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Abhay Ashtekar on Gödel Universes, Buddha's Poison Arrow, Time Travel, and Loop Quantum Cosmology
August 1, 2022
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The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze.
Culture, they analyze finance, economics, business, international affairs across every region. I'm particularly liking their new insider feature. It was just launched this month. It gives you, it gives me, a front row access to The Economist's internal editorial debates.
Where senior editors argue through the news with world leaders and policy makers in twice weekly long format shows. Basically an extremely high quality podcast. Whether it's scientific innovation or shifting global politics, The Economist provides comprehensive coverage beyond headlines. As a toe listener, you get a special discount. Head over to economist.com slash TOE to subscribe. That's economist.com slash TOE for your discount.
Professor Astakhar is the Eberly Professor of Physics and the Director of the Institute for Gravitational Physics and Geometry at Pennsylvania State University and is the man responsible for loop quantum cosmology. Roger Penrose has described Astakhar's approach to quantum gravity as the most important of all the attempts at quantizing general relativity. I'm proud to say
that this is Ashtakar's podcast premiere. In this part one, we cover what was there prior to the Big Bang, the myth of singularities, Buddha's parable of the poison arrow, as well as the inner versus outer world. Some of the physics can be a bit esoteric, especially the technicalities of loop QG, giving a taste as to what it's like to study the subject if you're interested. My name is Kurt Jaimungal. I'm a Torontonian filmmaker with a background in mathematical physics, dedicated to the explication of the variegated terrain of theories of everything,
that is primarily from a physics perspective, but as well as investigating what role consciousness has to play in the fundamental laws, provided these laws exist at all and are knowable to us. If you'd like to hear more podcasts like these, then do consider going to patreon.com slash Kurt Jaimungal.
It's support from the patrons and the sponsors that allow me to do this, to put out podcasts of this quality of this length consistently, as this is now what I'm able to do full time. Today's sponsor is Brilliant. Brilliant is a place to learn mathematics, science and engineering in an interactive form. Soon I would like to speak to Chiara Marletto on information theory. So I decided to take Brilliant's course on random variable distributions and information theory. And after taking that course, I could finally see why entropy is defined the way it is. There are plenty of other different courses.
You can even learn group theory, which is what's being referred to when you hear that the standard model, the internal gauge groups of the standard model are contingent on U1 cross SU2 cross SU3. Visit brilliance.org slash TOE, that is T-O-E, to get 20% off the annual subscription. And I personally, I recommend that you don't stop before four lessons. I think you'll be greatly surprised at the ease at which you can now comprehend subjects you previously had a difficult time grokking.
Alright, now part two will be in a few months, so note your questions down in the comments for me to ask the professor. Thank you and enjoy part one with the great Abhay Ashtakar making his podcast premiere on the Toe channel. Professor, I'm extremely honored to be here with you. You're one of the preeminent physicists of our era, and I think I speak on behalf of much of the audience when I say that we're lucky to be alive during the same time that you're alive, and it's an honor, man.
Thank you so much for joining me on tow. It was my pleasure because, I mean, it's one of the very rare places where people are interested in theory of everything, which includes not just the physical world, but also the inner world. And that has been my passion. So it is a very, very good match for me. The inner world you mentioned, we're going to get to that too. No, both, both the inner world as well as the outer world. I mean, not just
And not just the physics sense of theory of everything, but really theory of everything. Yes, everything. And that includes the overlap between those. And we gave or you gave a great analogy prior about the compatibility condition on a manifold on a sphere. We'll get to that. I'll give a bit of an overview for the audience as to what we're going to talk about roughly in order loop quantum gravity, because that's what you're most famous for. And loop quantum cosmology, the Big Bang,
black holes, the second law, so there's we deal with entropy at some point, and causality, perhaps even the arrow of time, the differences between the inner and the outer world, and what you believe are ingredients to a theory of everything, and perhaps even some of the philosophy of physics. Unfortunately, there were myriad technical issues, thus the audio of Achtekar's isn't as pristine as it could be. Keep listening as it improves with time. How about you give people an introduction as to how you view
What the outer world is and what the inner world is, perhaps what led you to that as well, that distinction, and also the utility of the inner world, which is generally discarded. Yeah, so the outer world, I just mean the physical universe at least in the habit of studying, it can be physics of what we're talking about, you know, it can be planets and stars and gravitational waves and cosmology and black holes. It can be just a tree outside my window up here and
So all those things, they all seem to have some laws and science has been incredibly successful in actually finding many, many of these laws and understanding why things happen in the external world that we see. But there also have been kind of old traditions which focused much more on the inner world.
And the problem there was not talking about kind of the best things that I have come across. I'm not talking about everybody. So the problem there was basically not that the outer world and phenomena, et cetera, et cetera, are not important. But somehow the central theme should be
Why is there suffering? And what would lead to lessening or elimination of suffering? There's a very, very beautiful story of the Buddha. So the statement is that one day a young monk came in the hour where people could go and ask questions and sat
I was meditating the other day and the following thoughts came to me. I should have looked this up before the conversation because I will probably not reproduce it completely. His name was Malanke Putta. Putta is Putra or son of Malanke. Malanke Putta says, well, sir, I was thinking about this and the following thoughts occurred to me.
Why is the universe finite or did it have a beginning? Did it always existed? I mean, so is it finite in time or what? Is the universe finite in space or is it infinite? These are the questions we asked today, right? Then he goes on about eight questions. That's why I said I should have looked at the other questions. These were the first two questions. And then he sort of says that well, does
Buddha exists after death or Buddha not exists after death or Buddha exists, both exist not at all, exists after death. So it goes on in first of the outer world and then you know with the more spiritual questions and so on. Buddha doesn't answer, keeps quiet. Then his Malayankaya Prataya is disappointed.
So he waits there very respectfully for whatever time was supposed to be appropriate and then leaves. Comes back a week later, says, I'm sorry, but those questions continue to bother me. I'm really troubled. And he repeats the questions again. I think there were eight questions again. Sounds like me. So Buddha doesn't answer again. And then a third time he comes and he says,
Every time I come, I've asked this question. He repeats the question. He says, it should be simple for you to say that you know the answers or you don't know the answers. And if you know the answers, what they are. Your silence does not please me. That was the one phrase he says. And basically, something that if he doesn't get his answers, he will leave the Sangha, you know, the community of the monks. And Buddha replies,
First of all, you didn't join Sangha conditionally. But of course, if you are to leave, you can give any time. Anybody can give any time. Nobody's bound here. And secondly, the reason I don't answer those questions is because they have nothing to do with the central problems that the Sangha is all about. And it has to do with sufferings.
Understanding those questions, understanding answers to those questions, exploring them and understanding them sufficiently will do nothing to the reduction of your suffering. And then I think Buddha gives an analogy. He says, supposing you go and, I forget the details, but you're wounded by an arrow.
And then the doctor comes and doctor wants to put something to it, some medicine. So you say, no, don't put the medicine. First, I have to know, where did you get those plants? How long were those plants marinated? Why this plant and not some other plant? Has this medicine been used always? If it was not used always, why did it start using now and what changed and so on and so forth?
But if you do that, he says, you will die before you are cured. He said the same thing is true with these questions about the external world. Now, what I like about this is not that he belittled the questions about the external world, but he just honestly said that this is not what he is, what he is about. I feel like it's like saying that, you know, somebody comes to physics class and asks questions about
Neuroscience or biology or something. You don't know the answers to those questions. You are in the wrong place. There is really a division between this external world and the internal world and it has grown.
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What I will say is for several centuries it has grown.
I think it's a pity because on the other hand, we are all human beings and we see the external world and we have the internal world. We cannot just deny the internal world. Again, in the talk of this, you said that philosophers of all time, they were interested in two things. One is the natural world, the natural philosophy. Secondly, wisdom. The wisdom was that you live what you believe.
And therefore you are a shining role model of what we believe. And then he goes on to say that today's scientists about that, they are no different from a lawyer or a banker or anybody else as far as their own wisdom is concerned or their own belief in practicing what they truly believe. And I think there's a lot of truth to that. And I think that's a pity.
that I think it should be much nicer if in fact more people were interested in both aspects of this world and so I think this was in the early 80s I think. I felt that I always been interested in internal work for whatever reason maybe because I was born in India it's not that my family was very spiritual or traditional something I don't know but I read some things you know I also read a lot of
The point was that there seems to be such a
such a system between the two things. And when I listen to scientists, for example, one thing that I like about science scientists very much compared to the people, experts in the internal world, is that one doesn't think one has the I mean, if you're not, yes, okay, if everything in this in the physics world that everything is going to be explained tomorrow, then people don't think that there is absolute truth.
I have no hesitation saying that Einstein was just wrong about many things. He was wrong about the cosmology constant. In fact, he was wrong about the Big Bang. First of all, when he heard about freedom of submission, he didn't believe in it.
Finally, when he understood Mathematics was right, he told Lametra, again Lametra, that in one of the Solway conferences, actually, that the idea of the Big Bang is completely repulsive to him. So it's completely repulsive. And then, same thing about Cosmogon constant, there is a whole idea about it. And then, actually, I told you about Lametra going in
Correcting is telling the Pope to behave differently. You also told Einstein explicitly long time ago, that why do you throw away, why do you say the cosmological constant cannot be there? It's not an aesthetic question. See, the aesthetics again, I mean, you and Einstein, right? It's not an aesthetic question. It's an observational question. It's either there or it's not there. And we see today that, anyway.
So, but nonetheless, we had no problem in saying that Einstein was wrong or that Bohr was wrong and various things. But that is not accepted in the internal world. You couldn't go in a conference and say, or group of those people and say, that was wrong. So, I think that this idea that there is absolute thing and you arrive there and then it's static, that I find not very pleasant and not very
scientific or not very useful attitude. It's an attitude which is self-limiting, I think. Well, scientists don't have that attitude, so that is good about it. But there is this problem, you know, you go and talk to these people and they want to dismiss science at once and you talk to scientists and they want to dismiss anything as big as going to the deep end.
But let me just close your eyes. There's a reality there, huge reality that you are dealing with all the time. And somehow that it is not interesting. And so I sometime in 80s, I thought that is really important. You know, what is the nature of reality? And each of them somehow think that, well, I can just extending, keep extending and then cover everything. And in terms of what they already extended.
and then like in science keeps progressing and progressing and progressing and you know, it's just, we just reached it. We don't know, right? And it may take infinite time to even describe the external world. We don't know that is going to happen in a finite amount of time. We'll make continuous progress and there's no question. It's deeply valuable. It's beautiful when you discover something new as there's no question about it. But then, so, so therefore I came up with this idea that maybe, you know, reality is
Perhaps if you at all want to model it, however incomplete that may be, maybe it's best modeled by a manifold picture, as I was mentioning to you the other day. It can be a more complicated manifold, but the simplest example would be just a two-dimensional sphere, the surface of a ball. And we know from the globe, from the Earth, looking at the maps and such things on the globe, that if you try to project it down on a plane,
Then you have to do the projected map. We can take this North Pole and then project each point of the globe, draw a straight line, and then we get a faithful picture of everything but the North Pole. It's a very distorted picture. It's not a second problem. Some areas look much bigger than they really are, and so on and so forth. But you get that picture. But you cannot cover the whole sphere with a single chart, single coordinate system, single X and Y things.
And so I felt that maybe that is true with reality, that there is an internal world and there is an external world. And the best case may be that you can try to cover more and more of the internal world and more and more of the external world, and they will give you some charts, so to say. And then the deep question is going to be about the overlap functions, because that is where the
The chart transitions. Yeah, the key thing about manifold lies, right? There's this compatibility of the two charts, compatibility of the coordinate system that they overlap. You can have a north pole chart, you can have a south pole chart, and around the equator, there are compatibility conditions that should be satisfied. In other words, the same phenomena can be looked at in two different ways, and they should be compatible with each other. And I think that is what is likely to happen, that as time goes on,
And in particular, for example, I was very surprised. I just heard about it only less than 10 years ago, maybe six years ago, something like that, about all these advances in neuroscience where they have been able to take the image of brain very much. But in particular, these advances had to do with some experiments with which people, I think his name is Brewer. He used to be in Yale, but now he has his own company somewhere else.
There's a paper in Procedures of National Academy about this, in which they actually took some monks, or non monks, who were trained in meditation, but solid long training in meditation, not beginning monks. And then he had them kind of brain scans while they were actually
began meditation and he purposely tried different kinds of meditation, you know, this compassion meditation that is a sensational meditation, feeling sensations and loving meditation. And they tried all those various techniques and they found that what happens is in all these practices is that the
A certain circuit in our brain, which is called DNN or default mode network, it's a rather big circuit. That is the circuit that is most active when we're in a normal state. And the way that we hold the world normally is through an internal dialogue. We are not necessarily conscious of it, but there's
There are other circuits which are more related to functional mode circuits. They don't slow down.
Now, for most people, even though all of them are very practiced monks, once the meditation, they came out of meditation, then the neurons started firing and the default mode started again. But there were a few exceptions. And these, by the way, are the ones which are... I first came across this in the book by Robert Wright.
called Why Buddhism is True. It's an interesting book. I mean, he was an evolutionary, he was a science writer for evolution psychology was his specialty. So it is tilted quite a bit towards evolution psychology. And I don't, I don't agree with some of the things that are said there. But it's a very good book. And then he reported this. And then I looked up the National Academy of Sciences journal and followed reading up here.
that there are a few people who were in that state even after they came out of meditation. They're always in that state. And it seems to me, and from the other things also that we've got some other time, Mark, that several reasons why I believe that this is a state of what used to be called enlightenment.
So it's not a state in which you have to go out in the Himalayas in the top cave or anything like that. It's really a state of mind. And almost all of them are, of course, very deeply practicing meditators and such things, but it may not be necessary. I mean, from what I hear, what I read about some of the people I respect is that it can also happen spontaneously. I mean, with some effort, but don't necessarily have to have
10 years of meditation or something like that in order to do this. So there are some mental states. So there is a possibility of actually having these overlap functions. Namely, science would say that somehow they were able to switch off the circuit. And when that happens, the sense of self disappears. And when sense of self disappears, then there is a
Very, very different perception. I mean, this is people that take psilocybin, for example. There is a very active group in Johns Hopkins who does research on that. And again, very respected, extremely respected people. And they are very solid researchers and doctors.
The experiences of those drugs is really exactly that, mainly switching off this circuit. And I think somebody said, right? Alan Watts, I think, said something like that, when you get the message, hang up the telephone. Which is to say, when you realize that the other states exist, don't keep taking this more and more.
So I think that there is enough of work going on and I'm not saying that this is therefore what do we solve in next five years, ten years, my lifetime or something of that sort. But I think it is possible to reach those states. I mean, I really know some people whose brains can show that and their writings show whatever they have told me and I have practiced.
I'm very hard-nosed. I don't want to take any advice. I'm also not inclined towards things like devotion, bhakti, and I'm not a religious person. But whatever makes complete sense to me, I try to adopt it. And this is one of the principles that they say. If you want to move towards, quote unquote, wisdom, you should live by what you understand and what you believe. It's not easy.
It's not easy at all, but I think it is not impossible. Because we could talk about the inner and the outer world for hours, we decided to save that for part two and to continue on with physics. Ensure that you note your questions for Ashtakar down either in the comments or somewhere else for part two, which will occur later this year. What is loop quantum gravity and how did you arrive at that approach? Right, so loop quantum gravity is a
is an approach to unifying general relativity with quantum physics and this is a long-standing open problem at one stage it was considered to be the biggest challenge in theoretical physics and in some circles it is still considered to be the biggest challenge although because of recent observations both in the cosmic microwave background and gravitational waves
Other frontiers have also opened up which are considered equally interesting. So I started out in general relativity and from the point of view of general relativity then the question is really how do we unify principles of general relativity with those of quantum physics. And there is a real problem right in the beginning because there is a really attention
I mean, general relativity at the conceptual level is a classical theory. So in that, you have a complete productivity. It's a very geometrical theory. It's sharp and precise. Quantum mechanics, on the other hand, is by inherently a probabilistic theory. We don't have certainty, but we only have probability amplitudes for various things to happen.
And the techniques that one uses are also very, very different techniques in quantum theory. In quantum theory, things like algebraic methods, Hilbert spaces, linear operators, and uncertainty principles, they play a major role. But the sort of interesting thing is that each theory, to begin with, has a claim on all of physics. In other words, general relativity would say not only is it a theory of gravity,
But it's also a theory of space-time structure. And of course, all interactions take place in space-time. And therefore, general relativity sort of tells you how to formulate the theories of other interactions, that there is a metric tensor field behind it, which also serves as a gravitational potential, but determines space-time geometry, determines causality. So it tells you that equations should be differential equations. They should be hyperbolic.
and so that you have got predictably and things propagate within the light cone of any point causality and so on so forth and everything is described by smooth tensor fields for example electromagnetic fields gravitational fields any other field whereas quantum physics to begin with is very different in quantum physics it also makes a claim on everything that all systems are quantum mechanical and they should be described therefore
in probabilistic terms. You should have quantum states or wave functions which only tell you about potentialities and only when measurements are done then these potentialities are turned into actualities. But on the other hand it says that the whole of physics should be described in these particular terms. So on the one hand we've got the geometry, tensor fields, smooth metric, light cone propagation etc and on the other hand we've got this
When I started out, this was considered to be the biggest open issue in theoretical physics. And my interest then was, how do we address this problem? How do we unify the principles of both those things? I came from the general relativity side. So for me, it was really important that there be no what people call background structures. So let me explain what this means.
So in quantum mechanics and even quantum field theory, like for example, when we do quantum electrodynamics and so on, we actually have background structures, which is really the space-time metric. Space-time metric is given. It's a stage on which various things happen. It is indifferent to the happenings. It is fixed. Nothing changes. Whereas in general relativity, there are no actors.
There is a drama of evolution, if you like. Space and time is not a spectator. It's also an actor. It's also a physical entity. You can act upon it. It acts back. Einstein's equations basically tell space time how to bend. And once you have got bent space time, that space time does matter how to move. And so there is a tension here because on the one hand, in general relativity,
There are no background structures. There is nothing which is sitting there, which is there's no stage. There's no arena. Everything is really acting with each other. There are no spectators, as I like to say, in this cosmic drama. So, but corner field theory for its very formulation really assumes that there is space time. For example, the Schrodinger equation in which time revolution, but even corner field theory, you know, you talk about
was a propagation, you say that if there are two fields of two so-called space-like separated points, so that there's no positive signal passes from one to another, then those fields commute. So these are fundamental commutation relations in the theory. And we don't have such a thing because we've got a dynamical metric, you know, so there's no fixed structure like that. And therefore, there is a tension. And coming from general relativity side, I felt that it was more important that
this background independence. The fact that there are no spectators in this cosmic evolution is something that should be put to forefront. And when I started out, all approaches coming from particle physics or quantum field theory side to quantum gravity were really based on this idea that there is a fixed Minkowski metric. And then when you take the gravitational field itself, for example, so that is represented, for example, by a curved metric G,
So what you do is you introduce by hand a flat Minkowski metric or called Minkowski metric and you take the difference g minus the flat metric, let's call it g naught and then that is considered to be the gravitation field and that was denoted by h and what just did perturbation theory in powers of h. So the approaches were completely perturbative and what I wanted to do was very much approach which is background independent
H is how much the metric differs from the flat case. The flat case metric is something that you put by hand. There is a gauge freedom there as one says. It is not something that is physically determined. The idea is that only when you sum over all the terms, then you will find that there is no dependence on this flat metric.
But there are questions about whether you can actually sum and that sum converges in a mathematical sense and so on and so forth. There are good partial answers to that in classical theory, but in quantum physics nothing converges, there are infinities, and so the problem is really open. Even in classical theory, it really is difficult to get.
If you start out with Minkowski space, which is a flat space, you know, it's like if you look at a two dimensional plane or three dimensional Euclidean space that you're familiar with, we're adding one dimension, which is time dimension, and it's all completely flat. So the metric there is basically minus the time difference squared plus the space difference squared. That is a metric. And so this is given to you once and for all. And then the statement is,
The H field, for example, is supposed to propagate on the light cones of this G naught metric that you are given once and for all. But on the other hand, G naught metric is just something put behind. And so therefore, to give fundamental meaning to these light cones is not appropriate. And I think by now people, particle physics even, the community sort of appreciates that, that that was not completely appropriate.
And then when you take with this flat spacetime metric, if you want to talk about black holes and so on, locally you can try to sum up the perturbation theory and get a locally black hole metric. But globally, black holes are very global concepts. This is not possible. So this was basically the idea. And then the question is how to go about doing this. And so there had been
Since the 1950s, attempts at formulating general relativity in a suitable way so that you can go to quantum mechanics, quantum physics, quantum gravity in a non-participative way without splitting this. So they were side-by-side attempts. The particle physics attempt was very much started with Feynman, but then taken over by many other people, particularly Bryce David and so on. And then on the non-participative side, we had Dirac,
And then Peter Bergman and his collaborators, old school and so on, they had developed a certain approach just called Hamiltonian methods or canonical gravity, as they call it, canonical. You can formulate any field theory in that particular language. And the advantage there was that one did not need to introduce a fictitious flat background metric.
But then the mathematics of that theory and which was then developed also by John Wheeler and his collaborators. But the mathematics of that theory had remained completely formal. And in other words, there are infinities because the system has infinite number of degrees of freedom. It's a field theory and every field theory, you want electromagnetic field light that has infinite local degrees of freedom. And then in many theories, we know perturbatively
how to handle it through renormalization, but general relativity turned out to be not renormalizable, but not quite a bit even finite. And so the question was, well, how do you then, you know, what do you do? What do you proceed? How do you? And so this was, this was not a problem for Dirac, Bergman, Wheeler, et cetera. And therefore they actually tried to go
that direction to address more basic questions, particularly Wheeler about, you know, what happens at the Big Bang and perhaps we can answer such questions where non-partiability methods are essential because near the Big Bang, the curvature is very, very large. So try to do an expansion in small curvature quantities is kind of a very bad method, if you like insuited method.
So this was there, but except that everything was very formal. People were writing down these equations which were formally written down. The famous Viradevit equation is a formal equation which was written down in the 70s or 60s actually. But even today, it is a formal equation. In other words, we do not have precise mathematical meaning to that equation. And so I wanted to go beyond that. And then I had three ingredients that came all together
The first was that there was a formulation of other interactions of physics, you know, the weak and electromagnetic interactions. And in those interactions, the interactions of popularly people who say forces are propagated by what people call vector potentials, or in geometry, you might call them connections.
It's a vector potential which couples locally to currents, for example, in electromagnetic theory. If you want a local coupling, one introduces a vector potential. Whereas in general relativity, we only had, we have a metric. I mean, there's a connection which it defines, but that's not at forefront. We have the metric, and the metric defines the light cause, it defines what you mean, gives meaning to hyperbolicity, differential equations, and so on and so forth. And so famously, for example, Weinberg had pointed out in his
And then I thought that maybe we can actually remove this wedge. The second ingredient that came at that time was really coming from
various ideas that people like Roger Penrose and Ted Newman and so on had introduced coming from Twister theory. And in Twister theory and so on, there is a certain sector of the theory which is exactly integrable. And that, I mean, in general relativity, the basic idea is a metric, but the invariantly defined things that defines a strong gravitational field or weak gravitational field is the so-called curvature, which is determined by the metric.
And this curvature, if you like, in Maxwell theory, is like the Maxwell tensor Fminu whose components are electric and magnetic fields. So we've got a similar tensor in general relativity is called the curvature tensor. And that curvature tensor, sometimes called the Riemann tensor, is obtained by commuting two derivative operators that are defined by the metric. And so there was this idea
that maybe what we should do is to take the connection as a fundamental quantity. And this idea somehow was suggested to me, I was a postdoc with Roger Penrose and just during that year that I was there for two years and just during that period, Roger invented what is called as nonlinear graviton. Which is called the what, sorry? It's called nonlinear graviton. A nonlinear graviton, okay. Nonlinear graviton. It's a Twister construction
It's a rich construction because it brings together theory of differential equations and algebraic geometry. The two things that were completely separate all along are brought together. And what Roger showed was that if you look at a certain simplified version of Einstein's equations, namely the following. What you do is you have got this curvature tensor.
But you can break up the curvature tensor into two parts, and they're called self-dual part and anti-self-dual part. And each of them, if you like, in Maxwell theory also, we can take the Maxwell tensor and divide into two parts called self-dual and anti-self-dual. And each of them defines a helicity of the photon. So these are eigenstates of the helicity operator. A photon is a spin-1 particle, and it has a rest mass zero, and therefore its angular momentum, its spin vector is pointed
Similarly, we can do this decomposition in the case of gravitational field.
And you can have self-dual and anti-self-dual solutions of Einstein's equations. These, however, are complex solutions of Einstein's equations. And now in quantum mechanics, it doesn't matter because the wave functions are complex. But in classical physics, we want real things. Now for the Maxwell case, it does not matter also because you can take two real, two complex things that are complex conjugates of each other. So you can just add them and you'll get the real Maxwell field. That is a real Maxwell field.
But general relativity is a nonlinear theory. So you cannot just add the self-dual curvature and anti-self-dual curvature to get some metric whose curvature will be the sum of the two, the real part. So you cannot get the real metric by adding because the theory is nonlinear. You cannot just superpose the self-dual solution and anti-self-dual solution to get a real solution. But nonetheless, the fact that
Self-duals, the mathematical structure of self-dual solutions is extremely simple. This is what Roger pointed out, that you can obtain, quote unquote, the more general solution of Einstein's equation, which is self-dual. This is, you know, a radical breakthrough in a way, that because equations are so complicated, but we can obtain the general solution of Einstein's equation using this method.
Ted Newman in Pittsburgh had another parallel construction and it turned out that the two are quite compatible with each other. They are exactly, one can go back and forth between the two. So I knew that there is this exactly integrable sector of general relativity. But again, I felt that that is still talking about complex general relativity.
And how do we construct a theory whose limit then would give you classical, usual, real general relativity with cosmology, black holes, and so on and so forth. And so that was my interest. My interest was that, well, on the one hand, these derivative operators or connections, they look like good objects to do things. But Penrose and Newman and Plobansky, they were three people, three slightly different approaches, but they turned out to be more or less equivalent.
They suggested that, well, we should be looking at self-dual things. So therefore, what I did was to say that maybe what we should do is take a real general relativity, but formulate it in terms of these self-dual variables, as they are called. In other words, you've got a derivative operator which acts on spinors. So spinors are fundamental objects that describe, for example, the electron, the neutrinos, the quarks,
in the standard model. The fundamental fermions are all fundamental particles. Massive particles are all fermions. And in the presence of a gravitational field, the equations they satisfy involves a certain derivative operator because they are differential equations. But these fundamental particles at the basic level
Right. So, very good. So,
If I look at, let's begin with the electromagnetic field. So we've got electric and magnetic fields, and one of the beautiful things about spatial relativity is that they can actually be combined in a covariant manner so that you've got the Maxwell field tensor. So it's a tensor whose, if you like, space-time component is the electric field and space-space component is the magnetic field.
Electric and magnetic fields are combined together already in spatial relativity. You shouldn't think of them as separately. If you have got an observer, that observer with his full velocity can decompose this tensor into electric and magnetic field. Another observer would decompose it in different ways. So what you have is really this field. And so what we have is a tensor field, which is called f. It has two spacetime indices. So let's call it f mu nu.
And if you have got a tensor, then one can take it mathematically. You can take what is called Hodge dual. So you've got a two-dimensional anti-symmetric tensor, and you can contract it with an epsilon mu nu alpha beta. So these are totally anti-symmetric tensor. And what you obtain is, again, what you obtain is the object with two anti-symmetric indices. So you get an object with the same
So it's a similar structure and so if you take this epsilon and operate it on a Maxwell field, you get another Maxwell field if you like and that is called the dual of the first one. It's dual because you operate it by epsilon. So what does it mean in terms of electric and magnetic fields? Well basically E goes to B and B goes to minus E. So you just do this rotation and that is what's dual. Now several dual is the one in which
The field is its own dual. But if you look at this duality operation in the space-time signature in the real world, which is time is always a minus and space is plus or vice versa, we usually use time as minus. So the distance is always minus the time interval squared plus the space interval squared. So in that signature, this operator, duality operator,
is actually, if you take a square, you get minus one. So it means that if you have a self-dual object, something which is equal to itself, if I again operate it by this... Equal to the Hodge of itself. Hodge dual, right, exactly. So then you'll get minus one. So therefore, the self-dual objects, if you do it twice, you get minus one. So therefore, the eigenvalues are plus or minus i. And so if it is plus i, it is called self-dual.
If it is minus i, it is called antiseptic. So in terms of electric and magnetic field and given observer, you can say that e plus ib, that complex field would be self-dual and e minus ib would be antiseptic.
Coming to gravity, gravity is very similar. The curvature tensor is like the Maxwell tensor. I'm so sorry. One more time. I'm so sorry, professor. I just want to always... Yes? It's okay? Yep. Every time your question... Great. Okay. Only because I want to make this physically clear. So just one note. Hodge... I may keep this or may not, but a Hodge dual. So if people know what a form is,
Let's say you have a manifold that's four dimensions and you have a form that's two dimensions, then you can take, there's a way of taking a two form and then identifying it with another two form. Well, the formula is just, you need this tensor field because you're talking, tell me how technical I can be. Yeah, yeah, yeah, you can get technical. And I need a four form or actually I need
a tensor field which is two covariant indices and two contravariant indices. And then these contravariant indices can contract with the form that you give me and therefore again obtain a covariant two form. So I need an object like that.
So what you need is technically called a conformal metric, a metric up to a multiplicative factor, then you can actually raise the indices of the four form that you have got in the manifold, if the manifold is orientable say, and then you can raise the indices and then you will get an object which has two down-stage indices if you like or covariant indices and two up-stage or contra-variant indices and then when you, when you, I got, maybe I should, I don't know, so it doesn't,
And then the statement is that I can contract the upstairs indices with the downstairs indices for the form and get again a form which has downstairs indices up here. But in the Lorenzian signature, which is minus plus plus plus, which is Minkowski signature, the square of the Hodge dual is minus one.
In the Riemannian signature, it is plus 2.
Douglas Goldstein, CFP®, Financial Planner & Investment Advisor
What I want to know is, what does it mean physically when you say that a theory is dual or self-dual? So for example, we could identify up and down with being a left-handed or a right-handed particle. Okay, so there's some correspondence between the math and then the physics. So what's the correspondence here between the math of being self-dual and then the physics? What's concretely happening when one says this theory is self-dual or not? Does that correspond to a particle? Does that correspond to a type of theory?
So in quantum mechanics, that corresponds to a particle with a given helicity. It's a photon, because it is a zero response particle, the photon actually has a spin which is aligned to its 4-momentum, not the energy momentum, it's like 4-momentum. And then it's either pointing along the 4-momentum or anti. And if it is pointing towards the 4-momentum, then it is helicity plus one and the other one is helicity minus one.
When it comes to mathematical representation of these states of the photon, then the ones which are pointing in one direction, one helicity, they correspond to Maxwell fields which are self-dual. And they're complex because wave functions are complex, there's no problem. And if it is other helicity, then that corresponds to the anti-self-dual. And in Maxwell theory it's nice because you can just add the two and get a real solution. That's very good.
And the idea that Roger had was that, and you can do the same thing with linearized gravity. In other words, this perturbative gravity that I told you about, which is in which you've got flat space, and then you've got a big gravitational field, and you can take the curvature tensor. So the curvature tensor in gravity has four indices, and it is anti-symmetric in the first two and anti-symmetric in the last two.
It's not like the epsilon form because it is not totally anti-symmetric, it is just anti-symmetric in the first two and anti-symmetric in the last two and then some other algebraic conditions appear and that's called the Riemann tensor and what you can do again is take this epsilon, take the Hodge dual on either of the two, it doesn't matter, you can take the Hodge dual either on the last two or the first two, it doesn't matter and then again you will get a tensor which will have four indices which will be anti-symmetric in these two and anti-symmetric in the other two
And then those indices are going to be and again the square of the Hodge duality operator is minus one and therefore you get the eigenfunctions are going to be complex. And if you look at linearized gravity,
And then you can talk about gravitons. The usual way that people talk about gravitons are all perturbative terms. So that really refers to linear gravity theory. And linearized gravity, the statement is that you can do exactly what we said in the Maxwell theory. Again, the only difference is that now the spin is two rather than one for the graviton, linearized gravity. And then again, it is zero response particle. So the spin is either aligned or anti-aligned. And if it's aligned, then it is
Can we talk about the helicity when the particle is not massless? Helicity is a social massless particle. It really replaces the motion of spin because the direction is already known. Whereas normally, if you had a massive vector boson, then it would have spin.
So it's not pointing along there. So what you know is that the spin is pointing always along, it is perpendicular to the full velocity. And so, but if the full velocity is null, then it's perpendicular itself, so it can spin can point along itself and that's it.
So there's one other way of understanding that with a mass, massive particle, if it's moving in a certain direction and it's spinning, you can boost yourself. You can move so that the particles moving over here, but the, but it would still be spinning here. So now it's moving, it's spinning in the opposite direction that it was, whereas before it was aligned. So then the helicity is not defined. The spin will transform like a vector. So if the full momentum will transform under Lorentz transformations, similarly the spin vector will transform.
But spin vector will transform like so-called pseudo vector, whereas the, in other words, if you change x, y, z, t, then the full momentum will go to minus its components of the reverse, whereas for the spin vector, the components will remain the same. It is like an ordinary quantum mechanics, non-reducible. So I have this long explanation about
So I just want to say where we were. So basically, you asked me about how do I start with this quantum gravity, the quantum gravity and so on. And so first thing was background independence and non-perdivity methods. The second thing was then, well, but how do you go about doing it? Because everything people had done, Dirac and Arnavides and Wiesner and Wheeler and Debit and so on, was very formal. And so how do you remove that formal things? The second point was, well, we've got this
All other interactions are really governed by this vector potentials or the derivative operator connection as one calls it in different geometry, whereas in gravity it is actually the metric that is what is used. And so one wanted to have more uniform way of dealing with all interactions. And then the third
thing that came was this idea that maybe what we should do is not use, so to say, the brute force derivative operator that the metric gives you, but only part of that derivative operator, which knows how to operate on left-handed spinors, which are the fundamental particles in our standard model, fundamental fermions. So these are the ones which are helicity. So we just look at those ones.
And then the statement was, that means that, well, we should not get rid of them. Metric is not a fundamental object, but even the derivative operator defines all of it is not fundamental object. Only a fraction of it which is extracted out, which is self-dual or anti-self-dual, it doesn't matter is your conventions, but supposing self-dual you extract it out, then that is going to be what we should be able to do.
That should be the fundamental object. And then we should formulate the theory thinking that that is a fundamental object and then go ahead. And then the nice thing was that if you did this, then one could write down a phase space of the theory, which is exactly like Yang-Mills theory, which govern other interactions, the weak, the electroweak and the strong interactions. So the weak electric, weak electromagnetic and strong interactions.
They're all governed by so-called Yang-Misting theory in which there is a connection. Here also now there is a connection. It just happens to be subtle. It's a gravitational connection which knows how fundamental particles move in presence of gravitational field. The electromagnetic connection tells you how electron charged particles move in the presence of electromagnetic field, external electromagnetic field.
Strong interaction vector potential A, that tells you how quarks move in presence of a gluon field. This connection is a gluon in that case. And now the statement was that you now take this fundamental constituents of matter which are fermions which have precise helicity
This is before the symmetry breaking. So they are precise helicity. So they are massless at that level. And then the statement is that you see how they move the gravitational field and what they are sensitive to is really this dual connection. So maybe we should choose that as a fundamental object. And to my surprise, it was a big surprise that the whole theory, real general relativity could be formulated
using this half the information somehow. And so that was a big surprise. So what happened is two things happened. First of all, the theory could be real general activity could be formulated. Whereas in twisters, even today, what we have is this subdual sector and antisubdual sector. We don't know how to combine them. Whereas in this formulation, you are really talking about real general activity. And secondly, kinematical level.
Before putting the information or the interactions and so on, detailed equations, what are the variables in terms of which you formulate your theory? In fact, in Einstein's autobiographical notes, he has this question that in formulation of a physical theory, the first question is what tools are you going to use? What are the basic mathematical variables which are going to capture your physical ideas? And only then what equations do they satisfy?
Sure. And here the statement is that these variables are the same for all interactions. That is very, to me this is very satisfying. On the other hand, the equations are satisfied quite different. So where does the difference come in? And another beautiful thing here is that the difference comes in precisely because you've got the in general relativity, there are no background fields. So when I write down the Lagrangian,
or the Hamiltonian in the Young-Mills theory or something. I'm allowed to use not only the Young-Mills fields, or in the case of Maxwell field, I'm allowed to use not only the tensor F-menu or electric and magnetic fields, but also the metric, just sitting there, spectator. I mean, it just is not doing anything, but I mean, it's not dynamically changing, it's sitting there. So I can use that to construct this Lagrangian density. But here I don't have anything, I don't have metric. So I have to write down equations using just these vector potentials, right?
But I don't have a background metric, you know. Now the funny thing is that if you really give yourself these variables, these connections and their conjugate momentum, which are like the electric fields, the analog in Maxwell theory would be the electric fields, then it turns out that there are very few equations you can write down.
And it literally is true that if you took a very bright undergraduate or first day graduate student and we would put them in the room and you tell them, write down the simplest equations you can write down. No background metric, no background fields. All you have is this connection and it's conjugate momentum. And the equations they will come down are precisely turned out to be Einstein's equations.
This is not how I arrived at it. I did it laboriously, which is I started with the usual formulation of Einstein's equations. I made a canonical transformation. I turned the theory on its head, as some friends of mine told me. And then the statement is that is it looking at upside down. So metric is no longer fundamentally variable. And then I did this canonical transformation, you certainly had these variables, which turned out to be a connection and that conjugate momentum.
And then I looked at, I mean, because I just did a canonical transformation, I could write down the equations which are equivalent to the Einstein's equation. Only later I realized that there aren't other equations you can write down. If you have background independence and if you want to have these connections, this is the only thing you can write down. And so that was a formulation of general relativity that I started with, which gave rise to this non-potential theory, quantum theory then.
So we had the advantage of actually using methods which are coming from very successful Yang-Mills theory, so-called Wilson loops or Wilson lines. And those methods were available already, but now we could take it into gravity and we could interpret geometry, space-time geometry in terms of those quantities which are used first only in the context of Yang-Mills theory. Now, much later, I think,
A little more than 10 years after I did this work. This work was done in 1986. So about 10 years later, I realized, I found out that, in fact, both Einstein and Schrödinger tried to give a formulation of this general relativity in which connection would be fundamentally variable. Exactly the same basic idea.
And it is a very fascinating chapter in history. So I just want to tell it to you for sure. I have audience, particularly. Einstein was in the Institute of Advanced Study in Princeton, and Schrodinger was in the Institute of Advanced Study in Dublin. And they kind of independently thought of this idea, but then they started corresponding. And then these letters are preserved.
And I think that they're available in the archives, not the usual archive, I mean, in the Surgeon Institute archive. And these are, there's a correspondence going back and forth, and this is across the ocean. And yet, you know, basically the letters are really one week apart.
So basically, as soon as they got the letter, they read it, understood it. I wrote these very detailed replies to each other. It's a very friendly and jovial thing, you know, in which Einstein sort of teased Shorinji by saying, oh, that idea of yours was cleverer than what a devil's grandmother could think of. And then, you know, Shorinji replies saying that, well, this is a bigger honor to me than, you know, all the medals that kings and various people have given me and so on.
So this was all happening and they were working on this theory, which was basically to formulate general relativity in terms of this connection. But they are using the connection, which is more like the metric connection, not the central connection, but the the the the derivative operator that comes from the metric up here. And then something happened, which is really weird. And the weird was that somehow Schrodinger thought that he had made a breakthrough. And he
That breakthrough, for those of you audience who might know about it, was basically to drop the condition that this connection, which is sometimes called Christoffel symbols. These Christoffel symbols normally in general relativity are symmetric or torsion free. So he allowed them to be anti-symmetric. And he thought that this was really a revolution.
And big idea, bigger. And then you give a press conference saying that, well, this is a completely new theory. It's much bigger and much more beautiful. And, you know, in general, you ask them to be symmetric. And so you even give an analogy of you say that, well, here is a horse and I want to train this horse, but poor horse, he cannot do everything. So what I'm going to do is to train him to jump over a fence. Right. But I'm going to tie the hind legs together and let it
first learn how to do it with his front legs. And the poor husk won't be able to do it. What you have to do is to, you know, let it use all the four legs. So so using that asking that the connect that this levituita symbol the connection be symmetric is like tying the hind legs of the horse. And I have freed it now. And privately, he won't discuss that you might probably get a second Nobel Prize and so on, so forth. And then he gave a seminar. And at that time, you may or may not know the history.
the Prime Minister, the Taoiseach, and then Ireland was a physicist. And so the Taoiseach came to the seminar and because Taoiseach came to the seminar, the press came to the seminar. And therefore there were headlines, the Irish newspaper, and these all, by the way, recorded in various places. There's a headline in Irish newspaper saying that Roger has made this great breakthrough and how generalitude is only a special case and so on and so forth.
And then New York Times managed to get a copy of the Irish Times before it actually appeared and send it to Schrodinger, to Oppenheimer and Einstein for comments. I don't know any comment of Oppenheimer. Oppenheimer might have just dismissed it completely. But Einstein prepared a very careful reply. And the reply said that he was very
taken aback because, you know, they are corresponding on the idea and suddenly showing the things that this is a great idea and he didn't think it was a great idea. He didn't think. And so Einstein gave this press release which said that, well, it is unwise for scientists to describe what is going on in technical work in simplistic terms because that gives the lay public the impression that science advances
through revolutions every day as if it was a banana Republic. And this was totally, and this appeared, of course, in New York Times. And then this was so shocking to Schrodinger when he heard about it. Unfortunately, Schrodinger did the second mistake of writing to Einstein saying that, you know, after the war, the living conditions of physicists are so bad here. So he thought that news like that will bring more money to physics and so on.
He was offended that Schrodinger went off and said that he found a breakthrough without conferring with Einstein first?
According to Moore's biography, it's called the Einstein-Schweiner eye, the Einstein's pick stack, the big mess that he has made with Einstein, and this is the whole thing. So this is an interesting story. Okay, so this is a long, let's go back to our mid-pop.
I have a quick naive question. There's something called the fundamental theorem of Riemannian geometry. So if you have torsion-free and something that's compatible with the metric, you get a unique connection. So if he throws out the torsion-free property, does the connection then become ambiguous or like you make a choice on it? Yes, so therefore there are new degrees of freedom.
Whatever the connection. So this anti-symmetric part of the torsion part is really a new degree of freedom. And you thought that was very important. I mean, this idea people are pursuing later also. It has not led to anything which is dramatic or even significant. But I mean, it's mathematical. It's a neat idea. It's just that it was not such a revolutionary as he thought. So coming back to the main point,
Coming back to the main point that the main ingredients were to formulate general relativity in turning it upside down, making metric as an emergent quantity and then the connection as being more fundamental variable.
And that is what is now has gone. So therefore, things which are called Wilson lines or Wilson loops become basic variables. And the word loop quantum gravity comes from those Wilson loops, even though these days nobody will use this loop so much as these lines. But just like string theory, you know, some name starts and then it becomes a name. So because string theory, there are brains and there are various other things equally important strings. But we still call it string theory. Similarly, here it is called loop quantum gravity.
The better name would be something I would say quantum Riemannian geometry because when you formulate it in this particular way then it turns out that basic geometrical objects like area of the screen that you're looking at right now, they all become operators in quantum theory and these operators have purely discrete spectrum.
And so really, geometry is quantized in the same sense as the energy, the angular momentum, the z-component angular momentum is quantized in hydrogen atom. And so this is important. I mean, it changes the picture of geometry completely. And so this is also something that you don't see in other approaches, either the Ville de Vitte approach,
Okay, here's some thoughts that occurred to me. Well, one is that you mentioned there's an area operator, and then I recall that there's someone named Theman, Thomas Theman, who said that we should have a volume operator and that better gives a semi classical limit of GR. So I just wanted to know what your thoughts were on that.
Right. So I'm one of the people who introduced the volume operator, studied its detailed properties. So I mean, like Lewandowski, and then Carlo Rovelli and Lee's volume independently developed, you know, this volume operator and also the area operators and so on. In the beginning, there were differences of opinion. There was some technical error in what Carlo and Lee had done, which is pointed out by Renata Lowell.
But, you know, at the end of it, sort of everything comes together and where I got a kind of geometry in which you've got volume, the area operator, volume operator. There's also a length operator. It's just that it's not as useful as a volume operator in the length operator. There's also a length operator. And the volume operator is something that is, that plays in what Thomas did, the T-man. T-man was a postdoc of mine and not many
When he began his work, he was a postbaka point, but the specific papers that he wrote, the series of papers on quantum spin dynamics, he started here, but then he finished elsewhere in Harroword and then he went to the Albert Einstein Institute. That's where he finished his work. So he used this volume operator very cleverly in order to write, to give a rigorous formulation of Einstein's quantum Einstein's equations.
That rigorous formulation is still being debated. It's not completely settled, but there is a huge progress. In fact, next month we've got this conference in Lyon, Loops 22. Every two years we have this conference and there is a talk by Madhavan Varadarajan who has made really very significant progress on this formulation of quantum Einstein's equation and he does use this volume operator that you mentioned.
Again, I don't know much about this, so my questions may be fatuous, so excuse me. So here's what I understand. So you have a fiber bundle, and you have a principal fiber bundle, which for people who are wondering what that is, it's like attaching a group to the manifold at each point.
The way that I learned it was that you attach a fiber P and then the P has a right action and that's G and it's free. And then on that you place a connection. Then a Yang-Mills field is when you take a section and then you pull back the connection locally.
Okay, so then I'm wondering, well, what the heck was what is Yang-Mills theory? What is its relationship to that? Well, as far as I can tell, Yang-Mills theory is just saying that the Lagrangian is somehow the curvature wedge, the hodge form of the curvature, and you take the trace of that. But I don't know if that's if that's all that there is to Yang-Mills. I'm sure there's more. Okay. No, that's the basic Yang-Mills theory. Exactly. What happens is that almost
Most of the plate times in Yang-Mills theory, that is to say, when people apply to gas to space-time, the topological considerations are not important. So these bundles are trivial. So it's true, it's a cross-section of a bundle, but if the bundle is trivial, then you can think of it as living in space-time itself. So most of the time, I mean, there are very interesting cases where this is not the
You cannot do it and then you get nice topological results and so on. But when you talk about Pertubatic QCD and so on, they're all living just on space time. You can think of, just like Maxwell theory, the fields live. Strictly speaking, Maxwell field also, there's a bundle. The group there is a U1 group rather than SU3, for example, for gluons. Here U1 group on the bundle and it's the same thing at the
Then what occurred to me was when you said that the metric is given in the Yang-Mills case, whereas in the general relativity case, it's not given. In the Yang-Mills case, when you say that it's given, is that because you take the Hodge dual and the Hodge dual assumes the metric or is it even more fundamental than that?
Okay, so now let's say we're on general relativity and what we have is the connection, then you're wondering, well, how do I recover
And that tells you how much curvature is enclosed in that ring.
Yes, yes, yes. And that's called the holonomy. Is that correct? Holonomy approach? Exactly. So that's how much curvature is enclosed. Okay, okay. So I'm just trying to make connections, make connections between the connections. Right, exactly. Yeah, but I think this, but as for undergraduates, senior undergraduates, it might be easier to sort of, so that is certainly true, but there's also a direct way of understanding constructing kind of spatial metrics.
metric in the spatial part of the matrix. And that is really that what you do is to take Yang-Mills connection that you've got, this gravitational connection you've got, and then you also have the phase space variables which are electric fields. Now normally electric field is just a vector in electromagnetic theory, but if the gauge group, if you have a gauge group which is higher dimension, in this case the gauge group is SU2 say, then
you've got kind of it's a matrix valued object it has and so it has it's a vector potential which takes values and matrices but the values are just SU2 value. Now SU2 is just three-dimensional is the rotation group is a double curve of the rotation group so you've got x direction rotation y direction z direction that's the group that you use for ordinary spinors in non-relativistic quantum mechanics the usual quantum mechanics up here.
And ordinary spinners, you know that you can just use a basis of Pauli matrices. And so you can think of both the vector potential and the electric field as carrying an internal index 1, 2, 3, which is basically component of the first Pauli metric, second Pauli metric, third Pauli metric. So it's a vector in space, but it also has an internal index.
which is like a spin is the internal space. It lives in some abstract space, which is not physical space. And so you've got a triplet of electric fields. And my main idea was that, well, if you have a triplet of electric fields, then you can take this triplet. Yes. And think of it as an orthonormal tri. Just define it. I mean, there's no metric, right?
So given these electric fields, these electric fields, I just define an orthonormal triad with this, and then that defines for me a metric, because if I know what three orthonormal vectors are, then that tells me what the, given any vector, I can decompose into that, and I know the metric. So in fact, the triad is like a square root of the metric. Metric is the square of the triad, just like the spinors are square root of vectors. Okay, interesting.
So basically, it's really the variable which is canonically conjugate to the connection to the derivative operator to set the connection. That is what is defining for you the spatial metric. Now, this is kind of a little bit of pedestrian way of doing it, but it's more intuitive. You can do it also co-variantly, and that is where the spin forms come into being.
But then you have to really think in terms of the Lawrence group at each point and
But I mean, it's just like, you know, normally how I explained to you in the very beginning, how I explained to the undergraduate in the beginning, how given the F mu nu, I can get electric and magnetic fields, but I can put them together to get F mu nu. So similarly, what I was just telling you about now is triad, but you can put them so that you actually get a four dimensional metric and not just a three dimensional metric. And that is what is done in spin forms.
When I look at a course on loop quantum gravity, one of the first lessons is on something called the four legs, but it has a it has a German name like wide bands or wide trends or what are those called the tetra? Are those tetraids? Okay, and that's what you're describing? Yeah. Okay. And so when you say that
that I know that I apologize for people who are wondering, like, these are such foolish questions, or so, or so technical, like, what's the point? Like, I'm just trying to clarify for myself, if you don't mind. So first, when they're being defined, it seems like it's, I was wondering, okay, so in general relativity, you say, okay, let me take a frame, let me go along with the frame. And let me just assume that frames or the normal. And then when I was hearing Tetra, I thought it was just talking about that. But then it sounded like they're saying,
Well, let me have another frame with those as the basis already. No? No, no, this is it. What you said is exactly that. It's just a frame. It's just a frame. And when I was talking about the internal indices, just index labels, these are 0, 1, 2, 3. But each of them is a vector. So there's a vector.
but I'm labeling one zero one two three so there's another index other than the vector index so there's a vector index like a mu yes but then there's also an i feel like an i goes from zero one two three yeah okay so that's where I get confused that's all right or initially was confused at least so let's say you have the four vector and then you call them at first like in the regular general relativity sense let's call this this e zero e one e two e three but then I'm saying I'm going to get another vector forget about
3 that are orthonormal and just get take one well that vector obviously can be decomposed in terms of these
Okay, so then you're saying, okay, Kurt, don't just take one vector, take another vector, those other indices, those are actually making reference to the original orthonormal basis. Okay, because I was wondering, like, why, why is there other indices at all? Why not just say in the same way you take these? Yeah, there's no other index. Your confusion was correct. I mean, there are no, there is no other index. I mean, you just assume that there was another index. No, I was not referring to another index at all. It's just those, but that index,
No, and then the statement is that if you get two other vectors, then I would like to know, for example, what is the magnitude of each of these vectors? What is the angle between those two vectors? And the statement is that if you give me the original four vectors, which are e is equal to e1 and e2, then I can just look at the components of this along v0, v1, v2, v3. And similarly, I can take w, w0, w1, w2, w3.
And then I know what the length is, the length is just minus V0 squared plus V1 squared plus, etc. And I know what the angle is, it's just V0. So that's what I mean by saying that if you give me four vectors, then I know the spacetime metric. If you give me three vectors, then I know the spatial.
Alright, okay, so now let's get to the more fun questions. So when you were working with Roger, you were a postdoc under Roger when you were working on this initially, and this seems like an extremely promising approach. So is Roger a proponent of loop or did he go off in another direction? Yeah, so in fact, just recently, I had some correspondence with the philosopher of science was visiting Oxford, he writes to me very often asking my views and such thing. And so Rogers, Roger has not followed it in very much. I mean, in his various books, he has said very
Why do you think that is? He's interested in quantum gravity. Yeah, but you know, everybody has 24 hours in a day and you have your own ideas and you feel that they are more... Oh, okay. So he has his own ideas. So he has his own idea. I mean the last
15 years or so, he has been, maybe even more, since the last 10, 15 years, he has been really doing this CCC, right? This one, the Confirmation Click Cosmology. So that's not even Twister theory, but it is, it is just by, so he's been focused on that. I mean, so it's not, I think it's one just, yep. I mean, but same thing is true with me. I mean, I think that Twister theory was very interesting. I started with it. I followed it very, very much until
the mid or late 1990s, but I haven't really followed the advances of whatever is happening in Oxford. Are there advances still? So there's someone or some people moving this Twister field forward? Yeah, this is a smaller group than there was before, but you know, particularly Lionel Mason in Oxford is doing very interesting work on scattering amplitudes and such things using Twister field. But for me the main, I don't see how to
use it very strongly to address the problems that interest me, for example, which has to do with, you know, classical general relativity has singularities, what happens to them? And so those questions, I think Twister theory is still very far from approaching and answering. Professor, what is Einstein's whole argument, H-O-L-E? Right. So when Einstein was developing this
At one stage, he got stuck because he had this basic idea that if you give yourself a theory, which has basic variables, as I was saying before, and you decided that metric was a basic variable. So if you give me some initial data for the metric at time t equals zero,
You give all the information that is needed, which is the metric, the spatial metric, and its time derivative. It's like giving the position and the velocity of a particle, if you like. Then the field should evolve and then should actually give you a solution. But then Einstein realized that because of the coordinate freedom in generativity, this is not true. I could give myself
a metric at the initial instant of time and its time derivative technically extensive curvature is what it's called it is about how this three manifold sits in the four manifold that is a time derivative of the metric. Then he found that well the solution is not unique because I could you could construct one solution and I can come and make a little motion what is mathematically called a diffeomorphism or
In pedestrian language, we call a coordinate transformation. And that coordinate transformation or diffeomorphism is identity everywhere, except in some region up here. So we started out here. And at the initial time, you're fixed to your surface completely. And you're not touching it. So the initial data is exactly the same. But I just change the metric up here. We are diffeomorphism or coordinate transformation.
which is identity outside, but it's not identity in some little region here. And that is the whole HOLE. Then there is again a solution of Einstein's equations. So somehow there wasn't a one-to-one correspondence between specification of the initial data and the solution. And therefore for a while, he really was completely stuck with this and saying that something wrong, how do we get out of it or something until the realization came that in fact,
You don't get a unique solution. You get a unique solution, modular coordinate transformation or modular diffimorphisms, which are identity on the initial slice because you fix the initial data. And so the coordinates or coordinate levels of a point don't have as really a physical significance. Their gauge dependent quantity is like the vector potential in electromagnetism, if you like, or Yang-Gill's theory. I mean, there's a gauge freedom there.
So in Yang-Mills theory also it's not true or in electromagnetism that if you give me a electric field, sorry the vector potential and the electric field. The electric field is like time derivative of the vector potential, it's like the velocity. I get a solution but the solution is not unique. I can make a gauge transformation, I can take the vector potential and add to it a gradient of a function, then function is zero everywhere except in some little region and that is equally a good solution.
So we should not ask that the vector potential should be unique, we should find out what the observables are and the observables should take unique values. So in electromagnetism it's simple, just calculate the electric and magnetic fields and then they are unique, there's no problem with the electric and magnetic fields at all. And now, so the question is about what about general relativity, things are conceptually subtle and then the reason is because we don't have simple observables because
You usually take tensor fields and you calculate the values in terms of components and the coordinates themselves don't have meaning. So you have to construct invariant quantities. So you can take, for example, curvature and contract all these indices with the metric and that is invariant. That would not change at all. So if you could choose, I mean, just conceptually, in practice, nobody has been able to do it and it's not going to be very useful either. But if you could choose four curvature
So this is what Einstein realized that in fact there is a gauge freedom and we just have to live with it.
and so that is the whole argument basically and this whole argument actually has a very interesting thing in loop quantum gravity because what are the basic tenet of loop quantum gravity is again that these points don't have physical meaning or the coordinate labels don't have physical meaning you should not have background structures so you have to compute observables you cannot just ask for example I cannot ask
I should not ask what is the area of the screen by itself, right? Mathematically, I can ask an object. But I should ask the question, formulate the question in physical terms, namely, the screen is invariantly defined as a discontinuity surface. There is no matter on this side of the screen and then suddenly there is a discontinuity. There's matter here on the screen itself.
So I define this screen as a discontinuity surface. And then I can ask, what is the area of this surface? Now, if I make a coordinate transformation, it acts on the metric. But it also acts on the matter field. It acts on everything. There are no spectators in this in this drama of evolution. So if I make a coordinate transformation, if I make a diffeomorphism,
If your morphism is an active way of talking about coordinate transformation, then this screen, for example, would bend, would look like that. But the metric would also bend. And the value of the area that the new metric will give on the new screen is the same as what the first metric gave on the screen. So this is an observer. The area of the screen is an observer. And the reason is because matter as well as geometry are both actors.
Okay, you gave away that the question made sense and then didn't make sense. Can you restate the first way in which it doesn't make sense? Yeah. So if I just say that, well, very good. So if I just say that, well, here is a certain square, right? What is the area? And the statement is that, well, I don't know, because if I take the square and if I act on by diffeomorphism, then I will get a metric, right?
And I have the same metrics that is given to me. Then I calculate this area and the area is going to be different. Okay. Okay. But the point is because the area is not invariant and the metric is not invariant and diffimorphism. But what you have to do is to define the surface in physical terms and apply the diffimorphism to everything. Metric is a physical quantity so you apply the diffimorphism to the metric and you apply the diffimorphism to this metric.
You apply them simultaneously, and then it's completely embedded. And that is very deeply embedded in loop quantum gravity. Our observables that we talk about are observables in this sense. And these are relational observables. I think Carlo must have talked about this. This relational view is very, very important in loop quantum gravity. I mean, the view is already there in classical general theory, but we take it very seriously, much more seriously in loop quantum gravity.
Okay, so we just talked about Einstein's whole argument, which is not talked about much. So I don't think anywhere else on the internet, actually, I did a YouTube search. And so this will be one of the only videos where Einstein's whole argument is referenced. By the way, as a side remark, you know, when I first saw it as a personal thing, when I first read this argument, there were tears in my eyes. I mean, this guy, where was he born? How could he figure this out? You know,
Why don't we stick for a moment longer on the Einstein whole argument. The way that it was explained was you have some system and then you evolve it forward and then there's a whole
and it doesn't matter if the hole is here or non-existent or it's larger, it still gives the same observable. Now, can you make that more concrete in terms of, let's say there's a ball, in terms of Newtonian, if you throw a ball, what would it be like? Give people an analogy. It would be like if the solution is a parabola, we understand, but the solution could also be a parabola minus the top. Give some analogy. No, the trouble is that there's no analogy in Newtonian terms because there's no motion gauge there.
Notion of gauge is critical in this thing. So anytime you have like Newtonian argument or the Newtonian ball or something like that, there is true that every initial data
In Maxwell theory, there is. I can give that example using Maxwell theory, but it is already a little bit abstract, which is basically that I can give you the initial data with the vector potential and its time derivative, which is the electric field. I can evolve it and I get a solution, but I can take
Take a little ball, a little region as a space, a little hole. And in that region, I just change the vector potential by vector potential. It goes to its original value plus gradient of a function, because the vector cannot take a gradient of any function. When I do that, the vector potential itself in that little region has changed. But you see that continues to satisfy the equation that was
So the point is that you should not try to see if the weakness holds for the vector potential but for observables and the observable for the Maxwell in this case is a magnetic field. It is a curl of this A and when adding the curl the gradient drops out. The curl of A and curl of A plus gradient of F is exactly the same.
So the E and B are exactly the same in Maxwell theory and that gauge in varying quantities and they are exactly the same.
It's just that in physics, sometimes you would think, well, I should be able to formulate things all in terms of gauge invariant quantities. I was sure that was possible when I was a student. But no, the statement is that if you wanted local physics, and locality is an important part here, then they cannot be formulated in a gauge invariant fashion.
In E&M, the potential is not observable. It's the electric in the magnetic field. Yeah, electric magnetic field. Isn't there the Aronoff-Bohm effect? Exactly. So how does one make sense of the whole argument there? Yeah, well, it's similar, but not exactly the same because there's no initial data, which is you're evolving in the Bohm-Aronoff effect. So what you have is solenoid.
So I think of this as a solenoid, just forget about it. This is a solenoid. And then the statement is that there is a current going through here. And so therefore you carefully adjust it so that actually there is no that the magnetic field is all here. There is zero magnetic field outside here. And then the interesting thing is that I see what the electron does if I start out here where there is zero magnetic field.
I go around and the statement is that there is actually a zero magnetic field. So you might say that nothing happens. But the statement is that there is in fact the holonomy. I mean you actually do get an effect up here because vector potential here is not zero. So it's not right to say that vector potential is not observed. Certain quantities are observable. Why? Because what you're measuring is what you said holonomy which is really
the circuit integral of a, but a dot dl is the same as b dot ds by stokes theorem. If I take a vector potential up here and do the circuit integral is the same as doing the surface integral
the flux of the magnetic field through the surface up here and there is so but you have to take the whole surface which is enclosed by this and that does include here so the electron doesn't see the surface but the electron actually sees and so that is a beautiful argument to say that well if you wanted to formulate everything in local terms then the vector potential is essential right because magnetic field was zero here magnetic field was zero but the electron still felt the electromagnetic field
Okay, another aspect that's not talked about much is Mach's principle. There are very few videos online about Mach's principle.
So why don't you explain what Mach's principle is, why Einstein thought it was so crucial, and what loop quantum gravity says about it? So the coin Mach's principle or Mach's conjecture was actually, this term was coined by Einstein. It didn't exist before, so Marx never called it a principle or something, it was really coined by Einstein at that time. And it played an important role in his formulation of
ideas about general activity. And this really goes back to Newtonian ideas about inertial frames and so on. And at that time, in Newtonian theory, it is certainly true that things like notion of centrifugal force were very important. If you're rotating, then in your arms go out. If you're doing a solid spinner, the water goes out. You dry the salad up here in that particular way. So
If you are not in inertial frame, if you are in a rotating frame, then there is centrifugal force. It looks like the notion of rotation is an absolute notion. But in Newtonian theory, there are local inertial frames. And so the question was, well, then, you know, how can you tell which frame is local inertial? And are you rotating or are you not rotating? And then the idea was that, well, you look at the distance stars.
And the frame defined by the stars is an inertial frame. And then on the other hand,
So if you're rotating with respect to it, then you... I'll be showing a picture of the Newtonian bucket-bott experiment. And as far as I understand, Newton used that to say, no, there is an absolute notion. I'm sorry. Yes, there is absolute space or an absolute notion of motion. And then someone else named Mach took it and said, actually, that same experiment proves that motion is relative, except you have to take into account something else. Right. Namely that it's really related to the distance stars, and it is really defined by... Yeah.
So Mark wanted to say that this is, and so the idea was that, well, non-local things, I mean, things over there, determine the local, the same kind of thing. And that idea sort of, Einstein in his writing and so on, has emphasized that played an important role. But in his later years, I think there is some work, historical, nice digging of work by historians of science, maybe Julian Barber from the other people. Then Einstein himself has said that, no, and as a mathematical sense in
Why is that the case?
As far as I know, most general relativity people don't think that that principle plays a deep role, or any role, depends on who you talk to, in the actually final theory that Einstein came up with. Which is why I never heard of it until recently, and I've studied general relativity and I've been taught courses in it, and almost no one else that's a student knows about Mach's principle. And the main point is that
I mean, the only way to formulate it is something, I don't want to get too technical, but basically, again, in terms of this initial value formulation that we talked about, namely, some of those Einstein's equations that we've got, the metric has 10 components and we've got 10 Einstein's equations on the metric. And Einstein's equations relate the curvature to the stationary tensor or to matter properties.
And the thing is that four of those equations are called constraint equations. In other words, they don't involve time derivatives. So they must involve just space derivatives. So they must hold at any instant of time without knowing what the time derivatives are. And an example is just given by in electromagnetism, you can think of E and B and you've got equations and you've got equation which says that divergence of E is equal to zero and divergence
without sources, divergence of E equal to zero and divergence of B equal to zero. If you have sources then divergence of E is equal to 4 pi times charge density and so on. But then they don't involve any time derivatives. But then you have got time derivative equations which says that E dot, the time derivative is curl B and B dot is minus curl E. So you get a
Now the same thing is true in Einstein's case. There are four equations which are called constraint equations and mathematically they are called elliptic equations. So elliptic equations are very rigid. The solutions are really given globally on an initial instant of time.
And so if you give me stationary tensor matter field, then I will be able to calculate for you. I have to solve this equation to get the initial metric in the extrinsic curvature. There is still some freedom, but a lot of it is completely determined. And so sometimes people might say that, well, so there is a max principle because matter doing out there is determining what the solution here could be.
But that's not completely right, because you also have local degrees of freedom, but that matter doesn't determine this solution completely. And of course, if you say that, then you would have to say also in electromagnetism, that there's a max principle, so our charge density out there determines what the electric field appears.
and the statement is that yes or no, yes in the sense that if there are no electromagnetic waves then the answer is yes, if it's static solution then the answer is yes, but if there are electromagnetic waves then part of the electric field is determined by the sources, charges, but part of it is just it has its own degrees of freedom and gravitational field has its own degrees of freedom and so that's one of the reasons why people don't take it seriously. I personally also don't take it seriously but I may be a
not a total minority but somewhat of a minority because I think that the whole notion of inertial frames which are so important in Newtonian physics. The whole point of general relativity was that it's lost. For your intuition you can talk about local inertial frames but I think that you can do any every calculation answer every physical question without ever talking about inertial frames.
And so this whole impetus that that was there about how do you know that you are inertial frame or you're not? Yeah. I mean, since you're talking about undergraduates, I mean, I mean, you know, when you teach this elementary course, there's always smart, I feel there's some smart undergraduates should ask this question, right? You said, wait a minute, you calculated the motion of the moon around the earth, saying that
Well, I mean the Earth's center of mass is an inertial frame and in that I applied Newton's laws and I solved it. But then Earth's frame was inertial, fine. But then when you talk about Earth's motion around the Sun, then you say Sun's frame is inertial and Earth is rotating. If Earth is rotating, it could have been an inertial frame. So isn't one of your calculations wrong?
And to me, at least, I mean, the real answer to this real answer to this question comes from general relativity. You don't need the notion of inertial frame. You're just calculating geodesics in the two cases. And then there's no problem at all. So I think this whole over emphasis on inertial frame, I don't mean it's useless notion. On the other hand, it's not essential. It's not something that, you know, on which any foundational issue should refer to. So that is the point about Marx's principle.
Okay so let's get to black holes. What does loop quantum gravity say about singularities and black holes? It would also be great if you could outline what a singularity is and why there are problems or some people think they're issues with the concept of them. So actually singularities in general relativity or any theory really arise because you start with some initial data which is completely regular and you evolve it using field equations.
And it may turn out that the field equations say that, in fact, that after a finite time, the fields become infinite. And if the field becomes infinite, you cannot evolve any further. And then you're stuck. And you just have no, no, no. So it's like the theory fails there. Theory comes to an end there. Now, something like that may happen in other theories, but one might just say that, well, it's not so bad because after all,
Maybe I just need to tweak something for that particular theory. I mean, I still have space time. I can ask the question about evolving and such. But in general relativity, the space time itself is defined by this evolution. So if the field becomes singular, the curvature diverges somewhere, then space time itself comes to an end. So it's not that particular initial data led to a problem. But in that space time, everything ends.
So historically, what happened was the following. So I think this is important for people to know.
that historically people started with cosmology, namely the freedom of solution, the initial singularity. So the US is starting with the singularity up here after Hubble's discovery. And by the way, it is really
who understood the physics of it completely, the Hubble's observation of what it meant and so on and so forth. And that's why the Hubble law was renamed Hubble-Lemaitre law recently by the astronomers. So there was actually this initial singularity. And that means that if you evolve back in time, space-time comes to an end, and so there was an absolute beginning. And this was a
issue about big contention and people were thinking both ways. Maybe some people thought that, well, this is good because that means that the biblical notion of you were starting at a finite time is reinforced by science. And again, a very interesting anecdote here is that George Gamow, who was one of the leading physicists at that time, who was working on nuclear synthesis,
and the notion of Big Bang really became more established with nuclear synthesis that they must have been a very hot phase of the early universe in which heavy elements were cooked because somehow when you look at the abundance of lithium, helium and that somehow and see how much of it is produced in stars, that is not really something that could be produced in stars. Enough of it could not be produced in stars. There must be some initially
There was some other mechanism by which this was produced, and therefore there was a hard initial phase of the universe. So Gamow actually wrote to Pope Pius XIV, I think, at that time, and saying that, well, look, you know, there was a hard phase of the universe, the universe was also born, and Pope got very excited. And so he next
The Vatican has a nice observatory, so the next conference that came, the Pope inaugurated by saying that it isn't just wonderful that science and religion are coming together and so on and so forth. And Lemaitre, who was associated with the observatory, had the hoodspot to go to the Pope with one senior person and convince the Pope that it's best not to mix religion and science.
So the singularities are very important, but people had various unease about it. In the 70s, very prominent British physicists and astronomers came up with this steady state university. Herman Bondy was working on it.
And of course, Fred Hoyle was the main pushing, Jay Narlikar was a student of his. So they were actually pushing this idea and in part because some people didn't feel that Big Bang was. In fact, the name Big Bang was, by the way, people don't know, was invented by Fred Hoyle in a pejorative way, in the sense of making fun of it and not seriously.
So the statement is that these big singularities, these initial singularities were troubling. So that is really the absolute beginning of time. And black holes, at least the simplest black holes, the Schwarzschild black holes and so on, they represent the absolute end of time because space time ends there and you cannot evolve. Classical general relativity fails and you cannot evolve. Not only classical general relativity, but you cannot evolve any field there because
So that is why it is so sort of important. The reason I spend a lot of time explaining about the Big Bang rather than right away in black holes is because for majority of the period in history, people were more worried about this absolute beginning than the absolute end, in part because it's relatively recently that people began to accept black holes as being reality.
Again, younger undergraduates won't realize this, but it is really true. I mean, I think when I was a graduate student, I had somebody who was a couple of years ahead of me, John Friedman, and he went to give talks. He was a student of Chandrasekhar's and they were talking about black holes. And in very prominent universities, prominent physicists would ask him afterwards, why are you working on this? It's not mathematical. It's not physics.
Astronomers also didn't take it seriously for the longest time. So that's why I began with them. I mean, the Singularity has been with us, but probably a lot of people for a long time, which is the cosmological Big Bang Singularity. And that's a meta commentary on the state of physics because some people would wonder, well, why do you care about high energy physics or extremely high energy physics when we can't reach there, when it seems like there's no predictions and so on? Well, the same argument was laid at black hole theory or studying black holes.
I agree but the question is always how comparing the argument is and again how comparing the argument is in the eye of the beholder. I mean to me as a graduate student and you know people who are doing general relativity it was obvious. There are a lot of black holes or something it was obvious. Why don't we see them? We don't see them because you know we don't have the techniques and we'll see them. We're confident about it all. I mean Chandana was 100% confident about it all otherwise he would not have spent 10 years of his life
thinking about these things. So that's what singularity is. So for the longest time then, people have believed that the singularity is the artifacts of general relativity, because we're assuming that Einstein's field equations are valid at arbitrary high densities and arbitrary high curvatures. Now, people don't realize this, but already in the 50s, in one of the editions which I have in one of my papers,
Einstein's book, Meaning of Relativity, one of the later editions, he has an explicit statement saying one may not assume the Big Bang singularity to be physical. He doesn't call it Big Bang, he says that the initial singularity to be
One should not assume that the initial singularity in the mathematical sense to be physical, because one may not assume the field equations, which is his own equations, at arbitrarily high densities of matter and field, by field even curvature. So Einstein himself had said that, by the way, but I mean, people still took it all very seriously. But I think there's a complete general consensus now that there is the
Is it correct to say that for the same reason that we can't evolve a black hole forward and so we say that that's the quote-unquote end of space-time is that the same reason why we consider the Big Bang to be the quote-unquote beginning in terms of just evolving it backward we can't? I mean in both those cases I'll qualify in a minute but that's the idea.
I just wanted to say that there is a short video which is called the meaning of the Big Bang or the new meaning of the Big Bang or something like that. It's only short, it's quite short like 15-20 minutes something and there were about seven of us who were interviewed including Stephen Hawking and Roger Penrose and
And we were interviewed in a completely separate location in our home institutions. And so we did not know who else was being interviewed, what they were saying. And we all had different approaches to quantum gravity and so on. But then all of us say exactly the same thing, that Big Bang is not a physical singularity. You know, there was an early hot phase of the universe that everybody agrees with that is important for nuclear synthesis and so on and so forth. But this in the inflationary model, for example, this phase comes after
the end of inflation. So certainly not before the onset of inflation, not before the Big Bang at all. And people say that, well, yeah, the idea that in early days, you know, when people form cosmic background and so on, they say, well, this is a signature of the Big Bang, you know, and that I think is not, it's not correct at all. That's a statement of here. It's not a signature of Big Bang because it happened way after. I mean, the, the hard phase really must happen before.
Way after as in many seconds or many microseconds or what? No, I think it is not way after, it's not that often. Yeah, so it is about, it's a fraction of a second, but in terms of plunk times way after fraction. Yes, yes, yes. 10 to 30 plunk times, 10 to 38 plunk times, something like that. So it's in that sense, way after. Even more. The end of the question is then after that, how many folds pass before the
So that is the idea and then the statement is that what
does loop quantum gravity wants to have to say about this and this has been one of the sort of solid ideas in loop quantum gravity namely that because we have got quantum Riemannian geometry rather than classical Riemannian geometry so we have to reformulate Einstein's equations in this new language. I like to say that well quantum gravity needs a new syntax and in loop quantum gravity the new syntax is
quantum Riemannian geometry. And now when you formulate Einstein's equation in terms of quantum Riemannian geometry, there are difficulties, of course, and that's why the problem is not completely solved. But what we can do is to go to physically interesting situations and apply it there. It's a bit like we don't still have complete QCD theory, quantum chromodynamics theory.
But we can go to physically interesting situations and you develop approximation techniques and then make predictions and then that same concern and such. So here the simple examples are simple situations that are physically interesting are provided by cosmology. So the Big Bang and the black holes. And then the reason why I think they're important, but also there is a lot of symmetry.
And because there's a lot of symmetry, then loop quantum gravity can make a lot of progress because many of these questions then simplify. I mean, technically, you should simplify that. So that area is called loop quantum cosmology. And the way loop quantum cosmology is done compared to other quantum cosmologies is really keeping an eye to full quantum gravity.
So it's true that one is in a simplified situation, but one doesn't sort of say that I don't know what the full theory is, and I'll just work in the simplified situation. This is what happens in Gile DeWitt cosmologist, because in the full theory there is no mathematically conceptual framework. We don't have Hilbert space, we don't know what to do and so on and so forth. Even at the kinematical level, even before you come down to dynamical equations,
What is the basic framework in terms of which to pose the questions is not clear in geometry dynamics. Whereas in loop quantum gravity, we have this rigorous framework, this quantum Riemannian geometry produces, provides us this rigorous framework. Therefore, we can take this rigorous framework and apply it in the simplified situations. And there's a precise sense that real theorems would say that this applied to this particular situation, there you've got a certain representation.
certain Hilbert spaces, certain ways of representing operators, those ways trickle down to these particular ways of doing operators. I'm not saying there are no ambiguities, but there are theorems which tell you what the assumptions are, so they will tell you what the ambiguities are, but there are higher order things. And within this, the statement is that Luke on cosmology has a precise mathematical framework,
And precisely because it encapsulates the quantum nature of geometry, the fact that the area operator has a discrete spectrum plays a very important role in this case. Because of that classical Einstein's equations receive quantum corrections. And these quantum corrections are such that the evolution of the quantum Einstein's equation doesn't break down in the singularity. You can continue across it. So
You can look at it at various levels. At the heuristic level, you can think of it as follows. This is space-time continuum is an approximation. And I've given this very often analogy because I think it really is a good analogy, which is that you look at, for example, my shirt up here. And my shirt up here is really, for all practical purposes, this is 2D method continuum. You want to see it's continuum. It's clear it's continuum.
You just have to take a magnifying glass and see that it is is woven by one-dimensional threads. There are constituents. It's not a continuum. It really is one-dimensional. It's not two-dimensional. But the threads are packed together so much that it looks like a two-dimensional continuum. And the statement is that the same is true with the quantum Riemannian geometry. Namely, our space-time continuum is an approximation like this shirt.
There are fundamental building blocks and these fundamental building blocks are come from these Wilson lines or these connections up here and there is a precise mathematical framework. That is what enables you to calculate the spectrum, the eigenvectors and eigenvalues of the area operator, the volume operator, length operator and so on and so forth. And what one finds is that the area has a non-zero minimum value.
So it's not a continuous thing because the spectrum is discrete, you've got zero of course, but then there's a gap and then there's the smallest eigenvalue and that is called the area gap. And then when you go to quantum Einstein's equations, this area gap plays a fundamental role.
Again, let me make a detour because we talked about holonomies just a while ago and we talked about Bohm-Aranoi effect which is also a holonomy. So what a holonomy does is to really look at the flux of curvature. So one way of defining the curvature is really in terms of holonomies and the statement is that you have to take the holonomy and you have to divide by shrink the loop until it shrinks to zero in classical generativity.
But in quantum Riemannian geometry, you don't do that. You can only shrink it up to a minimum area eigenvalue. And when you have shrunk it to a minimum eigenvalue, then you get an operator. And there's a fundamental non-locality for this curvature operator. But at the Planck scale, it's not because this area that encloses the order of Planck. Sorry, there's a non-locality associated with what? There's non-locality in the curvature operator. So the curvature is defined by
taking the holonomy around a closed loop and dividing it by the area like it's because the holonomy from electromagnetic field will be b magnetic field times area b.ds and then if you don't know what the magnetic field here is you want to divide by area and take the limit so the loop particular point up here but here we I mean you cannot shrink it to zero value because there's a
There's a minimum, so you shrink it to the minimum. So the spectrum starts at a non-zero value? There is a zero value, but then the statement is that you cannot shrink this loop to a zero value. I mean, if you shrink it to the zero value, the framework doesn't let you shrink it to the zero value. Because it's discrete? It's discrete. It's discrete. Exactly. It's discrete. The spectrum is discrete. So you come to the minimum non-zero value,
Then the statement is that you have this holonomy that gives you the curvature times if you like this area. But that's all you have. You cannot have curvature at a point. You just have, we are these operands. So therefore there's a non-locality at the Planck scale.
Sorry, to be clear, when you say that there's non-locality, are you referring to the connection changes from point to point? Is that what you mean or is that something different? No, the connection does change point to point, but the statement is that the curvature is calculated only by the connection.
and therefore I cannot define the formalism does not let me define the curvature at a given point. It only tells me what the curvature is, average curvature is on the surface of plank line along the holonomy. So in terms of surface, average curvature is in a plank line.
So therefore what happens is the curvature also has a maximum value. It cannot be infinite. There's a maximum value. And that maximum value
are surprisingly is related to the area gap. The matter density has a maximum value. And the matter density is which is really given by the goes like some constants divided by the area gap cube.
Now if you let the area gap go to zero, the classical limit, then the maximum value becomes infinite. But in loop quantum gravity, the area gap is a well-defined number, and therefore you've got a maximum. It's a very large number. Sure, sure. But it's finite. But the precise number is finite, exactly. And therefore, in loop quantum cosmology, what you do is you take a wave function of the universe. In other words, you first start out with the classical space time.
classical solution of Einstein's equations, like one of the Friedmann, Le Maitre, Roberts, and Walker cosmologies. And then you take a wave function which is very sharply peaked on that geometry at a given instant of time, at late time. So that wave function describes the geometry and you evolve it back in time. And as you evolve it back in time, it remains sharply peaked along some geometry.
If you want it forward in time, it remains sharply peak along geometry. It is the classical solution that is a function. But if you want back in time, then it follows the classical solution until the matter density or the curvature is about 1000 or 10,000 times the plan curvature and then it deviates. So the quantum correction becomes very important. It's almost negligible until the plan density is about
the classical trajectory is still in the peak of the wave function. You know, the wave function is sharply peaked, the classical wave trajectory is still in that wave function, you know, one standard deviation of the wave function. But then when that density is reached,
Then the wave packet is still sharply peaked but does not follow the classical trajectory. Classical trajectory would run into singularity. So if I think about singularity as being on the left side here and the classical trajectory is going into the singularity, left side here and the classical trajectory is going into the singularity, it's just your right side. Classical trajectory is run into singularity. What happens that it is approaching singularity and then bounces.
It bounces away from the cylinder. And again, by the time the curvature becomes 1,000 times, 1 upon 1,000 times the Planck curvature, or density is about 1 upon 1,000 times Planck density, then classical general relativity is again a good approximation. So there is a quantum bridge which joins a pre-Big Bang branch of the universe and the post-Big Bang branch of the universe.
So that is what is happening. And to me, the big surprise was when I first found this out, I didn't believe this. Maybe this is very special because we're using very special, very functional, special initial conditions. So I was working with two post docs, Tomasz Pawlowski and Param Singh. And they were the ones who were doing the HARC and the calculations, not the analytical part. I had done most of a lot of it.
And so I kept asking them to change these parameters, do this, do that, to see if it is robust. And after about six or eight months, I was convinced that it's really there. And then a couple of years later, we found analytical methods to get the same results with appropriate approximations. So by now, there are many, many different ways of checking this result, that in fact, the wave function does bounce. Is this what's called the Ashtakar bounce?
When I was speaking to Salvatore Pius, and I know I sent you a question from him, he kept referring to the Ashtakar bounce and he was saying, Kurt, you have to read conversations on quantum gravity. Ashtakar will blow your mind. He told me read all the conversations except yours and leave yours for last because he said yours is the best one. And he was super excited. So at some point later, we're going to get to his question.
All right, so that is what happens. And then cosmological models, people have done many things. First, it was done just by the simplest models, which are spatially flat, which correspond to our observed universe. It seems to be spatially flat. But then to make sure it is robust, people added spatial curvature to it. People added inflationary potentials to it. People added anisotropies to it. And collectively, we have found that the bounce is very robust. Now, nonetheless, in cosmology, things are
When it comes to black holes, it is the same question as you say is the end of the universe and as opposed to beginning of the universe for at least for the non rotating black holes. I will talk about rotating black holes just in a minute. So non rotating black holes are singularities against space like so it is really like the Big Bang singularity, but it's in the future. Its nature is very different.
part of the curvature which blows up at the Big Bang is very different from the part of the curvature which blows up at the Black Hole. And that is why Penrose often refers to the two as being very different and therefore they should be handled differently and so on and so forth. So therefore, as a result, we do not have as many tests and as much detailed investigation in the Black Hole case as we have in the Big Bang case. But there are
Fair number of calculations are having said that they appear in physical letters. People have a lot of references. People, you know, build on it and not just, you know, hundreds of papers written on the basis of those and so on. So it's not it's not a beginning stage by any means, but it's certainly also not not not really finished. So what do we know? So then again, what we find is that
It's somewhat different, but what we'll find is that there is actually a bounce across singularity. So the universe doesn't end at the singularity of the short shield space-time, but you can actually continue the evolution across that singularity. Now, what is it that happens? What are the differences?
Well, in the black hole case, as you know, there is an exterior region, which is the normal region that we live in and so on and so forth. And there is a region of black hole inside the horizon. And here what we're doing is to look at the region inside the horizon, because the singularity is inside the horizon here. And so you look at that region inside the horizon and then then you evolve. Then let's see what happens. But inside the horizon,
is called a trapped region. The reason is because light is trapped. So basically think of the horizon as being, you know, this is time and this is space. So I think of the horizon as being a null surface like that. And therefore if I light a beam of light up here, normally the beam of light would actually expand out and there will be part which also goes inside the light bulb so it contracts. But what we see is the one which is expanding out. So inside the black hole,
The expanding branch actually contracts and that is why it is called a trap tree. So this expanding what would be normally a light front which is expanding is actually contracting and goes into singularity. So inside the horizon both the quote-unquote outgoing branch and then outgoing light front and then going light front they are both contracting. Therefore that region is called a trap tree where
Sorry, when you say contracting, so the way that I'm visualizing it is with ordinary space-time diagrams and then the cones, they're just pointing toward the black hole. There's only cones point, okay. But once we are inside the black hole, already we are inside the black hole.
What you are saying is usually people draw those diagrams when you're outside. But now when you're inside them, the cones are pointing just straight into singularity. Nothing goes out because that region is stacked. So if the singularity is at the top of the page up here, then the statement is that if I got this is the horizon, then light rays coming from here
Just go and hit the singularity and that's it. They never reach you on the horizon. So that light front is not expanding out. That light front is actually contracting. Contracting goes into the horizon. So it's area of that light. Normally if I light a light bulb, spherical light bulb, then the area of the light front is expanding at a speed of light.
Here the area of that light front is actually contracting inside and that is why it's called a trapped region or contracting. And then what happens is that you come across a space-like surface which was a singularity before is now replaced by a regular surface. But this surface is a transition surface and on the other side what you have is really anti trapped region in which both light fronts are outgoing.
Both light fronts are expanding. In your room and my room, if I were to strike a match or light a light bulb, a spherical light bulb, then there will be what we see is an outgoing one. But of course, there's light also travels inside and that is just the incoming one that goes through there. So the interesting thing here is that on the other side of the singularity, both light fronts are expanding out. And so it is called anti-tractors.
In popular terms, the contracting region is called the black hole type of region. And this is called the white hole type of region. And that's why some people like Carlo, for example, like to think about as a transition from black hole to white hole. I don't like that terminology because both black holes and white holes have connotations of there being a singularity somewhere.
And there is no singularity here. It is just a trapped region where all the light fronts are contracting and anti-trapped region where they're all. So I think we understand a fair amount of what is happening. But if you want to know much more in detail about what happens in the black hole evaporation, that subject is still under investigation like in every other approach up here.
If I have time, let me just mention one thing. One is that, because this is often mentioned by people as being a real problem, a real paradox. So as you know, supposing I have a black hole which is formed, somehow I send in some matter, there's nothing else in the universe, I ignore everything else, and I send in some matter and it forms a black hole. Supposing it forms a black hole of one sort of mass. And then after that, nothing is falling into it from outside.
In classical generality, the black hole will just stay there. It's going to be one solar mass, it will just stay here. But because of Hawking effect, because of quantum tunneling, it is shrinking. And it is shrinking and shrinking and shrinking and shrinking and becoming smaller. And while it does, it's emitting this quanta. And this quanta are going up to infinity. And the big question is really the following, that this outgoing quanta look like they're in a thermal state.
which is a mixed state. It's not a pure state. Why is it not a pure state? Because these particles, this quanta are created in pairs. One particle goes out to infinity and its partner particle falls into the black hole. Now if it falls into the black hole, the two are correlated and therefore you're losing correlation. If you just look at infinity, you're not seeing what is happening inside, so you're losing correlations and that is why you've got a mixed state.
So it's like an ordinary quantum mechanics, except that it's happening in black holes. You're only seeing part of the system and therefore... Just as an aside for people, the difference between pure and mixed is... So a pure state is represented by a wave function, if you like, or by an element of a Hilbert space, either a vector or a ray in a Hilbert space, whereas a mixed state is represented by
state itself is represented by an operator. So basically it is like an operator in which I got just say for example if I just have spin up and spin down then I'm going to have a bra which is spin up, bra which is spin up and then some probability density plus bra which is spin down some probability density or rather spin up, spin down, spin down, spin up and some probability densities appear.
So it is a state which you cannot write as just a straight forward ket or straight forward wave function. And it is sort of basically saying that the state has kind of two subsystems and they're correlated. And if I now only look at one of the subsystems outside subsystem,
Then technically what one has to do is to trace over the states, the subsystem that we are not looking at. And when you take this trace of that, it becomes a density matrix or an operator because they're taking a trace of it and you're forgetting part of the information. So I think the simplest thing is to say that you forget part of the information.
Let me see if I can restate that. So most of the time when one is studying quantum mechanics, we hear about the wave function, but technically the wave function is for pure states. And even that it's not a unique member because you can take it. It should be a project, a member of a projective space. And then most of the time we're, we're dealing with our ignorance. We're dealing with mixed states.
which are operators, which are matrices instead of just a vector. So what I want to know is with these density operators, I believe they're called density operators as well, or is that false? I don't know the history, but there's a quantum mechanics. Whatever, it doesn't matter. So with these mixed states, do they arise only from our ignorance, from looking on the outside and core screening, or is there something inherent about the system that makes it mixed in some way?
Right. Now, I think that in the context of quantum mechanics, in the context of black hole evaporation, it is our ignorance. But it is fundamental ignorance because other particles go inside the black hole. So inside the horizon. And so that's our fundamental ignorance. But I mean, you could consider. Yeah, please go ahead. OK. So I went on the outside of the black hole. There's these virtual pairs and then one of them happens to go inside and the other one escapes.
So then does that mean equal amounts of matter and anti-matter are coming out of the black hole? Yeah. And is that okay that somehow doesn't violate some law because matter is what fell in but then sometimes anti-matter is what comes out? Yeah so the statement is that if for example you're going to charge black hole then there will be preferentially there will be preference of charging negative and there will be more
negative particles will come out but also positive charged particles will also come out. Now the black hole is shrinking and we understand. So the black hole is shrinking up here and then the statement is that we're looking at yeah and then and and so as a result of it more and more
thermal radiation is going out to infinity. In other words, the whole state is a pure state because it started with a pure state. But what is registered in infinity is only part of the state. And therefore, we're not looking at what is inside. And therefore, it is actually the state at infinity that we're looking at, quote unquote, appears to be mixed state. Now, the point is that this has
In my view, given rise to some confusion in the literature, quite some confusion in literature, because people take this event horizon as being absolute. And it is true in classical general relativity, but even in classical general relativity, there are things called dynamical horizons. You see, the event horizons are absolute, but they're also very not directly physical in this following sense.
You know, an event horizon might be forming in the room that you're sitting in right now. It's completely contained in the room that you're sitting right now. The reason is because it's still teleological. This is in response to what may happen a billion years from today, that there may be a collapse in the center of a galaxy somehow.
And then there will be a huge black hole. And if I trace back the event horizon, I have to trace back the event horizon. I don't know where it is until space time has ended, so to say. I can trace back the event horizon and then I'll find that, oh, it was actually fine. There's a component in this room right now. I don't feel anything locally. So event horizons are teleological. They are not
People are used to event horizons only in static situations like in the black hole or black hole or something. They don't think too much about the dynamical situations. I mean, simplifying, but a lot of people don't think enough in the in the dynamical situation. That's the point. In the dynamical situation, the statement is that event horizons like what I'm saying about just now can be very unphysical, can be very ghostly. But there are notions called
local, quasi-local notions and like in this room I can tell that there is no quasi-local horizons that in fact were developed here by Paul Stokes and I developed these things many years ago. This was in the context of vibration waves and black holes and not but is now has been used at starting from them also in quantum gravity because I was working both those areas up here and so if you take that more seriously then in fact
there isn't such an absolute end that there's no way for the information to come out. That you have to couple with the fact that in loop quantum gravity, singularity is resolved. You see, as long as there is singularity, then the kind of space-time diagram that Stephen Hawking was drawing initially, he changed his mind later, but initially he was drawing,
which our end singularity at the black hole singularity. Even when the black hole evaporates, the space time still has that singularity. And then that singularity can act as a sink of information. And therefore, it can happen that you start with a pure state, but you get a mixed state because some information failing to that singularity and it's completely inaccessible. But if in fact singularity is resolved and you don't have this absolute event horizon, then this information can come out.
at later times. And there is no a priori problem about the information coming out and the S-metrics being unitary. Now the S-metrics being unitary is not the same as saying S-metrics is identity. We're not saying that what comes out is what goes in. People often, I'm asked this question even in technical conferences by people who are outside quantum gravity, but they say, well, I don't understand. I mean, how can it be? Supposing I just take encyclopedia Britannica,
And I burn it. I lost information. So the point is that no, you're not lost information. Word information is funny. But you're lost information in the sense that those words that were written there, encyclopedia, are lost. But on the other hand, I had a state of the encyclopedia and the fire and everything. And then I had a final state. The final state, there's a lot of radiation that came on something, et cetera. And both those states are pure states, ultimately. And because they are pure states, I could
Information is not lost in the sense that there's a unit transformation which will bring me back. I mean in practice it is hopeless. So that is basically the statement up here that there's no, you can have a very complicated, I mean when we smash particles in CERN and then you get something else and obviously what you get out is completely different from what you started out with. But information is not lost in the sense that the S-metrics is still unitary. So that is a point.
Okay, so I think that, you know, S-metrics, we believe in Lupin-Gravity and most of us believe in Lupin-Gravity. Carlo and Rovelli and his group and I and my postdocs, so I have been working on parallel lines. Most of the time we have exactly, we are in agreement, but we're not in agreement on everything because there are open issues that we don't know which way it is going to go. And of course, with open issues, you always have prejudices about what is likely to happen because that's where you put more energy.
And so there are differences, but on the other hand, the overall picture that I just mentioned so far is common to many people working in loop one already. So we believe the information is not really lost. There's another issue that is very interesting that your audience might be quite interested, which is the following, which is a restricted form of information loss.
So let's not worry about singularity. I told you about singularity and things can come out and people might say, well, I don't know if singularity is resolved, etc. Let's not worry about it. There is still a problem, quote unquote, potential at the early stages. So supposing I take a solar mass black hole and I let it evaporate till it becomes a lunar mass.
So it is about a millionth of its mass now from what it is. But still it's a macroscopic object, this lunar mass black hole up here, right? So people have argued that even in this process, some semi-classical considerations are not going to be valid and something drastic could happen. And these people were claiming things like that means that even outside the event horizon of astrophysical black holes, quantum effects would be important and there would be
change our picture of understanding what is happening altogether. Since LIGO data which sort of shows no surprises vis-a-vis classical general relativity, these claims have been scaled back quite a lot. These ideas have been scaled back quite a lot that astrophysical black holes would encounter real problems. That has been scaled back quite a lot.
But nonetheless, people ask the following question. Supposing I go from solar mass to lunar mass. This process, by the way, is very slow. It takes 10 to the 76 years. The universe is only a billion years. I mean, 14 billion years. So this is huge compared to the life history of the universe up here. But still, the statement is that what is happening. So during this 10 to the 76 years, basically the solar mass
has become millionth of a solar mass. So most of the solar mass, solar mass minus a millionth of it has been radiated away. And its partner modes are all in here. So there's a huge number of partner modes. There's a huge amount of what, sorry? A partner modes, the modes which have gone away, the modes of the field, like radiation, which goes out, people call it modes, modes of the field. So these modes have gone away.
And their partners, you might call them particles. People don't use the word particle because in corner fields in curved space time, the notion of particle is not so sharply defined. So people talk about modes rather than particles. But the statement is that these modes, these particles, they're gone away and their partners are on the side. And so a huge number of correlations is lost, right? Because it's almost the same as the mass of the Sun, right? Mass of the Sun minus
So people say, well, wait a minute, I got this little thing with a millimeter size thing, right?
And how can it hold so many moors? There's moors, the partner moors are all here and there's just no way it can hold all these little moors. And there's more sophisticated arguments, but that's the basic argument up here. And therefore there's something, some semi-classical considerations must go wrong way before the solar mass black hole has shrunk to a lunar mass. That is the argument that is made.
But then when we look at more detail, first of all, not taking the event horizon so seriously, but looking at this quasi local horizons that I mentioned before. And we look at the back reaction. In other words, there is over 10 to 76 years, almost the whole solar mass of black hole, solar mass of black hole minus a millionth has fallen in it. So of course, that is going to change the geometry inside. It's not going to be the same geometry as before.
The question is, what is happening to this geometry dynamically? How is it changing? And what we find is, again, this is done independently by several people, the same conclusions, that what happens is that if you look at a space-like surface, constant time surface, inside the horizon of a black hole. So it is anchored on the horizon, and therefore it has a kind of a
two sphere here on the horizon, right? I mean, a two dimensional sphere up here. And then inside, it's like a tube, right? It goes inside. The space-like surface looks like a tube up here. Now, in the beginning, the tube has a Schwarzschild radius of a solar mass black hole, so it's about a kilometer radius. And the length up here is also kilometers, roughly comparable. It's not much difference. But in this 10 to 76 years, the
The aperture of the black hole, the portion from which it sort of communicates with the outer world, which ends on this quasi-local horizon, that shrinks. And that has shrunk to a millimeter now. But what happened to this tube? Amazingly, this tube gets longer and longer and longer and longer and longer. You can say, yeah, but how much? Well, it gets longer like 10 to the, I don't know, I forgot, I looked it before, but, you know, like 10 to the 80 light years.
light years not not centimeters light years so this tube is huge and long yes and it's pinched too and and it's pinched right exactly as it means it's sort of it's pitched and it's like longer longer and therefore you know this what people call modes which are inside the inside the inside this tube the part of the mode like an inflation they get elongated because this this thing was
Small and then just became longer and longer and longer. So inside the modes get elongated as the geometry becomes longer and longer, the length, proper length becomes and so they become what people call infrared, very low energy. Each of these particles or modes is going to be very low energy and therefore you can have lots of them without any problem.
And so there's no paradox in that sense, because if you take into account properly that it's not an event horizon, but a causal local horizon, and that these surfaces, you're taking into account the background, the back reaction of the geometry, the geometry changes so much that it is perfectly fine to accommodate a huge number of modes, even though the endpoint has only a millimeter
And therefore, you have this huge amount of energy, which is almost a solar mass of energy, a huge number of moles up there. And there's no problem. So this is kind of a, I mean, it's not a new idea. I've been looking at people, I've been working on it for six, seven, eight years, but a lot of people don't realize. That's relatively new.
Yeah, it's very interesting. So already the semi classical region where solar mass black hole becomes a lunar mass black hole, it looks like there is an apparent paradox. But in fact, if you look at the apparent paradoxes, how can a little thing like that hold so many more? And the point is that it's little thing only vis-a-vis the outer world is concerned. It has internal structure. This surface has internal structure, which is huge. Wheeler used to call it bags of gold.
Okay, now you just mentioned this word outer world, which we're going to get to. But how about we take a small break? Yeah, let's take a break. And then we'll get to we'll get to Salvatore Pius's question and then the inner world.
Professor, I have a question about ADM decomposition, where one assumes global hypervelicity to form a Cauchy surface and so on. And I'm curious, is that a reasonable assumption that this can always be done? Or does that reject a certain class of solutions to general relative to Einstein's equations? Yeah, so it does have
I mean, ADM decomposition has to do with dividing space time into space and time. It's a three plus one decomposition. And it breaks the manifest covariance of general relativity. But on the other hand, if you look at this, the space of solutions are exactly the same as the space of solution of general relativity. So it doesn't lose anything from general relativity, except if the space time is not globally hyperbolic.
And the global hyperbolicity condition, is that related at all to the cosmological constant or no?
No, it's not related to cosmological constants. So you could have globally hyperbolic, I mean, most people, most of the spacetimes people use in cosmology with the cosmological constant are all globally hyperbolic. There's no problem at all. But you could also construct non-globally hyperbolic spacetime with the cosmological constant. It's not very difficult, but people think of global hyperbolicity as a physically reasonable assumption. There's a widely, it doesn't mean that
other things that totally people should about on space time, but there's more exotic possibilities. So like, there are closed time like curves, at least in girdle, like there's a girdle universe, which is closed time like curves. And so, yeah. So when people say, hey, closed time like curves, or you can't, they're unphysical. Well, there's nothing about general relativity that says you can't have closed time like curves, correct? Right. So it is true that, that ADM framework and most of the
things that people do, you know, even classical general relativity and they use the ADM framework very heavily in numerical relativity and so on so forth. There are versions of ADM framework, but they use them very, very much. They all assume global hyperbolicity, you know, in the black hole
So I don't think you lose anything. Now the question is for something like quantum gravity or something like conceptual structure or something, would you do something without the 3 plus 1 decomposition? And in fact, you sent me some paper and that paper just begins with
I was asked to write an article and it is true that Lagrange himself actually suggested this very beautiful, I mean he laid the seeds of it, I should say, which is developed by other people later on. There's a very beautiful way of doing things without any
decomposition into space and time, even particle mechanics. The idea there is the phase space is not x and p or x and x dot at any instant of time, but the whole solution, dynamical solution, it's like the block in the universe. It's a whole solution of the entire particle trajectory is a point of the phase space. So it's called the covariant phase space combination. And I used, I mean, I developed that
for field theory when I was doing corner field theory in space-time in the 70s already. And then I'd taken these ideas and they were not used until then as far as I know for field theories. And then for this volume then I looked at general relativity in the covariant phase-space formulation, which does not use space-time in the space-time and space and time. And I showed that in fact you do get
Things like the ADM Hamiltonian and even the so-called, in presence of gravitational waves, you have got so-called bondy energy and bondy for momentum. Just like you have got ADM, I don't know if there's a reason of energy and free momentum, you also have the same quantities in presence of radiation, which actually decrease in time because the gravitational waves go away. ADM for momentum is conserved because it includes everything.
So we recovered all those things using covariant phase space formulation without any 3 plus 1 decomposition. So it's possible and I was at some time quite interested in thinking that whole quantum theory could be done with a covariant phase space but then as time went on I realized that no that's not really possible because basically
What quantum theory does, for example in quantum tunneling, is precisely allows certain, effectively is allowing trajectories which are not classically allowed, right? They're classically forbidden. There's something which is alpha particle inside the nucleus can actually come out. Classically it could not do that. There is a probability that it comes out, but classically there is no dynamical trajectory classically. The potential is such that there's no dynamical trajectory
that would allow you for the alpha particle classical dynamical trajectory to leave the nucleus and come out. Or mechanically, there is a probability that a stone on the ground could spontaneously come and break my window up here. It's a very minor probability. But there's a probability that that could happen. Classically, it cannot happen. There's no classical dynamical trajectory. There's a kinematical trajectory.
For those interested in hearing more about the Gödel universe, visit the link in the description as some physicists have animated it as well as they give more of an explanation as to what the Gödel metric is and its consequences. So the point is that all of quantum physics cannot be captured by if you restrict yourself from the beginning to the space of classical solutions.
And the covariant phase space is the space of classical solutions. It is isomorphic with the standard phase space, which is x and p phase space. Because if you give me an x and p, I get a unique dynamic trajectory. So the covariant phase space is like the canonical phase. I mean, mathematically it's equivalent or something. But as far as quantum theory is concerned, I feel that I still today feel that it's not possible to use base quantum
quantum theory, starting with the classical point of departure being the covariant phase space. I think you have to use, if you want to use a phase space, you do need to use a canonical phase space. Then you have these wave functions of x only, they're not a function of classical trajectories, space of classical trajectories up here. And so I think that there is, classically you can avoid 3 plus 1 splitting,
You mentioned, for people who are wondering what's the context, what the heck is this paper I referred to?
ADM decomposition is extremely important in loop quantum gravity and other approaches. And then on the Wikipedia page, there was some controversy that perhaps ADM decomposition is not always allowed or not always admissible. And so I was asking Professor Astrakhar,
What is his opinion on this? And can you take a look at this paper? So that's what that was about. OK, now you also mentioned Feynman's sum over all paths. And as far as I know, in loop quantum gravity, there's something similar where we sum over graphs, but it's not like we sum over all possible graphs. So you place some conditions on the graphs. And I'm curious, so are those conditions you feel like justified or eventually you want to get to some approach where you sum over quote unquote all graphs?
Some are all kinematically possible graphs. But the difference in loop quantum gravity is that, which is conceptually quite an interesting difference, that one is not looking at something or classical trajectories. In other words, because the classical trajectories would be, this is important, classical trajectories would be classical four geometries, all possible classical four geometries. Here what one is doing is one is
summing over trajectories which are in quantum Riemannian geometry from the beginning. So they are not smooth metrics but there are these two complexes with some data on them, colors two complexes as one says. But it is all possible, I mean the goal is all possible. In practice of course you know you do approximation just like what one does in quantum field theory. So therefore I start completely right to say that in loop quantum gravity one uses area framework
Let's get to Salvador Pais' question.
Okay, so the
I mean, I did go through what you have sent me. The super force is supposed to be given by, I think, Newton's constant divided by some power of the speed of light, so that the dimensions are the dimensions of force. There is no H bar in it at all. But it is claimed that some, at least in the couple of pages that you sent me, it was claimed that somehow it is the unification of all forces and the super force arising from there and so on. I mean, I don't see how
It's a completely classical idea and I don't see how it can be, it can incorporate weak interactions, strong interactions which are quintessentially quantum mechanical and even electromagnetic interaction because electroweak go hand in hand together because of unification. So I mean, I don't see how this super force can be anything like fundamental in any sense. As far as the quantum bounce is concerned, it is true that
I mean, as I was saying before, I was myself surprised that for the longest time, until, you know, the density becomes thousands of tens of thousands of plant density, classical picture is perfectly fine. And then suddenly, this new quantum effects take into picture. And in heuristic terms, one often says that gravitational force is normally attractive, but then
suddenly this quantum effect becomes, the quantum corrections become, they are always repulsive but they are completely repulsive and they suddenly dominate in this Planck regime and then overwhelm the classical gravitational attraction. That's what people say, that's what I say or other people say. I should say that this is one of those things in which people in physics literature, I mean advanced physics people or graduate students, they understand what it is meant. I mean there is no such thing as gravitational force
already in classical general relativity. But this is a way of just shorthand way of talking about the bounds. So I just want to make sure that that is also true, that force is not a fundamental concept either in classical general relativity or in quantum cosmology or quantum gravity. What we have is Lagrangians and Junians and propagators and so on and so on.
And also when a physicist uses the word force now, at least in high energy, they generally mean interactions. They don't mean F equals MA. Yeah, exactly. Exactly. I think that the word force should not be used because it terribly confuses people. I agree, but I'm not any sort of just English language to say that. Well,
Now briefly before we get to string theory and the comparison between loop and string, loop QG and string, talking about the Big Bang, we didn't get to what occurred before the Big Bang. So it depends on
Basically what one is doing in all these models is when it's starting at a given instant time as I said and then the post big bang in our brand of the universe whether universe away from a plank regime so that we can trust classical general relativity take a wave function which is sharply peaked and then you're volume it back. So if in fact in this post big bang picture what you have is a classical solution that your wave function is peaked at is the spatially flat
Freedman, Le Maitre, Robertson, and Walker universe, then what happens is that after the bounce, it joins on to another, especially flat universe, goes back. It's not necessarily symmetric. It depends on the initial state up here. It's not the time symmetry of all of it. It can be time symmetric, but it doesn't have to be time symmetric. It depends on the state that you have chosen, because there are many sharply picked states that you can choose from. But still, it's basically on the other side, there's another large
Spatially flat universe. And also if you started out with what is called open universes where there is spatial curvature, it's not spatially flat, but the spatial curvature is negative, then in the open universes it turns out that there's again a branch which is in the past like in spatially flat case. But if you started out with what is called positively curved spaces,
space sections, which is going to be a three sphere. So topology is that of a three dimensional sphere instead of a three dimensional space. Then you get classical relativity says that when you start with the Big Bang, the universe will actually expand out and then there will be a re-collapse and there is a big crunch. So in this case, what happens if you start with the Big Bang, I mean the general relativity says that. So now here if you start in the middle and you go back,
Let me just restate this because I want to make sure that the profundity of this isn't lost.
So if we rewind our universe back, we get to the Big Bang. And then the claim here is that a possibility is that prior to the Big Bang was another universe that from its perspective was crunching to a Big Bang, which produced hours because there's this bounce that occurs once you get to what's what we think of as the singularity. OK, then that's under the loop quantum cosmology model. OK, so from my understanding prior to 10 seconds ago,
It was, this is our universe. We're going back to the Big Bang. And then we think, well, this could have started from the crunch of another universe. So let's imagine that. Let's imagine it did. But then I was wondering, well, loop quantum cosmology says nothing about this other universe. Where did it come from? Does it just expand forever in that direction? Now you're saying that, oh, no, actually, it could, we could have infinite cycles. No, no, it depends on cosmology. No, it depends on your assumption. It's not, it depends on cosmology. Just like general religion, it doesn't have a
specific prediction. You have to tell me the matter content of the universe. So if the classical general relativity, you have what is called critical matter density. If the matter density in the universe is less than some amount, then the universe would be what they call spatially open. If it is exactly the critical density, then it is spatially flat. And if it is bigger than spatially
the critical value, then it is closed in the US. So classical general biology also doesn't, it's an observational question. And so, but these are the possibilities. And what I outlined was what happens in the three possibilities in loop quantum cosmology. In the three possibilities, in the possibility where the matter density is less than or equal to the critical density, you just have one bounce.
And then the statement is that, yeah, there are the universe, which is pre-boss bang. And there are a lot of ideas about, I mean, calculations about what was the nature of that universe, etc. But maybe that's going too far.
We'll have another discussion because we have so many physics questions, but we also want to get to some questions regarding consciousness. So the statement up here is that it really depends on the spatial topology. The spatial topology were closed, but then I should just add that one can say, oh, but then we know something about our universe today. So which one is it? So it looks that overwhelmingly that it is spatially flat. It's not closed universe.
I mean, it's not, there's always going to be some error in observation error, but it is supposed to be, I mean, there's all, there's a general picture people use is that the spatial effect. So, so in that case, there is, there is not a multiple bosses. Yeah, please go ahead. Sure. Let's compare string to loop. Oh, okay. Yeah. So string theory started with particle physics kind of emphasis and loop kind of gravity started with the general relativity emphasis.
So from the beginning, you know, the ideas were different. Particle physics was emphasizing field theoretical methods, and in the beginning was perturbative methods. But all the time, they also started giving up, paying more attention to the non-perturbative methods, and now much work is done in non-perturbative methods, particularly with this ADF-CFT formulation. So in that sense, I mean,
conceptually philosophically they're coming together and also the importance of background independence is something that is more and more appreciated as as the string theory went further and further away from the particular methods this was more and more appreciated. The difference is based still the difference namely that in string theory there isn't so much because of its origin particle physics there is so much emphasis on unification of all interactions whereas loop quantum gravity is not that
People are not interested. Of course, they're very interested. But the main goal is not unification of all interactions. The main goal is really quantum nature of geometry. Now, one might say, well, you could never understand quantum geometry until you bring non-interaction. That may be the case. But what we have seen is that we could actually understand electromagnetic interaction by itself. Then it was unified with electromagnetic interaction. And then people at some stage thought that
Really, to understand strong interactions, you need the grand unified field theory in which you've got all three, the electromagnetic, weak and strong interactions together. People tried that for a long time. They even had a prediction that proton should decay. The proton doesn't decay. And since proton doesn't decay, I think that idea is sort of pitted out that that should be the only way to do things. And people are just looking at QCD by itself.
And it's huge success looking at QCD by itself. So I don't see why looking at gravity and looking at the fundamental conceptual issues that are posed by gravity, which are unique because it is a theory of spacetime structure, is not going to teach us huge amount of things more. I mean, it has already taught us in classical relativity, you know, completely new physics, right, gravitational waves, Big Bang, black holes. So the question is, I mean, we can look for these qualitatively new things, like what happens
Now, because of this, I think partly because of this emphasis on unification, in string theory, there are all kinds of elements that were brought in. First was supersymmetry. Second was higher dimensions. And then there was positive
the negative cosmology constant and the point was that because you brought in supersymmetry and then you looked at the quote unquote natural ground state and there was a negative cosmology constant and so on and you know the conferences in string theory when people when first the idea came up that in fact the cosmological constant is positive and some preliminary evidence came up the conference in which very prominent string theories series are on record have said that
It can't be. It will go away. I mean, this is completely wrong because we know from supersymmetry that it must be negative. And it's not negative. It is positive. So there are these ingredients. I mean, these are not optional things in string theory. They lie at the foundation of string theory. Higher dimensions, supersymmetry, and the negative cosmology constant, none of which are seen in nature.
The people have tried hard looking for this and that. Now it doesn't mean that tomorrow people won't find it, but I should emphasize that even if they were to find supersymmetry, it doesn't mean string theory. There may be many theories using supersymmetric theory. So the case is not strong in terms of what observations are telling us today. And I don't think that string theory has given us reliable insights or good physical insights or
on which one can build on for future work about the nature of singularities or even about black hole evaporation today. There have been a lot of very bold ideas, but it's one of those things. These bold ideas are put forward. There's a rush of my papers, incredible. I mean, there was first various people in Stanford were talking about quantum Xerox machines in order to talk about black hole information, that modes which go out to infinity, information that goes out to infinity, somehow
Xerox somehow duplicated near the surface, near the horizon, of course, taking event horizon as being absolute. And somehow that's why you can get unitary. That's repeated now. Then there was a question. No, that was prior to ADF safety. And then there is, of course, ADF safety. And ADF safety, again, is something that is done in
negative cosmology constant and one doesn't really know much at all about even zero cosmology constant or positive cosmology constant in the universe. And so I think somehow one gets the impression that a lot of effort is being put in areas where one can actually get good mathematical results, solid mathematical results. So whether it has
much to do with our actual universe or not is seem to be secondary consideration. Perhaps this is driven by the idea that well just because we don't know much about the universe and if natural theory is found then the universe will obey it. They have said that about the cosmological constant. They have said that about supersymmetry. People are given even scales at which this should be found because they're natural and they're not. And there are examples in physics where
Very prominent people have talked about some natural ideas. I mean, one of the things that people don't know very much about is the following. Just in the end of 1800s, very prominent people, including Lord Kelvin, had really thought that what are atoms? Because people are realizing there are atoms and there are discrete spectral lines. People are just realizing that.
And their idea was that atoms are really vortices in ether because they believe in ether and atoms are vortices in ether and now what is it? So they thought well hydrogen atom seems to be the simplest atom so it's a circle. Then if you have got a next atom that you knew was the helium atom and the helium atom they thought was a truffle knot
It's one of those things. It's a knot in the knot theory. It's the simplest, beautiful knot. People use those knots on the boards and things like that. So there's a truffle knot. And then more and more complex atoms would become more and more complicated knotted structures of ether. So there are some lines in ether which are bent and which are knotted together. And they become the atoms. And these knots are vibrating. And that's why we see the spectrum. And these are very prominent people, we're saying that.
That's an extremely creative idea. I'm wondering how the heck do you come up with that? Absolutely creative idea. And then they convinced a Scottish mathematician Tate to think about knots. Knot theory was born out of this. The whole thing started because they thought that atoms are knots in ether.
That's how it started. It's a beautiful mathematical idea, beautiful bold idea. They talked about variety. They talked about how discreetness might come because of this, you know, why vibrational modes, because the closed thing. Vibrational modes are quantized and that might explain that atomic structure. Michael Atiyah, who was a very famous mathematician, has a very nice little book on this and the origin of Nocturian, how it came about. Very, very small book. So
So these things happened. Then there was another big thing from my community, John Wheeler. John Wheeler was a very imaginative person and everything. And he thought that elementary particles were chemistry of geometry. It's a little like this idea, I feel like. But now, not at the atomic level, but at the level of elementary particles. And again, he thought that there were some
In general relativity, there are some structures which are purely gravitational, some complicated. So it's not now one dimensional, but more complicated structures which are called geons, topologically built and such things. How do you spell that? Geons? Geons, right. And he had, you know, he talked about elementary particles, chemistry and geometry.
I may be misremembering, but I think there's even the last chapter of the textbook gravitation of Mislut von Wheeler might have a chapter on this, might have a section on the chemistry of geometry, which is this idea. Again, it's a very beautiful idea that everything after all is just geometry, that this all comes from expectations of geometry, that topological expectations and all elementary particles are just that sort of thing. This clever idea did not work.
So I think that just because some mathematical structures look very natural and nice, and there is enough precedent that that doesn't imply that they have anything to do with our actual physical world. And it will be good for us to keep that in mind. I mean, it may have, but this confidence and
I have to quote Alan Greenspan, who was the head of the Federal Reserve. You know, you called about exuberance. Something exuberance, right? And unfettered exuberance. That, I think, is not necessary. I mean, we can have bold ideas. We can put forward them. But to take the viewpoint that that is the only solution is not something that is really called for.
And so now the question is, what is happening today? How do string theory and loop on gravity or any other approach? Where are we today about it? So there is a very nice article on the web page of the Institute for Advanced Study by somebody who was a journalist in residence there about the current status of string theory. And the title and the abstract actually say explicitly that string theory has not lived up to its promise of
You don't see that to be the case or no? No, I do see that to be the case. I agree with that. So, but it has evolved in that direction, right? And in the sense of, you know, very, very
Mirror Symmetry
They did not know how to find these functions for them in condensed matter physics, but then they use this idea about some kind of a duality, and therefore they could calculate it in the weak field, in the weak coupling constant limit in gravity, and then they could calculate those functions. So these are extremely rich toolbox, and I think it's something great to have that toolbox up here. But toolbox is very different from theory of everything, as it is great. And I think that, you know, that
They're admitting, leading string theories were quoted in this article, and they're admitting that it's not really that, but it's just a second rebirth and therefore it's going to remain. And I have no qualms about it. I think I agree, it is a very rich toolbox. But I think toolbox is not
What would this string theorist say to you? They're like, okay, you say this about us, but hey, all the loop people. Yeah, so I don't know. I mean, it depends on which string theories. Okay, let's pick David Gross. David Gross has openly said somewhere, right, that it is bullshit. So I think that is difficult.
Okay, so that's what he would say. Okay, so let's pick someone who has a bit more of a specific criticism. But I mean, somebody like Gary Horowitz, I mean, he has told me several times, Gary is one who has worked, because he also began in general relativity, so we can speak similar language. Until, when was it? Until 2008 or 2009. Every year, I used to write notes on what progress and main things in string theory, and I used to
I used to talk with Gary and find out various things. One of my former postdocs, Don Meroff, is a senior figure in string theory, also in Santa Barbara. So, we talk and so on. Don had done some early work in loop on gravity, so he knows that subject as well. When we talk, we have an open disagreement. When we talk, to me it is much more reasonable in the sense of
There's no irrational exuberance. There is much more, yeah, this is the word, but we believe that this is pointing direction in this particular way and we're excited about this. That's good. It's an interesting idea. We tell them what they're doing. These guys can resolve singularities and that's a good thing. So
It's a regular scientific discussion. It's not kind of political polemics. But there are enough of them. So that's good. There are enough of them. We can have this discussion. We are far from having the final say. If people claim that we're very close, I wouldn't agree with them either. On the other hand, I do think that
Here's a quick statement from Ed Whitten and this comes from the book Conversations on Quantum Gravity.
The interviewer says, due to the lack of experimental data, there exists a plethora of different approaches to quantizing gravity. Which of these approaches, in your opinion, is closer to a true description of nature and why? Then Ed Whitten said this, I think your premise is misleading. String theory is the only idea about quantum gravity with any substance. One sign is that where critics have had an interesting idea, so non-commutative geometry, black hole entropy, twister theory, they have tended to be absorbed as a part of string theory.
I don't know if I want to say names, I was just debating about that. I think everybody is entitled to their opinion and I just have two remarks. There is a remark that I like very much by Richard Feynman.
And the remark says that you should have a reality check. And so he says, it doesn't matter how beautiful your idea is. It doesn't matter what your name is. If your theory is not realized in nature, it is wrong. And I kind of feel that one should keep that in mind. That's my first remark, that very nice comment of Richard Feynman's. And the second is,
that there was this conference, which was 25th anniversary of KITP. And that, you know, they invited some people that happened to be invited me as a representative of Nukron Gravity, I suppose. And there, there's a prominent sync theories or kind of a tea break or coffee break.
were chatting and he said, he repeated to me what you just read. And this was a while ago at which by far the number one computer company or company in the world, financial institution world was Microsoft. So he said, well, you know, string theory is like Microsoft. And
What Microsoft has done successfully is that anytime there's a competition or something, they are successfully incorporated in that. So it becomes part of Microsoft. And he said, he was nice, very nice, but he said, the same thing is true with string theory, that we have incorporated a matrix model, we have incorporated conformal field theory, and we have incorporated noncommutative geometry. On the other hand, he says,
Look quantum gravity is the one thing that we're not incorporated and look quantum gravity is like Apple's. And at that time, I didn't say anything. It's like Apple's like Apple, Apple. Oh, like Apple computer. OK, as opposed to Microsoft. Yes, yes, yes. And so I think this conversation was very illuminating. Yeah. But the success being Microsoft and
That was a model of success at the time of Microsoft incorporating everything together. And Apple didn't do that. And we are today where we are. So I think people can take their judgment about
He said that there was a principle of duality, which is extremely vaguely named because there are many principles of duality in physics and mathematics.
I emailed him and I said, what are you referring to him? Then he wasn't, he didn't get back to me. But he said in the book that there's this principle of duality that a statement in loop quantum gravity becomes a statement in string theory and vice versa, or that he conjectures that there's one because there seems to be some for a certain class of questions. I didn't find any more information other than that. And either way, Lee seems to think that both loop and string are somehow approximations of some other real theory.
Rather than it seems like you're on the more you're on the approach that well Firstly loop is not claiming to be a toe to be a grand unified theory. It's a quantum theory of geometry, which is quote-unquote quantum theory of gravity Okay, so firstly there's that and so it sounds a bit more like you're you have a tempered view of loop quantum gravity and Lee has a more expansive view that incorporates both
Where do you agree and disagree? And do you have any references for me to look up this principle of duality? Because I'm still looking to read something concrete about it. Well, I don't have good recollection of dates about when Lee might have said that. But there are instances. For example, when we're talking about this work on black hole entropy that I've done with John Byes and
In that work, again somehow this idea about punctured spheres was playing a big role and again the gauge theories and then if I look at the string theory idea, the brain and then there were also punctures on the brain that were made by strings and then
And so at one stage, I mean, we thought that there was actually some relation. It is also true that, you know, if you take Lee and Carlo and I wrote a paper, which is called Gravitons on Loops, in which we, these are linearized gravitons. So we formulated the theory in terms of kind of thicker loops. We introduced a notion of form factor of the loop and such thing. And the point was that if we just
You start with completely in the beginning, then you find that there is a graviton, there is an anti-symmetric tensor, there is a dilaton, and that's what people call bosonic strengths. And so it looked like in the early days that they may be saying similar things in different words, and it still might be that some of the things are similar. But I think my view is that
The way that the things are developed since then, both in loop quantum gravity and string theory, they've become much more diverse than before. There are people in loop quantum gravities, for example, Laura Friedel and people associated with him in Perimeter, they do talk about kind of possible holography in loop quantum gravity and so on and so forth. I don't think that string theory people take it very seriously.
So I don't know where it is going to go, where it is going to go. So what I'm saying is that in the initial stage, this duality that Lee was talking about might have been about just a couple of examples I gave there. There is some idea that same kind of concepts appear in both approaches. But I think that over time, instead of more and more such connections, there have been less and less such connections.
Professor, I'm sure you're aware, and Carlo Ravelli's brought this up, that physicists of the past were extremely philosophical. And then now there's this excoriation of philosophy in Academy, where it's seen as, that's ill-defined, that's superstitious in some manner, and it's going to lead you off the deep end, even though, as you outlined, well, many of the physicists aren't attached particularly to reality with their musings mathematically. Do you think that
This is true. Physicists have lost their way. Is it a negative or a positive in terms of abandoning philosophy? The physicists should be more philosophical. I think there's been a branching of ways, but it's not something that is most recent. So if I go back in time, philosophy was often natural philosophy. I mean, if you look at Socrates and Plato and
Indian philosophy side or something like Brahmagupta was astronomer and they were interested in the natural world and they're also interested in philosophy and in fact a lot of philosophy was philosophy of natural philosophy which is then sometime I think around the time of Galileo and Kepler and Newton we had a branching a little bit namely science I mean in some sense this
Natural philosophy was too successful in that it bred science, particularly physics and astronomy, initially. And so somehow science, I mean, for this long time has actually taken over that side of philosophy. There is a very beautiful book by the father and son team, which is called
The Philosopher and the Monk. The French philosopher is Francois Ravel. That is his pen name. The Philosopher and the Monk. The Philosopher and the Monk. And Francois Ravel, the father, was a philosopher. He was a real figure in France, a very influential figure in France.
He was very strongly, first of all, anti-religious against the Catholic Church. And then he was also anti-communist, which left him in no man's land. And his son, Mathieu Ricard, who actually started as a neuroscientist, and he got his PhD with one of the Nobel laureates in Paris. I forget now the name.
Now there are a couple of them, so I'll get them mixed up. And then at a postdoc opportunity as a postdoc to go to Stanford, he had the offer and he was ready to go. But in the meanwhile, he had also met some Buddhist monks and had gone to India and so on and so on. And due to his father's horror, he actually relinquished.
science and went into became a Buddhist monk and he is the Dalai Lama's chief French translator. You find him every many places sometimes it's called the happiest man etc etc. That's not important. The important thing is that Maurice Ravel has sort of said it's a nice account of you know how philosophy has developed and not developed and so on so forth that sometime around that you know around the Galileo Newton
Somehow philosophy lost this natural philosophy to science. And it also had wisdom aspect. You can play to it. There is really wisdom aspect. And he somehow felt that that wisdom aspect somehow was stolen by more religious traditions. And so he is, I mean, he himself is a philosopher, but he sort of felt that somehow the field has gotten diluted because of, you know,
In some ways, other branches grew much more. And I mean, I kind of I'm quoting him because I feel that there is some large grain of truth in this. So if you look at, for example, the beginning of 20th century, I mean, there's a very important lecture by Max Planck, who says, philosophers of today sit in physics departments.
And he says that their names are Albert Einstein and Niels Bohr. So there are there are these going in that direction, right? Some of the fruits. So I think that this really has happened. And I know that really in the 1930s, there were philosophers in Oxford. It's not a little place. We are arguing that on philosophical grounds, spatial relativity could possibly not be right.
And so there has been and so I'm just saying these things because these things have somehow led to a deep mistrust in a lot of physics communities about, you know, utility and usefulness of philosophy and philosophy of science and so on. However, I find personally that there is a new generation, a newer generation, not so new because there are tenured professors now and so on and so on.
of philosophers of science who actually understand the physics and mathematics that is needed. And that is always a problem, right? You need so much mathematical background to understand what physical concepts are and then to be able to evaluate them. Otherwise you are always years and years behind. But there are a few, there are not, you can probably maybe 20 or so that I want to know.
less than 20, who actually are able to do this. I think that those people can contribute greatly. I mean, they should be taken more seriously by the physics community than they are. So I kind of feel that physics has become very specific and very technical and so on and so forth. So it is true that
that physicists dismiss philosophy altogether. I think that is too harsh and too uncalled for stand. But on the other hand, I think it's also true that a lot of philosophy people don't really know science. I mean, it just becomes difficult just because of this specialization and so on and so forth. But I think that with this young generation, there is hope and useful things that can be useful.
Can you give me an example, perhaps a concrete example or a specific one where someone of our generation was able to merge philosophy and physics and contribute something that perhaps just soul physics couldn't do? When I say soul physics, I mean, S-O-L-E without the soul of the S-O-U-L. Yeah, that people from
that I happen to know are from the Pittsburgh School of Philosophy of Science, who, for example, have worked on things like the time reversal invariance. And they formulated the way that time reversal is actually analyzed in physics communities and so on and so forth.
And one of them actually, yeah, I don't want to go into too many details because I various names of principles and so on, because in order to explain too much of that. But they formulated the ways that they sort of codified thoughts by saying that, well, this is a way of looking at time reversal mechanics. This is another way of looking at time reversal mechanics, et cetera, et cetera.
example, pointed out that maybe there are more general ways of looking at time reversal invariance and there is, I think in part because people in Pittsburgh were, because the gravity group is strong there, Carlo was there for a while, long time ago, and so on. So the gravity group is strong there and so that they are familiar with some of the
topics that the forefront topics in physics. So they were aware in quantum gravity and so you know they were raising questions such as what would happen in quantum gravity because many of the things that one uses to talk about time reversal invariance are so deeply rooted in Poincare group and so the question is well if gravity everything and particularly quantum gravity what would happen to it and these arguments will not go through and unitary and unitary operators and
So I think that was quite insightful. So that is an example in which they were able to formulate, they were able to kind of classify the effects, the arguments that physicists had made into categories. And then from those categories say that, well,
If you wanted to generalize physics further and include quantum gravity, then one would have to rethink about time reversal invariance. I thought that was quite insightful and actually it led me to think about time reversal quite a bit and realizing that in fact you don't need much of the machinery that is usually used to talk about time reversal in quantum mechanics.
Sorry, is time reversal distinct from time travel? Yeah. So time reversal, that's that. So, I mean, they clarified, you know, that there's a
The question is about time reversal in basic laws of physics. I mean, because people also say that entropy increasing means that, you know, you don't have time reversal. I mean, people say that, well, the glass fell down and it was broke and then it's not, it's not spontaneous. But the point is that that's not true, right? Because if I just took the final state and reversed all the in classical mechanics and reverse all the velocity, they should actually come back. I mean, the point is that those initial conditions
form such as tiny fraction of the whole phase space that is very unlikely. And so that made a very clean distinction. They made the clean distinction between that's not what they were talking about. They were talking about time reverse in the fundamental laws of physics. And that's what is true with respect to that time reversal is actually valid in the k on dk.
So there's fundamental and then you know that they're bringing in CPT and usually one says and time reverse is violated one day what one shows that CP is violated and then one says that I got a CPT theorem and therefore time reverse is violated but then their argument was that well but CPT theorems completely depend on spatial or artistic local quantum field theories and if you don't have spatial or artistic quantum field theory then you can't make such arguments so it was it was quite so that's an example.
in which I think younger people making, understanding first of all what the physical literature is saying and understanding enough about unitarity and community operators, what we need, what we don't need and such things and then then making nice statement. I think his name is Brian Roberts and I think he's, they have already written a book, he was writing a book on this thing. I just know because
The links to the philosopher and the monk as well as Brian Roberts, his work, or at least his Google scholar page will be in the description. Professor, thank you so much. It's been quite a ride, more than four hours. Okay, let's do this again at some point. We'll communicate over email and we'll see you also how this one goes online and see what the reception is like. Sounds very good. Okay. Take care now. Take care, professor. Okay.
Transcribed by https://otter.ai
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"text": " The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze."
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"text": " Professor Astakhar is the Eberly Professor of Physics and the Director of the Institute for Gravitational Physics and Geometry at Pennsylvania State University and is the man responsible for loop quantum cosmology. Roger Penrose has described Astakhar's approach to quantum gravity as the most important of all the attempts at quantizing general relativity. I'm proud to say"
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"text": " that this is Ashtakar's podcast premiere. In this part one, we cover what was there prior to the Big Bang, the myth of singularities, Buddha's parable of the poison arrow, as well as the inner versus outer world. Some of the physics can be a bit esoteric, especially the technicalities of loop QG, giving a taste as to what it's like to study the subject if you're interested. My name is Kurt Jaimungal. I'm a Torontonian filmmaker with a background in mathematical physics, dedicated to the explication of the variegated terrain of theories of everything,"
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"text": " that is primarily from a physics perspective, but as well as investigating what role consciousness has to play in the fundamental laws, provided these laws exist at all and are knowable to us. If you'd like to hear more podcasts like these, then do consider going to patreon.com slash Kurt Jaimungal."
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"text": " It's support from the patrons and the sponsors that allow me to do this, to put out podcasts of this quality of this length consistently, as this is now what I'm able to do full time. Today's sponsor is Brilliant. Brilliant is a place to learn mathematics, science and engineering in an interactive form. Soon I would like to speak to Chiara Marletto on information theory. So I decided to take Brilliant's course on random variable distributions and information theory. And after taking that course, I could finally see why entropy is defined the way it is. There are plenty of other different courses."
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"text": " Alright, now part two will be in a few months, so note your questions down in the comments for me to ask the professor. Thank you and enjoy part one with the great Abhay Ashtakar making his podcast premiere on the Toe channel. Professor, I'm extremely honored to be here with you. You're one of the preeminent physicists of our era, and I think I speak on behalf of much of the audience when I say that we're lucky to be alive during the same time that you're alive, and it's an honor, man."
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"text": " Thank you so much for joining me on tow. It was my pleasure because, I mean, it's one of the very rare places where people are interested in theory of everything, which includes not just the physical world, but also the inner world. And that has been my passion. So it is a very, very good match for me. The inner world you mentioned, we're going to get to that too. No, both, both the inner world as well as the outer world. I mean, not just"
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"text": " And not just the physics sense of theory of everything, but really theory of everything. Yes, everything. And that includes the overlap between those. And we gave or you gave a great analogy prior about the compatibility condition on a manifold on a sphere. We'll get to that. I'll give a bit of an overview for the audience as to what we're going to talk about roughly in order loop quantum gravity, because that's what you're most famous for. And loop quantum cosmology, the Big Bang,"
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"text": " black holes, the second law, so there's we deal with entropy at some point, and causality, perhaps even the arrow of time, the differences between the inner and the outer world, and what you believe are ingredients to a theory of everything, and perhaps even some of the philosophy of physics. Unfortunately, there were myriad technical issues, thus the audio of Achtekar's isn't as pristine as it could be. Keep listening as it improves with time. How about you give people an introduction as to how you view"
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"text": " What the outer world is and what the inner world is, perhaps what led you to that as well, that distinction, and also the utility of the inner world, which is generally discarded. Yeah, so the outer world, I just mean the physical universe at least in the habit of studying, it can be physics of what we're talking about, you know, it can be planets and stars and gravitational waves and cosmology and black holes. It can be just a tree outside my window up here and"
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"text": " So all those things, they all seem to have some laws and science has been incredibly successful in actually finding many, many of these laws and understanding why things happen in the external world that we see. But there also have been kind of old traditions which focused much more on the inner world."
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"text": " And the problem there was not talking about kind of the best things that I have come across. I'm not talking about everybody. So the problem there was basically not that the outer world and phenomena, et cetera, et cetera, are not important. But somehow the central theme should be"
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"text": " Why is there suffering? And what would lead to lessening or elimination of suffering? There's a very, very beautiful story of the Buddha. So the statement is that one day a young monk came in the hour where people could go and ask questions and sat"
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"text": " I was meditating the other day and the following thoughts came to me. I should have looked this up before the conversation because I will probably not reproduce it completely. His name was Malanke Putta. Putta is Putra or son of Malanke. Malanke Putta says, well, sir, I was thinking about this and the following thoughts occurred to me."
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"text": " Why is the universe finite or did it have a beginning? Did it always existed? I mean, so is it finite in time or what? Is the universe finite in space or is it infinite? These are the questions we asked today, right? Then he goes on about eight questions. That's why I said I should have looked at the other questions. These were the first two questions. And then he sort of says that well, does"
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"text": " Buddha exists after death or Buddha not exists after death or Buddha exists, both exist not at all, exists after death. So it goes on in first of the outer world and then you know with the more spiritual questions and so on. Buddha doesn't answer, keeps quiet. Then his Malayankaya Prataya is disappointed."
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"text": " So he waits there very respectfully for whatever time was supposed to be appropriate and then leaves. Comes back a week later, says, I'm sorry, but those questions continue to bother me. I'm really troubled. And he repeats the questions again. I think there were eight questions again. Sounds like me. So Buddha doesn't answer again. And then a third time he comes and he says,"
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"text": " Every time I come, I've asked this question. He repeats the question. He says, it should be simple for you to say that you know the answers or you don't know the answers. And if you know the answers, what they are. Your silence does not please me. That was the one phrase he says. And basically, something that if he doesn't get his answers, he will leave the Sangha, you know, the community of the monks. And Buddha replies,"
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"text": " First of all, you didn't join Sangha conditionally. But of course, if you are to leave, you can give any time. Anybody can give any time. Nobody's bound here. And secondly, the reason I don't answer those questions is because they have nothing to do with the central problems that the Sangha is all about. And it has to do with sufferings."
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"text": " Understanding those questions, understanding answers to those questions, exploring them and understanding them sufficiently will do nothing to the reduction of your suffering. And then I think Buddha gives an analogy. He says, supposing you go and, I forget the details, but you're wounded by an arrow."
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"text": " And then the doctor comes and doctor wants to put something to it, some medicine. So you say, no, don't put the medicine. First, I have to know, where did you get those plants? How long were those plants marinated? Why this plant and not some other plant? Has this medicine been used always? If it was not used always, why did it start using now and what changed and so on and so forth?"
},
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"text": " But if you do that, he says, you will die before you are cured. He said the same thing is true with these questions about the external world. Now, what I like about this is not that he belittled the questions about the external world, but he just honestly said that this is not what he is, what he is about. I feel like it's like saying that, you know, somebody comes to physics class and asks questions about"
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"text": " Neuroscience or biology or something. You don't know the answers to those questions. You are in the wrong place. There is really a division between this external world and the internal world and it has grown."
},
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"text": " Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal. Now what to do with your unwanted bills? Ever seen an origami version of the Miami Bull?"
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"text": " What I will say is for several centuries it has grown."
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"text": " I think it's a pity because on the other hand, we are all human beings and we see the external world and we have the internal world. We cannot just deny the internal world. Again, in the talk of this, you said that philosophers of all time, they were interested in two things. One is the natural world, the natural philosophy. Secondly, wisdom. The wisdom was that you live what you believe."
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"text": " And therefore you are a shining role model of what we believe. And then he goes on to say that today's scientists about that, they are no different from a lawyer or a banker or anybody else as far as their own wisdom is concerned or their own belief in practicing what they truly believe. And I think there's a lot of truth to that. And I think that's a pity."
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"text": " that I think it should be much nicer if in fact more people were interested in both aspects of this world and so I think this was in the early 80s I think. I felt that I always been interested in internal work for whatever reason maybe because I was born in India it's not that my family was very spiritual or traditional something I don't know but I read some things you know I also read a lot of"
},
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"text": " The point was that there seems to be such a"
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"text": " such a system between the two things. And when I listen to scientists, for example, one thing that I like about science scientists very much compared to the people, experts in the internal world, is that one doesn't think one has the I mean, if you're not, yes, okay, if everything in this in the physics world that everything is going to be explained tomorrow, then people don't think that there is absolute truth."
},
{
"end_time": 910.52,
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"text": " I have no hesitation saying that Einstein was just wrong about many things. He was wrong about the cosmology constant. In fact, he was wrong about the Big Bang. First of all, when he heard about freedom of submission, he didn't believe in it."
},
{
"end_time": 940.401,
"index": 34,
"start_time": 911.015,
"text": " Finally, when he understood Mathematics was right, he told Lametra, again Lametra, that in one of the Solway conferences, actually, that the idea of the Big Bang is completely repulsive to him. So it's completely repulsive. And then, same thing about Cosmogon constant, there is a whole idea about it. And then, actually, I told you about Lametra going in"
},
{
"end_time": 967.534,
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"start_time": 940.964,
"text": " Correcting is telling the Pope to behave differently. You also told Einstein explicitly long time ago, that why do you throw away, why do you say the cosmological constant cannot be there? It's not an aesthetic question. See, the aesthetics again, I mean, you and Einstein, right? It's not an aesthetic question. It's an observational question. It's either there or it's not there. And we see today that, anyway."
},
{
"end_time": 994.735,
"index": 36,
"start_time": 968.063,
"text": " So, but nonetheless, we had no problem in saying that Einstein was wrong or that Bohr was wrong and various things. But that is not accepted in the internal world. You couldn't go in a conference and say, or group of those people and say, that was wrong. So, I think that this idea that there is absolute thing and you arrive there and then it's static, that I find not very pleasant and not very"
},
{
"end_time": 1022.056,
"index": 37,
"start_time": 997.005,
"text": " scientific or not very useful attitude. It's an attitude which is self-limiting, I think. Well, scientists don't have that attitude, so that is good about it. But there is this problem, you know, you go and talk to these people and they want to dismiss science at once and you talk to scientists and they want to dismiss anything as big as going to the deep end."
},
{
"end_time": 1051.357,
"index": 38,
"start_time": 1023.08,
"text": " But let me just close your eyes. There's a reality there, huge reality that you are dealing with all the time. And somehow that it is not interesting. And so I sometime in 80s, I thought that is really important. You know, what is the nature of reality? And each of them somehow think that, well, I can just extending, keep extending and then cover everything. And in terms of what they already extended."
},
{
"end_time": 1081.323,
"index": 39,
"start_time": 1051.8,
"text": " and then like in science keeps progressing and progressing and progressing and you know, it's just, we just reached it. We don't know, right? And it may take infinite time to even describe the external world. We don't know that is going to happen in a finite amount of time. We'll make continuous progress and there's no question. It's deeply valuable. It's beautiful when you discover something new as there's no question about it. But then, so, so therefore I came up with this idea that maybe, you know, reality is"
},
{
"end_time": 1109.121,
"index": 40,
"start_time": 1081.613,
"text": " Perhaps if you at all want to model it, however incomplete that may be, maybe it's best modeled by a manifold picture, as I was mentioning to you the other day. It can be a more complicated manifold, but the simplest example would be just a two-dimensional sphere, the surface of a ball. And we know from the globe, from the Earth, looking at the maps and such things on the globe, that if you try to project it down on a plane,"
},
{
"end_time": 1138.951,
"index": 41,
"start_time": 1109.514,
"text": " Then you have to do the projected map. We can take this North Pole and then project each point of the globe, draw a straight line, and then we get a faithful picture of everything but the North Pole. It's a very distorted picture. It's not a second problem. Some areas look much bigger than they really are, and so on and so forth. But you get that picture. But you cannot cover the whole sphere with a single chart, single coordinate system, single X and Y things."
},
{
"end_time": 1161.937,
"index": 42,
"start_time": 1139.48,
"text": " And so I felt that maybe that is true with reality, that there is an internal world and there is an external world. And the best case may be that you can try to cover more and more of the internal world and more and more of the external world, and they will give you some charts, so to say. And then the deep question is going to be about the overlap functions, because that is where the"
},
{
"end_time": 1191.084,
"index": 43,
"start_time": 1162.619,
"text": " The chart transitions. Yeah, the key thing about manifold lies, right? There's this compatibility of the two charts, compatibility of the coordinate system that they overlap. You can have a north pole chart, you can have a south pole chart, and around the equator, there are compatibility conditions that should be satisfied. In other words, the same phenomena can be looked at in two different ways, and they should be compatible with each other. And I think that is what is likely to happen, that as time goes on,"
},
{
"end_time": 1222.415,
"index": 44,
"start_time": 1192.483,
"text": " And in particular, for example, I was very surprised. I just heard about it only less than 10 years ago, maybe six years ago, something like that, about all these advances in neuroscience where they have been able to take the image of brain very much. But in particular, these advances had to do with some experiments with which people, I think his name is Brewer. He used to be in Yale, but now he has his own company somewhere else."
},
{
"end_time": 1250.862,
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"start_time": 1223.217,
"text": " There's a paper in Procedures of National Academy about this, in which they actually took some monks, or non monks, who were trained in meditation, but solid long training in meditation, not beginning monks. And then he had them kind of brain scans while they were actually"
},
{
"end_time": 1274.77,
"index": 46,
"start_time": 1251.152,
"text": " began meditation and he purposely tried different kinds of meditation, you know, this compassion meditation that is a sensational meditation, feeling sensations and loving meditation. And they tried all those various techniques and they found that what happens is in all these practices is that the"
},
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"end_time": 1299.65,
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"text": " A certain circuit in our brain, which is called DNN or default mode network, it's a rather big circuit. That is the circuit that is most active when we're in a normal state. And the way that we hold the world normally is through an internal dialogue. We are not necessarily conscious of it, but there's"
},
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"text": " There are other circuits which are more related to functional mode circuits. They don't slow down."
},
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"text": " Now, for most people, even though all of them are very practiced monks, once the meditation, they came out of meditation, then the neurons started firing and the default mode started again. But there were a few exceptions. And these, by the way, are the ones which are... I first came across this in the book by Robert Wright."
},
{
"end_time": 1389.582,
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"text": " called Why Buddhism is True. It's an interesting book. I mean, he was an evolutionary, he was a science writer for evolution psychology was his specialty. So it is tilted quite a bit towards evolution psychology. And I don't, I don't agree with some of the things that are said there. But it's a very good book. And then he reported this. And then I looked up the National Academy of Sciences journal and followed reading up here."
},
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"end_time": 1413.097,
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"text": " that there are a few people who were in that state even after they came out of meditation. They're always in that state. And it seems to me, and from the other things also that we've got some other time, Mark, that several reasons why I believe that this is a state of what used to be called enlightenment."
},
{
"end_time": 1443.148,
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"start_time": 1414.258,
"text": " So it's not a state in which you have to go out in the Himalayas in the top cave or anything like that. It's really a state of mind. And almost all of them are, of course, very deeply practicing meditators and such things, but it may not be necessary. I mean, from what I hear, what I read about some of the people I respect is that it can also happen spontaneously. I mean, with some effort, but don't necessarily have to have"
},
{
"end_time": 1470.418,
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"start_time": 1444.053,
"text": " 10 years of meditation or something like that in order to do this. So there are some mental states. So there is a possibility of actually having these overlap functions. Namely, science would say that somehow they were able to switch off the circuit. And when that happens, the sense of self disappears. And when sense of self disappears, then there is a"
},
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"end_time": 1498.66,
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"start_time": 1471.476,
"text": " Very, very different perception. I mean, this is people that take psilocybin, for example. There is a very active group in Johns Hopkins who does research on that. And again, very respected, extremely respected people. And they are very solid researchers and doctors."
},
{
"end_time": 1527.995,
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"start_time": 1499.206,
"text": " The experiences of those drugs is really exactly that, mainly switching off this circuit. And I think somebody said, right? Alan Watts, I think, said something like that, when you get the message, hang up the telephone. Which is to say, when you realize that the other states exist, don't keep taking this more and more."
},
{
"end_time": 1556.391,
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"start_time": 1528.558,
"text": " So I think that there is enough of work going on and I'm not saying that this is therefore what do we solve in next five years, ten years, my lifetime or something of that sort. But I think it is possible to reach those states. I mean, I really know some people whose brains can show that and their writings show whatever they have told me and I have practiced."
},
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"end_time": 1585.759,
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"text": " I'm very hard-nosed. I don't want to take any advice. I'm also not inclined towards things like devotion, bhakti, and I'm not a religious person. But whatever makes complete sense to me, I try to adopt it. And this is one of the principles that they say. If you want to move towards, quote unquote, wisdom, you should live by what you understand and what you believe. It's not easy."
},
{
"end_time": 1614.565,
"index": 58,
"start_time": 1586.834,
"text": " It's not easy at all, but I think it is not impossible. Because we could talk about the inner and the outer world for hours, we decided to save that for part two and to continue on with physics. Ensure that you note your questions for Ashtakar down either in the comments or somewhere else for part two, which will occur later this year. What is loop quantum gravity and how did you arrive at that approach? Right, so loop quantum gravity is a"
},
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"end_time": 1642.142,
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"start_time": 1615.503,
"text": " is an approach to unifying general relativity with quantum physics and this is a long-standing open problem at one stage it was considered to be the biggest challenge in theoretical physics and in some circles it is still considered to be the biggest challenge although because of recent observations both in the cosmic microwave background and gravitational waves"
},
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"end_time": 1671.732,
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"start_time": 1642.739,
"text": " Other frontiers have also opened up which are considered equally interesting. So I started out in general relativity and from the point of view of general relativity then the question is really how do we unify principles of general relativity with those of quantum physics. And there is a real problem right in the beginning because there is a really attention"
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"text": " I mean, general relativity at the conceptual level is a classical theory. So in that, you have a complete productivity. It's a very geometrical theory. It's sharp and precise. Quantum mechanics, on the other hand, is by inherently a probabilistic theory. We don't have certainty, but we only have probability amplitudes for various things to happen."
},
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"end_time": 1731.783,
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"text": " And the techniques that one uses are also very, very different techniques in quantum theory. In quantum theory, things like algebraic methods, Hilbert spaces, linear operators, and uncertainty principles, they play a major role. But the sort of interesting thing is that each theory, to begin with, has a claim on all of physics. In other words, general relativity would say not only is it a theory of gravity,"
},
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"end_time": 1761.357,
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"text": " But it's also a theory of space-time structure. And of course, all interactions take place in space-time. And therefore, general relativity sort of tells you how to formulate the theories of other interactions, that there is a metric tensor field behind it, which also serves as a gravitational potential, but determines space-time geometry, determines causality. So it tells you that equations should be differential equations. They should be hyperbolic."
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"end_time": 1788.404,
"index": 64,
"start_time": 1761.869,
"text": " and so that you have got predictably and things propagate within the light cone of any point causality and so on so forth and everything is described by smooth tensor fields for example electromagnetic fields gravitational fields any other field whereas quantum physics to begin with is very different in quantum physics it also makes a claim on everything that all systems are quantum mechanical and they should be described therefore"
},
{
"end_time": 1817.432,
"index": 65,
"start_time": 1788.814,
"text": " in probabilistic terms. You should have quantum states or wave functions which only tell you about potentialities and only when measurements are done then these potentialities are turned into actualities. But on the other hand it says that the whole of physics should be described in these particular terms. So on the one hand we've got the geometry, tensor fields, smooth metric, light cone propagation etc and on the other hand we've got this"
},
{
"end_time": 1847.671,
"index": 66,
"start_time": 1817.91,
"text": " When I started out, this was considered to be the biggest open issue in theoretical physics. And my interest then was, how do we address this problem? How do we unify the principles of both those things? I came from the general relativity side. So for me, it was really important that there be no what people call background structures. So let me explain what this means."
},
{
"end_time": 1876.988,
"index": 67,
"start_time": 1848.626,
"text": " So in quantum mechanics and even quantum field theory, like for example, when we do quantum electrodynamics and so on, we actually have background structures, which is really the space-time metric. Space-time metric is given. It's a stage on which various things happen. It is indifferent to the happenings. It is fixed. Nothing changes. Whereas in general relativity, there are no actors."
},
{
"end_time": 1902.927,
"index": 68,
"start_time": 1877.398,
"text": " There is a drama of evolution, if you like. Space and time is not a spectator. It's also an actor. It's also a physical entity. You can act upon it. It acts back. Einstein's equations basically tell space time how to bend. And once you have got bent space time, that space time does matter how to move. And so there is a tension here because on the one hand, in general relativity,"
},
{
"end_time": 1930.572,
"index": 69,
"start_time": 1903.712,
"text": " There are no background structures. There is nothing which is sitting there, which is there's no stage. There's no arena. Everything is really acting with each other. There are no spectators, as I like to say, in this cosmic drama. So, but corner field theory for its very formulation really assumes that there is space time. For example, the Schrodinger equation in which time revolution, but even corner field theory, you know, you talk about"
},
{
"end_time": 1960.401,
"index": 70,
"start_time": 1931.749,
"text": " was a propagation, you say that if there are two fields of two so-called space-like separated points, so that there's no positive signal passes from one to another, then those fields commute. So these are fundamental commutation relations in the theory. And we don't have such a thing because we've got a dynamical metric, you know, so there's no fixed structure like that. And therefore, there is a tension. And coming from general relativity side, I felt that it was more important that"
},
{
"end_time": 1990.111,
"index": 71,
"start_time": 1960.896,
"text": " this background independence. The fact that there are no spectators in this cosmic evolution is something that should be put to forefront. And when I started out, all approaches coming from particle physics or quantum field theory side to quantum gravity were really based on this idea that there is a fixed Minkowski metric. And then when you take the gravitational field itself, for example, so that is represented, for example, by a curved metric G,"
},
{
"end_time": 2019.224,
"index": 72,
"start_time": 1990.589,
"text": " So what you do is you introduce by hand a flat Minkowski metric or called Minkowski metric and you take the difference g minus the flat metric, let's call it g naught and then that is considered to be the gravitation field and that was denoted by h and what just did perturbation theory in powers of h. So the approaches were completely perturbative and what I wanted to do was very much approach which is background independent"
},
{
"end_time": 2049.002,
"index": 73,
"start_time": 2019.514,
"text": " H is how much the metric differs from the flat case. The flat case metric is something that you put by hand. There is a gauge freedom there as one says. It is not something that is physically determined. The idea is that only when you sum over all the terms, then you will find that there is no dependence on this flat metric."
},
{
"end_time": 2071.664,
"index": 74,
"start_time": 2049.923,
"text": " But there are questions about whether you can actually sum and that sum converges in a mathematical sense and so on and so forth. There are good partial answers to that in classical theory, but in quantum physics nothing converges, there are infinities, and so the problem is really open. Even in classical theory, it really is difficult to get."
},
{
"end_time": 2101.834,
"index": 75,
"start_time": 2072.073,
"text": " If you start out with Minkowski space, which is a flat space, you know, it's like if you look at a two dimensional plane or three dimensional Euclidean space that you're familiar with, we're adding one dimension, which is time dimension, and it's all completely flat. So the metric there is basically minus the time difference squared plus the space difference squared. That is a metric. And so this is given to you once and for all. And then the statement is,"
},
{
"end_time": 2130.179,
"index": 76,
"start_time": 2103.473,
"text": " The H field, for example, is supposed to propagate on the light cones of this G naught metric that you are given once and for all. But on the other hand, G naught metric is just something put behind. And so therefore, to give fundamental meaning to these light cones is not appropriate. And I think by now people, particle physics even, the community sort of appreciates that, that that was not completely appropriate."
},
{
"end_time": 2155.384,
"index": 77,
"start_time": 2130.503,
"text": " And then when you take with this flat spacetime metric, if you want to talk about black holes and so on, locally you can try to sum up the perturbation theory and get a locally black hole metric. But globally, black holes are very global concepts. This is not possible. So this was basically the idea. And then the question is how to go about doing this. And so there had been"
},
{
"end_time": 2185.794,
"index": 78,
"start_time": 2156.305,
"text": " Since the 1950s, attempts at formulating general relativity in a suitable way so that you can go to quantum mechanics, quantum physics, quantum gravity in a non-participative way without splitting this. So they were side-by-side attempts. The particle physics attempt was very much started with Feynman, but then taken over by many other people, particularly Bryce David and so on. And then on the non-participative side, we had Dirac,"
},
{
"end_time": 2209.07,
"index": 79,
"start_time": 2186.766,
"text": " And then Peter Bergman and his collaborators, old school and so on, they had developed a certain approach just called Hamiltonian methods or canonical gravity, as they call it, canonical. You can formulate any field theory in that particular language. And the advantage there was that one did not need to introduce a fictitious flat background metric."
},
{
"end_time": 2239.923,
"index": 80,
"start_time": 2210.401,
"text": " But then the mathematics of that theory and which was then developed also by John Wheeler and his collaborators. But the mathematics of that theory had remained completely formal. And in other words, there are infinities because the system has infinite number of degrees of freedom. It's a field theory and every field theory, you want electromagnetic field light that has infinite local degrees of freedom. And then in many theories, we know perturbatively"
},
{
"end_time": 2260.776,
"index": 81,
"start_time": 2240.384,
"text": " how to handle it through renormalization, but general relativity turned out to be not renormalizable, but not quite a bit even finite. And so the question was, well, how do you then, you know, what do you do? What do you proceed? How do you? And so this was, this was not a problem for Dirac, Bergman, Wheeler, et cetera. And therefore they actually tried to go"
},
{
"end_time": 2283.37,
"index": 82,
"start_time": 2261.254,
"text": " that direction to address more basic questions, particularly Wheeler about, you know, what happens at the Big Bang and perhaps we can answer such questions where non-partiability methods are essential because near the Big Bang, the curvature is very, very large. So try to do an expansion in small curvature quantities is kind of a very bad method, if you like insuited method."
},
{
"end_time": 2313.66,
"index": 83,
"start_time": 2284.718,
"text": " So this was there, but except that everything was very formal. People were writing down these equations which were formally written down. The famous Viradevit equation is a formal equation which was written down in the 70s or 60s actually. But even today, it is a formal equation. In other words, we do not have precise mathematical meaning to that equation. And so I wanted to go beyond that. And then I had three ingredients that came all together"
},
{
"end_time": 2337.875,
"index": 84,
"start_time": 2314.292,
"text": " The first was that there was a formulation of other interactions of physics, you know, the weak and electromagnetic interactions. And in those interactions, the interactions of popularly people who say forces are propagated by what people call vector potentials, or in geometry, you might call them connections."
},
{
"end_time": 2368.063,
"index": 85,
"start_time": 2338.251,
"text": " It's a vector potential which couples locally to currents, for example, in electromagnetic theory. If you want a local coupling, one introduces a vector potential. Whereas in general relativity, we only had, we have a metric. I mean, there's a connection which it defines, but that's not at forefront. We have the metric, and the metric defines the light cause, it defines what you mean, gives meaning to hyperbolicity, differential equations, and so on and so forth. And so famously, for example, Weinberg had pointed out in his"
},
{
"end_time": 2392.858,
"index": 86,
"start_time": 2368.541,
"text": " And then I thought that maybe we can actually remove this wedge. The second ingredient that came at that time was really coming from"
},
{
"end_time": 2420.418,
"index": 87,
"start_time": 2393.353,
"text": " various ideas that people like Roger Penrose and Ted Newman and so on had introduced coming from Twister theory. And in Twister theory and so on, there is a certain sector of the theory which is exactly integrable. And that, I mean, in general relativity, the basic idea is a metric, but the invariantly defined things that defines a strong gravitational field or weak gravitational field is the so-called curvature, which is determined by the metric."
},
{
"end_time": 2449.616,
"index": 88,
"start_time": 2421.476,
"text": " And this curvature, if you like, in Maxwell theory, is like the Maxwell tensor Fminu whose components are electric and magnetic fields. So we've got a similar tensor in general relativity is called the curvature tensor. And that curvature tensor, sometimes called the Riemann tensor, is obtained by commuting two derivative operators that are defined by the metric. And so there was this idea"
},
{
"end_time": 2479.462,
"index": 89,
"start_time": 2450.401,
"text": " that maybe what we should do is to take the connection as a fundamental quantity. And this idea somehow was suggested to me, I was a postdoc with Roger Penrose and just during that year that I was there for two years and just during that period, Roger invented what is called as nonlinear graviton. Which is called the what, sorry? It's called nonlinear graviton. A nonlinear graviton, okay. Nonlinear graviton. It's a Twister construction"
},
{
"end_time": 2508.319,
"index": 90,
"start_time": 2480.589,
"text": " It's a rich construction because it brings together theory of differential equations and algebraic geometry. The two things that were completely separate all along are brought together. And what Roger showed was that if you look at a certain simplified version of Einstein's equations, namely the following. What you do is you have got this curvature tensor."
},
{
"end_time": 2538.285,
"index": 91,
"start_time": 2508.78,
"text": " But you can break up the curvature tensor into two parts, and they're called self-dual part and anti-self-dual part. And each of them, if you like, in Maxwell theory also, we can take the Maxwell tensor and divide into two parts called self-dual and anti-self-dual. And each of them defines a helicity of the photon. So these are eigenstates of the helicity operator. A photon is a spin-1 particle, and it has a rest mass zero, and therefore its angular momentum, its spin vector is pointed"
},
{
"end_time": 2567.739,
"index": 92,
"start_time": 2538.865,
"text": " Similarly, we can do this decomposition in the case of gravitational field."
},
{
"end_time": 2597.227,
"index": 93,
"start_time": 2568.285,
"text": " And you can have self-dual and anti-self-dual solutions of Einstein's equations. These, however, are complex solutions of Einstein's equations. And now in quantum mechanics, it doesn't matter because the wave functions are complex. But in classical physics, we want real things. Now for the Maxwell case, it does not matter also because you can take two real, two complex things that are complex conjugates of each other. So you can just add them and you'll get the real Maxwell field. That is a real Maxwell field."
},
{
"end_time": 2622.244,
"index": 94,
"start_time": 2598.029,
"text": " But general relativity is a nonlinear theory. So you cannot just add the self-dual curvature and anti-self-dual curvature to get some metric whose curvature will be the sum of the two, the real part. So you cannot get the real metric by adding because the theory is nonlinear. You cannot just superpose the self-dual solution and anti-self-dual solution to get a real solution. But nonetheless, the fact that"
},
{
"end_time": 2646.135,
"index": 95,
"start_time": 2623.097,
"text": " Self-duals, the mathematical structure of self-dual solutions is extremely simple. This is what Roger pointed out, that you can obtain, quote unquote, the more general solution of Einstein's equation, which is self-dual. This is, you know, a radical breakthrough in a way, that because equations are so complicated, but we can obtain the general solution of Einstein's equation using this method."
},
{
"end_time": 2667.995,
"index": 96,
"start_time": 2647.21,
"text": " Ted Newman in Pittsburgh had another parallel construction and it turned out that the two are quite compatible with each other. They are exactly, one can go back and forth between the two. So I knew that there is this exactly integrable sector of general relativity. But again, I felt that that is still talking about complex general relativity."
},
{
"end_time": 2696.749,
"index": 97,
"start_time": 2668.712,
"text": " And how do we construct a theory whose limit then would give you classical, usual, real general relativity with cosmology, black holes, and so on and so forth. And so that was my interest. My interest was that, well, on the one hand, these derivative operators or connections, they look like good objects to do things. But Penrose and Newman and Plobansky, they were three people, three slightly different approaches, but they turned out to be more or less equivalent."
},
{
"end_time": 2726.647,
"index": 98,
"start_time": 2698.387,
"text": " They suggested that, well, we should be looking at self-dual things. So therefore, what I did was to say that maybe what we should do is take a real general relativity, but formulate it in terms of these self-dual variables, as they are called. In other words, you've got a derivative operator which acts on spinors. So spinors are fundamental objects that describe, for example, the electron, the neutrinos, the quarks,"
},
{
"end_time": 2753.063,
"index": 99,
"start_time": 2726.852,
"text": " in the standard model. The fundamental fermions are all fundamental particles. Massive particles are all fermions. And in the presence of a gravitational field, the equations they satisfy involves a certain derivative operator because they are differential equations. But these fundamental particles at the basic level"
},
{
"end_time": 2782.756,
"index": 100,
"start_time": 2753.985,
"text": " Right. So, very good. So,"
},
{
"end_time": 2809.48,
"index": 101,
"start_time": 2784.548,
"text": " If I look at, let's begin with the electromagnetic field. So we've got electric and magnetic fields, and one of the beautiful things about spatial relativity is that they can actually be combined in a covariant manner so that you've got the Maxwell field tensor. So it's a tensor whose, if you like, space-time component is the electric field and space-space component is the magnetic field."
},
{
"end_time": 2838.063,
"index": 102,
"start_time": 2809.684,
"text": " Electric and magnetic fields are combined together already in spatial relativity. You shouldn't think of them as separately. If you have got an observer, that observer with his full velocity can decompose this tensor into electric and magnetic field. Another observer would decompose it in different ways. So what you have is really this field. And so what we have is a tensor field, which is called f. It has two spacetime indices. So let's call it f mu nu."
},
{
"end_time": 2869.258,
"index": 103,
"start_time": 2839.497,
"text": " And if you have got a tensor, then one can take it mathematically. You can take what is called Hodge dual. So you've got a two-dimensional anti-symmetric tensor, and you can contract it with an epsilon mu nu alpha beta. So these are totally anti-symmetric tensor. And what you obtain is, again, what you obtain is the object with two anti-symmetric indices. So you get an object with the same"
},
{
"end_time": 2897.244,
"index": 104,
"start_time": 2869.616,
"text": " So it's a similar structure and so if you take this epsilon and operate it on a Maxwell field, you get another Maxwell field if you like and that is called the dual of the first one. It's dual because you operate it by epsilon. So what does it mean in terms of electric and magnetic fields? Well basically E goes to B and B goes to minus E. So you just do this rotation and that is what's dual. Now several dual is the one in which"
},
{
"end_time": 2927.21,
"index": 105,
"start_time": 2898.797,
"text": " The field is its own dual. But if you look at this duality operation in the space-time signature in the real world, which is time is always a minus and space is plus or vice versa, we usually use time as minus. So the distance is always minus the time interval squared plus the space interval squared. So in that signature, this operator, duality operator,"
},
{
"end_time": 2955.828,
"index": 106,
"start_time": 2927.756,
"text": " is actually, if you take a square, you get minus one. So it means that if you have a self-dual object, something which is equal to itself, if I again operate it by this... Equal to the Hodge of itself. Hodge dual, right, exactly. So then you'll get minus one. So therefore, the self-dual objects, if you do it twice, you get minus one. So therefore, the eigenvalues are plus or minus i. And so if it is plus i, it is called self-dual."
},
{
"end_time": 2971.169,
"index": 107,
"start_time": 2956.152,
"text": " If it is minus i, it is called antiseptic. So in terms of electric and magnetic field and given observer, you can say that e plus ib, that complex field would be self-dual and e minus ib would be antiseptic."
},
{
"end_time": 2998.012,
"index": 108,
"start_time": 2972.722,
"text": " Coming to gravity, gravity is very similar. The curvature tensor is like the Maxwell tensor. I'm so sorry. One more time. I'm so sorry, professor. I just want to always... Yes? It's okay? Yep. Every time your question... Great. Okay. Only because I want to make this physically clear. So just one note. Hodge... I may keep this or may not, but a Hodge dual. So if people know what a form is,"
},
{
"end_time": 3023.404,
"index": 109,
"start_time": 2998.575,
"text": " Let's say you have a manifold that's four dimensions and you have a form that's two dimensions, then you can take, there's a way of taking a two form and then identifying it with another two form. Well, the formula is just, you need this tensor field because you're talking, tell me how technical I can be. Yeah, yeah, yeah, you can get technical. And I need a four form or actually I need"
},
{
"end_time": 3041.118,
"index": 110,
"start_time": 3024.138,
"text": " a tensor field which is two covariant indices and two contravariant indices. And then these contravariant indices can contract with the form that you give me and therefore again obtain a covariant two form. So I need an object like that."
},
{
"end_time": 3070.708,
"index": 111,
"start_time": 3042.022,
"text": " So what you need is technically called a conformal metric, a metric up to a multiplicative factor, then you can actually raise the indices of the four form that you have got in the manifold, if the manifold is orientable say, and then you can raise the indices and then you will get an object which has two down-stage indices if you like or covariant indices and two up-stage or contra-variant indices and then when you, when you, I got, maybe I should, I don't know, so it doesn't,"
},
{
"end_time": 3088.882,
"index": 112,
"start_time": 3070.998,
"text": " And then the statement is that I can contract the upstairs indices with the downstairs indices for the form and get again a form which has downstairs indices up here. But in the Lorenzian signature, which is minus plus plus plus, which is Minkowski signature, the square of the Hodge dual is minus one."
},
{
"end_time": 3101.459,
"index": 113,
"start_time": 3089.633,
"text": " In the Riemannian signature, it is plus 2."
},
{
"end_time": 3121.732,
"index": 114,
"start_time": 3101.903,
"text": " Douglas Goldstein, CFP®, Financial Planner & Investment Advisor"
},
{
"end_time": 3149.275,
"index": 115,
"start_time": 3122.671,
"text": " What I want to know is, what does it mean physically when you say that a theory is dual or self-dual? So for example, we could identify up and down with being a left-handed or a right-handed particle. Okay, so there's some correspondence between the math and then the physics. So what's the correspondence here between the math of being self-dual and then the physics? What's concretely happening when one says this theory is self-dual or not? Does that correspond to a particle? Does that correspond to a type of theory?"
},
{
"end_time": 3180.026,
"index": 116,
"start_time": 3150.179,
"text": " So in quantum mechanics, that corresponds to a particle with a given helicity. It's a photon, because it is a zero response particle, the photon actually has a spin which is aligned to its 4-momentum, not the energy momentum, it's like 4-momentum. And then it's either pointing along the 4-momentum or anti. And if it is pointing towards the 4-momentum, then it is helicity plus one and the other one is helicity minus one."
},
{
"end_time": 3209.428,
"index": 117,
"start_time": 3180.657,
"text": " When it comes to mathematical representation of these states of the photon, then the ones which are pointing in one direction, one helicity, they correspond to Maxwell fields which are self-dual. And they're complex because wave functions are complex, there's no problem. And if it is other helicity, then that corresponds to the anti-self-dual. And in Maxwell theory it's nice because you can just add the two and get a real solution. That's very good."
},
{
"end_time": 3231.954,
"index": 118,
"start_time": 3210.196,
"text": " And the idea that Roger had was that, and you can do the same thing with linearized gravity. In other words, this perturbative gravity that I told you about, which is in which you've got flat space, and then you've got a big gravitational field, and you can take the curvature tensor. So the curvature tensor in gravity has four indices, and it is anti-symmetric in the first two and anti-symmetric in the last two."
},
{
"end_time": 3261.51,
"index": 119,
"start_time": 3232.193,
"text": " It's not like the epsilon form because it is not totally anti-symmetric, it is just anti-symmetric in the first two and anti-symmetric in the last two and then some other algebraic conditions appear and that's called the Riemann tensor and what you can do again is take this epsilon, take the Hodge dual on either of the two, it doesn't matter, you can take the Hodge dual either on the last two or the first two, it doesn't matter and then again you will get a tensor which will have four indices which will be anti-symmetric in these two and anti-symmetric in the other two"
},
{
"end_time": 3284.428,
"index": 120,
"start_time": 3261.869,
"text": " And then those indices are going to be and again the square of the Hodge duality operator is minus one and therefore you get the eigenfunctions are going to be complex. And if you look at linearized gravity,"
},
{
"end_time": 3314.77,
"index": 121,
"start_time": 3284.957,
"text": " And then you can talk about gravitons. The usual way that people talk about gravitons are all perturbative terms. So that really refers to linear gravity theory. And linearized gravity, the statement is that you can do exactly what we said in the Maxwell theory. Again, the only difference is that now the spin is two rather than one for the graviton, linearized gravity. And then again, it is zero response particle. So the spin is either aligned or anti-aligned. And if it's aligned, then it is"
},
{
"end_time": 3343.848,
"index": 122,
"start_time": 3315.862,
"text": " Can we talk about the helicity when the particle is not massless? Helicity is a social massless particle. It really replaces the motion of spin because the direction is already known. Whereas normally, if you had a massive vector boson, then it would have spin."
},
{
"end_time": 3360.452,
"index": 123,
"start_time": 3344.343,
"text": " So it's not pointing along there. So what you know is that the spin is pointing always along, it is perpendicular to the full velocity. And so, but if the full velocity is null, then it's perpendicular itself, so it can spin can point along itself and that's it."
},
{
"end_time": 3388.899,
"index": 124,
"start_time": 3361.152,
"text": " So there's one other way of understanding that with a mass, massive particle, if it's moving in a certain direction and it's spinning, you can boost yourself. You can move so that the particles moving over here, but the, but it would still be spinning here. So now it's moving, it's spinning in the opposite direction that it was, whereas before it was aligned. So then the helicity is not defined. The spin will transform like a vector. So if the full momentum will transform under Lorentz transformations, similarly the spin vector will transform."
},
{
"end_time": 3414.957,
"index": 125,
"start_time": 3389.275,
"text": " But spin vector will transform like so-called pseudo vector, whereas the, in other words, if you change x, y, z, t, then the full momentum will go to minus its components of the reverse, whereas for the spin vector, the components will remain the same. It is like an ordinary quantum mechanics, non-reducible. So I have this long explanation about"
},
{
"end_time": 3445.776,
"index": 126,
"start_time": 3416.032,
"text": " So I just want to say where we were. So basically, you asked me about how do I start with this quantum gravity, the quantum gravity and so on. And so first thing was background independence and non-perdivity methods. The second thing was then, well, but how do you go about doing it? Because everything people had done, Dirac and Arnavides and Wiesner and Wheeler and Debit and so on, was very formal. And so how do you remove that formal things? The second point was, well, we've got this"
},
{
"end_time": 3471.698,
"index": 127,
"start_time": 3447.244,
"text": " All other interactions are really governed by this vector potentials or the derivative operator connection as one calls it in different geometry, whereas in gravity it is actually the metric that is what is used. And so one wanted to have more uniform way of dealing with all interactions. And then the third"
},
{
"end_time": 3499.121,
"index": 128,
"start_time": 3471.937,
"text": " thing that came was this idea that maybe what we should do is not use, so to say, the brute force derivative operator that the metric gives you, but only part of that derivative operator, which knows how to operate on left-handed spinors, which are the fundamental particles in our standard model, fundamental fermions. So these are the ones which are helicity. So we just look at those ones."
},
{
"end_time": 3523.626,
"index": 129,
"start_time": 3499.974,
"text": " And then the statement was, that means that, well, we should not get rid of them. Metric is not a fundamental object, but even the derivative operator defines all of it is not fundamental object. Only a fraction of it which is extracted out, which is self-dual or anti-self-dual, it doesn't matter is your conventions, but supposing self-dual you extract it out, then that is going to be what we should be able to do."
},
{
"end_time": 3551.954,
"index": 130,
"start_time": 3524.326,
"text": " That should be the fundamental object. And then we should formulate the theory thinking that that is a fundamental object and then go ahead. And then the nice thing was that if you did this, then one could write down a phase space of the theory, which is exactly like Yang-Mills theory, which govern other interactions, the weak, the electroweak and the strong interactions. So the weak electric, weak electromagnetic and strong interactions."
},
{
"end_time": 3581.493,
"index": 131,
"start_time": 3552.244,
"text": " They're all governed by so-called Yang-Misting theory in which there is a connection. Here also now there is a connection. It just happens to be subtle. It's a gravitational connection which knows how fundamental particles move in presence of gravitational field. The electromagnetic connection tells you how electron charged particles move in the presence of electromagnetic field, external electromagnetic field."
},
{
"end_time": 3607.381,
"index": 132,
"start_time": 3581.766,
"text": " Strong interaction vector potential A, that tells you how quarks move in presence of a gluon field. This connection is a gluon in that case. And now the statement was that you now take this fundamental constituents of matter which are fermions which have precise helicity"
},
{
"end_time": 3634.684,
"index": 133,
"start_time": 3607.739,
"text": " This is before the symmetry breaking. So they are precise helicity. So they are massless at that level. And then the statement is that you see how they move the gravitational field and what they are sensitive to is really this dual connection. So maybe we should choose that as a fundamental object. And to my surprise, it was a big surprise that the whole theory, real general relativity could be formulated"
},
{
"end_time": 3664.343,
"index": 134,
"start_time": 3635.213,
"text": " using this half the information somehow. And so that was a big surprise. So what happened is two things happened. First of all, the theory could be real general activity could be formulated. Whereas in twisters, even today, what we have is this subdual sector and antisubdual sector. We don't know how to combine them. Whereas in this formulation, you are really talking about real general activity. And secondly, kinematical level."
},
{
"end_time": 3694.445,
"index": 135,
"start_time": 3664.94,
"text": " Before putting the information or the interactions and so on, detailed equations, what are the variables in terms of which you formulate your theory? In fact, in Einstein's autobiographical notes, he has this question that in formulation of a physical theory, the first question is what tools are you going to use? What are the basic mathematical variables which are going to capture your physical ideas? And only then what equations do they satisfy?"
},
{
"end_time": 3723.166,
"index": 136,
"start_time": 3694.872,
"text": " Sure. And here the statement is that these variables are the same for all interactions. That is very, to me this is very satisfying. On the other hand, the equations are satisfied quite different. So where does the difference come in? And another beautiful thing here is that the difference comes in precisely because you've got the in general relativity, there are no background fields. So when I write down the Lagrangian,"
},
{
"end_time": 3753.148,
"index": 137,
"start_time": 3723.439,
"text": " or the Hamiltonian in the Young-Mills theory or something. I'm allowed to use not only the Young-Mills fields, or in the case of Maxwell field, I'm allowed to use not only the tensor F-menu or electric and magnetic fields, but also the metric, just sitting there, spectator. I mean, it just is not doing anything, but I mean, it's not dynamically changing, it's sitting there. So I can use that to construct this Lagrangian density. But here I don't have anything, I don't have metric. So I have to write down equations using just these vector potentials, right?"
},
{
"end_time": 3780.026,
"index": 138,
"start_time": 3753.746,
"text": " But I don't have a background metric, you know. Now the funny thing is that if you really give yourself these variables, these connections and their conjugate momentum, which are like the electric fields, the analog in Maxwell theory would be the electric fields, then it turns out that there are very few equations you can write down."
},
{
"end_time": 3804.872,
"index": 139,
"start_time": 3781.817,
"text": " And it literally is true that if you took a very bright undergraduate or first day graduate student and we would put them in the room and you tell them, write down the simplest equations you can write down. No background metric, no background fields. All you have is this connection and it's conjugate momentum. And the equations they will come down are precisely turned out to be Einstein's equations."
},
{
"end_time": 3831.169,
"index": 140,
"start_time": 3805.333,
"text": " This is not how I arrived at it. I did it laboriously, which is I started with the usual formulation of Einstein's equations. I made a canonical transformation. I turned the theory on its head, as some friends of mine told me. And then the statement is that is it looking at upside down. So metric is no longer fundamentally variable. And then I did this canonical transformation, you certainly had these variables, which turned out to be a connection and that conjugate momentum."
},
{
"end_time": 3859.582,
"index": 141,
"start_time": 3831.817,
"text": " And then I looked at, I mean, because I just did a canonical transformation, I could write down the equations which are equivalent to the Einstein's equation. Only later I realized that there aren't other equations you can write down. If you have background independence and if you want to have these connections, this is the only thing you can write down. And so that was a formulation of general relativity that I started with, which gave rise to this non-potential theory, quantum theory then."
},
{
"end_time": 3889.155,
"index": 142,
"start_time": 3860.196,
"text": " So we had the advantage of actually using methods which are coming from very successful Yang-Mills theory, so-called Wilson loops or Wilson lines. And those methods were available already, but now we could take it into gravity and we could interpret geometry, space-time geometry in terms of those quantities which are used first only in the context of Yang-Mills theory. Now, much later, I think,"
},
{
"end_time": 3918.234,
"index": 143,
"start_time": 3890.828,
"text": " A little more than 10 years after I did this work. This work was done in 1986. So about 10 years later, I realized, I found out that, in fact, both Einstein and Schrödinger tried to give a formulation of this general relativity in which connection would be fundamentally variable. Exactly the same basic idea."
},
{
"end_time": 3942.244,
"index": 144,
"start_time": 3919.121,
"text": " And it is a very fascinating chapter in history. So I just want to tell it to you for sure. I have audience, particularly. Einstein was in the Institute of Advanced Study in Princeton, and Schrodinger was in the Institute of Advanced Study in Dublin. And they kind of independently thought of this idea, but then they started corresponding. And then these letters are preserved."
},
{
"end_time": 3961.51,
"index": 145,
"start_time": 3942.739,
"text": " And I think that they're available in the archives, not the usual archive, I mean, in the Surgeon Institute archive. And these are, there's a correspondence going back and forth, and this is across the ocean. And yet, you know, basically the letters are really one week apart."
},
{
"end_time": 3991.664,
"index": 146,
"start_time": 3961.869,
"text": " So basically, as soon as they got the letter, they read it, understood it. I wrote these very detailed replies to each other. It's a very friendly and jovial thing, you know, in which Einstein sort of teased Shorinji by saying, oh, that idea of yours was cleverer than what a devil's grandmother could think of. And then, you know, Shorinji replies saying that, well, this is a bigger honor to me than, you know, all the medals that kings and various people have given me and so on."
},
{
"end_time": 4018.592,
"index": 147,
"start_time": 3992.244,
"text": " So this was all happening and they were working on this theory, which was basically to formulate general relativity in terms of this connection. But they are using the connection, which is more like the metric connection, not the central connection, but the the the the derivative operator that comes from the metric up here. And then something happened, which is really weird. And the weird was that somehow Schrodinger thought that he had made a breakthrough. And he"
},
{
"end_time": 4039.787,
"index": 148,
"start_time": 4019.172,
"text": " That breakthrough, for those of you audience who might know about it, was basically to drop the condition that this connection, which is sometimes called Christoffel symbols. These Christoffel symbols normally in general relativity are symmetric or torsion free. So he allowed them to be anti-symmetric. And he thought that this was really a revolution."
},
{
"end_time": 4070.435,
"index": 149,
"start_time": 4040.657,
"text": " And big idea, bigger. And then you give a press conference saying that, well, this is a completely new theory. It's much bigger and much more beautiful. And, you know, in general, you ask them to be symmetric. And so you even give an analogy of you say that, well, here is a horse and I want to train this horse, but poor horse, he cannot do everything. So what I'm going to do is to train him to jump over a fence. Right. But I'm going to tie the hind legs together and let it"
},
{
"end_time": 4101.084,
"index": 150,
"start_time": 4071.186,
"text": " first learn how to do it with his front legs. And the poor husk won't be able to do it. What you have to do is to, you know, let it use all the four legs. So so using that asking that the connect that this levituita symbol the connection be symmetric is like tying the hind legs of the horse. And I have freed it now. And privately, he won't discuss that you might probably get a second Nobel Prize and so on, so forth. And then he gave a seminar. And at that time, you may or may not know the history."
},
{
"end_time": 4127.961,
"index": 151,
"start_time": 4101.425,
"text": " the Prime Minister, the Taoiseach, and then Ireland was a physicist. And so the Taoiseach came to the seminar and because Taoiseach came to the seminar, the press came to the seminar. And therefore there were headlines, the Irish newspaper, and these all, by the way, recorded in various places. There's a headline in Irish newspaper saying that Roger has made this great breakthrough and how generalitude is only a special case and so on and so forth."
},
{
"end_time": 4153.882,
"index": 152,
"start_time": 4128.746,
"text": " And then New York Times managed to get a copy of the Irish Times before it actually appeared and send it to Schrodinger, to Oppenheimer and Einstein for comments. I don't know any comment of Oppenheimer. Oppenheimer might have just dismissed it completely. But Einstein prepared a very careful reply. And the reply said that he was very"
},
{
"end_time": 4182.125,
"index": 153,
"start_time": 4154.241,
"text": " taken aback because, you know, they are corresponding on the idea and suddenly showing the things that this is a great idea and he didn't think it was a great idea. He didn't think. And so Einstein gave this press release which said that, well, it is unwise for scientists to describe what is going on in technical work in simplistic terms because that gives the lay public the impression that science advances"
},
{
"end_time": 4210.845,
"index": 154,
"start_time": 4182.517,
"text": " through revolutions every day as if it was a banana Republic. And this was totally, and this appeared, of course, in New York Times. And then this was so shocking to Schrodinger when he heard about it. Unfortunately, Schrodinger did the second mistake of writing to Einstein saying that, you know, after the war, the living conditions of physicists are so bad here. So he thought that news like that will bring more money to physics and so on."
},
{
"end_time": 4241.323,
"index": 155,
"start_time": 4211.664,
"text": " He was offended that Schrodinger went off and said that he found a breakthrough without conferring with Einstein first?"
},
{
"end_time": 4258.763,
"index": 156,
"start_time": 4241.937,
"text": " According to Moore's biography, it's called the Einstein-Schweiner eye, the Einstein's pick stack, the big mess that he has made with Einstein, and this is the whole thing. So this is an interesting story. Okay, so this is a long, let's go back to our mid-pop."
},
{
"end_time": 4278.302,
"index": 157,
"start_time": 4260.026,
"text": " I have a quick naive question. There's something called the fundamental theorem of Riemannian geometry. So if you have torsion-free and something that's compatible with the metric, you get a unique connection. So if he throws out the torsion-free property, does the connection then become ambiguous or like you make a choice on it? Yes, so therefore there are new degrees of freedom."
},
{
"end_time": 4303.439,
"index": 158,
"start_time": 4278.302,
"text": " Whatever the connection. So this anti-symmetric part of the torsion part is really a new degree of freedom. And you thought that was very important. I mean, this idea people are pursuing later also. It has not led to anything which is dramatic or even significant. But I mean, it's mathematical. It's a neat idea. It's just that it was not such a revolutionary as he thought. So coming back to the main point,"
},
{
"end_time": 4317.585,
"index": 159,
"start_time": 4303.831,
"text": " Coming back to the main point that the main ingredients were to formulate general relativity in turning it upside down, making metric as an emergent quantity and then the connection as being more fundamental variable."
},
{
"end_time": 4346.596,
"index": 160,
"start_time": 4318.046,
"text": " And that is what is now has gone. So therefore, things which are called Wilson lines or Wilson loops become basic variables. And the word loop quantum gravity comes from those Wilson loops, even though these days nobody will use this loop so much as these lines. But just like string theory, you know, some name starts and then it becomes a name. So because string theory, there are brains and there are various other things equally important strings. But we still call it string theory. Similarly, here it is called loop quantum gravity."
},
{
"end_time": 4372.5,
"index": 161,
"start_time": 4347.142,
"text": " The better name would be something I would say quantum Riemannian geometry because when you formulate it in this particular way then it turns out that basic geometrical objects like area of the screen that you're looking at right now, they all become operators in quantum theory and these operators have purely discrete spectrum."
},
{
"end_time": 4398.763,
"index": 162,
"start_time": 4373.831,
"text": " And so really, geometry is quantized in the same sense as the energy, the angular momentum, the z-component angular momentum is quantized in hydrogen atom. And so this is important. I mean, it changes the picture of geometry completely. And so this is also something that you don't see in other approaches, either the Ville de Vitte approach,"
},
{
"end_time": 4429.599,
"index": 163,
"start_time": 4399.974,
"text": " Okay, here's some thoughts that occurred to me. Well, one is that you mentioned there's an area operator, and then I recall that there's someone named Theman, Thomas Theman, who said that we should have a volume operator and that better gives a semi classical limit of GR. So I just wanted to know what your thoughts were on that."
},
{
"end_time": 4456.34,
"index": 164,
"start_time": 4430.213,
"text": " Right. So I'm one of the people who introduced the volume operator, studied its detailed properties. So I mean, like Lewandowski, and then Carlo Rovelli and Lee's volume independently developed, you know, this volume operator and also the area operators and so on. In the beginning, there were differences of opinion. There was some technical error in what Carlo and Lee had done, which is pointed out by Renata Lowell."
},
{
"end_time": 4481.288,
"index": 165,
"start_time": 4456.8,
"text": " But, you know, at the end of it, sort of everything comes together and where I got a kind of geometry in which you've got volume, the area operator, volume operator. There's also a length operator. It's just that it's not as useful as a volume operator in the length operator. There's also a length operator. And the volume operator is something that is, that plays in what Thomas did, the T-man. T-man was a postdoc of mine and not many"
},
{
"end_time": 4511.903,
"index": 166,
"start_time": 4481.954,
"text": " When he began his work, he was a postbaka point, but the specific papers that he wrote, the series of papers on quantum spin dynamics, he started here, but then he finished elsewhere in Harroword and then he went to the Albert Einstein Institute. That's where he finished his work. So he used this volume operator very cleverly in order to write, to give a rigorous formulation of Einstein's quantum Einstein's equations."
},
{
"end_time": 4539.684,
"index": 167,
"start_time": 4512.824,
"text": " That rigorous formulation is still being debated. It's not completely settled, but there is a huge progress. In fact, next month we've got this conference in Lyon, Loops 22. Every two years we have this conference and there is a talk by Madhavan Varadarajan who has made really very significant progress on this formulation of quantum Einstein's equation and he does use this volume operator that you mentioned."
},
{
"end_time": 4557.056,
"index": 168,
"start_time": 4540.708,
"text": " Again, I don't know much about this, so my questions may be fatuous, so excuse me. So here's what I understand. So you have a fiber bundle, and you have a principal fiber bundle, which for people who are wondering what that is, it's like attaching a group to the manifold at each point."
},
{
"end_time": 4576.152,
"index": 169,
"start_time": 4557.261,
"text": " The way that I learned it was that you attach a fiber P and then the P has a right action and that's G and it's free. And then on that you place a connection. Then a Yang-Mills field is when you take a section and then you pull back the connection locally."
},
{
"end_time": 4599.991,
"index": 170,
"start_time": 4576.732,
"text": " Okay, so then I'm wondering, well, what the heck was what is Yang-Mills theory? What is its relationship to that? Well, as far as I can tell, Yang-Mills theory is just saying that the Lagrangian is somehow the curvature wedge, the hodge form of the curvature, and you take the trace of that. But I don't know if that's if that's all that there is to Yang-Mills. I'm sure there's more. Okay. No, that's the basic Yang-Mills theory. Exactly. What happens is that almost"
},
{
"end_time": 4625.401,
"index": 171,
"start_time": 4600.674,
"text": " Most of the plate times in Yang-Mills theory, that is to say, when people apply to gas to space-time, the topological considerations are not important. So these bundles are trivial. So it's true, it's a cross-section of a bundle, but if the bundle is trivial, then you can think of it as living in space-time itself. So most of the time, I mean, there are very interesting cases where this is not the"
},
{
"end_time": 4650.913,
"index": 172,
"start_time": 4625.913,
"text": " You cannot do it and then you get nice topological results and so on. But when you talk about Pertubatic QCD and so on, they're all living just on space time. You can think of, just like Maxwell theory, the fields live. Strictly speaking, Maxwell field also, there's a bundle. The group there is a U1 group rather than SU3, for example, for gluons. Here U1 group on the bundle and it's the same thing at the"
},
{
"end_time": 4678.183,
"index": 173,
"start_time": 4651.254,
"text": " Then what occurred to me was when you said that the metric is given in the Yang-Mills case, whereas in the general relativity case, it's not given. In the Yang-Mills case, when you say that it's given, is that because you take the Hodge dual and the Hodge dual assumes the metric or is it even more fundamental than that?"
},
{
"end_time": 4703.695,
"index": 174,
"start_time": 4678.865,
"text": " Okay, so now let's say we're on general relativity and what we have is the connection, then you're wondering, well, how do I recover"
},
{
"end_time": 4731.834,
"index": 175,
"start_time": 4704.753,
"text": " And that tells you how much curvature is enclosed in that ring."
},
{
"end_time": 4762.244,
"index": 176,
"start_time": 4732.329,
"text": " Yes, yes, yes. And that's called the holonomy. Is that correct? Holonomy approach? Exactly. So that's how much curvature is enclosed. Okay, okay. So I'm just trying to make connections, make connections between the connections. Right, exactly. Yeah, but I think this, but as for undergraduates, senior undergraduates, it might be easier to sort of, so that is certainly true, but there's also a direct way of understanding constructing kind of spatial metrics."
},
{
"end_time": 4790.981,
"index": 177,
"start_time": 4763.166,
"text": " metric in the spatial part of the matrix. And that is really that what you do is to take Yang-Mills connection that you've got, this gravitational connection you've got, and then you also have the phase space variables which are electric fields. Now normally electric field is just a vector in electromagnetic theory, but if the gauge group, if you have a gauge group which is higher dimension, in this case the gauge group is SU2 say, then"
},
{
"end_time": 4817.705,
"index": 178,
"start_time": 4791.664,
"text": " you've got kind of it's a matrix valued object it has and so it has it's a vector potential which takes values and matrices but the values are just SU2 value. Now SU2 is just three-dimensional is the rotation group is a double curve of the rotation group so you've got x direction rotation y direction z direction that's the group that you use for ordinary spinors in non-relativistic quantum mechanics the usual quantum mechanics up here."
},
{
"end_time": 4843.712,
"index": 179,
"start_time": 4818.319,
"text": " And ordinary spinners, you know that you can just use a basis of Pauli matrices. And so you can think of both the vector potential and the electric field as carrying an internal index 1, 2, 3, which is basically component of the first Pauli metric, second Pauli metric, third Pauli metric. So it's a vector in space, but it also has an internal index."
},
{
"end_time": 4869.684,
"index": 180,
"start_time": 4844.189,
"text": " which is like a spin is the internal space. It lives in some abstract space, which is not physical space. And so you've got a triplet of electric fields. And my main idea was that, well, if you have a triplet of electric fields, then you can take this triplet. Yes. And think of it as an orthonormal tri. Just define it. I mean, there's no metric, right?"
},
{
"end_time": 4900.35,
"index": 181,
"start_time": 4870.401,
"text": " So given these electric fields, these electric fields, I just define an orthonormal triad with this, and then that defines for me a metric, because if I know what three orthonormal vectors are, then that tells me what the, given any vector, I can decompose into that, and I know the metric. So in fact, the triad is like a square root of the metric. Metric is the square of the triad, just like the spinors are square root of vectors. Okay, interesting."
},
{
"end_time": 4928.541,
"index": 182,
"start_time": 4900.725,
"text": " So basically, it's really the variable which is canonically conjugate to the connection to the derivative operator to set the connection. That is what is defining for you the spatial metric. Now, this is kind of a little bit of pedestrian way of doing it, but it's more intuitive. You can do it also co-variantly, and that is where the spin forms come into being."
},
{
"end_time": 4936.459,
"index": 183,
"start_time": 4928.695,
"text": " But then you have to really think in terms of the Lawrence group at each point and"
},
{
"end_time": 4962.927,
"index": 184,
"start_time": 4936.971,
"text": " But I mean, it's just like, you know, normally how I explained to you in the very beginning, how I explained to the undergraduate in the beginning, how given the F mu nu, I can get electric and magnetic fields, but I can put them together to get F mu nu. So similarly, what I was just telling you about now is triad, but you can put them so that you actually get a four dimensional metric and not just a three dimensional metric. And that is what is done in spin forms."
},
{
"end_time": 4989.309,
"index": 185,
"start_time": 4964.548,
"text": " When I look at a course on loop quantum gravity, one of the first lessons is on something called the four legs, but it has a it has a German name like wide bands or wide trends or what are those called the tetra? Are those tetraids? Okay, and that's what you're describing? Yeah. Okay. And so when you say that"
},
{
"end_time": 5019.292,
"index": 186,
"start_time": 4989.735,
"text": " that I know that I apologize for people who are wondering, like, these are such foolish questions, or so, or so technical, like, what's the point? Like, I'm just trying to clarify for myself, if you don't mind. So first, when they're being defined, it seems like it's, I was wondering, okay, so in general relativity, you say, okay, let me take a frame, let me go along with the frame. And let me just assume that frames or the normal. And then when I was hearing Tetra, I thought it was just talking about that. But then it sounded like they're saying,"
},
{
"end_time": 5044.172,
"index": 187,
"start_time": 5020.077,
"text": " Well, let me have another frame with those as the basis already. No? No, no, this is it. What you said is exactly that. It's just a frame. It's just a frame. And when I was talking about the internal indices, just index labels, these are 0, 1, 2, 3. But each of them is a vector. So there's a vector."
},
{
"end_time": 5072.79,
"index": 188,
"start_time": 5044.667,
"text": " but I'm labeling one zero one two three so there's another index other than the vector index so there's a vector index like a mu yes but then there's also an i feel like an i goes from zero one two three yeah okay so that's where I get confused that's all right or initially was confused at least so let's say you have the four vector and then you call them at first like in the regular general relativity sense let's call this this e zero e one e two e three but then I'm saying I'm going to get another vector forget about"
},
{
"end_time": 5077.978,
"index": 189,
"start_time": 5072.79,
"text": " 3 that are orthonormal and just get take one well that vector obviously can be decomposed in terms of these"
},
{
"end_time": 5104.94,
"index": 190,
"start_time": 5078.524,
"text": " Okay, so then you're saying, okay, Kurt, don't just take one vector, take another vector, those other indices, those are actually making reference to the original orthonormal basis. Okay, because I was wondering, like, why, why is there other indices at all? Why not just say in the same way you take these? Yeah, there's no other index. Your confusion was correct. I mean, there are no, there is no other index. I mean, you just assume that there was another index. No, I was not referring to another index at all. It's just those, but that index,"
},
{
"end_time": 5132.466,
"index": 191,
"start_time": 5105.486,
"text": " No, and then the statement is that if you get two other vectors, then I would like to know, for example, what is the magnitude of each of these vectors? What is the angle between those two vectors? And the statement is that if you give me the original four vectors, which are e is equal to e1 and e2, then I can just look at the components of this along v0, v1, v2, v3. And similarly, I can take w, w0, w1, w2, w3."
},
{
"end_time": 5150.196,
"index": 192,
"start_time": 5132.807,
"text": " And then I know what the length is, the length is just minus V0 squared plus V1 squared plus, etc. And I know what the angle is, it's just V0. So that's what I mean by saying that if you give me four vectors, then I know the spacetime metric. If you give me three vectors, then I know the spatial."
},
{
"end_time": 5180.708,
"index": 193,
"start_time": 5151.544,
"text": " Alright, okay, so now let's get to the more fun questions. So when you were working with Roger, you were a postdoc under Roger when you were working on this initially, and this seems like an extremely promising approach. So is Roger a proponent of loop or did he go off in another direction? Yeah, so in fact, just recently, I had some correspondence with the philosopher of science was visiting Oxford, he writes to me very often asking my views and such thing. And so Rogers, Roger has not followed it in very much. I mean, in his various books, he has said very"
},
{
"end_time": 5206.92,
"index": 194,
"start_time": 5181.237,
"text": " Why do you think that is? He's interested in quantum gravity. Yeah, but you know, everybody has 24 hours in a day and you have your own ideas and you feel that they are more... Oh, okay. So he has his own ideas. So he has his own idea. I mean the last"
},
{
"end_time": 5238.029,
"index": 195,
"start_time": 5208.49,
"text": " 15 years or so, he has been, maybe even more, since the last 10, 15 years, he has been really doing this CCC, right? This one, the Confirmation Click Cosmology. So that's not even Twister theory, but it is, it is just by, so he's been focused on that. I mean, so it's not, I think it's one just, yep. I mean, but same thing is true with me. I mean, I think that Twister theory was very interesting. I started with it. I followed it very, very much until"
},
{
"end_time": 5267.892,
"index": 196,
"start_time": 5239.002,
"text": " the mid or late 1990s, but I haven't really followed the advances of whatever is happening in Oxford. Are there advances still? So there's someone or some people moving this Twister field forward? Yeah, this is a smaller group than there was before, but you know, particularly Lionel Mason in Oxford is doing very interesting work on scattering amplitudes and such things using Twister field. But for me the main, I don't see how to"
},
{
"end_time": 5298.234,
"index": 197,
"start_time": 5268.524,
"text": " use it very strongly to address the problems that interest me, for example, which has to do with, you know, classical general relativity has singularities, what happens to them? And so those questions, I think Twister theory is still very far from approaching and answering. Professor, what is Einstein's whole argument, H-O-L-E? Right. So when Einstein was developing this"
},
{
"end_time": 5326.169,
"index": 198,
"start_time": 5298.882,
"text": " At one stage, he got stuck because he had this basic idea that if you give yourself a theory, which has basic variables, as I was saying before, and you decided that metric was a basic variable. So if you give me some initial data for the metric at time t equals zero,"
},
{
"end_time": 5355.486,
"index": 199,
"start_time": 5326.527,
"text": " You give all the information that is needed, which is the metric, the spatial metric, and its time derivative. It's like giving the position and the velocity of a particle, if you like. Then the field should evolve and then should actually give you a solution. But then Einstein realized that because of the coordinate freedom in generativity, this is not true. I could give myself"
},
{
"end_time": 5383.951,
"index": 200,
"start_time": 5355.896,
"text": " a metric at the initial instant of time and its time derivative technically extensive curvature is what it's called it is about how this three manifold sits in the four manifold that is a time derivative of the metric. Then he found that well the solution is not unique because I could you could construct one solution and I can come and make a little motion what is mathematically called a diffeomorphism or"
},
{
"end_time": 5409.394,
"index": 201,
"start_time": 5384.206,
"text": " In pedestrian language, we call a coordinate transformation. And that coordinate transformation or diffeomorphism is identity everywhere, except in some region up here. So we started out here. And at the initial time, you're fixed to your surface completely. And you're not touching it. So the initial data is exactly the same. But I just change the metric up here. We are diffeomorphism or coordinate transformation."
},
{
"end_time": 5438.097,
"index": 202,
"start_time": 5409.94,
"text": " which is identity outside, but it's not identity in some little region here. And that is the whole HOLE. Then there is again a solution of Einstein's equations. So somehow there wasn't a one-to-one correspondence between specification of the initial data and the solution. And therefore for a while, he really was completely stuck with this and saying that something wrong, how do we get out of it or something until the realization came that in fact,"
},
{
"end_time": 5468.78,
"index": 203,
"start_time": 5439.224,
"text": " You don't get a unique solution. You get a unique solution, modular coordinate transformation or modular diffimorphisms, which are identity on the initial slice because you fix the initial data. And so the coordinates or coordinate levels of a point don't have as really a physical significance. Their gauge dependent quantity is like the vector potential in electromagnetism, if you like, or Yang-Gill's theory. I mean, there's a gauge freedom there."
},
{
"end_time": 5496.442,
"index": 204,
"start_time": 5469.275,
"text": " So in Yang-Mills theory also it's not true or in electromagnetism that if you give me a electric field, sorry the vector potential and the electric field. The electric field is like time derivative of the vector potential, it's like the velocity. I get a solution but the solution is not unique. I can make a gauge transformation, I can take the vector potential and add to it a gradient of a function, then function is zero everywhere except in some little region and that is equally a good solution."
},
{
"end_time": 5525.282,
"index": 205,
"start_time": 5496.971,
"text": " So we should not ask that the vector potential should be unique, we should find out what the observables are and the observables should take unique values. So in electromagnetism it's simple, just calculate the electric and magnetic fields and then they are unique, there's no problem with the electric and magnetic fields at all. And now, so the question is about what about general relativity, things are conceptually subtle and then the reason is because we don't have simple observables because"
},
{
"end_time": 5554.411,
"index": 206,
"start_time": 5525.947,
"text": " You usually take tensor fields and you calculate the values in terms of components and the coordinates themselves don't have meaning. So you have to construct invariant quantities. So you can take, for example, curvature and contract all these indices with the metric and that is invariant. That would not change at all. So if you could choose, I mean, just conceptually, in practice, nobody has been able to do it and it's not going to be very useful either. But if you could choose four curvature"
},
{
"end_time": 5579.138,
"index": 207,
"start_time": 5555.043,
"text": " So this is what Einstein realized that in fact there is a gauge freedom and we just have to live with it."
},
{
"end_time": 5607.688,
"index": 208,
"start_time": 5580.282,
"text": " and so that is the whole argument basically and this whole argument actually has a very interesting thing in loop quantum gravity because what are the basic tenet of loop quantum gravity is again that these points don't have physical meaning or the coordinate labels don't have physical meaning you should not have background structures so you have to compute observables you cannot just ask for example I cannot ask"
},
{
"end_time": 5634.735,
"index": 209,
"start_time": 5608.046,
"text": " I should not ask what is the area of the screen by itself, right? Mathematically, I can ask an object. But I should ask the question, formulate the question in physical terms, namely, the screen is invariantly defined as a discontinuity surface. There is no matter on this side of the screen and then suddenly there is a discontinuity. There's matter here on the screen itself."
},
{
"end_time": 5660.64,
"index": 210,
"start_time": 5635.128,
"text": " So I define this screen as a discontinuity surface. And then I can ask, what is the area of this surface? Now, if I make a coordinate transformation, it acts on the metric. But it also acts on the matter field. It acts on everything. There are no spectators in this in this drama of evolution. So if I make a coordinate transformation, if I make a diffeomorphism,"
},
{
"end_time": 5688.882,
"index": 211,
"start_time": 5661.118,
"text": " If your morphism is an active way of talking about coordinate transformation, then this screen, for example, would bend, would look like that. But the metric would also bend. And the value of the area that the new metric will give on the new screen is the same as what the first metric gave on the screen. So this is an observer. The area of the screen is an observer. And the reason is because matter as well as geometry are both actors."
},
{
"end_time": 5719.07,
"index": 212,
"start_time": 5689.172,
"text": " Okay, you gave away that the question made sense and then didn't make sense. Can you restate the first way in which it doesn't make sense? Yeah. So if I just say that, well, very good. So if I just say that, well, here is a certain square, right? What is the area? And the statement is that, well, I don't know, because if I take the square and if I act on by diffeomorphism, then I will get a metric, right?"
},
{
"end_time": 5748.302,
"index": 213,
"start_time": 5719.855,
"text": " And I have the same metrics that is given to me. Then I calculate this area and the area is going to be different. Okay. Okay. But the point is because the area is not invariant and the metric is not invariant and diffimorphism. But what you have to do is to define the surface in physical terms and apply the diffimorphism to everything. Metric is a physical quantity so you apply the diffimorphism to the metric and you apply the diffimorphism to this metric."
},
{
"end_time": 5778.848,
"index": 214,
"start_time": 5748.848,
"text": " You apply them simultaneously, and then it's completely embedded. And that is very deeply embedded in loop quantum gravity. Our observables that we talk about are observables in this sense. And these are relational observables. I think Carlo must have talked about this. This relational view is very, very important in loop quantum gravity. I mean, the view is already there in classical general theory, but we take it very seriously, much more seriously in loop quantum gravity."
},
{
"end_time": 5805.862,
"index": 215,
"start_time": 5779.548,
"text": " Okay, so we just talked about Einstein's whole argument, which is not talked about much. So I don't think anywhere else on the internet, actually, I did a YouTube search. And so this will be one of the only videos where Einstein's whole argument is referenced. By the way, as a side remark, you know, when I first saw it as a personal thing, when I first read this argument, there were tears in my eyes. I mean, this guy, where was he born? How could he figure this out? You know,"
},
{
"end_time": 5829.36,
"index": 216,
"start_time": 5806.169,
"text": " Why don't we stick for a moment longer on the Einstein whole argument. The way that it was explained was you have some system and then you evolve it forward and then there's a whole"
},
{
"end_time": 5857.568,
"index": 217,
"start_time": 5829.855,
"text": " and it doesn't matter if the hole is here or non-existent or it's larger, it still gives the same observable. Now, can you make that more concrete in terms of, let's say there's a ball, in terms of Newtonian, if you throw a ball, what would it be like? Give people an analogy. It would be like if the solution is a parabola, we understand, but the solution could also be a parabola minus the top. Give some analogy. No, the trouble is that there's no analogy in Newtonian terms because there's no motion gauge there."
},
{
"end_time": 5869.189,
"index": 218,
"start_time": 5858.114,
"text": " Notion of gauge is critical in this thing. So anytime you have like Newtonian argument or the Newtonian ball or something like that, there is true that every initial data"
},
{
"end_time": 5896.561,
"index": 219,
"start_time": 5870.009,
"text": " In Maxwell theory, there is. I can give that example using Maxwell theory, but it is already a little bit abstract, which is basically that I can give you the initial data with the vector potential and its time derivative, which is the electric field. I can evolve it and I get a solution, but I can take"
},
{
"end_time": 5924.548,
"index": 220,
"start_time": 5896.954,
"text": " Take a little ball, a little region as a space, a little hole. And in that region, I just change the vector potential by vector potential. It goes to its original value plus gradient of a function, because the vector cannot take a gradient of any function. When I do that, the vector potential itself in that little region has changed. But you see that continues to satisfy the equation that was"
},
{
"end_time": 5952.005,
"index": 221,
"start_time": 5925.486,
"text": " So the point is that you should not try to see if the weakness holds for the vector potential but for observables and the observable for the Maxwell in this case is a magnetic field. It is a curl of this A and when adding the curl the gradient drops out. The curl of A and curl of A plus gradient of F is exactly the same."
},
{
"end_time": 5960.145,
"index": 222,
"start_time": 5952.722,
"text": " So the E and B are exactly the same in Maxwell theory and that gauge in varying quantities and they are exactly the same."
},
{
"end_time": 5983.712,
"index": 223,
"start_time": 5961.459,
"text": " It's just that in physics, sometimes you would think, well, I should be able to formulate things all in terms of gauge invariant quantities. I was sure that was possible when I was a student. But no, the statement is that if you wanted local physics, and locality is an important part here, then they cannot be formulated in a gauge invariant fashion."
},
{
"end_time": 6007.602,
"index": 224,
"start_time": 5984.258,
"text": " In E&M, the potential is not observable. It's the electric in the magnetic field. Yeah, electric magnetic field. Isn't there the Aronoff-Bohm effect? Exactly. So how does one make sense of the whole argument there? Yeah, well, it's similar, but not exactly the same because there's no initial data, which is you're evolving in the Bohm-Aronoff effect. So what you have is solenoid."
},
{
"end_time": 6037.398,
"index": 225,
"start_time": 6007.841,
"text": " So I think of this as a solenoid, just forget about it. This is a solenoid. And then the statement is that there is a current going through here. And so therefore you carefully adjust it so that actually there is no that the magnetic field is all here. There is zero magnetic field outside here. And then the interesting thing is that I see what the electron does if I start out here where there is zero magnetic field."
},
{
"end_time": 6066.561,
"index": 226,
"start_time": 6037.739,
"text": " I go around and the statement is that there is actually a zero magnetic field. So you might say that nothing happens. But the statement is that there is in fact the holonomy. I mean you actually do get an effect up here because vector potential here is not zero. So it's not right to say that vector potential is not observed. Certain quantities are observable. Why? Because what you're measuring is what you said holonomy which is really"
},
{
"end_time": 6085.435,
"index": 227,
"start_time": 6067.278,
"text": " the circuit integral of a, but a dot dl is the same as b dot ds by stokes theorem. If I take a vector potential up here and do the circuit integral is the same as doing the surface integral"
},
{
"end_time": 6112.637,
"index": 228,
"start_time": 6086.049,
"text": " the flux of the magnetic field through the surface up here and there is so but you have to take the whole surface which is enclosed by this and that does include here so the electron doesn't see the surface but the electron actually sees and so that is a beautiful argument to say that well if you wanted to formulate everything in local terms then the vector potential is essential right because magnetic field was zero here magnetic field was zero but the electron still felt the electromagnetic field"
},
{
"end_time": 6140.657,
"index": 229,
"start_time": 6113.319,
"text": " Okay, another aspect that's not talked about much is Mach's principle. There are very few videos online about Mach's principle."
},
{
"end_time": 6169.804,
"index": 230,
"start_time": 6141.288,
"text": " So why don't you explain what Mach's principle is, why Einstein thought it was so crucial, and what loop quantum gravity says about it? So the coin Mach's principle or Mach's conjecture was actually, this term was coined by Einstein. It didn't exist before, so Marx never called it a principle or something, it was really coined by Einstein at that time. And it played an important role in his formulation of"
},
{
"end_time": 6199.104,
"index": 231,
"start_time": 6170.981,
"text": " ideas about general activity. And this really goes back to Newtonian ideas about inertial frames and so on. And at that time, in Newtonian theory, it is certainly true that things like notion of centrifugal force were very important. If you're rotating, then in your arms go out. If you're doing a solid spinner, the water goes out. You dry the salad up here in that particular way. So"
},
{
"end_time": 6223.882,
"index": 232,
"start_time": 6199.65,
"text": " If you are not in inertial frame, if you are in a rotating frame, then there is centrifugal force. It looks like the notion of rotation is an absolute notion. But in Newtonian theory, there are local inertial frames. And so the question was, well, then, you know, how can you tell which frame is local inertial? And are you rotating or are you not rotating? And then the idea was that, well, you look at the distance stars."
},
{
"end_time": 6234.241,
"index": 233,
"start_time": 6224.787,
"text": " And the frame defined by the stars is an inertial frame. And then on the other hand,"
},
{
"end_time": 6263.882,
"index": 234,
"start_time": 6235.111,
"text": " So if you're rotating with respect to it, then you... I'll be showing a picture of the Newtonian bucket-bott experiment. And as far as I understand, Newton used that to say, no, there is an absolute notion. I'm sorry. Yes, there is absolute space or an absolute notion of motion. And then someone else named Mach took it and said, actually, that same experiment proves that motion is relative, except you have to take into account something else. Right. Namely that it's really related to the distance stars, and it is really defined by... Yeah."
},
{
"end_time": 6293.712,
"index": 235,
"start_time": 6264.07,
"text": " So Mark wanted to say that this is, and so the idea was that, well, non-local things, I mean, things over there, determine the local, the same kind of thing. And that idea sort of, Einstein in his writing and so on, has emphasized that played an important role. But in his later years, I think there is some work, historical, nice digging of work by historians of science, maybe Julian Barber from the other people. Then Einstein himself has said that, no, and as a mathematical sense in"
},
{
"end_time": 6309.906,
"index": 236,
"start_time": 6294.206,
"text": " Why is that the case?"
},
{
"end_time": 6337.483,
"index": 237,
"start_time": 6310.179,
"text": " As far as I know, most general relativity people don't think that that principle plays a deep role, or any role, depends on who you talk to, in the actually final theory that Einstein came up with. Which is why I never heard of it until recently, and I've studied general relativity and I've been taught courses in it, and almost no one else that's a student knows about Mach's principle. And the main point is that"
},
{
"end_time": 6367.5,
"index": 238,
"start_time": 6338.712,
"text": " I mean, the only way to formulate it is something, I don't want to get too technical, but basically, again, in terms of this initial value formulation that we talked about, namely, some of those Einstein's equations that we've got, the metric has 10 components and we've got 10 Einstein's equations on the metric. And Einstein's equations relate the curvature to the stationary tensor or to matter properties."
},
{
"end_time": 6395.111,
"index": 239,
"start_time": 6369.462,
"text": " And the thing is that four of those equations are called constraint equations. In other words, they don't involve time derivatives. So they must involve just space derivatives. So they must hold at any instant of time without knowing what the time derivatives are. And an example is just given by in electromagnetism, you can think of E and B and you've got equations and you've got equation which says that divergence of E is equal to zero and divergence"
},
{
"end_time": 6417.295,
"index": 240,
"start_time": 6395.691,
"text": " without sources, divergence of E equal to zero and divergence of B equal to zero. If you have sources then divergence of E is equal to 4 pi times charge density and so on. But then they don't involve any time derivatives. But then you have got time derivative equations which says that E dot, the time derivative is curl B and B dot is minus curl E. So you get a"
},
{
"end_time": 6447.944,
"index": 241,
"start_time": 6418.166,
"text": " Now the same thing is true in Einstein's case. There are four equations which are called constraint equations and mathematically they are called elliptic equations. So elliptic equations are very rigid. The solutions are really given globally on an initial instant of time."
},
{
"end_time": 6474.292,
"index": 242,
"start_time": 6448.49,
"text": " And so if you give me stationary tensor matter field, then I will be able to calculate for you. I have to solve this equation to get the initial metric in the extrinsic curvature. There is still some freedom, but a lot of it is completely determined. And so sometimes people might say that, well, so there is a max principle because matter doing out there is determining what the solution here could be."
},
{
"end_time": 6495.452,
"index": 243,
"start_time": 6474.872,
"text": " But that's not completely right, because you also have local degrees of freedom, but that matter doesn't determine this solution completely. And of course, if you say that, then you would have to say also in electromagnetism, that there's a max principle, so our charge density out there determines what the electric field appears."
},
{
"end_time": 6522.944,
"index": 244,
"start_time": 6495.64,
"text": " and the statement is that yes or no, yes in the sense that if there are no electromagnetic waves then the answer is yes, if it's static solution then the answer is yes, but if there are electromagnetic waves then part of the electric field is determined by the sources, charges, but part of it is just it has its own degrees of freedom and gravitational field has its own degrees of freedom and so that's one of the reasons why people don't take it seriously. I personally also don't take it seriously but I may be a"
},
{
"end_time": 6547.244,
"index": 245,
"start_time": 6523.404,
"text": " not a total minority but somewhat of a minority because I think that the whole notion of inertial frames which are so important in Newtonian physics. The whole point of general relativity was that it's lost. For your intuition you can talk about local inertial frames but I think that you can do any every calculation answer every physical question without ever talking about inertial frames."
},
{
"end_time": 6575.486,
"index": 246,
"start_time": 6547.654,
"text": " And so this whole impetus that that was there about how do you know that you are inertial frame or you're not? Yeah. I mean, since you're talking about undergraduates, I mean, I mean, you know, when you teach this elementary course, there's always smart, I feel there's some smart undergraduates should ask this question, right? You said, wait a minute, you calculated the motion of the moon around the earth, saying that"
},
{
"end_time": 6601.664,
"index": 247,
"start_time": 6576.254,
"text": " Well, I mean the Earth's center of mass is an inertial frame and in that I applied Newton's laws and I solved it. But then Earth's frame was inertial, fine. But then when you talk about Earth's motion around the Sun, then you say Sun's frame is inertial and Earth is rotating. If Earth is rotating, it could have been an inertial frame. So isn't one of your calculations wrong?"
},
{
"end_time": 6631.442,
"index": 248,
"start_time": 6603.217,
"text": " And to me, at least, I mean, the real answer to this real answer to this question comes from general relativity. You don't need the notion of inertial frame. You're just calculating geodesics in the two cases. And then there's no problem at all. So I think this whole over emphasis on inertial frame, I don't mean it's useless notion. On the other hand, it's not essential. It's not something that, you know, on which any foundational issue should refer to. So that is the point about Marx's principle."
},
{
"end_time": 6660.213,
"index": 249,
"start_time": 6632.722,
"text": " Okay so let's get to black holes. What does loop quantum gravity say about singularities and black holes? It would also be great if you could outline what a singularity is and why there are problems or some people think they're issues with the concept of them. So actually singularities in general relativity or any theory really arise because you start with some initial data which is completely regular and you evolve it using field equations."
},
{
"end_time": 6688.763,
"index": 250,
"start_time": 6660.879,
"text": " And it may turn out that the field equations say that, in fact, that after a finite time, the fields become infinite. And if the field becomes infinite, you cannot evolve any further. And then you're stuck. And you just have no, no, no. So it's like the theory fails there. Theory comes to an end there. Now, something like that may happen in other theories, but one might just say that, well, it's not so bad because after all,"
},
{
"end_time": 6717.244,
"index": 251,
"start_time": 6689.172,
"text": " Maybe I just need to tweak something for that particular theory. I mean, I still have space time. I can ask the question about evolving and such. But in general relativity, the space time itself is defined by this evolution. So if the field becomes singular, the curvature diverges somewhere, then space time itself comes to an end. So it's not that particular initial data led to a problem. But in that space time, everything ends."
},
{
"end_time": 6747.619,
"index": 252,
"start_time": 6717.978,
"text": " So historically, what happened was the following. So I think this is important for people to know."
},
{
"end_time": 6771.903,
"index": 253,
"start_time": 6748.131,
"text": " that historically people started with cosmology, namely the freedom of solution, the initial singularity. So the US is starting with the singularity up here after Hubble's discovery. And by the way, it is really"
},
{
"end_time": 6800.52,
"index": 254,
"start_time": 6772.961,
"text": " who understood the physics of it completely, the Hubble's observation of what it meant and so on and so forth. And that's why the Hubble law was renamed Hubble-Lemaitre law recently by the astronomers. So there was actually this initial singularity. And that means that if you evolve back in time, space-time comes to an end, and so there was an absolute beginning. And this was a"
},
{
"end_time": 6830.452,
"index": 255,
"start_time": 6802.125,
"text": " issue about big contention and people were thinking both ways. Maybe some people thought that, well, this is good because that means that the biblical notion of you were starting at a finite time is reinforced by science. And again, a very interesting anecdote here is that George Gamow, who was one of the leading physicists at that time, who was working on nuclear synthesis,"
},
{
"end_time": 6860.35,
"index": 256,
"start_time": 6830.623,
"text": " and the notion of Big Bang really became more established with nuclear synthesis that they must have been a very hot phase of the early universe in which heavy elements were cooked because somehow when you look at the abundance of lithium, helium and that somehow and see how much of it is produced in stars, that is not really something that could be produced in stars. Enough of it could not be produced in stars. There must be some initially"
},
{
"end_time": 6890.486,
"index": 257,
"start_time": 6860.913,
"text": " There was some other mechanism by which this was produced, and therefore there was a hard initial phase of the universe. So Gamow actually wrote to Pope Pius XIV, I think, at that time, and saying that, well, look, you know, there was a hard phase of the universe, the universe was also born, and Pope got very excited. And so he next"
},
{
"end_time": 6915.265,
"index": 258,
"start_time": 6891.118,
"text": " The Vatican has a nice observatory, so the next conference that came, the Pope inaugurated by saying that it isn't just wonderful that science and religion are coming together and so on and so forth. And Lemaitre, who was associated with the observatory, had the hoodspot to go to the Pope with one senior person and convince the Pope that it's best not to mix religion and science."
},
{
"end_time": 6945.845,
"index": 259,
"start_time": 6915.998,
"text": " So the singularities are very important, but people had various unease about it. In the 70s, very prominent British physicists and astronomers came up with this steady state university. Herman Bondy was working on it."
},
{
"end_time": 6972.108,
"index": 260,
"start_time": 6946.459,
"text": " And of course, Fred Hoyle was the main pushing, Jay Narlikar was a student of his. So they were actually pushing this idea and in part because some people didn't feel that Big Bang was. In fact, the name Big Bang was, by the way, people don't know, was invented by Fred Hoyle in a pejorative way, in the sense of making fun of it and not seriously."
},
{
"end_time": 7001.186,
"index": 261,
"start_time": 6972.875,
"text": " So the statement is that these big singularities, these initial singularities were troubling. So that is really the absolute beginning of time. And black holes, at least the simplest black holes, the Schwarzschild black holes and so on, they represent the absolute end of time because space time ends there and you cannot evolve. Classical general relativity fails and you cannot evolve. Not only classical general relativity, but you cannot evolve any field there because"
},
{
"end_time": 7029.531,
"index": 262,
"start_time": 7001.578,
"text": " So that is why it is so sort of important. The reason I spend a lot of time explaining about the Big Bang rather than right away in black holes is because for majority of the period in history, people were more worried about this absolute beginning than the absolute end, in part because it's relatively recently that people began to accept black holes as being reality."
},
{
"end_time": 7056.766,
"index": 263,
"start_time": 7030.282,
"text": " Again, younger undergraduates won't realize this, but it is really true. I mean, I think when I was a graduate student, I had somebody who was a couple of years ahead of me, John Friedman, and he went to give talks. He was a student of Chandrasekhar's and they were talking about black holes. And in very prominent universities, prominent physicists would ask him afterwards, why are you working on this? It's not mathematical. It's not physics."
},
{
"end_time": 7085.896,
"index": 264,
"start_time": 7057.142,
"text": " Astronomers also didn't take it seriously for the longest time. So that's why I began with them. I mean, the Singularity has been with us, but probably a lot of people for a long time, which is the cosmological Big Bang Singularity. And that's a meta commentary on the state of physics because some people would wonder, well, why do you care about high energy physics or extremely high energy physics when we can't reach there, when it seems like there's no predictions and so on? Well, the same argument was laid at black hole theory or studying black holes."
},
{
"end_time": 7114.991,
"index": 265,
"start_time": 7086.254,
"text": " I agree but the question is always how comparing the argument is and again how comparing the argument is in the eye of the beholder. I mean to me as a graduate student and you know people who are doing general relativity it was obvious. There are a lot of black holes or something it was obvious. Why don't we see them? We don't see them because you know we don't have the techniques and we'll see them. We're confident about it all. I mean Chandana was 100% confident about it all otherwise he would not have spent 10 years of his life"
},
{
"end_time": 7144.957,
"index": 266,
"start_time": 7115.452,
"text": " thinking about these things. So that's what singularity is. So for the longest time then, people have believed that the singularity is the artifacts of general relativity, because we're assuming that Einstein's field equations are valid at arbitrary high densities and arbitrary high curvatures. Now, people don't realize this, but already in the 50s, in one of the editions which I have in one of my papers,"
},
{
"end_time": 7167.295,
"index": 267,
"start_time": 7145.435,
"text": " Einstein's book, Meaning of Relativity, one of the later editions, he has an explicit statement saying one may not assume the Big Bang singularity to be physical. He doesn't call it Big Bang, he says that the initial singularity to be"
},
{
"end_time": 7197.005,
"index": 268,
"start_time": 7168.285,
"text": " One should not assume that the initial singularity in the mathematical sense to be physical, because one may not assume the field equations, which is his own equations, at arbitrarily high densities of matter and field, by field even curvature. So Einstein himself had said that, by the way, but I mean, people still took it all very seriously. But I think there's a complete general consensus now that there is the"
},
{
"end_time": 7227.381,
"index": 269,
"start_time": 7197.756,
"text": " Is it correct to say that for the same reason that we can't evolve a black hole forward and so we say that that's the quote-unquote end of space-time is that the same reason why we consider the Big Bang to be the quote-unquote beginning in terms of just evolving it backward we can't? I mean in both those cases I'll qualify in a minute but that's the idea."
},
{
"end_time": 7247.995,
"index": 270,
"start_time": 7227.637,
"text": " I just wanted to say that there is a short video which is called the meaning of the Big Bang or the new meaning of the Big Bang or something like that. It's only short, it's quite short like 15-20 minutes something and there were about seven of us who were interviewed including Stephen Hawking and Roger Penrose and"
},
{
"end_time": 7278.404,
"index": 271,
"start_time": 7249.07,
"text": " And we were interviewed in a completely separate location in our home institutions. And so we did not know who else was being interviewed, what they were saying. And we all had different approaches to quantum gravity and so on. But then all of us say exactly the same thing, that Big Bang is not a physical singularity. You know, there was an early hot phase of the universe that everybody agrees with that is important for nuclear synthesis and so on and so forth. But this in the inflationary model, for example, this phase comes after"
},
{
"end_time": 7308.046,
"index": 272,
"start_time": 7279.394,
"text": " the end of inflation. So certainly not before the onset of inflation, not before the Big Bang at all. And people say that, well, yeah, the idea that in early days, you know, when people form cosmic background and so on, they say, well, this is a signature of the Big Bang, you know, and that I think is not, it's not correct at all. That's a statement of here. It's not a signature of Big Bang because it happened way after. I mean, the, the hard phase really must happen before."
},
{
"end_time": 7337.432,
"index": 273,
"start_time": 7308.387,
"text": " Way after as in many seconds or many microseconds or what? No, I think it is not way after, it's not that often. Yeah, so it is about, it's a fraction of a second, but in terms of plunk times way after fraction. Yes, yes, yes. 10 to 30 plunk times, 10 to 38 plunk times, something like that. So it's in that sense, way after. Even more. The end of the question is then after that, how many folds pass before the"
},
{
"end_time": 7367.722,
"index": 274,
"start_time": 7338.097,
"text": " So that is the idea and then the statement is that what"
},
{
"end_time": 7398.422,
"index": 275,
"start_time": 7368.439,
"text": " does loop quantum gravity wants to have to say about this and this has been one of the sort of solid ideas in loop quantum gravity namely that because we have got quantum Riemannian geometry rather than classical Riemannian geometry so we have to reformulate Einstein's equations in this new language. I like to say that well quantum gravity needs a new syntax and in loop quantum gravity the new syntax is"
},
{
"end_time": 7426.903,
"index": 276,
"start_time": 7399.121,
"text": " quantum Riemannian geometry. And now when you formulate Einstein's equation in terms of quantum Riemannian geometry, there are difficulties, of course, and that's why the problem is not completely solved. But what we can do is to go to physically interesting situations and apply it there. It's a bit like we don't still have complete QCD theory, quantum chromodynamics theory."
},
{
"end_time": 7455.094,
"index": 277,
"start_time": 7427.21,
"text": " But we can go to physically interesting situations and you develop approximation techniques and then make predictions and then that same concern and such. So here the simple examples are simple situations that are physically interesting are provided by cosmology. So the Big Bang and the black holes. And then the reason why I think they're important, but also there is a lot of symmetry."
},
{
"end_time": 7480.93,
"index": 278,
"start_time": 7455.452,
"text": " And because there's a lot of symmetry, then loop quantum gravity can make a lot of progress because many of these questions then simplify. I mean, technically, you should simplify that. So that area is called loop quantum cosmology. And the way loop quantum cosmology is done compared to other quantum cosmologies is really keeping an eye to full quantum gravity."
},
{
"end_time": 7507.415,
"index": 279,
"start_time": 7481.374,
"text": " So it's true that one is in a simplified situation, but one doesn't sort of say that I don't know what the full theory is, and I'll just work in the simplified situation. This is what happens in Gile DeWitt cosmologist, because in the full theory there is no mathematically conceptual framework. We don't have Hilbert space, we don't know what to do and so on and so forth. Even at the kinematical level, even before you come down to dynamical equations,"
},
{
"end_time": 7534.77,
"index": 280,
"start_time": 7507.858,
"text": " What is the basic framework in terms of which to pose the questions is not clear in geometry dynamics. Whereas in loop quantum gravity, we have this rigorous framework, this quantum Riemannian geometry produces, provides us this rigorous framework. Therefore, we can take this rigorous framework and apply it in the simplified situations. And there's a precise sense that real theorems would say that this applied to this particular situation, there you've got a certain representation."
},
{
"end_time": 7564.48,
"index": 281,
"start_time": 7535.111,
"text": " certain Hilbert spaces, certain ways of representing operators, those ways trickle down to these particular ways of doing operators. I'm not saying there are no ambiguities, but there are theorems which tell you what the assumptions are, so they will tell you what the ambiguities are, but there are higher order things. And within this, the statement is that Luke on cosmology has a precise mathematical framework,"
},
{
"end_time": 7594.394,
"index": 282,
"start_time": 7565.162,
"text": " And precisely because it encapsulates the quantum nature of geometry, the fact that the area operator has a discrete spectrum plays a very important role in this case. Because of that classical Einstein's equations receive quantum corrections. And these quantum corrections are such that the evolution of the quantum Einstein's equation doesn't break down in the singularity. You can continue across it. So"
},
{
"end_time": 7622.551,
"index": 283,
"start_time": 7594.872,
"text": " You can look at it at various levels. At the heuristic level, you can think of it as follows. This is space-time continuum is an approximation. And I've given this very often analogy because I think it really is a good analogy, which is that you look at, for example, my shirt up here. And my shirt up here is really, for all practical purposes, this is 2D method continuum. You want to see it's continuum. It's clear it's continuum."
},
{
"end_time": 7649.053,
"index": 284,
"start_time": 7622.79,
"text": " You just have to take a magnifying glass and see that it is is woven by one-dimensional threads. There are constituents. It's not a continuum. It really is one-dimensional. It's not two-dimensional. But the threads are packed together so much that it looks like a two-dimensional continuum. And the statement is that the same is true with the quantum Riemannian geometry. Namely, our space-time continuum is an approximation like this shirt."
},
{
"end_time": 7673.183,
"index": 285,
"start_time": 7649.531,
"text": " There are fundamental building blocks and these fundamental building blocks are come from these Wilson lines or these connections up here and there is a precise mathematical framework. That is what enables you to calculate the spectrum, the eigenvectors and eigenvalues of the area operator, the volume operator, length operator and so on and so forth. And what one finds is that the area has a non-zero minimum value."
},
{
"end_time": 7691.049,
"index": 286,
"start_time": 7673.814,
"text": " So it's not a continuous thing because the spectrum is discrete, you've got zero of course, but then there's a gap and then there's the smallest eigenvalue and that is called the area gap. And then when you go to quantum Einstein's equations, this area gap plays a fundamental role."
},
{
"end_time": 7723.37,
"index": 287,
"start_time": 7694.07,
"text": " Again, let me make a detour because we talked about holonomies just a while ago and we talked about Bohm-Aranoi effect which is also a holonomy. So what a holonomy does is to really look at the flux of curvature. So one way of defining the curvature is really in terms of holonomies and the statement is that you have to take the holonomy and you have to divide by shrink the loop until it shrinks to zero in classical generativity."
},
{
"end_time": 7752.756,
"index": 288,
"start_time": 7724.497,
"text": " But in quantum Riemannian geometry, you don't do that. You can only shrink it up to a minimum area eigenvalue. And when you have shrunk it to a minimum eigenvalue, then you get an operator. And there's a fundamental non-locality for this curvature operator. But at the Planck scale, it's not because this area that encloses the order of Planck. Sorry, there's a non-locality associated with what? There's non-locality in the curvature operator. So the curvature is defined by"
},
{
"end_time": 7782.227,
"index": 289,
"start_time": 7753.541,
"text": " taking the holonomy around a closed loop and dividing it by the area like it's because the holonomy from electromagnetic field will be b magnetic field times area b.ds and then if you don't know what the magnetic field here is you want to divide by area and take the limit so the loop particular point up here but here we I mean you cannot shrink it to zero value because there's a"
},
{
"end_time": 7809.787,
"index": 290,
"start_time": 7782.568,
"text": " There's a minimum, so you shrink it to the minimum. So the spectrum starts at a non-zero value? There is a zero value, but then the statement is that you cannot shrink this loop to a zero value. I mean, if you shrink it to the zero value, the framework doesn't let you shrink it to the zero value. Because it's discrete? It's discrete. It's discrete. Exactly. It's discrete. The spectrum is discrete. So you come to the minimum non-zero value,"
},
{
"end_time": 7831.135,
"index": 291,
"start_time": 7811.63,
"text": " Then the statement is that you have this holonomy that gives you the curvature times if you like this area. But that's all you have. You cannot have curvature at a point. You just have, we are these operands. So therefore there's a non-locality at the Planck scale."
},
{
"end_time": 7858.643,
"index": 292,
"start_time": 7831.476,
"text": " Sorry, to be clear, when you say that there's non-locality, are you referring to the connection changes from point to point? Is that what you mean or is that something different? No, the connection does change point to point, but the statement is that the curvature is calculated only by the connection."
},
{
"end_time": 7883.336,
"index": 293,
"start_time": 7860.486,
"text": " and therefore I cannot define the formalism does not let me define the curvature at a given point. It only tells me what the curvature is, average curvature is on the surface of plank line along the holonomy. So in terms of surface, average curvature is in a plank line."
},
{
"end_time": 7911.715,
"index": 294,
"start_time": 7883.592,
"text": " So therefore what happens is the curvature also has a maximum value. It cannot be infinite. There's a maximum value. And that maximum value"
},
{
"end_time": 7928.831,
"index": 295,
"start_time": 7912.125,
"text": " are surprisingly is related to the area gap. The matter density has a maximum value. And the matter density is which is really given by the goes like some constants divided by the area gap cube."
},
{
"end_time": 7956.459,
"index": 296,
"start_time": 7930.026,
"text": " Now if you let the area gap go to zero, the classical limit, then the maximum value becomes infinite. But in loop quantum gravity, the area gap is a well-defined number, and therefore you've got a maximum. It's a very large number. Sure, sure. But it's finite. But the precise number is finite, exactly. And therefore, in loop quantum cosmology, what you do is you take a wave function of the universe. In other words, you first start out with the classical space time."
},
{
"end_time": 7984.326,
"index": 297,
"start_time": 7957.568,
"text": " classical solution of Einstein's equations, like one of the Friedmann, Le Maitre, Roberts, and Walker cosmologies. And then you take a wave function which is very sharply peaked on that geometry at a given instant of time, at late time. So that wave function describes the geometry and you evolve it back in time. And as you evolve it back in time, it remains sharply peaked along some geometry."
},
{
"end_time": 8014.497,
"index": 298,
"start_time": 7985.811,
"text": " If you want it forward in time, it remains sharply peak along geometry. It is the classical solution that is a function. But if you want back in time, then it follows the classical solution until the matter density or the curvature is about 1000 or 10,000 times the plan curvature and then it deviates. So the quantum correction becomes very important. It's almost negligible until the plan density is about"
},
{
"end_time": 8043.336,
"index": 299,
"start_time": 8014.855,
"text": " the classical trajectory is still in the peak of the wave function. You know, the wave function is sharply peaked, the classical wave trajectory is still in that wave function, you know, one standard deviation of the wave function. But then when that density is reached,"
},
{
"end_time": 8074.684,
"index": 300,
"start_time": 8044.991,
"text": " Then the wave packet is still sharply peaked but does not follow the classical trajectory. Classical trajectory would run into singularity. So if I think about singularity as being on the left side here and the classical trajectory is going into the singularity, left side here and the classical trajectory is going into the singularity, it's just your right side. Classical trajectory is run into singularity. What happens that it is approaching singularity and then bounces."
},
{
"end_time": 8103.78,
"index": 301,
"start_time": 8075.179,
"text": " It bounces away from the cylinder. And again, by the time the curvature becomes 1,000 times, 1 upon 1,000 times the Planck curvature, or density is about 1 upon 1,000 times Planck density, then classical general relativity is again a good approximation. So there is a quantum bridge which joins a pre-Big Bang branch of the universe and the post-Big Bang branch of the universe."
},
{
"end_time": 8133.78,
"index": 302,
"start_time": 8105.111,
"text": " So that is what is happening. And to me, the big surprise was when I first found this out, I didn't believe this. Maybe this is very special because we're using very special, very functional, special initial conditions. So I was working with two post docs, Tomasz Pawlowski and Param Singh. And they were the ones who were doing the HARC and the calculations, not the analytical part. I had done most of a lot of it."
},
{
"end_time": 8162.841,
"index": 303,
"start_time": 8134.104,
"text": " And so I kept asking them to change these parameters, do this, do that, to see if it is robust. And after about six or eight months, I was convinced that it's really there. And then a couple of years later, we found analytical methods to get the same results with appropriate approximations. So by now, there are many, many different ways of checking this result, that in fact, the wave function does bounce. Is this what's called the Ashtakar bounce?"
},
{
"end_time": 8193.404,
"index": 304,
"start_time": 8163.933,
"text": " When I was speaking to Salvatore Pius, and I know I sent you a question from him, he kept referring to the Ashtakar bounce and he was saying, Kurt, you have to read conversations on quantum gravity. Ashtakar will blow your mind. He told me read all the conversations except yours and leave yours for last because he said yours is the best one. And he was super excited. So at some point later, we're going to get to his question."
},
{
"end_time": 8223.831,
"index": 305,
"start_time": 8194.872,
"text": " All right, so that is what happens. And then cosmological models, people have done many things. First, it was done just by the simplest models, which are spatially flat, which correspond to our observed universe. It seems to be spatially flat. But then to make sure it is robust, people added spatial curvature to it. People added inflationary potentials to it. People added anisotropies to it. And collectively, we have found that the bounce is very robust. Now, nonetheless, in cosmology, things are"
},
{
"end_time": 8249.377,
"index": 306,
"start_time": 8224.343,
"text": " When it comes to black holes, it is the same question as you say is the end of the universe and as opposed to beginning of the universe for at least for the non rotating black holes. I will talk about rotating black holes just in a minute. So non rotating black holes are singularities against space like so it is really like the Big Bang singularity, but it's in the future. Its nature is very different."
},
{
"end_time": 8279.94,
"index": 307,
"start_time": 8250.538,
"text": " part of the curvature which blows up at the Big Bang is very different from the part of the curvature which blows up at the Black Hole. And that is why Penrose often refers to the two as being very different and therefore they should be handled differently and so on and so forth. So therefore, as a result, we do not have as many tests and as much detailed investigation in the Black Hole case as we have in the Big Bang case. But there are"
},
{
"end_time": 8307.005,
"index": 308,
"start_time": 8280.52,
"text": " Fair number of calculations are having said that they appear in physical letters. People have a lot of references. People, you know, build on it and not just, you know, hundreds of papers written on the basis of those and so on. So it's not it's not a beginning stage by any means, but it's certainly also not not not really finished. So what do we know? So then again, what we find is that"
},
{
"end_time": 8336.613,
"index": 309,
"start_time": 8307.381,
"text": " It's somewhat different, but what we'll find is that there is actually a bounce across singularity. So the universe doesn't end at the singularity of the short shield space-time, but you can actually continue the evolution across that singularity. Now, what is it that happens? What are the differences?"
},
{
"end_time": 8366.613,
"index": 310,
"start_time": 8337.329,
"text": " Well, in the black hole case, as you know, there is an exterior region, which is the normal region that we live in and so on and so forth. And there is a region of black hole inside the horizon. And here what we're doing is to look at the region inside the horizon, because the singularity is inside the horizon here. And so you look at that region inside the horizon and then then you evolve. Then let's see what happens. But inside the horizon,"
},
{
"end_time": 8397.466,
"index": 311,
"start_time": 8367.858,
"text": " is called a trapped region. The reason is because light is trapped. So basically think of the horizon as being, you know, this is time and this is space. So I think of the horizon as being a null surface like that. And therefore if I light a beam of light up here, normally the beam of light would actually expand out and there will be part which also goes inside the light bulb so it contracts. But what we see is the one which is expanding out. So inside the black hole,"
},
{
"end_time": 8427.381,
"index": 312,
"start_time": 8398.814,
"text": " The expanding branch actually contracts and that is why it is called a trap tree. So this expanding what would be normally a light front which is expanding is actually contracting and goes into singularity. So inside the horizon both the quote-unquote outgoing branch and then outgoing light front and then going light front they are both contracting. Therefore that region is called a trap tree where"
},
{
"end_time": 8455.401,
"index": 313,
"start_time": 8428.063,
"text": " Sorry, when you say contracting, so the way that I'm visualizing it is with ordinary space-time diagrams and then the cones, they're just pointing toward the black hole. There's only cones point, okay. But once we are inside the black hole, already we are inside the black hole."
},
{
"end_time": 8480.794,
"index": 314,
"start_time": 8456.408,
"text": " What you are saying is usually people draw those diagrams when you're outside. But now when you're inside them, the cones are pointing just straight into singularity. Nothing goes out because that region is stacked. So if the singularity is at the top of the page up here, then the statement is that if I got this is the horizon, then light rays coming from here"
},
{
"end_time": 8507.91,
"index": 315,
"start_time": 8481.459,
"text": " Just go and hit the singularity and that's it. They never reach you on the horizon. So that light front is not expanding out. That light front is actually contracting. Contracting goes into the horizon. So it's area of that light. Normally if I light a light bulb, spherical light bulb, then the area of the light front is expanding at a speed of light."
},
{
"end_time": 8537.295,
"index": 316,
"start_time": 8508.507,
"text": " Here the area of that light front is actually contracting inside and that is why it's called a trapped region or contracting. And then what happens is that you come across a space-like surface which was a singularity before is now replaced by a regular surface. But this surface is a transition surface and on the other side what you have is really anti trapped region in which both light fronts are outgoing."
},
{
"end_time": 8567.278,
"index": 317,
"start_time": 8537.927,
"text": " Both light fronts are expanding. In your room and my room, if I were to strike a match or light a light bulb, a spherical light bulb, then there will be what we see is an outgoing one. But of course, there's light also travels inside and that is just the incoming one that goes through there. So the interesting thing here is that on the other side of the singularity, both light fronts are expanding out. And so it is called anti-tractors."
},
{
"end_time": 8596.988,
"index": 318,
"start_time": 8568.933,
"text": " In popular terms, the contracting region is called the black hole type of region. And this is called the white hole type of region. And that's why some people like Carlo, for example, like to think about as a transition from black hole to white hole. I don't like that terminology because both black holes and white holes have connotations of there being a singularity somewhere."
},
{
"end_time": 8626.101,
"index": 319,
"start_time": 8597.568,
"text": " And there is no singularity here. It is just a trapped region where all the light fronts are contracting and anti-trapped region where they're all. So I think we understand a fair amount of what is happening. But if you want to know much more in detail about what happens in the black hole evaporation, that subject is still under investigation like in every other approach up here."
},
{
"end_time": 8654.889,
"index": 320,
"start_time": 8627.739,
"text": " If I have time, let me just mention one thing. One is that, because this is often mentioned by people as being a real problem, a real paradox. So as you know, supposing I have a black hole which is formed, somehow I send in some matter, there's nothing else in the universe, I ignore everything else, and I send in some matter and it forms a black hole. Supposing it forms a black hole of one sort of mass. And then after that, nothing is falling into it from outside."
},
{
"end_time": 8685.333,
"index": 321,
"start_time": 8655.555,
"text": " In classical generality, the black hole will just stay there. It's going to be one solar mass, it will just stay here. But because of Hawking effect, because of quantum tunneling, it is shrinking. And it is shrinking and shrinking and shrinking and shrinking and becoming smaller. And while it does, it's emitting this quanta. And this quanta are going up to infinity. And the big question is really the following, that this outgoing quanta look like they're in a thermal state."
},
{
"end_time": 8715.162,
"index": 322,
"start_time": 8685.742,
"text": " which is a mixed state. It's not a pure state. Why is it not a pure state? Because these particles, this quanta are created in pairs. One particle goes out to infinity and its partner particle falls into the black hole. Now if it falls into the black hole, the two are correlated and therefore you're losing correlation. If you just look at infinity, you're not seeing what is happening inside, so you're losing correlations and that is why you've got a mixed state."
},
{
"end_time": 8742.125,
"index": 323,
"start_time": 8715.333,
"text": " So it's like an ordinary quantum mechanics, except that it's happening in black holes. You're only seeing part of the system and therefore... Just as an aside for people, the difference between pure and mixed is... So a pure state is represented by a wave function, if you like, or by an element of a Hilbert space, either a vector or a ray in a Hilbert space, whereas a mixed state is represented by"
},
{
"end_time": 8771.118,
"index": 324,
"start_time": 8743.49,
"text": " state itself is represented by an operator. So basically it is like an operator in which I got just say for example if I just have spin up and spin down then I'm going to have a bra which is spin up, bra which is spin up and then some probability density plus bra which is spin down some probability density or rather spin up, spin down, spin down, spin up and some probability densities appear."
},
{
"end_time": 8795.742,
"index": 325,
"start_time": 8771.63,
"text": " So it is a state which you cannot write as just a straight forward ket or straight forward wave function. And it is sort of basically saying that the state has kind of two subsystems and they're correlated. And if I now only look at one of the subsystems outside subsystem,"
},
{
"end_time": 8818.046,
"index": 326,
"start_time": 8796.391,
"text": " Then technically what one has to do is to trace over the states, the subsystem that we are not looking at. And when you take this trace of that, it becomes a density matrix or an operator because they're taking a trace of it and you're forgetting part of the information. So I think the simplest thing is to say that you forget part of the information."
},
{
"end_time": 8838.729,
"index": 327,
"start_time": 8819.053,
"text": " Let me see if I can restate that. So most of the time when one is studying quantum mechanics, we hear about the wave function, but technically the wave function is for pure states. And even that it's not a unique member because you can take it. It should be a project, a member of a projective space. And then most of the time we're, we're dealing with our ignorance. We're dealing with mixed states."
},
{
"end_time": 8868.114,
"index": 328,
"start_time": 8839.224,
"text": " which are operators, which are matrices instead of just a vector. So what I want to know is with these density operators, I believe they're called density operators as well, or is that false? I don't know the history, but there's a quantum mechanics. Whatever, it doesn't matter. So with these mixed states, do they arise only from our ignorance, from looking on the outside and core screening, or is there something inherent about the system that makes it mixed in some way?"
},
{
"end_time": 8894.036,
"index": 329,
"start_time": 8868.422,
"text": " Right. Now, I think that in the context of quantum mechanics, in the context of black hole evaporation, it is our ignorance. But it is fundamental ignorance because other particles go inside the black hole. So inside the horizon. And so that's our fundamental ignorance. But I mean, you could consider. Yeah, please go ahead. OK. So I went on the outside of the black hole. There's these virtual pairs and then one of them happens to go inside and the other one escapes."
},
{
"end_time": 8922.756,
"index": 330,
"start_time": 8894.616,
"text": " So then does that mean equal amounts of matter and anti-matter are coming out of the black hole? Yeah. And is that okay that somehow doesn't violate some law because matter is what fell in but then sometimes anti-matter is what comes out? Yeah so the statement is that if for example you're going to charge black hole then there will be preferentially there will be preference of charging negative and there will be more"
},
{
"end_time": 8947.005,
"index": 331,
"start_time": 8923.114,
"text": " negative particles will come out but also positive charged particles will also come out. Now the black hole is shrinking and we understand. So the black hole is shrinking up here and then the statement is that we're looking at yeah and then and and so as a result of it more and more"
},
{
"end_time": 8974.889,
"index": 332,
"start_time": 8948.063,
"text": " thermal radiation is going out to infinity. In other words, the whole state is a pure state because it started with a pure state. But what is registered in infinity is only part of the state. And therefore, we're not looking at what is inside. And therefore, it is actually the state at infinity that we're looking at, quote unquote, appears to be mixed state. Now, the point is that this has"
},
{
"end_time": 9002.432,
"index": 333,
"start_time": 8975.299,
"text": " In my view, given rise to some confusion in the literature, quite some confusion in literature, because people take this event horizon as being absolute. And it is true in classical general relativity, but even in classical general relativity, there are things called dynamical horizons. You see, the event horizons are absolute, but they're also very not directly physical in this following sense."
},
{
"end_time": 9025.623,
"index": 334,
"start_time": 9002.927,
"text": " You know, an event horizon might be forming in the room that you're sitting in right now. It's completely contained in the room that you're sitting right now. The reason is because it's still teleological. This is in response to what may happen a billion years from today, that there may be a collapse in the center of a galaxy somehow."
},
{
"end_time": 9047.193,
"index": 335,
"start_time": 9026.254,
"text": " And then there will be a huge black hole. And if I trace back the event horizon, I have to trace back the event horizon. I don't know where it is until space time has ended, so to say. I can trace back the event horizon and then I'll find that, oh, it was actually fine. There's a component in this room right now. I don't feel anything locally. So event horizons are teleological. They are not"
},
{
"end_time": 9076.22,
"index": 336,
"start_time": 9047.637,
"text": " People are used to event horizons only in static situations like in the black hole or black hole or something. They don't think too much about the dynamical situations. I mean, simplifying, but a lot of people don't think enough in the in the dynamical situation. That's the point. In the dynamical situation, the statement is that event horizons like what I'm saying about just now can be very unphysical, can be very ghostly. But there are notions called"
},
{
"end_time": 9105.981,
"index": 337,
"start_time": 9076.8,
"text": " local, quasi-local notions and like in this room I can tell that there is no quasi-local horizons that in fact were developed here by Paul Stokes and I developed these things many years ago. This was in the context of vibration waves and black holes and not but is now has been used at starting from them also in quantum gravity because I was working both those areas up here and so if you take that more seriously then in fact"
},
{
"end_time": 9133.063,
"index": 338,
"start_time": 9106.425,
"text": " there isn't such an absolute end that there's no way for the information to come out. That you have to couple with the fact that in loop quantum gravity, singularity is resolved. You see, as long as there is singularity, then the kind of space-time diagram that Stephen Hawking was drawing initially, he changed his mind later, but initially he was drawing,"
},
{
"end_time": 9162.892,
"index": 339,
"start_time": 9133.541,
"text": " which our end singularity at the black hole singularity. Even when the black hole evaporates, the space time still has that singularity. And then that singularity can act as a sink of information. And therefore, it can happen that you start with a pure state, but you get a mixed state because some information failing to that singularity and it's completely inaccessible. But if in fact singularity is resolved and you don't have this absolute event horizon, then this information can come out."
},
{
"end_time": 9192.841,
"index": 340,
"start_time": 9163.695,
"text": " at later times. And there is no a priori problem about the information coming out and the S-metrics being unitary. Now the S-metrics being unitary is not the same as saying S-metrics is identity. We're not saying that what comes out is what goes in. People often, I'm asked this question even in technical conferences by people who are outside quantum gravity, but they say, well, I don't understand. I mean, how can it be? Supposing I just take encyclopedia Britannica,"
},
{
"end_time": 9221.203,
"index": 341,
"start_time": 9193.114,
"text": " And I burn it. I lost information. So the point is that no, you're not lost information. Word information is funny. But you're lost information in the sense that those words that were written there, encyclopedia, are lost. But on the other hand, I had a state of the encyclopedia and the fire and everything. And then I had a final state. The final state, there's a lot of radiation that came on something, et cetera. And both those states are pure states, ultimately. And because they are pure states, I could"
},
{
"end_time": 9247.142,
"index": 342,
"start_time": 9221.613,
"text": " Information is not lost in the sense that there's a unit transformation which will bring me back. I mean in practice it is hopeless. So that is basically the statement up here that there's no, you can have a very complicated, I mean when we smash particles in CERN and then you get something else and obviously what you get out is completely different from what you started out with. But information is not lost in the sense that the S-metrics is still unitary. So that is a point."
},
{
"end_time": 9275.759,
"index": 343,
"start_time": 9247.551,
"text": " Okay, so I think that, you know, S-metrics, we believe in Lupin-Gravity and most of us believe in Lupin-Gravity. Carlo and Rovelli and his group and I and my postdocs, so I have been working on parallel lines. Most of the time we have exactly, we are in agreement, but we're not in agreement on everything because there are open issues that we don't know which way it is going to go. And of course, with open issues, you always have prejudices about what is likely to happen because that's where you put more energy."
},
{
"end_time": 9298.882,
"index": 344,
"start_time": 9276.357,
"text": " And so there are differences, but on the other hand, the overall picture that I just mentioned so far is common to many people working in loop one already. So we believe the information is not really lost. There's another issue that is very interesting that your audience might be quite interested, which is the following, which is a restricted form of information loss."
},
{
"end_time": 9322.978,
"index": 345,
"start_time": 9299.292,
"text": " So let's not worry about singularity. I told you about singularity and things can come out and people might say, well, I don't know if singularity is resolved, etc. Let's not worry about it. There is still a problem, quote unquote, potential at the early stages. So supposing I take a solar mass black hole and I let it evaporate till it becomes a lunar mass."
},
{
"end_time": 9353.029,
"index": 346,
"start_time": 9325.145,
"text": " So it is about a millionth of its mass now from what it is. But still it's a macroscopic object, this lunar mass black hole up here, right? So people have argued that even in this process, some semi-classical considerations are not going to be valid and something drastic could happen. And these people were claiming things like that means that even outside the event horizon of astrophysical black holes, quantum effects would be important and there would be"
},
{
"end_time": 9376.8,
"index": 347,
"start_time": 9353.37,
"text": " change our picture of understanding what is happening altogether. Since LIGO data which sort of shows no surprises vis-a-vis classical general relativity, these claims have been scaled back quite a lot. These ideas have been scaled back quite a lot that astrophysical black holes would encounter real problems. That has been scaled back quite a lot."
},
{
"end_time": 9406.664,
"index": 348,
"start_time": 9378.865,
"text": " But nonetheless, people ask the following question. Supposing I go from solar mass to lunar mass. This process, by the way, is very slow. It takes 10 to the 76 years. The universe is only a billion years. I mean, 14 billion years. So this is huge compared to the life history of the universe up here. But still, the statement is that what is happening. So during this 10 to the 76 years, basically the solar mass"
},
{
"end_time": 9437.995,
"index": 349,
"start_time": 9408.677,
"text": " has become millionth of a solar mass. So most of the solar mass, solar mass minus a millionth of it has been radiated away. And its partner modes are all in here. So there's a huge number of partner modes. There's a huge amount of what, sorry? A partner modes, the modes which have gone away, the modes of the field, like radiation, which goes out, people call it modes, modes of the field. So these modes have gone away."
},
{
"end_time": 9468.012,
"index": 350,
"start_time": 9438.712,
"text": " And their partners, you might call them particles. People don't use the word particle because in corner fields in curved space time, the notion of particle is not so sharply defined. So people talk about modes rather than particles. But the statement is that these modes, these particles, they're gone away and their partners are on the side. And so a huge number of correlations is lost, right? Because it's almost the same as the mass of the Sun, right? Mass of the Sun minus"
},
{
"end_time": 9496.22,
"index": 351,
"start_time": 9468.507,
"text": " So people say, well, wait a minute, I got this little thing with a millimeter size thing, right?"
},
{
"end_time": 9522.039,
"index": 352,
"start_time": 9496.8,
"text": " And how can it hold so many moors? There's moors, the partner moors are all here and there's just no way it can hold all these little moors. And there's more sophisticated arguments, but that's the basic argument up here. And therefore there's something, some semi-classical considerations must go wrong way before the solar mass black hole has shrunk to a lunar mass. That is the argument that is made."
},
{
"end_time": 9553.046,
"index": 353,
"start_time": 9523.2,
"text": " But then when we look at more detail, first of all, not taking the event horizon so seriously, but looking at this quasi local horizons that I mentioned before. And we look at the back reaction. In other words, there is over 10 to 76 years, almost the whole solar mass of black hole, solar mass of black hole minus a millionth has fallen in it. So of course, that is going to change the geometry inside. It's not going to be the same geometry as before."
},
{
"end_time": 9582.739,
"index": 354,
"start_time": 9554.275,
"text": " The question is, what is happening to this geometry dynamically? How is it changing? And what we find is, again, this is done independently by several people, the same conclusions, that what happens is that if you look at a space-like surface, constant time surface, inside the horizon of a black hole. So it is anchored on the horizon, and therefore it has a kind of a"
},
{
"end_time": 9611.596,
"index": 355,
"start_time": 9583.353,
"text": " two sphere here on the horizon, right? I mean, a two dimensional sphere up here. And then inside, it's like a tube, right? It goes inside. The space-like surface looks like a tube up here. Now, in the beginning, the tube has a Schwarzschild radius of a solar mass black hole, so it's about a kilometer radius. And the length up here is also kilometers, roughly comparable. It's not much difference. But in this 10 to 76 years, the"
},
{
"end_time": 9641.834,
"index": 356,
"start_time": 9612.619,
"text": " The aperture of the black hole, the portion from which it sort of communicates with the outer world, which ends on this quasi-local horizon, that shrinks. And that has shrunk to a millimeter now. But what happened to this tube? Amazingly, this tube gets longer and longer and longer and longer and longer. You can say, yeah, but how much? Well, it gets longer like 10 to the, I don't know, I forgot, I looked it before, but, you know, like 10 to the 80 light years."
},
{
"end_time": 9669.599,
"index": 357,
"start_time": 9643.183,
"text": " light years not not centimeters light years so this tube is huge and long yes and it's pinched too and and it's pinched right exactly as it means it's sort of it's pitched and it's like longer longer and therefore you know this what people call modes which are inside the inside the inside this tube the part of the mode like an inflation they get elongated because this this thing was"
},
{
"end_time": 9697.739,
"index": 358,
"start_time": 9670.009,
"text": " Small and then just became longer and longer and longer. So inside the modes get elongated as the geometry becomes longer and longer, the length, proper length becomes and so they become what people call infrared, very low energy. Each of these particles or modes is going to be very low energy and therefore you can have lots of them without any problem."
},
{
"end_time": 9728.114,
"index": 359,
"start_time": 9699.616,
"text": " And so there's no paradox in that sense, because if you take into account properly that it's not an event horizon, but a causal local horizon, and that these surfaces, you're taking into account the background, the back reaction of the geometry, the geometry changes so much that it is perfectly fine to accommodate a huge number of modes, even though the endpoint has only a millimeter"
},
{
"end_time": 9758.166,
"index": 360,
"start_time": 9728.643,
"text": " And therefore, you have this huge amount of energy, which is almost a solar mass of energy, a huge number of moles up there. And there's no problem. So this is kind of a, I mean, it's not a new idea. I've been looking at people, I've been working on it for six, seven, eight years, but a lot of people don't realize. That's relatively new."
},
{
"end_time": 9787.585,
"index": 361,
"start_time": 9758.899,
"text": " Yeah, it's very interesting. So already the semi classical region where solar mass black hole becomes a lunar mass black hole, it looks like there is an apparent paradox. But in fact, if you look at the apparent paradoxes, how can a little thing like that hold so many more? And the point is that it's little thing only vis-a-vis the outer world is concerned. It has internal structure. This surface has internal structure, which is huge. Wheeler used to call it bags of gold."
},
{
"end_time": 9814.309,
"index": 362,
"start_time": 9788.097,
"text": " Okay, now you just mentioned this word outer world, which we're going to get to. But how about we take a small break? Yeah, let's take a break. And then we'll get to we'll get to Salvatore Pius's question and then the inner world."
},
{
"end_time": 9844.377,
"index": 363,
"start_time": 9819.565,
"text": " Professor, I have a question about ADM decomposition, where one assumes global hypervelicity to form a Cauchy surface and so on. And I'm curious, is that a reasonable assumption that this can always be done? Or does that reject a certain class of solutions to general relative to Einstein's equations? Yeah, so it does have"
},
{
"end_time": 9874.36,
"index": 364,
"start_time": 9845.026,
"text": " I mean, ADM decomposition has to do with dividing space time into space and time. It's a three plus one decomposition. And it breaks the manifest covariance of general relativity. But on the other hand, if you look at this, the space of solutions are exactly the same as the space of solution of general relativity. So it doesn't lose anything from general relativity, except if the space time is not globally hyperbolic."
},
{
"end_time": 9902.039,
"index": 365,
"start_time": 9875.111,
"text": " And the global hyperbolicity condition, is that related at all to the cosmological constant or no?"
},
{
"end_time": 9932.056,
"index": 366,
"start_time": 9902.978,
"text": " No, it's not related to cosmological constants. So you could have globally hyperbolic, I mean, most people, most of the spacetimes people use in cosmology with the cosmological constant are all globally hyperbolic. There's no problem at all. But you could also construct non-globally hyperbolic spacetime with the cosmological constant. It's not very difficult, but people think of global hyperbolicity as a physically reasonable assumption. There's a widely, it doesn't mean that"
},
{
"end_time": 9961.032,
"index": 367,
"start_time": 9932.5,
"text": " other things that totally people should about on space time, but there's more exotic possibilities. So like, there are closed time like curves, at least in girdle, like there's a girdle universe, which is closed time like curves. And so, yeah. So when people say, hey, closed time like curves, or you can't, they're unphysical. Well, there's nothing about general relativity that says you can't have closed time like curves, correct? Right. So it is true that, that ADM framework and most of the"
},
{
"end_time": 9977.039,
"index": 368,
"start_time": 9961.271,
"text": " things that people do, you know, even classical general relativity and they use the ADM framework very heavily in numerical relativity and so on so forth. There are versions of ADM framework, but they use them very, very much. They all assume global hyperbolicity, you know, in the black hole"
},
{
"end_time": 10007.398,
"index": 369,
"start_time": 9977.995,
"text": " So I don't think you lose anything. Now the question is for something like quantum gravity or something like conceptual structure or something, would you do something without the 3 plus 1 decomposition? And in fact, you sent me some paper and that paper just begins with"
},
{
"end_time": 10037.073,
"index": 370,
"start_time": 10007.739,
"text": " I was asked to write an article and it is true that Lagrange himself actually suggested this very beautiful, I mean he laid the seeds of it, I should say, which is developed by other people later on. There's a very beautiful way of doing things without any"
},
{
"end_time": 10066.357,
"index": 371,
"start_time": 10038.114,
"text": " decomposition into space and time, even particle mechanics. The idea there is the phase space is not x and p or x and x dot at any instant of time, but the whole solution, dynamical solution, it's like the block in the universe. It's a whole solution of the entire particle trajectory is a point of the phase space. So it's called the covariant phase space combination. And I used, I mean, I developed that"
},
{
"end_time": 10095.981,
"index": 372,
"start_time": 10066.732,
"text": " for field theory when I was doing corner field theory in space-time in the 70s already. And then I'd taken these ideas and they were not used until then as far as I know for field theories. And then for this volume then I looked at general relativity in the covariant phase-space formulation, which does not use space-time in the space-time and space and time. And I showed that in fact you do get"
},
{
"end_time": 10125.862,
"index": 373,
"start_time": 10096.493,
"text": " Things like the ADM Hamiltonian and even the so-called, in presence of gravitational waves, you have got so-called bondy energy and bondy for momentum. Just like you have got ADM, I don't know if there's a reason of energy and free momentum, you also have the same quantities in presence of radiation, which actually decrease in time because the gravitational waves go away. ADM for momentum is conserved because it includes everything."
},
{
"end_time": 10151.664,
"index": 374,
"start_time": 10126.203,
"text": " So we recovered all those things using covariant phase space formulation without any 3 plus 1 decomposition. So it's possible and I was at some time quite interested in thinking that whole quantum theory could be done with a covariant phase space but then as time went on I realized that no that's not really possible because basically"
},
{
"end_time": 10182.91,
"index": 375,
"start_time": 10155.486,
"text": " What quantum theory does, for example in quantum tunneling, is precisely allows certain, effectively is allowing trajectories which are not classically allowed, right? They're classically forbidden. There's something which is alpha particle inside the nucleus can actually come out. Classically it could not do that. There is a probability that it comes out, but classically there is no dynamical trajectory classically. The potential is such that there's no dynamical trajectory"
},
{
"end_time": 10212.995,
"index": 376,
"start_time": 10183.387,
"text": " that would allow you for the alpha particle classical dynamical trajectory to leave the nucleus and come out. Or mechanically, there is a probability that a stone on the ground could spontaneously come and break my window up here. It's a very minor probability. But there's a probability that that could happen. Classically, it cannot happen. There's no classical dynamical trajectory. There's a kinematical trajectory."
},
{
"end_time": 10242.346,
"index": 377,
"start_time": 10213.985,
"text": " For those interested in hearing more about the Gödel universe, visit the link in the description as some physicists have animated it as well as they give more of an explanation as to what the Gödel metric is and its consequences. So the point is that all of quantum physics cannot be captured by if you restrict yourself from the beginning to the space of classical solutions."
},
{
"end_time": 10273.251,
"index": 378,
"start_time": 10243.66,
"text": " And the covariant phase space is the space of classical solutions. It is isomorphic with the standard phase space, which is x and p phase space. Because if you give me an x and p, I get a unique dynamic trajectory. So the covariant phase space is like the canonical phase. I mean, mathematically it's equivalent or something. But as far as quantum theory is concerned, I feel that I still today feel that it's not possible to use base quantum"
},
{
"end_time": 10302.841,
"index": 379,
"start_time": 10273.524,
"text": " quantum theory, starting with the classical point of departure being the covariant phase space. I think you have to use, if you want to use a phase space, you do need to use a canonical phase space. Then you have these wave functions of x only, they're not a function of classical trajectories, space of classical trajectories up here. And so I think that there is, classically you can avoid 3 plus 1 splitting,"
},
{
"end_time": 10319.394,
"index": 380,
"start_time": 10303.575,
"text": " You mentioned, for people who are wondering what's the context, what the heck is this paper I referred to?"
},
{
"end_time": 10335.486,
"index": 381,
"start_time": 10320.435,
"text": " ADM decomposition is extremely important in loop quantum gravity and other approaches. And then on the Wikipedia page, there was some controversy that perhaps ADM decomposition is not always allowed or not always admissible. And so I was asking Professor Astrakhar,"
},
{
"end_time": 10362.005,
"index": 382,
"start_time": 10335.486,
"text": " What is his opinion on this? And can you take a look at this paper? So that's what that was about. OK, now you also mentioned Feynman's sum over all paths. And as far as I know, in loop quantum gravity, there's something similar where we sum over graphs, but it's not like we sum over all possible graphs. So you place some conditions on the graphs. And I'm curious, so are those conditions you feel like justified or eventually you want to get to some approach where you sum over quote unquote all graphs?"
},
{
"end_time": 10389.804,
"index": 383,
"start_time": 10362.551,
"text": " Some are all kinematically possible graphs. But the difference in loop quantum gravity is that, which is conceptually quite an interesting difference, that one is not looking at something or classical trajectories. In other words, because the classical trajectories would be, this is important, classical trajectories would be classical four geometries, all possible classical four geometries. Here what one is doing is one is"
},
{
"end_time": 10421.476,
"index": 384,
"start_time": 10391.817,
"text": " summing over trajectories which are in quantum Riemannian geometry from the beginning. So they are not smooth metrics but there are these two complexes with some data on them, colors two complexes as one says. But it is all possible, I mean the goal is all possible. In practice of course you know you do approximation just like what one does in quantum field theory. So therefore I start completely right to say that in loop quantum gravity one uses area framework"
},
{
"end_time": 10451.084,
"index": 385,
"start_time": 10421.903,
"text": " Let's get to Salvador Pais' question."
},
{
"end_time": 10481.374,
"index": 386,
"start_time": 10452.005,
"text": " Okay, so the"
},
{
"end_time": 10511.135,
"index": 387,
"start_time": 10482.449,
"text": " I mean, I did go through what you have sent me. The super force is supposed to be given by, I think, Newton's constant divided by some power of the speed of light, so that the dimensions are the dimensions of force. There is no H bar in it at all. But it is claimed that some, at least in the couple of pages that you sent me, it was claimed that somehow it is the unification of all forces and the super force arising from there and so on. I mean, I don't see how"
},
{
"end_time": 10541.596,
"index": 388,
"start_time": 10511.92,
"text": " It's a completely classical idea and I don't see how it can be, it can incorporate weak interactions, strong interactions which are quintessentially quantum mechanical and even electromagnetic interaction because electroweak go hand in hand together because of unification. So I mean, I don't see how this super force can be anything like fundamental in any sense. As far as the quantum bounce is concerned, it is true that"
},
{
"end_time": 10572.312,
"index": 389,
"start_time": 10542.602,
"text": " I mean, as I was saying before, I was myself surprised that for the longest time, until, you know, the density becomes thousands of tens of thousands of plant density, classical picture is perfectly fine. And then suddenly, this new quantum effects take into picture. And in heuristic terms, one often says that gravitational force is normally attractive, but then"
},
{
"end_time": 10601.442,
"index": 390,
"start_time": 10572.517,
"text": " suddenly this quantum effect becomes, the quantum corrections become, they are always repulsive but they are completely repulsive and they suddenly dominate in this Planck regime and then overwhelm the classical gravitational attraction. That's what people say, that's what I say or other people say. I should say that this is one of those things in which people in physics literature, I mean advanced physics people or graduate students, they understand what it is meant. I mean there is no such thing as gravitational force"
},
{
"end_time": 10627.892,
"index": 391,
"start_time": 10601.937,
"text": " already in classical general relativity. But this is a way of just shorthand way of talking about the bounds. So I just want to make sure that that is also true, that force is not a fundamental concept either in classical general relativity or in quantum cosmology or quantum gravity. What we have is Lagrangians and Junians and propagators and so on and so on."
},
{
"end_time": 10651.8,
"index": 392,
"start_time": 10629.514,
"text": " And also when a physicist uses the word force now, at least in high energy, they generally mean interactions. They don't mean F equals MA. Yeah, exactly. Exactly. I think that the word force should not be used because it terribly confuses people. I agree, but I'm not any sort of just English language to say that. Well,"
},
{
"end_time": 10679.428,
"index": 393,
"start_time": 10652.415,
"text": " Now briefly before we get to string theory and the comparison between loop and string, loop QG and string, talking about the Big Bang, we didn't get to what occurred before the Big Bang. So it depends on"
},
{
"end_time": 10709.582,
"index": 394,
"start_time": 10679.821,
"text": " Basically what one is doing in all these models is when it's starting at a given instant time as I said and then the post big bang in our brand of the universe whether universe away from a plank regime so that we can trust classical general relativity take a wave function which is sharply peaked and then you're volume it back. So if in fact in this post big bang picture what you have is a classical solution that your wave function is peaked at is the spatially flat"
},
{
"end_time": 10740.299,
"index": 395,
"start_time": 10710.35,
"text": " Freedman, Le Maitre, Robertson, and Walker universe, then what happens is that after the bounce, it joins on to another, especially flat universe, goes back. It's not necessarily symmetric. It depends on the initial state up here. It's not the time symmetry of all of it. It can be time symmetric, but it doesn't have to be time symmetric. It depends on the state that you have chosen, because there are many sharply picked states that you can choose from. But still, it's basically on the other side, there's another large"
},
{
"end_time": 10770.896,
"index": 396,
"start_time": 10740.896,
"text": " Spatially flat universe. And also if you started out with what is called open universes where there is spatial curvature, it's not spatially flat, but the spatial curvature is negative, then in the open universes it turns out that there's again a branch which is in the past like in spatially flat case. But if you started out with what is called positively curved spaces,"
},
{
"end_time": 10800.964,
"index": 397,
"start_time": 10771.391,
"text": " space sections, which is going to be a three sphere. So topology is that of a three dimensional sphere instead of a three dimensional space. Then you get classical relativity says that when you start with the Big Bang, the universe will actually expand out and then there will be a re-collapse and there is a big crunch. So in this case, what happens if you start with the Big Bang, I mean the general relativity says that. So now here if you start in the middle and you go back,"
},
{
"end_time": 10827.432,
"index": 398,
"start_time": 10801.596,
"text": " Let me just restate this because I want to make sure that the profundity of this isn't lost."
},
{
"end_time": 10854.053,
"index": 399,
"start_time": 10827.79,
"text": " So if we rewind our universe back, we get to the Big Bang. And then the claim here is that a possibility is that prior to the Big Bang was another universe that from its perspective was crunching to a Big Bang, which produced hours because there's this bounce that occurs once you get to what's what we think of as the singularity. OK, then that's under the loop quantum cosmology model. OK, so from my understanding prior to 10 seconds ago,"
},
{
"end_time": 10882.244,
"index": 400,
"start_time": 10854.582,
"text": " It was, this is our universe. We're going back to the Big Bang. And then we think, well, this could have started from the crunch of another universe. So let's imagine that. Let's imagine it did. But then I was wondering, well, loop quantum cosmology says nothing about this other universe. Where did it come from? Does it just expand forever in that direction? Now you're saying that, oh, no, actually, it could, we could have infinite cycles. No, no, it depends on cosmology. No, it depends on your assumption. It's not, it depends on cosmology. Just like general religion, it doesn't have a"
},
{
"end_time": 10910.725,
"index": 401,
"start_time": 10882.637,
"text": " specific prediction. You have to tell me the matter content of the universe. So if the classical general relativity, you have what is called critical matter density. If the matter density in the universe is less than some amount, then the universe would be what they call spatially open. If it is exactly the critical density, then it is spatially flat. And if it is bigger than spatially"
},
{
"end_time": 10937.654,
"index": 402,
"start_time": 10911.135,
"text": " the critical value, then it is closed in the US. So classical general biology also doesn't, it's an observational question. And so, but these are the possibilities. And what I outlined was what happens in the three possibilities in loop quantum cosmology. In the three possibilities, in the possibility where the matter density is less than or equal to the critical density, you just have one bounce."
},
{
"end_time": 10952.654,
"index": 403,
"start_time": 10938.797,
"text": " And then the statement is that, yeah, there are the universe, which is pre-boss bang. And there are a lot of ideas about, I mean, calculations about what was the nature of that universe, etc. But maybe that's going too far."
},
{
"end_time": 10980.555,
"index": 404,
"start_time": 10953.37,
"text": " We'll have another discussion because we have so many physics questions, but we also want to get to some questions regarding consciousness. So the statement up here is that it really depends on the spatial topology. The spatial topology were closed, but then I should just add that one can say, oh, but then we know something about our universe today. So which one is it? So it looks that overwhelmingly that it is spatially flat. It's not closed universe."
},
{
"end_time": 11010.367,
"index": 405,
"start_time": 10980.981,
"text": " I mean, it's not, there's always going to be some error in observation error, but it is supposed to be, I mean, there's all, there's a general picture people use is that the spatial effect. So, so in that case, there is, there is not a multiple bosses. Yeah, please go ahead. Sure. Let's compare string to loop. Oh, okay. Yeah. So string theory started with particle physics kind of emphasis and loop kind of gravity started with the general relativity emphasis."
},
{
"end_time": 11039.923,
"index": 406,
"start_time": 11010.657,
"text": " So from the beginning, you know, the ideas were different. Particle physics was emphasizing field theoretical methods, and in the beginning was perturbative methods. But all the time, they also started giving up, paying more attention to the non-perturbative methods, and now much work is done in non-perturbative methods, particularly with this ADF-CFT formulation. So in that sense, I mean,"
},
{
"end_time": 11070.043,
"index": 407,
"start_time": 11041.169,
"text": " conceptually philosophically they're coming together and also the importance of background independence is something that is more and more appreciated as as the string theory went further and further away from the particular methods this was more and more appreciated. The difference is based still the difference namely that in string theory there isn't so much because of its origin particle physics there is so much emphasis on unification of all interactions whereas loop quantum gravity is not that"
},
{
"end_time": 11097.261,
"index": 408,
"start_time": 11070.367,
"text": " People are not interested. Of course, they're very interested. But the main goal is not unification of all interactions. The main goal is really quantum nature of geometry. Now, one might say, well, you could never understand quantum geometry until you bring non-interaction. That may be the case. But what we have seen is that we could actually understand electromagnetic interaction by itself. Then it was unified with electromagnetic interaction. And then people at some stage thought that"
},
{
"end_time": 11124.906,
"index": 409,
"start_time": 11098.524,
"text": " Really, to understand strong interactions, you need the grand unified field theory in which you've got all three, the electromagnetic, weak and strong interactions together. People tried that for a long time. They even had a prediction that proton should decay. The proton doesn't decay. And since proton doesn't decay, I think that idea is sort of pitted out that that should be the only way to do things. And people are just looking at QCD by itself."
},
{
"end_time": 11154.002,
"index": 410,
"start_time": 11125.418,
"text": " And it's huge success looking at QCD by itself. So I don't see why looking at gravity and looking at the fundamental conceptual issues that are posed by gravity, which are unique because it is a theory of spacetime structure, is not going to teach us huge amount of things more. I mean, it has already taught us in classical relativity, you know, completely new physics, right, gravitational waves, Big Bang, black holes. So the question is, I mean, we can look for these qualitatively new things, like what happens"
},
{
"end_time": 11183.49,
"index": 411,
"start_time": 11154.394,
"text": " Now, because of this, I think partly because of this emphasis on unification, in string theory, there are all kinds of elements that were brought in. First was supersymmetry. Second was higher dimensions. And then there was positive"
},
{
"end_time": 11213.558,
"index": 412,
"start_time": 11184.053,
"text": " the negative cosmology constant and the point was that because you brought in supersymmetry and then you looked at the quote unquote natural ground state and there was a negative cosmology constant and so on and you know the conferences in string theory when people when first the idea came up that in fact the cosmological constant is positive and some preliminary evidence came up the conference in which very prominent string theories series are on record have said that"
},
{
"end_time": 11238.865,
"index": 413,
"start_time": 11214.053,
"text": " It can't be. It will go away. I mean, this is completely wrong because we know from supersymmetry that it must be negative. And it's not negative. It is positive. So there are these ingredients. I mean, these are not optional things in string theory. They lie at the foundation of string theory. Higher dimensions, supersymmetry, and the negative cosmology constant, none of which are seen in nature."
},
{
"end_time": 11267.568,
"index": 414,
"start_time": 11239.65,
"text": " The people have tried hard looking for this and that. Now it doesn't mean that tomorrow people won't find it, but I should emphasize that even if they were to find supersymmetry, it doesn't mean string theory. There may be many theories using supersymmetric theory. So the case is not strong in terms of what observations are telling us today. And I don't think that string theory has given us reliable insights or good physical insights or"
},
{
"end_time": 11296.664,
"index": 415,
"start_time": 11267.978,
"text": " on which one can build on for future work about the nature of singularities or even about black hole evaporation today. There have been a lot of very bold ideas, but it's one of those things. These bold ideas are put forward. There's a rush of my papers, incredible. I mean, there was first various people in Stanford were talking about quantum Xerox machines in order to talk about black hole information, that modes which go out to infinity, information that goes out to infinity, somehow"
},
{
"end_time": 11321.186,
"index": 416,
"start_time": 11297.125,
"text": " Xerox somehow duplicated near the surface, near the horizon, of course, taking event horizon as being absolute. And somehow that's why you can get unitary. That's repeated now. Then there was a question. No, that was prior to ADF safety. And then there is, of course, ADF safety. And ADF safety, again, is something that is done in"
},
{
"end_time": 11346.869,
"index": 417,
"start_time": 11321.817,
"text": " negative cosmology constant and one doesn't really know much at all about even zero cosmology constant or positive cosmology constant in the universe. And so I think somehow one gets the impression that a lot of effort is being put in areas where one can actually get good mathematical results, solid mathematical results. So whether it has"
},
{
"end_time": 11376.51,
"index": 418,
"start_time": 11347.108,
"text": " much to do with our actual universe or not is seem to be secondary consideration. Perhaps this is driven by the idea that well just because we don't know much about the universe and if natural theory is found then the universe will obey it. They have said that about the cosmological constant. They have said that about supersymmetry. People are given even scales at which this should be found because they're natural and they're not. And there are examples in physics where"
},
{
"end_time": 11406.578,
"index": 419,
"start_time": 11377.5,
"text": " Very prominent people have talked about some natural ideas. I mean, one of the things that people don't know very much about is the following. Just in the end of 1800s, very prominent people, including Lord Kelvin, had really thought that what are atoms? Because people are realizing there are atoms and there are discrete spectral lines. People are just realizing that."
},
{
"end_time": 11433.131,
"index": 420,
"start_time": 11407.193,
"text": " And their idea was that atoms are really vortices in ether because they believe in ether and atoms are vortices in ether and now what is it? So they thought well hydrogen atom seems to be the simplest atom so it's a circle. Then if you have got a next atom that you knew was the helium atom and the helium atom they thought was a truffle knot"
},
{
"end_time": 11463.507,
"index": 421,
"start_time": 11433.814,
"text": " It's one of those things. It's a knot in the knot theory. It's the simplest, beautiful knot. People use those knots on the boards and things like that. So there's a truffle knot. And then more and more complex atoms would become more and more complicated knotted structures of ether. So there are some lines in ether which are bent and which are knotted together. And they become the atoms. And these knots are vibrating. And that's why we see the spectrum. And these are very prominent people, we're saying that."
},
{
"end_time": 11489.104,
"index": 422,
"start_time": 11463.814,
"text": " That's an extremely creative idea. I'm wondering how the heck do you come up with that? Absolutely creative idea. And then they convinced a Scottish mathematician Tate to think about knots. Knot theory was born out of this. The whole thing started because they thought that atoms are knots in ether."
},
{
"end_time": 11516.8,
"index": 423,
"start_time": 11490.23,
"text": " That's how it started. It's a beautiful mathematical idea, beautiful bold idea. They talked about variety. They talked about how discreetness might come because of this, you know, why vibrational modes, because the closed thing. Vibrational modes are quantized and that might explain that atomic structure. Michael Atiyah, who was a very famous mathematician, has a very nice little book on this and the origin of Nocturian, how it came about. Very, very small book. So"
},
{
"end_time": 11542.756,
"index": 424,
"start_time": 11517.517,
"text": " So these things happened. Then there was another big thing from my community, John Wheeler. John Wheeler was a very imaginative person and everything. And he thought that elementary particles were chemistry of geometry. It's a little like this idea, I feel like. But now, not at the atomic level, but at the level of elementary particles. And again, he thought that there were some"
},
{
"end_time": 11568.558,
"index": 425,
"start_time": 11543.148,
"text": " In general relativity, there are some structures which are purely gravitational, some complicated. So it's not now one dimensional, but more complicated structures which are called geons, topologically built and such things. How do you spell that? Geons? Geons, right. And he had, you know, he talked about elementary particles, chemistry and geometry."
},
{
"end_time": 11597.705,
"index": 426,
"start_time": 11569.514,
"text": " I may be misremembering, but I think there's even the last chapter of the textbook gravitation of Mislut von Wheeler might have a chapter on this, might have a section on the chemistry of geometry, which is this idea. Again, it's a very beautiful idea that everything after all is just geometry, that this all comes from expectations of geometry, that topological expectations and all elementary particles are just that sort of thing. This clever idea did not work."
},
{
"end_time": 11628.49,
"index": 427,
"start_time": 11598.507,
"text": " So I think that just because some mathematical structures look very natural and nice, and there is enough precedent that that doesn't imply that they have anything to do with our actual physical world. And it will be good for us to keep that in mind. I mean, it may have, but this confidence and"
},
{
"end_time": 11657.295,
"index": 428,
"start_time": 11628.848,
"text": " I have to quote Alan Greenspan, who was the head of the Federal Reserve. You know, you called about exuberance. Something exuberance, right? And unfettered exuberance. That, I think, is not necessary. I mean, we can have bold ideas. We can put forward them. But to take the viewpoint that that is the only solution is not something that is really called for."
},
{
"end_time": 11687.329,
"index": 429,
"start_time": 11657.875,
"text": " And so now the question is, what is happening today? How do string theory and loop on gravity or any other approach? Where are we today about it? So there is a very nice article on the web page of the Institute for Advanced Study by somebody who was a journalist in residence there about the current status of string theory. And the title and the abstract actually say explicitly that string theory has not lived up to its promise of"
},
{
"end_time": 11717.278,
"index": 430,
"start_time": 11687.551,
"text": " You don't see that to be the case or no? No, I do see that to be the case. I agree with that. So, but it has evolved in that direction, right? And in the sense of, you know, very, very"
},
{
"end_time": 11737.432,
"index": 431,
"start_time": 11718.66,
"text": " Mirror Symmetry"
},
{
"end_time": 11767.654,
"index": 432,
"start_time": 11738.148,
"text": " They did not know how to find these functions for them in condensed matter physics, but then they use this idea about some kind of a duality, and therefore they could calculate it in the weak field, in the weak coupling constant limit in gravity, and then they could calculate those functions. So these are extremely rich toolbox, and I think it's something great to have that toolbox up here. But toolbox is very different from theory of everything, as it is great. And I think that, you know, that"
},
{
"end_time": 11790.247,
"index": 433,
"start_time": 11768.131,
"text": " They're admitting, leading string theories were quoted in this article, and they're admitting that it's not really that, but it's just a second rebirth and therefore it's going to remain. And I have no qualms about it. I think I agree, it is a very rich toolbox. But I think toolbox is not"
},
{
"end_time": 11819.07,
"index": 434,
"start_time": 11791.135,
"text": " What would this string theorist say to you? They're like, okay, you say this about us, but hey, all the loop people. Yeah, so I don't know. I mean, it depends on which string theories. Okay, let's pick David Gross. David Gross has openly said somewhere, right, that it is bullshit. So I think that is difficult."
},
{
"end_time": 11848.114,
"index": 435,
"start_time": 11819.582,
"text": " Okay, so that's what he would say. Okay, so let's pick someone who has a bit more of a specific criticism. But I mean, somebody like Gary Horowitz, I mean, he has told me several times, Gary is one who has worked, because he also began in general relativity, so we can speak similar language. Until, when was it? Until 2008 or 2009. Every year, I used to write notes on what progress and main things in string theory, and I used to"
},
{
"end_time": 11876.903,
"index": 436,
"start_time": 11848.643,
"text": " I used to talk with Gary and find out various things. One of my former postdocs, Don Meroff, is a senior figure in string theory, also in Santa Barbara. So, we talk and so on. Don had done some early work in loop on gravity, so he knows that subject as well. When we talk, we have an open disagreement. When we talk, to me it is much more reasonable in the sense of"
},
{
"end_time": 11902.944,
"index": 437,
"start_time": 11877.381,
"text": " There's no irrational exuberance. There is much more, yeah, this is the word, but we believe that this is pointing direction in this particular way and we're excited about this. That's good. It's an interesting idea. We tell them what they're doing. These guys can resolve singularities and that's a good thing. So"
},
{
"end_time": 11931.476,
"index": 438,
"start_time": 11903.353,
"text": " It's a regular scientific discussion. It's not kind of political polemics. But there are enough of them. So that's good. There are enough of them. We can have this discussion. We are far from having the final say. If people claim that we're very close, I wouldn't agree with them either. On the other hand, I do think that"
},
{
"end_time": 11947.363,
"index": 439,
"start_time": 11932.329,
"text": " Here's a quick statement from Ed Whitten and this comes from the book Conversations on Quantum Gravity."
},
{
"end_time": 11977.722,
"index": 440,
"start_time": 11947.858,
"text": " The interviewer says, due to the lack of experimental data, there exists a plethora of different approaches to quantizing gravity. Which of these approaches, in your opinion, is closer to a true description of nature and why? Then Ed Whitten said this, I think your premise is misleading. String theory is the only idea about quantum gravity with any substance. One sign is that where critics have had an interesting idea, so non-commutative geometry, black hole entropy, twister theory, they have tended to be absorbed as a part of string theory."
},
{
"end_time": 12007.056,
"index": 441,
"start_time": 11978.268,
"text": " I don't know if I want to say names, I was just debating about that. I think everybody is entitled to their opinion and I just have two remarks. There is a remark that I like very much by Richard Feynman."
},
{
"end_time": 12036.988,
"index": 442,
"start_time": 12007.756,
"text": " And the remark says that you should have a reality check. And so he says, it doesn't matter how beautiful your idea is. It doesn't matter what your name is. If your theory is not realized in nature, it is wrong. And I kind of feel that one should keep that in mind. That's my first remark, that very nice comment of Richard Feynman's. And the second is,"
},
{
"end_time": 12067.073,
"index": 443,
"start_time": 12037.756,
"text": " that there was this conference, which was 25th anniversary of KITP. And that, you know, they invited some people that happened to be invited me as a representative of Nukron Gravity, I suppose. And there, there's a prominent sync theories or kind of a tea break or coffee break."
},
{
"end_time": 12090.93,
"index": 444,
"start_time": 12067.5,
"text": " were chatting and he said, he repeated to me what you just read. And this was a while ago at which by far the number one computer company or company in the world, financial institution world was Microsoft. So he said, well, you know, string theory is like Microsoft. And"
},
{
"end_time": 12119.155,
"index": 445,
"start_time": 12091.954,
"text": " What Microsoft has done successfully is that anytime there's a competition or something, they are successfully incorporated in that. So it becomes part of Microsoft. And he said, he was nice, very nice, but he said, the same thing is true with string theory, that we have incorporated a matrix model, we have incorporated conformal field theory, and we have incorporated noncommutative geometry. On the other hand, he says,"
},
{
"end_time": 12147.671,
"index": 446,
"start_time": 12119.957,
"text": " Look quantum gravity is the one thing that we're not incorporated and look quantum gravity is like Apple's. And at that time, I didn't say anything. It's like Apple's like Apple, Apple. Oh, like Apple computer. OK, as opposed to Microsoft. Yes, yes, yes. And so I think this conversation was very illuminating. Yeah. But the success being Microsoft and"
},
{
"end_time": 12165.538,
"index": 447,
"start_time": 12148.763,
"text": " That was a model of success at the time of Microsoft incorporating everything together. And Apple didn't do that. And we are today where we are. So I think people can take their judgment about"
},
{
"end_time": 12185.811,
"index": 448,
"start_time": 12166.22,
"text": " He said that there was a principle of duality, which is extremely vaguely named because there are many principles of duality in physics and mathematics."
},
{
"end_time": 12213.677,
"index": 449,
"start_time": 12186.271,
"text": " I emailed him and I said, what are you referring to him? Then he wasn't, he didn't get back to me. But he said in the book that there's this principle of duality that a statement in loop quantum gravity becomes a statement in string theory and vice versa, or that he conjectures that there's one because there seems to be some for a certain class of questions. I didn't find any more information other than that. And either way, Lee seems to think that both loop and string are somehow approximations of some other real theory."
},
{
"end_time": 12237.261,
"index": 450,
"start_time": 12214.497,
"text": " Rather than it seems like you're on the more you're on the approach that well Firstly loop is not claiming to be a toe to be a grand unified theory. It's a quantum theory of geometry, which is quote-unquote quantum theory of gravity Okay, so firstly there's that and so it sounds a bit more like you're you have a tempered view of loop quantum gravity and Lee has a more expansive view that incorporates both"
},
{
"end_time": 12267.415,
"index": 451,
"start_time": 12238.387,
"text": " Where do you agree and disagree? And do you have any references for me to look up this principle of duality? Because I'm still looking to read something concrete about it. Well, I don't have good recollection of dates about when Lee might have said that. But there are instances. For example, when we're talking about this work on black hole entropy that I've done with John Byes and"
},
{
"end_time": 12296.237,
"index": 452,
"start_time": 12267.756,
"text": " In that work, again somehow this idea about punctured spheres was playing a big role and again the gauge theories and then if I look at the string theory idea, the brain and then there were also punctures on the brain that were made by strings and then"
},
{
"end_time": 12326.561,
"index": 453,
"start_time": 12296.561,
"text": " And so at one stage, I mean, we thought that there was actually some relation. It is also true that, you know, if you take Lee and Carlo and I wrote a paper, which is called Gravitons on Loops, in which we, these are linearized gravitons. So we formulated the theory in terms of kind of thicker loops. We introduced a notion of form factor of the loop and such thing. And the point was that if we just"
},
{
"end_time": 12353.114,
"index": 454,
"start_time": 12327.193,
"text": " You start with completely in the beginning, then you find that there is a graviton, there is an anti-symmetric tensor, there is a dilaton, and that's what people call bosonic strengths. And so it looked like in the early days that they may be saying similar things in different words, and it still might be that some of the things are similar. But I think my view is that"
},
{
"end_time": 12380.742,
"index": 455,
"start_time": 12354.258,
"text": " The way that the things are developed since then, both in loop quantum gravity and string theory, they've become much more diverse than before. There are people in loop quantum gravities, for example, Laura Friedel and people associated with him in Perimeter, they do talk about kind of possible holography in loop quantum gravity and so on and so forth. I don't think that string theory people take it very seriously."
},
{
"end_time": 12413.08,
"index": 456,
"start_time": 12383.183,
"text": " So I don't know where it is going to go, where it is going to go. So what I'm saying is that in the initial stage, this duality that Lee was talking about might have been about just a couple of examples I gave there. There is some idea that same kind of concepts appear in both approaches. But I think that over time, instead of more and more such connections, there have been less and less such connections."
},
{
"end_time": 12444.821,
"index": 457,
"start_time": 12415.196,
"text": " Professor, I'm sure you're aware, and Carlo Ravelli's brought this up, that physicists of the past were extremely philosophical. And then now there's this excoriation of philosophy in Academy, where it's seen as, that's ill-defined, that's superstitious in some manner, and it's going to lead you off the deep end, even though, as you outlined, well, many of the physicists aren't attached particularly to reality with their musings mathematically. Do you think that"
},
{
"end_time": 12475.776,
"index": 458,
"start_time": 12445.981,
"text": " This is true. Physicists have lost their way. Is it a negative or a positive in terms of abandoning philosophy? The physicists should be more philosophical. I think there's been a branching of ways, but it's not something that is most recent. So if I go back in time, philosophy was often natural philosophy. I mean, if you look at Socrates and Plato and"
},
{
"end_time": 12506.527,
"index": 459,
"start_time": 12476.988,
"text": " Indian philosophy side or something like Brahmagupta was astronomer and they were interested in the natural world and they're also interested in philosophy and in fact a lot of philosophy was philosophy of natural philosophy which is then sometime I think around the time of Galileo and Kepler and Newton we had a branching a little bit namely science I mean in some sense this"
},
{
"end_time": 12536.613,
"index": 460,
"start_time": 12506.834,
"text": " Natural philosophy was too successful in that it bred science, particularly physics and astronomy, initially. And so somehow science, I mean, for this long time has actually taken over that side of philosophy. There is a very beautiful book by the father and son team, which is called"
},
{
"end_time": 12563.507,
"index": 461,
"start_time": 12537.244,
"text": " The Philosopher and the Monk. The French philosopher is Francois Ravel. That is his pen name. The Philosopher and the Monk. The Philosopher and the Monk. And Francois Ravel, the father, was a philosopher. He was a real figure in France, a very influential figure in France."
},
{
"end_time": 12590.06,
"index": 462,
"start_time": 12564.804,
"text": " He was very strongly, first of all, anti-religious against the Catholic Church. And then he was also anti-communist, which left him in no man's land. And his son, Mathieu Ricard, who actually started as a neuroscientist, and he got his PhD with one of the Nobel laureates in Paris. I forget now the name."
},
{
"end_time": 12613.404,
"index": 463,
"start_time": 12590.401,
"text": " Now there are a couple of them, so I'll get them mixed up. And then at a postdoc opportunity as a postdoc to go to Stanford, he had the offer and he was ready to go. But in the meanwhile, he had also met some Buddhist monks and had gone to India and so on and so on. And due to his father's horror, he actually relinquished."
},
{
"end_time": 12642.5,
"index": 464,
"start_time": 12614.138,
"text": " science and went into became a Buddhist monk and he is the Dalai Lama's chief French translator. You find him every many places sometimes it's called the happiest man etc etc. That's not important. The important thing is that Maurice Ravel has sort of said it's a nice account of you know how philosophy has developed and not developed and so on so forth that sometime around that you know around the Galileo Newton"
},
{
"end_time": 12673.2,
"index": 465,
"start_time": 12643.302,
"text": " Somehow philosophy lost this natural philosophy to science. And it also had wisdom aspect. You can play to it. There is really wisdom aspect. And he somehow felt that that wisdom aspect somehow was stolen by more religious traditions. And so he is, I mean, he himself is a philosopher, but he sort of felt that somehow the field has gotten diluted because of, you know,"
},
{
"end_time": 12703.148,
"index": 466,
"start_time": 12673.882,
"text": " In some ways, other branches grew much more. And I mean, I kind of I'm quoting him because I feel that there is some large grain of truth in this. So if you look at, for example, the beginning of 20th century, I mean, there's a very important lecture by Max Planck, who says, philosophers of today sit in physics departments."
},
{
"end_time": 12730.128,
"index": 467,
"start_time": 12703.933,
"text": " And he says that their names are Albert Einstein and Niels Bohr. So there are there are these going in that direction, right? Some of the fruits. So I think that this really has happened. And I know that really in the 1930s, there were philosophers in Oxford. It's not a little place. We are arguing that on philosophical grounds, spatial relativity could possibly not be right."
},
{
"end_time": 12760.435,
"index": 468,
"start_time": 12732.056,
"text": " And so there has been and so I'm just saying these things because these things have somehow led to a deep mistrust in a lot of physics communities about, you know, utility and usefulness of philosophy and philosophy of science and so on. However, I find personally that there is a new generation, a newer generation, not so new because there are tenured professors now and so on and so on."
},
{
"end_time": 12790.35,
"index": 469,
"start_time": 12760.759,
"text": " of philosophers of science who actually understand the physics and mathematics that is needed. And that is always a problem, right? You need so much mathematical background to understand what physical concepts are and then to be able to evaluate them. Otherwise you are always years and years behind. But there are a few, there are not, you can probably maybe 20 or so that I want to know."
},
{
"end_time": 12819.053,
"index": 470,
"start_time": 12790.811,
"text": " less than 20, who actually are able to do this. I think that those people can contribute greatly. I mean, they should be taken more seriously by the physics community than they are. So I kind of feel that physics has become very specific and very technical and so on and so forth. So it is true that"
},
{
"end_time": 12849.77,
"index": 471,
"start_time": 12819.94,
"text": " that physicists dismiss philosophy altogether. I think that is too harsh and too uncalled for stand. But on the other hand, I think it's also true that a lot of philosophy people don't really know science. I mean, it just becomes difficult just because of this specialization and so on and so forth. But I think that with this young generation, there is hope and useful things that can be useful."
},
{
"end_time": 12876.357,
"index": 472,
"start_time": 12850.52,
"text": " Can you give me an example, perhaps a concrete example or a specific one where someone of our generation was able to merge philosophy and physics and contribute something that perhaps just soul physics couldn't do? When I say soul physics, I mean, S-O-L-E without the soul of the S-O-U-L. Yeah, that people from"
},
{
"end_time": 12908.456,
"index": 473,
"start_time": 12879.087,
"text": " that I happen to know are from the Pittsburgh School of Philosophy of Science, who, for example, have worked on things like the time reversal invariance. And they formulated the way that time reversal is actually analyzed in physics communities and so on and so forth."
},
{
"end_time": 12939.138,
"index": 474,
"start_time": 12910.026,
"text": " And one of them actually, yeah, I don't want to go into too many details because I various names of principles and so on, because in order to explain too much of that. But they formulated the ways that they sort of codified thoughts by saying that, well, this is a way of looking at time reversal mechanics. This is another way of looking at time reversal mechanics, et cetera, et cetera."
},
{
"end_time": 12963.473,
"index": 475,
"start_time": 12940.196,
"text": " example, pointed out that maybe there are more general ways of looking at time reversal invariance and there is, I think in part because people in Pittsburgh were, because the gravity group is strong there, Carlo was there for a while, long time ago, and so on. So the gravity group is strong there and so that they are familiar with some of the"
},
{
"end_time": 12994.155,
"index": 476,
"start_time": 12964.787,
"text": " topics that the forefront topics in physics. So they were aware in quantum gravity and so you know they were raising questions such as what would happen in quantum gravity because many of the things that one uses to talk about time reversal invariance are so deeply rooted in Poincare group and so the question is well if gravity everything and particularly quantum gravity what would happen to it and these arguments will not go through and unitary and unitary operators and"
},
{
"end_time": 13022.449,
"index": 477,
"start_time": 12994.838,
"text": " So I think that was quite insightful. So that is an example in which they were able to formulate, they were able to kind of classify the effects, the arguments that physicists had made into categories. And then from those categories say that, well,"
},
{
"end_time": 13051.084,
"index": 478,
"start_time": 13023.473,
"text": " If you wanted to generalize physics further and include quantum gravity, then one would have to rethink about time reversal invariance. I thought that was quite insightful and actually it led me to think about time reversal quite a bit and realizing that in fact you don't need much of the machinery that is usually used to talk about time reversal in quantum mechanics."
},
{
"end_time": 13079.872,
"index": 479,
"start_time": 13051.63,
"text": " Sorry, is time reversal distinct from time travel? Yeah. So time reversal, that's that. So, I mean, they clarified, you know, that there's a"
},
{
"end_time": 13108.319,
"index": 480,
"start_time": 13080.316,
"text": " The question is about time reversal in basic laws of physics. I mean, because people also say that entropy increasing means that, you know, you don't have time reversal. I mean, people say that, well, the glass fell down and it was broke and then it's not, it's not spontaneous. But the point is that that's not true, right? Because if I just took the final state and reversed all the in classical mechanics and reverse all the velocity, they should actually come back. I mean, the point is that those initial conditions"
},
{
"end_time": 13131.817,
"index": 481,
"start_time": 13109.019,
"text": " form such as tiny fraction of the whole phase space that is very unlikely. And so that made a very clean distinction. They made the clean distinction between that's not what they were talking about. They were talking about time reverse in the fundamental laws of physics. And that's what is true with respect to that time reversal is actually valid in the k on dk."
},
{
"end_time": 13161.425,
"index": 482,
"start_time": 13132.466,
"text": " So there's fundamental and then you know that they're bringing in CPT and usually one says and time reverse is violated one day what one shows that CP is violated and then one says that I got a CPT theorem and therefore time reverse is violated but then their argument was that well but CPT theorems completely depend on spatial or artistic local quantum field theories and if you don't have spatial or artistic quantum field theory then you can't make such arguments so it was it was quite so that's an example."
},
{
"end_time": 13189.104,
"index": 483,
"start_time": 13162.483,
"text": " in which I think younger people making, understanding first of all what the physical literature is saying and understanding enough about unitarity and community operators, what we need, what we don't need and such things and then then making nice statement. I think his name is Brian Roberts and I think he's, they have already written a book, he was writing a book on this thing. I just know because"
},
{
"end_time": 13219.48,
"index": 484,
"start_time": 13190.384,
"text": " The links to the philosopher and the monk as well as Brian Roberts, his work, or at least his Google scholar page will be in the description. Professor, thank you so much. It's been quite a ride, more than four hours. Okay, let's do this again at some point. We'll communicate over email and we'll see you also how this one goes online and see what the reception is like. Sounds very good. Okay. Take care now. Take care, professor. Okay."
},
{
"end_time": 13243.797,
"index": 485,
"start_time": 13220.213,
"text": " Transcribed by https://otter.ai"
}
]
}No transcript available.