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Claudia de Rham: The Theory of Gravity That Shouldn't Exist
April 9, 2025
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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.
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When I was doing my PhD, I had just bought into all of these theorems. They were written by very famous people, but we realized that we were able to violate these NERGO theorems. General relativity can't be the final answer.
What if gravity itself has mass? This seemingly simple question challenges decades of foundational physics. In this second conversation with Professor Claudia Durham of Imperial College London, we venture even deeper into her revolutionary theory. Durham didn't set out to overturn any established physics, she was searching for an explanation for the cosmos's accelerating expansion.
However, in doing so, she discovered that the impossible may indeed be possible. Gravity itself may have mass. This is known as massive gravity.
This potentially solves the so-called cosmological constant problem that has puzzled physicists for nearly a century. As we explore the implications of this mass of gravity, we talk about, well, what does that even mean? We'll also discover how symmetries emerge from chaos, why energy may be a concept that we need to abandon in dynamically curved space-time, and what recent cosmic observations tell us about the fate of our universe.
Tell me about a time where there was some established physics theorem and you found a way around it. What was that theorem or folklore or concept and how? How did you find a way to circumvent it? So one thing I've done is related to a no-go theorem related to massive gravity. So maybe I need to unfold this a little bit, what massive gravity is and what the no-go theorem is.
We understand gravity thanks to Einstein's theory of general relativity. And there's a little bit of this tell that tells us that, oh, we don't know how to reconcile gravity with quantum field theory. Actually, that's not quite true in Einstein's theory of general relativity. We do understand how we can describe gravity as a particle.
we can call this particle the graviton and that doesn't matter too much but we do understand that very well so we can embed gravity as in Einstein theory of general relativity into a standard field theory framework and represent the force of gravity a little bit like the other forces of the standard model of particle physics like the electromagnetic force and so for instance we know how gravitational waves are a little bit the analog of electromagnetic waves
and we can ask ourselves in principle the question as to the gravitational waves which are carried by light. We can in principle ask ourselves the question as to light which are electromagnetic waves whether the particle that carries them
maybe a massive particle so in the standard model as we understand it at the moment we think of light we think of electromagnetic waves as being a massless phenomenon carried by a massless particle but in principle we can think of it as a massive particle and we can put a bound on how massive the photon the particle carrier of light would be and there's no issue with that we have bounds from observations on how heavy if you were
Electromagnetism or light would be and so we can ask ourselves the same question in fact for gravity this a very.
Sensible question to ask ourselves. In fact, it's the first question we should really ask ourselves when we think of gravity as being carried by a fundamental particle like the graviton. You may ask yourself, what is the mass of this particle? Is it massless or could in principle have a mass? And if so, what is the constraints from observations on that mass?
And this is where the hiccup comes in. This question was already been addressed or tried to be addressed almost now, a hundred years ago, already since a Fiat St. Pauli in 1939. They already tried to establish whether it would be possible for the graviton or a field that would behave like the graviton to be a massive particle. And it comes up with all sorts of different luggage along the way.
And they realized that it is in principle if you just wanted it to be completely independent, completely isolated from anything else. But we don't want the graviton to be completely isolated from anything else. We like it to be interacting. We want it to be the structure of space time. We like it to be realizing the reality in which we live in. And therefore we can't just think of the graviton as being an isolated particle not interacting with anything else.
In fact, this is a virtue of gravity that it interacts with everything. This is based in universality, the equivalence principle of general relativity, which tells us that everything and anyone interacts with gravity and gravity interacts with everything and everyone. So as soon as you want to think of gravity, you also need to think of it as interacting with everything else.
And so this is where the issue came in. People were able to give a mass to the graviton or to think of how to give a mass to the graviton. But as soon as this graviton started interacting with other particles or even with itself, there seemed to be a no-go theorem. So,
A challenge which was impossible to overcome to the point where people came up with serums that told you exactly what would go wrong if you were trying to think of even in theory of having a mass for the graviton.
The Nogo theorem came under different names but they were always boiling down to the same aspect which is that as soon as you think of the graviton having a mass then you start exciting some modes
for gravitational waves which would carry negative energy and so maybe we can go to a notion of energy in a bit but for now we can just think of having some modes for polarizations of gravitational waves which would have negative energy and so in principle as soon as you think of the graviton being massive and interacting with the rest of the world you could have some processes
getting energy and taking this energy with an infinite negative pool of energy of the massive mode of the graviton and that would lead to a complete instability in fact an instantaneous instability of even the fabric of space-time as we know it. So that's the course of the matter for why we can't in principle or there was no-go theorems as to why we couldn't give a mass to the graviton so there was no-go on massive gravity.
This came up in various different formulations throughout the decades, particularly in the 70s, again in the 80s and in 2000. In fact, when I was doing my PhD, when I was doing my postdocs, I had just bought into all of these theorems. They were written by very famous people, then I'm going to name them, but I was certainly not going to go and contradict them in any way.
But we realized that we were able to build a model based originally from extra dimension.
which in fact was violating these NERGO theorems. So it was based on extra dimensions and so that's why we thought we could get some leverage from that but in fact we could in principle just represent it from a four-dimensional point of view and when we look at it from a four-dimensional point of view we saw that the NERGO theorems should be that I would tell us that something could go wrong
wasn't going wrong at the order that was predicted so this really motivated to better understand what were the assumption behind those no go theorems and what were the real implications and we realized that.
In fact, it was way too quick. The assumptions were good, but the realization of those assumption into no-go theorems were always using some shortcuts, which in fact could be overcome. And so there was many different realizations of those theorems in different languages.
But we got the motivation to really look into each and every single one of them when we realized that, in fact, there was much more to it. And so then realizing that there was a way to bypass this no-go theorem, we then realized how to, in fact, completely formulate a theory of massive gravity which was free from all of the pathologies that people thought should exist before that.
So you weren't looking to evade the theorem initially or outwit the people who formulated it. What was it that motivated you then in that direction? What was the spark that let you think, okay, maybe grass, sorry, grass is massive. Maybe gravity is massive.
So what we wanted to do other time, and in fact I still think it's a good idea, precisely how to realize it is challenging, but what we wanted to do other time is try to understand whether we could tackle the cosmological constant problem related to the late time acceleration of the universe with a better understanding of gravity at large distances. And at the time there was all sorts of work based on extra dimensions
Because it was realized from string theory that you could have extra dimensions out there. And in fact, from M theory, one of these extra dimensions could be large in the sense that it could be even millimeter size. So there was all sorts of different ideas in trying to understand what is the representation of gravity from a four-dimensional point of view and whether the leakage
of gravity within the extra dimensions could in fact lead to modification of the behavior of gravity on large cosmological distances and this could help us understanding how to tackle the cosmological constant problem. The cosmological constant problem is very much as the interface between quantum particle physics and gravity and it's coming from the fact that we would have expected
To have all of the vacuum energy, the quantum vacuum energy of all the particles that we know of to gravitate and to gravitate with an amount that effectively the universe not only should be accelerating, but should be accelerating by many, many orders of magnitude larger as compared to what is being observed.
And this in fact, this cosmological problem or this quantum vacuum energy problem is also been known since almost a hundred years now since Pauli and even other people before him. At the start of quantum quantum field theory very much so people realize that if you consider the quantum vacuum energy of electrons simply of electrons
This should populate space time and lead to an accelerated expansion of the universe, which would mean a space between the earth and the moon would accelerate so fast that we shouldn't be able to see the moon anymore. And this is something that was postulated, that was written down, that was understood as a challenge already since Pauli at the very, very start of the formulation of quantum field theory or even quantum mechanics, in fact. And so faced with this problem,
People thought that there was something one could one was missing in how a cosmological constant or how quantum vacuum energy was was gravitating and maybe for a symmetry reason or another reason that evades us as the moment really the universe is not accelerating and so that was the lure actually for almost 80 years until it was realized that
The universe is accelerating. The universe is not flat. It is expanding, but this expansion is also accelerating. And this is really the challenge because we would be happier if we would say for a reason or another, I don't know what's happening, but there's no acceleration altogether. So all of this quantum vacuum energy, even though it should lead to an accelerated expansion of the universe, let's just forget about it. And there may be some other phenomenon coming in the game.
The issues very much when all of a sudden we realize that the expansion of the universe is accelerating but bad really just a ridiculously small amount. So what is it is this is quantum vacuum energy leading to an acceleration of the universe or it's not and then we need to add something else but no formulation is perfect.
So what we were trying to do at the time is trying to understand whether it is this quantum vacuum energy that leads to an accelerated expansion of the universe but not as much as one would have anticipated according to Einstein's theory of gene relativity because gravity is actually leaking in the extra dimension and so this is something we don't see on short distances in the
on solar system scales, on galactic scales, on cluster of galaxy scales, but it's something that we start seeing on very large cosmological distances, on the distances where we really see the accelerated expansion of the universe.
So that was the idea at the time. Not at all to go back into a theorem led by my great heroes, but much more into trying to tackle these issues. And we thought at the time we knew that it would be challenging to come up with a model which was purely four dimensional because of all those no go theorems. So that's why we were basing ourself on extra dimensions.
where the effect of the extra dimension may look like non-local from our four-dimensional perspective so may look may be expressed in a slightly different way and yet could lead to effectively an accelerated expansion of the universe. I have a variety of questions about energy and we'll get to what is energy shortly especially what is negative energy but let's talk about dark energy so to be clear dark energy is a placeholder for our ignorance regarding the cosmic acceleration
And then vacuum energy is seen as a natural candidate. But the problem is that it predicts these absurdly high acceleration rates. That's right. So is there another reason other than that the vacuum energy is canceled? So supersymmetry would say that the vacuum energy contributions are canceled. Is there another reason that the vacuum energy shouldn't even factor in to
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Thanks to Verso for supporting this episode and supporting my health. And that should have bearing on the cosmological constant. So the answer is we don't know. We don't know for sure. We don't really know. So even, for instance, if we take supersymmetry as an example, it is an amazing symmetry that would cancel the contributions when the symmetry is being satisfied. So it is very possible that the realization
at high energy is supersymmetric so if we discover new particles at the NHC or next particle collider or anything else,
We will start seeing some signs of supersymmetry. That is still very much possible and it is still very much possible that supersymmetry is being restored at a given scale. But the world that we experiencing at low energy is clearly not supersymmetric. There's not a clear partner for each, for instance Boson, there's not a clear
Famine partner so super symmetry the reality it has to be broken below a given scale this is observations this is the reality of the world that we live in so even if they were super symmetry that would cancel all of the high energy contributions the contributions from the particles of the standard model so the contribution from the particles that we know we are made out of electrons the top quarks the Higgs etc.
they should in principle lead to a contribution to the quantum vacuum energy which is not cancelled out by supersymmetry. So there may be another symmetry out there but supersymmetry is doing an amazing job of potentially cancelling out all of the contribution beyond let's say even TeV scale but below that we still need to face the fact that we have a leftover from the standard model which will not cancel by supersymmetry.
It is a little tricky when we say when we say the quantum vacuum energy of for instance loops of electrons lead to contribution to they interact with gravity on a loop lead to quantum
It is a little bit tricky when we say that loop of the particles of the standard model lead to a contribution to the quantum vacuum energy. In fact, what we're doing there is compute some loops, which technically are infinite. And so we need to do a renormalization procedure. And if we do the most conservative
I'm regularization if i do friends is what i call dimension regularization so i'm not putting a cutoff at high energy and i'm doing any of this i'm just looking at how the contribution of this bubble diagrams this loops flows with energy i see that for each massive particle.
It leads to contribution which scales like the mass of this particle to the power of four. And this is the most conservative way to do things. So it is still possible that we don't understand everything in this regularization and renormalization procedure. That is very possible.
However, we understand this renormalization procedure extremely well for all sorts of other loops which we then go and compute and compare with scattering processes at the LHC and they give a flow and regularization scales of all sorts of different things which we know, understand extremely, extremely well.
So it is a little bit puzzling to think that we know so well how to compute those things when gravity is not part of the game and all of a sudden now all i do is a sandwich some gravity on external legs i'm not i don't need really to deal with quantum gravity in the sense of looking at an ultimate high energy completion of.
quantum gravity at or beyond the plank scale that's not at all what i'm doing i'm just looking at the quantum effective field description of gravity which we do on a daily basis i do it on the board and we do look for observations of that in the sky we do we think we know very well how to do that and yet as soon as i start
Putting in some external legs which are gravitons so I want to look at the effect of these loop diagrams of let's say electrons on external legs which are graviton which in effect I'm wanting to see how this loop of electrons loops of virtual electrons for instance lead to an effect to an interaction with space-time that's really what we're doing all of a sudden
What we get as a result seems to be completely inconsistent with observations. So probably it is true that something is going on there and we don't understand that so well, but it is very puzzling because everything else we understand it so well. Why is it the case that when I think of it in the case of Graviton that stops being so sensible?
We don't know. The answer is we don't know. You can go into string theory landscape and think of there being a landscape of different possibilities where the leftover cosmological constant, the leftover vacuum energy could take many different values and we just happen to be living in a realization where the leftover is just the right value.
Because if you wasn't that right value, we wouldn't be here to ask ourselves that question. That is always a possibility. But then but then it's a little bit unsatisfying because we don't know how to probe that possibility. We don't know how to probe alternatives to that. We sort of giving up on trying to find a more dynamical, a more fundamental reason as to why the effect of all of the loops is not leading to what we would have expected.
Does philosophy inform your physics research and by philosophy you can count causality and thinking about lawfulness or the foundation of time into your answer? So those questions like causality, like unitarity, like the flow of time, that definitely informs all of our research, all of our results,
All of the way we think about things in fact causality is really intrinsic to a lot of the question that we asking ourselves and so for instance we are we looking at effective descriptions effective quantum field theory descriptions.
for some phenomenon around us we always want to make sure that they satisfy some basic criteria of basic I would call them basic physics you can call them philosophy if you want to we would like it to be to satisfy some notion of causality this is essential for us and that manifests itself in many different ways we for instance you can think of it the notion of causality at zeroth order you can think of it as saying
Phenomenology where I'm not able to go backwards in time and kill my grandfather so that I'm not there anymore. That's at the basic level. But in fact when you represent that into a model where you think that Lorentz invariance is a fundamental symmetry then that tells you that you shouldn't be able to have processes that go faster than light.
In fact, it's not really that it's a bit more precise than that, but we can embed those concepts into much more formal, much more rigorous ways to clarify how to move forward. There's no notion of unitarity as well, which in some sense is a very simple concept for us to think about. It's really to say that if
If I think of the possibilities of a different outcome and so in quantum physics we know that things are not deterministic. I can do an experiment over and over again.
For each time, for each realization, I won't know exactly what the outcome will be, but what I know is what the probability of a given outcome will be. And so we are thinking everything the realization is really very much into probability or amplitude of probabilities of different outcomes. But we want the sum of all of these probabilities to sum up to one.
And we want those probabilities is individual probabilities never to be negative so i never wanted to be a real number and so that seems to be trivial statements.
If i play the lottery i shouldn't have more than 100 chances to win and i shouldn't be able to have a negative chance to win because i can't quite make sense of that this seems like completely trivial statements that guide our everyday life in fact is structural in the way we live our lives if we didn't have this notion then all hell will break loose we'll be able to play the lottery over and over and over again and just take advantage of this so it sort of sets up
The structure of the reality in which we live in, and in the same way, this notion of unitarity sets up the reality of the physics with which we work, and so the models with which we work. So to put up a counterpoint, last time we touched on ghosts, and there were these good ghosts, which are the fidei of popov ghosts, and then the more problematic one, like desser, and I don't know how to pronounce balware. I would say boulevard deser ghost.
The Klein-Gordon equation initially faced rejection over negative probabilities and I believe Schrodinger came up with it first and just didn't even publish about it because
Do you see that there's some other point of view where what's seen as a fatal flaw here is no longer?
For negative probabilities or unitarity or even locality conditions. So as you say, we certainly use ghosts in some formulation, like for the father of ghosts, we use those ghosts almost as a trick. We we when we have when we have some symmetries, for instance, it's easier for us to work with our feminism where we take too much into account.
And then we use those fadif of ghosts or related ghosts to cancel out contribution that we know shouldn't have been there in the first place. And we do that a lot in many different things, but they are under control and you have to think of them as a mathematical trick. You have to think of this as a formulation. We give too much away and then we know how to control what we've given too much away and we know how to remove those things.
So in that sense, it's a negative, it violates unitarity in the sense that it has a negative contribution and negative energy, but of just the right amount to remove the positive contribution that we had added on. And so in that sense, that is completely under control. Now there are other situations like the bullwad as a ghost, where this is not something which has been added to
Remove another contribution is just something that comes in and it's on and it's on from its own accord and you can see you can see in the case of the ball what is a ghost why starts becoming problematic and it's particularly problematic because you're dealing with modes related to space time.
And so let's just imagine a little bit what you mean by gravitational waves. We have observed gravitational waves and the way we have observed them is them distorting space within our interferometer, distorting the space between two mirrors in our interferometer. And so they make the space between the interferometer evolve in time.
But you can in principle we are dealing with a theory of space time you can in principle sake of having the same thing with time and then if you start having a mode for gravitational waves which allows you to jiggle things in time as well then this is also related to some level of causality violation and so.
This notion of breaking unitarity with some of those ghosts can be linked directly to a violation of causality and as soon as you enable for that possibility to happen then you are opening a whole pandora box of pathologies which are not under control.
Because this is not something that we engineered precisely so as to remove another contribution because we were lazy in some sense in the in the first place it's something that just populate just based on by its own accord is not under control so you may say well it does have.
He's on that does he have its own way of thinking of it you can i mean in some sense from the formalism yes you can you can you can analyze it is a pathology and as a scientist you can analyze it you can try to understand it you can look at the structure and it has some a lot of interesting features in its own right but at the same time you know that this mode it is a pathology you can't have it in
In your space time as a fully dynamical degree of freedom in its own right that that you can't have and it is a little bit different as compared to saying that you have an instability.
So for instance the Higgs potential is unstable within some range and you may think that this instability may be the sign of a pathology but that is in fact just a time evolution and it's just a transition a transitioning behavior from one point to another and you can think for instance that the whole evolution of the universe is something that signals some level of instability because we are going into a different configuration we are evolving
in the evolution of the universe those are not they're not pathologies they are just the reality and we may not like the thing is never necessarily pleasant to be in an unstable configuration but we can deal with it and and that may just be the reality the issue with the ghost is that we know that that tells us there's no vacuum there's no ground zero around which we can think about about our theories
And so we can't even start looking at the model into how to represent anything. As soon as you have this actual negative kinetic energy mode, a genuine degree of freedom that delivers energy when it moves, we know that there's no ground zero in which we can start thinking of our whole quantum field theory framework. So in that sense, we can't even start doing anything.
So speaking of energy, what is energy, especially in general relativity? What is gravitational energy? And what is this criteria or wishlist that you would like a well-defined definition of energy to have, like locality or covariance or what have you? Yeah, okay. So for me, I don't have so much about wishlist for energy because I
I don't have the need of having this concept as being as fundamental as we may have otherwise have. I think we're very much driven by
almost a Newtonian perspective of things being static in time and this symmetry in time tells us that there's an associated conserved quantity which we have which we call energy. So it's almost a luxury to have energy as a conserved quantity and as a well defined quantity that we can rely on and we can rely on to predict phenomena and to understand how you can borrow energy from one system
Give it to another system and that the whole energy within a box, let's say, should be conserved. Now, as you said yourself, when you have gravity in the game, things become much more complicated. There's no local conserved, ordinary conserved notion of energy in the same way that we would think we should have otherwise. And that in our everyday life,
We follow the rules as if the notion of energy was conserved. This is related to the fact that gravity is in fact a spin to particle so it behaves slightly differently and so the stress energy tensor is no longer conserved, ordinarily conserved. It's covariantly conserved but that means that the conservation
of the quantities related like energy they're not absolutely conserved there's a borrowing or there's a trade-off between the energy of what we call matter let's say and the energy of space-time. A system can borrow energy from the space-time or just dwell energy into the space-time and that disturbs us a little bit.
And we know this maybe a simple example to think about which helps us a little bit into making the analogy into how we think of energy being conserved in normal system and how different things are with gravity. Let me just imagine that I have two stars. Let me imagine I can start having one star and that star is emitting light. It's emitting electromagnetic waves.
And so that star is losing energy at one point, it will die and that's sad, but that's life. Um, it's losing energy, but this energy has been carried by the electromagnetic waves has been carried by light. And so in principle, if I take that star and then I were to draw a sphere around that star, I can compute the amount of energy lost by that star, but also the flux of energy, uh, carried by light, by electromagnetic waves.
within that sphere around or that box whatever around that star and I have a complete trade-off between the amount of energy being lost by that star and the flux of light going through that surface and so we have this very well understood notion of conservation or trade-off of energy in a normal system. Now if I do the same thing with gravity
So let me just imagine, instead of having one star, let me just imagine I have two stars. I can do that as well. And so they will lose energy through light. They radiate light, but they also radiate gravitational waves. We actually need two stars rather than one.
For gravitational waves to be radiated and that we know. In fact, there are some systems where they lose more energy through gravitational waves than they lose energy through radiation of light. So it's not something which is simply innocent. It's actually it can be quite substantial. So for some system, they lose most of their energy through the radiation of gravitational waves.
and you could in principle ask yourself if you could do the same thing let me just draw a sphere that encompass those two stars and let me think of the energy lost by that system of two stars so they're losing the they're losing the chemical energy they're losing some energy inside each of the stars but they're also losing some of their potential energy because they're getting closer and closer together
I can think I'm a little bit further away from these two systems of stars. I drew a sphere around them and I compute the flux of gravitational waves through that surface and the flux of light through that surface and that doesn't work in the same way. There's no such a notion of local at a given finite distance away from these two stars.
Of energy which is concerned for that system i would really need to go to infinity if it's asymptotically flat at infinity if i recover flat space time at infinity and then i'll be able to finally define a whole notion of energy which will be conserved but only because i'm in flat space time asymptotically and only in that case i'm able to define a local standard notion of energy.
And that's because the notion of energy is very much a consequence of
some symmetries of the space time. You need to have a time like killing vector to have a conserved charge, a conserved quantity related to that. All of this is actually I should say, I want to say because it's important, all of these concepts is actually thanks to Amy Noether that understood very much that she pioneered all of this fundamental connection between
Symmetry and conserved charges and nowadays we understand the whole world we understand it so this notion of symmetry is that the building blocks of everything that we how we represent reality around us three classification of different symmetries and those different symmetries come in with as a consequence with conserved charges but only one we have.
what I'll call time translation invariance or that flat space time has, or something related to a time like Keeling vector. So this is the same thing, a symmetry in time, if you want, then I can have the luxury as a present to have a conserved charge associated with it, which I can call the energy. But in a normal gravitational setup where I have space time,
This is not the case and there's not going to be any local gauge environment quantity which is an observable and that directly tells me that there's no such a thing as a local ordinary conserved notion of energy even if integrated within a given volume that doesn't happen. So for those two stars you really need to go to infinity to define this notion of conserved energy.
And that's if you're lucky and you are asymptotically flat in the world in which we live in now. Right. How reasonable is that assumption? No, that's not. You can make it mathematically. You can make it theoretically. But the world we live in is not like that. We know we are living.
in an accelerating expanding universe something which i'll call is close to doceta not minkowski it's a different topology it's a different asymptotics and so that we know there's not going to be such a thing as a conserved notion of energy you know for instance that you can in in an accelerated expanding universe
just in an expanding universe in fact you can create out of the vacuum some physical particles and so as time goes on you have some particles being created constantly being created and you can think of this as being created with a finite amount of energy which is borrowed from this bath which is space-time you can just borrow energy from from space-time which if it's not flat and if it's curved as it would be the case in a
accelerated expanding universe. That bothers us a little bit but it doesn't mean that is not right. It just means that the rules of the games are in fact quite different in the presence of gravity and this ability in fact to actually take in energy from the vacuum. So we can still make traction in defining some quantities which are conserved ordinarily and then as you mentioned in your
Actually, I have a popular article that I wrote on Substack called What is Energy Actually, which goes into technical detail into what general relativity conceptualizes as energy and why it's ill-defined. A link to that article will be in the description. I'm also recording a video version of that, so that link will be in the description as well.
Taking some pseudo stress energy tensor to compensate that but but that you really need to think of it as. Borrowing borrowing what is happening from from from space time itself and that that has slightly different rules of the games it doesn't make them wrong and it's but it's only in some very special limits that was standard notion of energy as you want.
to satisfy with being local, being gauge environment, being conserved, ordinary conserved will be present but typically is not. Perhaps this is one of the reasons why for instance holography ADS-CFT has become so so popular because you are living in ADS, let's say the gravitational theory is in ADS which is a curved
but the boundary it has a boundary as you can think of its gravity in a box which has a boundary and on the boundary of ads where actually the cft is living on the boundary of ads you have a time like killing vectors so you have a symmetry associated with that along the time direction and so then you have the luxury of having uh conserved quantity which is energy related to this
I'm sorry in the concept of holography in a DSC FT correspondence you have the CFT been described in flat space and then themselves they have a notion of energy and just like you have on the boundary of ADS you have a time like killing vector and a notion of conserved energy as you would want it in there now if you wanted to do the same thing for not ADS.
cft correspondence not in the same holographic description if you wanted to do it in the setter cft correspondence because we leave in something which is close to the setter within the expanded
Accelerating universe then in fact the the boundary of the setter wouldn't would would would not be a boundary which has a time like killing vector so you wouldn't have an authority on that boundary and you wouldn't have a conservation of energy on that boundary so this is one of the reasons why it's actually quite the reality of the world we live in the fact again the fact that the universe
Firstly, you're an exceptional explainer. You're great at being a public science communicator.
And I want to know how did you develop that skill and has that translated to new physics for you? When I say has that translated to new physics, what I mean is have the insights that you've gleaned from simplifying for a general audience led to new research?
So I don't know that I can answer the first question other than this if this is something that you like doing the more you do it I think the more the easier it become and you learn a lot from the questions that people ask. I think the key thing is being able to relate to the way people are thinking in the different challenges they may have in trying to address
i'm some of the concepts i think i think this is probably one of the essential things i don't know if it's easy to explain to others but i think the listening part is the most essential part of i think you know when you understand.
How people think about things and why some concept that you may have taken for granted and you may not have questioned them yourself because you don't think of it like that. You realize how other people think about it, how they address it and what are the stumbling blocks for them. I think it's very enriching for everybody. It has been very enriching for me. Sometimes I was, you're in the bus and you talk with someone, just someone next to you on the bus
first of all being able to see that the things that we are studying sometimes we go so deep in the research and it becomes so technical that you forget where everything comes in and so being able just to explain those concepts
To someone else who's not at all fluent in that language and go back to what actually was the original passion is really great and seeing that this is something they can connect with because a lot of the questions we asking ourselves people connect without they want to know they want to know what is the origin of space time.
What is a black hole? What is space time? What is gravity? Why are we here? What is going to happen to us? All of those questions that we all have them and we're all excited about it. Everybody I think is excited about looking at the sky and trying to understand the world that surrounds us. But then in trying to connect with those people and seeing what that question means for them and how they would go along addressing some of the questions
that we all ask ourselves. I think it's very enriching for everybody. So I think this is very much something you can build on. Of course, it's not that the perspective necessarily helps me understanding whether it's a factor of two or pi in my equation, but putting things together in the bigger picture and understanding how things are connected with one another is very enriching. And I think this is really where it comes in.
And so to answer your question, I think yes, it does help a lot in making progress in research. I often describe it a little bit like a chess player where you see this. I don't play chess. My daughter plays chess, but you can see these people playing chess and they don't need the pieces anymore. They don't think about one step at a time. They think about the whole game as a whole. And so being able to embrace enough
Experience in understanding what is the done long term dynamics of a game knowing how knowing how i started and what are the different possibilities of outcome. I can think of this a little bit in physics as well where.
The math and the logic and all of this formulation they are the basis but if you're able to gain enough intuition you can extrapolate yourself from that and use much more your creativity to understand where things are going without needing to go sit down and do every single step along the way. You'll do that eventually but
To get the bigger picture you start with having embraced all of this intuition which is coming from all sorts of different people you spoke with in all sorts of different backgrounds and then from that you understand where things are going what does it mean what does it mean if i have two electrons capturing and i have an interaction with a graviton there but also when i push that to higher energy and i include a contribution from other things you have a bigger picture of what will happen and from that what it means
I think you want to understand what he means and how different things are connected with one another. And so I do think it does help and it does help to gain some intuition and just put aside a little bit all of the formulation if you can and use your creativity to free yourself a little bit and that's how you make progress. You need a bit of both of course you need to have built in from all of this
I should also state that you have a book called The Beauty of Falling which will be on screen and the link will be in the description.
So while we're on the subject of dark energy, there are the DESI results that hint that dark energy may be dynamical. What does that mean? And what do you make of it? And does it have any bearing on massive gravity? So it's really exciting. Any departure from a cosmological constant would be extremely exciting.
It precisely what he means i would say is a little too early to just to tell i think that there's a lot of signals which are sometimes below three sigma which come and go and so before it's actually very much there and has sufficient significance it's going to be hard to tell whether
Is going to survive or not but it's true that is going into more and more into this direction so first of all having some dynamical dark energy would be extremely exciting for many different reasons just the fact that is not the vanilla model that one would have expected.
Is telling you that there's some signs from new physics and that is very much what we need we need traction into something new that tells us where to go where to look for more information on what is leading to the expansion of the universe anything which is done i make all is really.
fascinating because it tells us it may uncover the reasoning as to why we have an accelerated expansion of the universe with precisely that amount of magnitude and not a little bit more or not a little bit less if it is dynamical.
Then you can understand that much more dynamically. Having dynamical dark energy would tell you that there's actually other degrees of freedom out there and so there may even be a particle, a field, related to that. That would be really fascinating because it tells us that there's something else to discover there. So having dynamical dark energy to me would be fascinating because it tells you that it's not just a cosmological constant which is kind of boring and we're stuck with that problem as to why it has
That particular value having dynamical dark energy could tell us that it didn't always have this value. It's something that evolves in time. And so it gives us really different new clues to the to the problem. One thing, though, is that we call it dynamical dark energy. Really what it is is an equation of state parameter, which is not constant in time. This is based on the observations.
But it could be due to many different things. It could either be that the actual source for the accelerator expansion of the universe evolves in time, or it could be that the dictionary between this source, between this dark energy or cosmological constant and its effect on the evolution of the universe is what evolves in time. And that would lead to, for instance, a modification of gravity.
If it's true that there is dynamical dark energy, what it tells us is that there's something new out there precisely where it is. If it's in the source, if it's in the gravitational side, if it's in between that, that will have to be uncovered. What do you mean by the source? So the source would be dark energy itself being not just a cosmological constant, but being something that evolves in time. So that's possibly the simplest possible.
this could be the simplest possibility although you need to understand what this field is and why it evolves in time or what we know is that this is what we observe and if we observe something that appears to be evolving in time it could still be the case that we have a cosmological constant but the effect of this cosmological constant on the evolution of the universe is what evolves in time and so it's in the translation between what
is present in its effect on the evolution of the universe that's where the time dependence comes in and if that were the case then that would hint towards a model of modified gravity where as time goes on or when the scales involves change then the effect of a particular source for instance a cosmological constant is different and so leads to a slightly different rate of acceleration of the universe.
And that would really be so incredibly fascinating. One thing which is very interesting, it's a little early still, but one thing which is very interesting is that at the moment observations seem to be suggest that it's going towards even smaller than minus one equation of state parameter. And that is quite puzzling because normal matter, normal energy,
doesn't even need to be matter normal energy as we as we know it even quantum vacuum energy typically is behaving with the opposite behavior so with an equation of state parameter which is slightly larger than minus one.
Having some an equation of state parameter w as it's called being smaller than minus one would mean that the evolution of the acceleration of the expansion of the universe would mean that the accelerated expansion of the universe would even go faster and faster. So the Hubble rate would go even faster and faster in time and so that could lead to a big rip.
universe is not only accelerating but this acceleration is going faster and faster to the point where even if you consider the space between in cosmic voice of space between two two clusters of galaxies will be ripped apart. So we don't know it's too early to tell but definitely
How do i make a dark energy goes would have incredible consequences for the future of a universe what is the destiny what is the fate of a universe depends on the precise behavior of dark energy and that so it's amazing i think to us being able
to look in the sky and see those results from daisy and then from that determine what is the fate not of us on earth but the fate of the very structure of space time in the universe is incredible really um we don't know for sure right now but but either way is going to be fascinating i'll put a link on screen to the new desi results there's an article from the economist
I know you said that your approach is agnostic to whatever the final quantum gravity theory may be. However, one of the initial motivating reasons to go into string theory was that as a side effect it produced a massless spin-to-field.
So it didn't produce a massive one. I don't know if the fervor would have initially been as intense had it produced a massive one. So how do you make sense of the disparity between the string approaches to quantum gravity, which predominantly have massless spin two field and then, and then yours. And if massiveness is up for grabs, then is spin two-ness up for grabs? Like maybe grab a tongue. Like what is up for grabs? Just a moment. Don't go anywhere. Hey, I see you inching away.
Don't be like the economy. Instead, read The Economist. I thought all The Economist was was something that CEOs read to stay up to date on world trends. And that's true, but that's not only true. What I found more than useful for myself, personally, is their coverage of math, physics, philosophy, and AI, especially how something is perceived by other countries and how it may impact markets.
For instance the economist had an interview with some of the people behind deep seek the week deep seek was launched no one else had that another example is the economist has this fantastic article on the recent dark energy data which surpasses even scientific americans coverage in my opinion they also have the charts of everything like the chart version of this channel it's something which is a pleasure to scroll through and learn from.
Links to all of these will be in the description of course. Now the economist commitment to rigorous journalism means that you get a clear picture of the world's most significant developments. I am personally interested in the more scientific ones like this one on extending life via mitochondrial transplants which creates actually a new field of medicine.
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Thanks for tuning in and now let's get back to the exploration of the mysteries of our universe.
Yeah good good good amazing question let me just start by telling you that in fact the first model of string theory bosonic string theory actually came in with a massive spin-2 field. It was unstable and that was in a supersymmetric version and there was all sorts of different problems but in fact the first model of string theory came up with a massive spin-2 particle.
That doesn't mean that i do believe that a massive spin to grab it on a woodcut would come from strength area i don't i don't i don't think so the moment indication seem to suggest quite the quite the opposite but this is just to say in fact we. We have many different realizations and we never know for sure what is gonna be the final outcome.
Now we have learned a lot from understanding what is possible to come from string theory in fact and what are potential high energy completion of massive gravitons. So I think unlike the approach of remaining quite agnostic in precisely what the high energy completion is,
so long as it satisfies some basic rules that we discussed about earlier like causality, like unitarity and it doesn't need to be string theory per se but we want however physics manifests itself at very high energy we want it to be so that it satisfies these very simple rules without which I don't think we can even make sense of reality anymore and we don't even need to have a notion of
I want causality to be satisfied. These are very much the ground rules for what we want to base ourselves on.
And then it can be string theory, or then it can be something quite different. It doesn't matter. From that, you can actually make contact with how physics manifests itself at low energy. And we know that there are some models that I can come up with NASA models that I can write down. And that seems quite consistent at low energy. And I can even convince myself that they could be good representations for what happens in the world that
That i observe in the experiments that we make and they seem to be self-consistent within the remit in which we want to probe them and yet those models in fact we know they will never be imbeddable they will never have a representation of high energy or they will never come from a high energy
Representation of physics, which is consistent, which is unitary and which is causal, for instance. And so this good outcomes, because then we can carve out a whole region of models. We have carved out all sorts of different ways to represent the world, which otherwise would have seemed consistent, but we know it's not consistent with having high energy completion, which is unitary or causal or those kind of kind of base rules. Now for massive gravity.
At zero order it is already challenging because of all the modes that come in to be embeddable in a standard high energy completion. If in addition I want the high energy completion to be weakly coupled in the sense that I have a standard perturbative approach all the way up to high energy then we know nowadays that this will not happen.
What is a disaster for a massive gravity some of my colleagues would say that's a disaster for string theory but in the reality is that even in string theory is not the case that it necessarily needs to be weekly coupled we are we have to make a distinction between what is.
easier to keep traction on what is easier to calculate where we can actually make more predictions and make more progress and the realm of all sorts of other possibilities and this is what the distinction is a lot of the time we go much further in directions which are
easier to calculate, that's the truth of the matter. When things are weakly coupled, when things are more perturbative, it's much easier to make traction in some directions and in those directions we know that we're not going to be able to make contact with massive gravity. The graviton will have to be massless and that's the end of the story. So that is definitely true. And so in all of the string theory realizations that we have at the moment, we can't
Make space for a massive gravity will have to be a mass less gravity has to be a master's gravity. So they can be massive spin to fields and in fact we do believe in string theory that we believe there will be massive spin to fill but there's never such a case where you have.
What we call a gap, a separation of scales between a small remit where you have massive spin to fields for instance and a large gap and then nothing else so that we can treat those massive spin to fields as being a low energy effective description for the world in which we live in. It's always a continuum of states in between. So that is the nature of it. Does it mean that massive gravity is ruled out?
Possibly, I don't know. It is in tension with the standard realization of string theory. That is definitely true. I would say, though, that better understanding how you can have a realization which builds on this strong coupling, which is very challenging to keep track of and very challenging to get predictable, observable from is actually interesting in its own right.
I don't know whether this is going to be ultimately realized but I still think that this is an interesting direction to study and it is possible that ultimately even for our standard completion of the world in which we live in, we're going to need to rely on a strongly coupled high energy completion that may just be the reality.
and in that if that's the case then it would be much easier to understand how to make sense of it in sort of a toy model as it is the case in massive gravity as opposed to a fully fledged theory of quantum gravity. That is for the mass of the of the graviton. For the spin
So long as you follow a standard approach where you think of the spin first of all that's also a consequence of a symmetry which is Lorentz invariance so everything that
A lot of the things I'm thinking about that people would be thinking about in string theory and in a lot of high energy completion are still within the remit that Lorentz environments is a fundamental symmetry. So the world in which we live in right now is not Lorentz environment, but that's a continuous breaking. And if I were to zoom into a very small region of space time, you'd think that you recover this Lorentz environments.
And so if you have Lorentz invariance you have all sorts of related quantities associated with it and one of them like the notion of mass and another one is a notion of spin which is discretized and you can have a spin zero like a scalar field and in fact there are
Before general activity there were models for gravity which were based just on a scalar field spin zero gravity. Now we know this is completely incompatible with observation you can't have gravity being just a spin zero particle you would you wouldn't get gravitational waves but you wouldn't even get the right behavior in the solar system so we can't have that.
spin one particle that corresponds in fact to the photon. The photon is a spin one particle. It's massless. You can have massive spin one particles like the W and the Z bosons. We also know that the graviton cannot be a spin one particle. It has to be at least a spin two particle. So really the question is could it be the case that the graviton is not a spin two particle but it's a higher spin particle
the spin two subspace of a higher spin particle
In fact it's quite challenging we know just to have a higher spin particle interacting just by itself without having an infinite tower of other higher spin particles being present as well that that we know and in fact string theory is just that it is a spin two and a whole higher spin tower of other particles that that come in along the way that's what that's where string theory is. So in that sense
Part of string theory is having the spin two as one of the states but a whole tower of higher spin so we in fact embrace this spinness for grab in many of the models of quantum gravity. We know that we can't just stop at one given spin. The thing with spin two
and higher spin is that as soon as you switch on, as soon as you have a spin to particle, and I'm not talking about a mass here, just in gravity itself, as soon as you have a spin to particle, we know that its behavior as you go to high and high energy, it grows too fast with energy to be consistent at high energy. And so you actually need to have an infinite tower of higher spin states
Where when you resume everything together that's what's taming down the high energy behavior of him talking about amplitudes of probabilities and things like that but we know. Already in if you take to my activity you have the.
This is the only way to have
Are you working on a theory that gives mass
I am actually working on a theory. I can tell you one question I have. It's related. Well, it's lots of questions that I have every day. There are these, let's say, swan plant conjectures or landscape conjectures. One of them is called the weak gravity conjecture.
We would think for many different reasons which are very well founded that in fact gravity should be the weakest force there is and we can think of this around a black hole, we can think of a black hole having a mass but also having a charge with respect to not necessarily electromagnetism but it could be an electric charge but also another kind of charge
We want to be able for the black hole to evaporate its charge faster than it evaporates its mass because as it evaporates we don't want it to become too charged and become a critical black hole which would lead to a naked singularity. So this is a very very simplified way to explain the weak gravity conjecture in the sense that we would like
to being able to evaporate into charge more rapidly than evaporate into the mass if you want or we would like the gravity to ultimately be the weakest force around.
So a lot of my work is trying to understand how to think of this weak gravity conjecture and whether we know that from the high energy completion of quantum gravity, whatever it is, the ultimate completion of everything in fact, we can derive this weak gravity conjecture or slightly modified versions of this weak gravity conjecture.
But something else I want to work about related to your question is the long gravity conjecture. So I told you that in I don't know how much I want to go into that. Don't start working. Is it because it's too new? It's too new. Yeah. Now, let me just say, one question I have is if if we if we know that one question I have is,
If you were the case of gravity on could have a mass and the photon could have a mass in principle. Now I know that I can't embed that in a weekly coupled high energy completion. But let me allow for myself to have a strongly couple high energy completion where some of the bounds that have been derived are not quite as
So let me enable this possibility and think about whether it could be the case that the graviton could have a mass, in fact the photon could have a mass, in fact every particles have a mass, it may be just very very small. And the bound we have on the photon mass, observationally, that's nothing to do with me, but observationally there's reason to believe that from the coherence of magnetic fields in galaxies
The bound on the photon mass is of the order of 10 to the minus 20 electron volt. I should say in fact there's some very nice papers by some colleagues of mine, Giyad Vali and Lasha, who've gone through this analysis again and I think they have some very nice results in showing that there's a little bit more leeway into that. Anyways, let me accept that
In principle the photon could have a mass and if that were the case the bond is not so stringent. In fact the bond is weaker as compared to the bond we have on the graviton mass just from observations. Now I'd like to understand whether from being able to embed these theories in a consistent high energy completion not necessarily weakly couple them but it could be strongly coupled even whether
It is the case whether it would be possible for the photon to be lighter than the graviton or not. And I think that's an interesting question and it's alright because if we can come up with a way to understand as to why the graviton should always be lighter than the photon, it can be massless but if you had a mass it has to be lighter than the photon and in fact lighter than any of the other particles that exist,
It would tell you that at long distances, gravity is always the force that survives. So it would be a long gravity phenomenon in some sense. All the other forces in nature will have to be switching off faster than gravity. So that's just one idea I've been trying to think about for breakfast, but there's lots of things that come up every day.
So our audience largely comprises researchers in math, physics and philosophy, but there's also a substantial part, a portion that is lay is not educated in physics at the university level. So I just want to distinguish something here. You said gravity could be lighter than the photon. Someone may think, well, the photon is light. The photon is light as in when you're saying it's lighter, you mean it has less mass.
I don't know if people know who are not physicists how difficult it was what you did in 2010 and how radical this approach is.
Because if I recall correctly from our first conversation, you said diffusomorphism invariance in GR may be approximate, maybe something that emerges. Am I recalling correctly? Yeah, so this is something that I think is quite interesting in that if you take a textbook on general relativity, on Einstein's theory of gravity, or if you teach it or even historically, it's always
seems to be the case that you have these pillars there you have the equivalence principle you have this sort of even assumptions and we call them sometimes Einstein principles on which Einstein's theory of general relativity is being built and if we phrase it like that it may almost seem like these are for grab and I can just remove them and I have a completely different theory which maybe would be consistent in its own right and
It may be more historical or it may be because those are actually conceptually very important frameworks. For instance, the notion of covariance, the notion of the fact that every observer is equivalent and I can change my quantum system but you shouldn't change the laws of physics and that's related to a symmetry which we call coordinate diffimorphism invariance, diff invariance.
Now you may think that this is built in and general relativity emerges from that. And in fact, if you take that perspective, you can ask yourself whether you can get rid of this symmetry.
Maybe it's not necessarily comfortable to do that but you can ask yourself whether you can get rid of that symmetry and then you get up with a much more general theory of gravity which is not based on the symmetry but a lot of other possibilities emerge.
And in fact you can go through this and realize that all other possibility for which they're not they're breaking different variants at least in the kinetic term in the way the dynamics of gravity is being built in if you allow yourself you enable yourself to include some
potential correction, which would break that symmetry. You see that those potential correction automatically lead to pathologies, which are those goals like pathologies that completely rule out that theory. So I think this is quite interesting because it tells us that we don't need to base ourselves necessarily on these principles. We don't need to base ourselves necessarily on those notion of symmetries to build our theories.
We can start with in principle it will be much more complicated but we can start with something which is much more messy much more complicated and much more flexible and then you realize that the only thing that makes sense.
is what is what is the substructure for which a symmetry just pops out and so it in fact gives you a motivation as to why the symmetry has to be there if the symmetry wasn't there the theory would not be stable and it's not so it's not that we simply stubborn and we can't think things in a different way or we just focus on particular framework where it has a given level of symmetry
is in fact the symmetry is essential to protect the theory against all sorts of pathologies. And if it wasn't there, the world simply would be completely unstable to the point where there wouldn't be any structure of reality. So the only possibility is for this symmetry to emerge. Now, if diffeomorphism invariance emerges,
then, and if theomorphism invariance is analogous in Yang-Mills to gauge automorphism invariance, then is gauge invariance approximate? Is there room for that? So I would say the same thing that in Yang-Mills, for instance, you know that the symmetry is there to preserve the stability of the theory. And that's the same thing in electromagnetism as well, where you have some notion of gauge invariance there as well.
You can break that gauge invariance in electromagnetism by adding not a change in the kinetic structure, because you know that this will lead to pathologies. You can break it for other terms, some other what I call irrelevant operators, a mass term. So in principle you can add a mass to the photon that breaks the gauge invariance that you have for electromagnetism. But even if you do break it softly at the level of the mass,
You can't break it at the level of the structure. Sorry, you can't break it at the level of the kinetics. So even in models that consider the photon to be massive, the dynamics of the photon themselves through the Maxwell structure has to be preserved exactly in the way it is.
And so even if you enable yourself in the same way to start with something which even softly break the gauge invariance in electromagnetism, you'll restore this gauge invariance by stability for the standard kinetics of the photon. So there's a conceptual clash between quantum theories, external and absolute time, and then general relativity's dynamical spacetime.
You mentioned that massive gravity needs to be embedded in QFT. So does constructing a quantum theory of massive gravity give you some clue about time? Like maybe it's due to the inherent scale introduced by the graviton mass. Do you have an answer to the problem of time? I don't have an answer to the problem of time, but it does give you a framework where indeed you
Because you set up the scene much more clearly or you are forced to set up some parts of the scene from the outset, it's a curse but also it's an ability to work with those things from the beginning. So there's a lot of things that were
On the face of it, it is much more complicated in massive gravity, but possibly embracing those things and understanding how to make sense of those. So the scale of the mass and indeed the breaking of the time different invariance may enable you to then understand how to make sense of it at the quantum level in a way that would otherwise have appeared much more challenging in a fully fledged theory of quantum gravity.
Einstein had a whole argument, H-O-L-E argument, and that led him to say that diffeomorphism, I believe that may be among some other factors, but that was one of the principal factors that led him to diffeomorphism invariance because he wanted to retain determinism in GR. So does removing diffeomorphism invariance then at the fundamental scale reintroduce indeterminism into GR?
I think it's hard to tell at this stage. I think we're not really there because I mean perturbatively we would get the same thing that is okay. We understand how to, we can restore that symmetry if you want and you can think of other degrees of freedom there that will restore that symmetry. I think that really the question
Is what happens when you are in a regime where things are no longer perturbative and are so strongly coupled that the potential outcome of that is quite different as compared to what you had started with. But that is also very complicated to look into. So I honestly, I can't tell you at the moment. I don't know. What are gravitational rainbows? It's like rainbows. What are rainbows? What are rainbows? Rainbows?
Just the fact that light as it travels through a medium, let's say through water, through glass, will be affected by the medium slightly differently depending on its frequency and we understand that because as light goes through a medium it will interact with whatever matter is in that medium in a way which is
If the wavelength of the light the color of the light is quite similar to the relevant scale in that medium it will interact strongly with that and it will be slowed down by matter by the atoms in that medium and if it's very high frequency it will just zoom through completely unaffected and so the speed of light in water is in fact dependent on its color
And because of that, as we shine light through water, through a droplet of water, when it just rain in the sky, we see that light comes out of this droplet of water in a way which is different depending on the different frequency, the different colors of light. So we see this pattern in the sky.
Now you can do exactly the same thing for gravitational waves. Gravitation waves are traveling through the universe and most of the universe we think is empty but still we think that most of the universe is filled with dark energy. That's what leads to the accelerated expansion of the universe.
What is dark energy precisely I don't know and we know more or less how it interacts roughly with gravity but we don't know precisely how it interacts with gravity in a frequency dependent way at very very low frequencies. So it's possible that as gravitational waves are just traveling through the universe they are interacting with dark energy in a way which is frequency dependent.
And so that's the case we will see that gravitational waves with different colors or different frequencies will have been affected every so slightly by dark energy all the things along the way in a way which depends in the in the colors.
Of course, we're not going to look in the sky and see a beautiful rainbow in the same way as we see it for light, because we can't see gravitational waves with our eyes. So it's not going to look so pretty just like that. But in principle, the same type of phenomena can happen. And so we know, for instance, that there's different systems that emit gravitational waves, and they do so within a range of frequencies.
The system that we have observed for the merging of black holes or neutron stars that we have observed so far, the gravitational waves emitted a relatively high frequency within that spectrum and so they zoomed through the universe completely unaffected by dark energy or anything else.
But if we were looking at system, which are supermassive black holes starting their journey much further away, the frequency they met to start with will be much lower. So more towards the red of the spectrum in comparison. And so they can start being much more affected by the medium of the universe, for instance, by dark energy.
And then you could observe that the speed of very low frequency gravitational waves, we're talking very, very low of the order of 10 to the minus 30 electron volt. So 10 or so orders of magnitude below what we have observed so far. But potentially we can observe that those would propagate at a speed ever so slightly smaller than those are very high frequency. And so that would distort the signal that we observe.
That would be a gravitational window. Whether they exist or not, I don't know. That depends a little bit on what dark energy is. It depends how gravity interacts with dark energy. It depends on lots of different things. But it is something that we should keep our mind open for because this is a way to distinguish between different models. This is a new way to observe the universe. It's a new way to interrogate an environment and ask ourselves, is this happening or not?
Suppose we could do a double slit experiment in ideal conditions with gravitons. Would we expect an interference pattern? Yes, we are dealing with gravitational waves. So yes, in principle, you would expect the same thing for gravitational waves as you do for light. Yeah, there are waves, so you would expect that.
So is there something different about gravity that acts as an observation or measurement in the measurement problem sense? So one thing which is different with gravity as compared to the other things is the fact that it's so weak. The strength of gravity is making it quite unique and especially
Possibly the reason why we actually can be here and ask ourselves that question, but gravity is much weaker as a force as compared to everything else. So this has a direct impact in ability to in fact
detect the fundamental particle of gravity in the same way as we have been able to detect the fundamental particle of light we know how to make sense of a single electron we know how to make sense of a single photon we can do experiments with that and we can look at the effect of a single photon that we can do but for gravity because it's so so weak the effect of gravitational waves is already the way we observe on earth they've been so weak
We're just observing gravitational waves. We see light all the time. We're sensitive to light and it drops energy in our retina. We can see light all the time. We interact with it quite strongly in some sense. With gravity, we interact with it very, very weakly. And so it's only when we have a coherent state on so many gravitons all together
that the effect is sufficiently large to being able to observe a gravitational waves passing through. Now if you were just to think of the effect of a single graviton in the same way as you think of the effect of a single photon, it's not only challenging at the moment to observe a single graviton with interferometers, that would go below Heisenberg uncertainty principle. So you can ask
yourself if I have a single graviton going through our interferometers, a single one of those with a given momentum which is associated with the length of the interferometer will lead to a displacement of space, an effective displacement of the mirrors in an interferometer which is too small to be observable. It's not just a technical engineering challenge
It goes below Heisenberg uncertainty principles that is quite different as compared to everything else that we know so we know that to prove the quantum nature of gravity observationally is going to be challenging so there's one side of that but then there's another side which makes it even
more problematic is that if you try really to probe gravity in a way which becomes stronger and stronger you have this sort of protection mechanism where it creates a black hole and so it sort of protect itself from even being able to being observed in stronger and stronger environments. So probing the quantum nature of gravity and being able to observe it in interesting regions
We do know it's going to be very, very challenging. I'd like to get to some of your latest research. So you've been working on positivity bounds derived from the S matrix theory and how they constrain massive gravity. So can you please talk about that and explain what positive bounds are?
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So positivity bounds are in fact something quite intuitive I would say. If you think of having ultimate high energy completion of whatever it is. I don't know exactly what physics looks like at high energy. I may not have any fields there to describe reality. I may need to have
Use a different tool, I may need to use strings, I may need to use something else yet I haven't even thought about. I don't know but it doesn't matter too much because what I'm thinking about is amplitude of probabilities of given outcomes and I don't really need to understand what the other fundamental blocks of nature at very high energy.
but what i do know is when i make a link between high energy and i go down to low and low energy i can sum up probabilities and so for instance if i if i am at low energy and i take two electrons let's say i take two particles and i scatter them together at a given energy they're gonna interact and lots of different things can happen and what can happen depends a
high energy physics but all other additional contribution should adopt positively to some quantities related to the amplitude of probability so whatever if i have all the particles that come in there that come and play along in the game
All they can do is add up for a new outcome which will give an additional positive contribution to the realm of possibilities. So this is really what the positivity bounds are in some sense. It's embedded in this notion of unitarity but you don't need to go into the details. It's very much into thinking that when you have
When i scatter things so the scattering this is what is encoded in this as matrix and that's why we're talking about the s metrics i can look at the different possible outcomes and if i have more and more physics coming in at high energy that opens more and more possibilities or it happens some more and more contributions to the potential outcomes but they will bring in positive contribution i don't want anything
which may lead me to negative contributions because otherwise I could simply focus on this and end up with a probability which is doesn't make sense which is negative let's say. So these are what the positivity bounds are.
Conceptually, you can think they're quite simple. They're quite simple to understand that things should add up constructively and positively. Of course, it's a bit more mathematical than that. What I'm saying is a little bit simplified. It's not entirely correct, I should say, but it's just to give you the gist of it, a little bit of the taste of it.
But the beauty of this is that it enables you to make a connection between an unknown high energy completion. I don't know what it is. All I know is possibilities, contribution to an amplitude of probability at high energy and then some potential outcome at low energy and some realization, some models at low energy.
And so I can from that have a model at low energy, which I'll call it an effective description. It's a effective quantum field description for the world at low energy. For instance, the standard model of particle physics, I can think of it as a low energy, effective quantum field theory. It's valid up to a given energy scale.
And even general relativity, I can think of it as an effective quantum field description. It's a quantum field theory and an effective one, which makes sense. It makes complete sense. It's consistent. Everything goes well. There's absolutely no problem up to a given energy scale. And it's only when I start looking at things at a high energy scale and I can think of doing scattering processes,
That involves gravity. When I start doing this at energy scales, which are comparable to the Planck scale, then I start producing black holes and all sorts of funny things happen. And if I were just to take general relativity with nothing else at high energy, I would seem to break this outcome of unitarity, break this notion that the probability should sum up to one.
So this is really the issue and this is why we know that something else has to come up to compensate for that. But now I can just take effective descriptions at low energy the quantum field theories and just consider amplitudes of probability at low energy and ask myself whether their behavior and their behavior as a function of energy and different parameters which are related
To some extent to energy is consistent with what I would have expected had it come from a consistent high energy theory. And so, as I mentioned before, for some of those models, we already know that they will not be consistent. An interesting thing is that sometimes you can look at it at low energy.
And nothing wrong seem to happen in principle they could be an ok description as an effective perturbative quantum field theory they may be consistent but then we know that in fact they're never gonna be linked.
To link them to a high-energy completion something bad has to happen somewhere along the way there needs to be some negative contribution somewhere along the way and that can't happen otherwise we could just focus on this negative contribution and everything will be unstable everything will be bad. So now you can do that for all sorts of theories that you have out there including for massive gravity.
Now for Massive Gravity, there's a very nice paper actually by Chang and Roman from 2015 or 2016, maybe it was 2016. It's called Positive Science in Massive Gravity. So Massive Gravity comes up with different parameters.
for interactions is a different parameters that come in and then they show that there's an island of possibility among this parameter space where those positivity bounds are satisfied. So for the theory to be consistent and to be embeddable with a high energy completion, you need to be within a region of parameter space. And that was quite nice because before
In fact we anticipated that there would be no region of parameter space where it would ever be embeddable in a standard high energy completion and you always needed something which is quite different. So even the possibility for this to happen is quite interesting in its own right.
And then there's been a series of other papers since then that show that if you make further assumption and you push those bounds further and further in particular if you make some assumption which are stronger based on weekly couple high energy completion then you can't have the theory being.
embedded massive gravity being embeddable in a standard high energy completion so that we know so for massive gravity to have a high energy completion it can't be just a weakly coupled more let me say perturbative approach I have something more in mind when I say that but it can't be just a weakly coupled high energy completion it will have to be something quite different which may be interesting but makes it also quite challenging so this is the the statue of that
I think to my mind this is really
Very interesting, but it's also very challenging. So what we know is that you have to redress some of the coupling constants that come in in the situation and the roles of the games become quite different, but also very challenging to keep track of. So very little progress has been made in those directions for massive gravity. For other things, a lot of progress has been made, but not for massive gravity.
But another completely different direction is simply to use those positivity bounds not for massive gravity but all sorts of different effective descriptions that we have out there. And for instance for particle physics we understand now that we have the standard model of particle physics that includes the Higgs but if you were to ask the community 10 years ago even 13 years ago they would have told you that
One would have hoped to observe something beyond the standard model, which is based on particular models coming from high-energy realizations. So either some signs of supersymmetry or some particular models that would have come in. And the reality is nothing has emerged. We haven't seen anything beyond the standard of particle physics, but we know that it will be hard for it to be just the standard of particle physics. We would have expected something else to come in.
At the very least we know that we have to couple it with gravity at some point that the neutrinos have masses maybe that's not really the big issue but at some point of this before the plan scale something has to come in and we believe that something will have to come in even at a much lower energy scale than that.
But before we were driven much more by beautiful, very well thought out, specific realizations at high energy, some specific models which come out with their specific signatures at low energy. And unfortunately nothing has been found along those realms.
So nowadays quite a different approach has been taken where people are looking at what we call the SMEFT, the standard model effective field theory, where instead of looking for specific model dependent signatures, they're looking for all possibilities. So they parameterize the corrections that you can have
Beyond the standard model of particle physics, it's the SMEFT, so you're looking at corrections which will become more and more important than high energy that go beyond the standard model of particle physics. But there's thousands of those and so those positivity bounds can enable us to see where in this big region of parameter space you have, you can be
connected with a sensible high energy completion and which regions you are not and so that allows us to make tractions and focus in sensible regions in parameter space for physics beyond the standard model without being focused on specific model dependent on a focusing on a consistent high energy completion and this consistency is just a notion of causality and unitarity.
When people hear the terms high energy realization, UV completion, high energy completion, are those all synonyms? And then what would be a synonym for the viewer or listener so that they can understand it more? Is it final theory? Is it a more final theory? What does that mean? Yeah, so it means slightly different things depending on the context. For this discussion, when I talk about high energy completion, I really mean
Something that in principle could be probed at infinitely high energy. You know that general relativity is an extremely good description of the world we live in up to some given energy scale. But we know that if I were to probe Einstein's theory of general relativity at too high energy, things go wrong. It's not longer consistent. It's no longer consistent as a quantum field theory.
And so some new physics has to come in. It could be that there's never really gonna be a finite end of the story. It could be that we understand what is the next layer of physics beyond general relativity. We have let's say string theory and then things go on and then we realize there's something beyond that and there's something beyond that etc. But what we want to know is what at the very least what happens
within a consistent quantum theory of gravity at energy scales beyond the Planck scale. But in some sense it doesn't matter too much whether it's the final word or whether it continues like a fractal
Realization because all we asking ourselves is for physics have a manifest itself to be consistent in the sense that we want causality there and we want some notion of unitarity the probabilities some up to one and so it doesn't matter if it's an infinite.
infinity of models that we need to go deeper and deeper and deeper or if it stops and we'll get to a point where we understood everything and that's it it's string theory everything stops there and we have all the tools at our disposal to compute anything you want I don't know probably I will never know within my lifetime and probably in the next generation will also find it quite challenging to know and that's why we don't want to be too committed into
Add that being a finite mess in our knowledge or whether we gonna keep pursuing knowledge deeper and deeper levels to get more and more precise into what makes a structure of reality and it doesn't matter all that matters is that we know.
That what we have access to right now is not the final story and there have to be something else out there for which we don't have direct contact with at the moment because we don't have the tools to fully describe what's going on there. Now, the last time we spoke, you discussed longitudinal modes in the context of Einstein screening, if I'm not mistaken, and how that overcomes the VDVZ issue.
So does the presence of this mode in Massive Gravity leave imprints on the CMB that are different than standard cosmology? That's an excellent question and the answer is probably, although we don't know yet. So what is quite likely is that
The presence of this mode means that depending on the scale you're looking at, you change every so slightly how easy or challenging it is for structures to form. So for the structure we see in a universe, the clusters of galaxies and the filament of dark matter, they got seeded by original quantum fluctuations in the very beginning of the universe and then there's been gravitational collapse
around them and things being patched around those seeds and those structure. But if you change every so slightly the strength of gravity because of this longitudinal mode that will affect the spectrum of those structures and it affects every so slightly differently depending on the size of the structure and depending as well on when they got formed in
Devolution of the universe whether it was early on or later on so we would expect a slightly different realization of this and in fact there's some very nice work by Mark Wyman and Justin Corey where they look in at the different ways structure get form depending on how strongly this longitudinal mode start kicking in through the history of our universe now for the CMB
One would believe, one would think that at the time of the imprint on the CNB, this is coming from quantum fluctuations at the very beginning of the universe, the energy scales involved at that time are so high that the longitudinal mode would be completely screened.
Because it's we're dealing with very high energy scale so that probably is not where one would expect to see the best signatures for the longitudinal mode but really being able to come up with a precise calculation requires us to being able to follow the whole evolution of the universe in a fear of massive gravity which is very challenging.
But there's been some other work being done where just from the fact that not only you have a longitudinal mode but just the standard tensor mode, the standard what you call gravitational waves are massive, that would change the spectrum of gravitational waves fluctuations at the beginning of the universe. And if we did observe primordial gravitational waves,
which could be imprinted on the cosmic micro background through polarization of the CMB. This would come in with a particular spectrum, which depends on the alley, depends on the angular momentum and angular distance, depends on the frequency if you want, and that will
be affected by the scale, the mass of the graviton. In particular, if you observe primordial gravitational waves, so for instance, if you observe a polarization in the cosmic microwave background that you can trace down directly to primordial gravitational waves as opposed to anything else like dust along the way or anything else. And if those came in at very, very low, very large distances, let's say very, very large angular distances,
then that would tell you that the graviton has to be effectively massless at the time of emission and therefore that could put a constraint on the graviton mass. So the spectrum of the polarization of the CMB may enable us to put some constraints on the graviton mass and there's some very nice papers being done in the focus just on the effect of the mass on the standard tensor mode of gravitational waves.
What about the spectrum of Hawking radiation or the temperature? Is there any introduction of decays into the massive gravitons? Yeah, so that's an excellent question. In principle, yeah, you can start looking at those things. In fact, yes, it's a very nice paper by Rachel Rosen, which has looked at the effect of the thermodynamics of the massive graviton and the correction. So the reality is
What happens is that you introduce a new scale, which is the graviton mass, in the spectrum.
And so she has followed through the differences that comes in in the thermodynamics lows in a theory of massive gravity. In fact, in normal processes, the mass is so small as compared to the other scales involved, it makes a very little difference. But it's still very interesting to see how you recover the standard smooth massless limit in the limit where the mass becomes very small.
So Claudia, thank you for spending two hours with me. I appreciate that. Yeah, thank you. Thanks. So it's great talking to you. I want to know before I talk about what is it that you're currently working on and where people can find out more about you. And by the way, there's the beauty of falling, which will be on screen and link in the description as well. What's your current assessment of emergent gravity proposals?
You know I really like to stay agnostic. There's so many good ideas out there but at the moment my work is very much making connection between those and low energy physics in terms of observables in a way where I don't want to commit too much into what is emerging gravity, what is the realization because to me I mean it
Ideally a lot of those ideas are jeweled to one another and I would love it if in fact it's not just one realization or another is if we see a correspondence between these different ways to think about it. So I'm going to be speaking with Ted Jacobson soon and I'm curious if you have any questions for him.
What do you think he's doing that's wrong or what questions come up to you? Don't put me on the spot for that. No, I don't want to go into that. Okay. I see him every so often, so I'll talk to him offline. You'll talk to him yourself. All right. All right. Great. Yeah.
Okay, so what are you most excited about now that you're pursuing? Yeah, every day I have a new idea and I like to pursue. So one thing I'm quite excited about is to try to understand whether again moving into this notion of symmetries where they emerge from more fundamental principle. So in a lot of the way we're thinking about things, we think of symmetries as a guiding principle because it helps us to
Put an order into things and to keep things under control but sometimes it's almost like a way to simplify our life and in a lot of the work we're starting to see we realize that it's not up for grab actually they have to be there those symmetries emerging from all sorts of different requirements which we thought
we're just there to make our life simpler but in fact it may be that high energy completion actually requires a level of symmetry which from a low energy perspective we didn't think we needed to but the high energy world is becoming more and more symmetric so symmetries just emerge as you go to high and higher energy and that's just based not only on stability if it were
but an even more fundamental principle like again unitarity. So that's one of the things I'm quite excited to look into into it and what type of symmetries are actually emerging is an interesting question in itself. Are there any experiments that you're looking forward to? So I love the daisy experiment to be pushed further but I mean the next decade is just going to be incredible in terms of observations from
I'm
all of those things it's really gonna enable us to not only see the universe to the different structure but also get a whole spectrum of gravitational waves ideally going all the way up to nanohertz all the way up to a hundred hertz and connecting between these different frequencies of gravitational waves is gonna give us such a handle on gravity to me that's so exciting it's no it's really it's incredible the wealth of data we're gonna have
I've received several messages, emails and comments from professors saying that they recommend theories of everything to their students and that's fantastic. If you're a professor or a lecturer and there's a particular standout episode that your students can benefit from, please do share and as always feel free to contact me.
Hey Kurt, you've spoken to so many people in the fields of theoretical physics, philosophy, and consciousness. What are your thoughts?
While I remain impartial in interviews, this substack is a way to peer into my present deliberations on these topics. Also, thank you to our partner, The Economist.
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"text": " Tell me about a time where there was some established physics theorem and you found a way around it. What was that theorem or folklore or concept and how? How did you find a way to circumvent it? So one thing I've done is related to a no-go theorem related to massive gravity. So maybe I need to unfold this a little bit, what massive gravity is and what the no-go theorem is."
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"text": " We understand gravity thanks to Einstein's theory of general relativity. And there's a little bit of this tell that tells us that, oh, we don't know how to reconcile gravity with quantum field theory. Actually, that's not quite true in Einstein's theory of general relativity. We do understand how we can describe gravity as a particle."
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"text": " for gravitational waves which would carry negative energy and so maybe we can go to a notion of energy in a bit but for now we can just think of having some modes for polarizations of gravitational waves which would have negative energy and so in principle as soon as you think of the graviton being massive and interacting with the rest of the world you could have some processes"
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"text": " getting energy and taking this energy with an infinite negative pool of energy of the massive mode of the graviton and that would lead to a complete instability in fact an instantaneous instability of even the fabric of space-time as we know it. So that's the course of the matter for why we can't in principle or there was no-go theorems as to why we couldn't give a mass to the graviton so there was no-go on massive gravity."
},
{
"end_time": 552.295,
"index": 23,
"start_time": 524.309,
"text": " This came up in various different formulations throughout the decades, particularly in the 70s, again in the 80s and in 2000. In fact, when I was doing my PhD, when I was doing my postdocs, I had just bought into all of these theorems. They were written by very famous people, then I'm going to name them, but I was certainly not going to go and contradict them in any way."
},
{
"end_time": 559.462,
"index": 24,
"start_time": 552.295,
"text": " But we realized that we were able to build a model based originally from extra dimension."
},
{
"end_time": 585.674,
"index": 25,
"start_time": 560.316,
"text": " which in fact was violating these NERGO theorems. So it was based on extra dimensions and so that's why we thought we could get some leverage from that but in fact we could in principle just represent it from a four-dimensional point of view and when we look at it from a four-dimensional point of view we saw that the NERGO theorems should be that I would tell us that something could go wrong"
},
{
"end_time": 600.179,
"index": 26,
"start_time": 585.674,
"text": " wasn't going wrong at the order that was predicted so this really motivated to better understand what were the assumption behind those no go theorems and what were the real implications and we realized that."
},
{
"end_time": 617.278,
"index": 27,
"start_time": 600.674,
"text": " In fact, it was way too quick. The assumptions were good, but the realization of those assumption into no-go theorems were always using some shortcuts, which in fact could be overcome. And so there was many different realizations of those theorems in different languages."
},
{
"end_time": 645.094,
"index": 28,
"start_time": 617.688,
"text": " But we got the motivation to really look into each and every single one of them when we realized that, in fact, there was much more to it. And so then realizing that there was a way to bypass this no-go theorem, we then realized how to, in fact, completely formulate a theory of massive gravity which was free from all of the pathologies that people thought should exist before that."
},
{
"end_time": 664.548,
"index": 29,
"start_time": 647.329,
"text": " So you weren't looking to evade the theorem initially or outwit the people who formulated it. What was it that motivated you then in that direction? What was the spark that let you think, okay, maybe grass, sorry, grass is massive. Maybe gravity is massive."
},
{
"end_time": 693.422,
"index": 30,
"start_time": 665.333,
"text": " So what we wanted to do other time, and in fact I still think it's a good idea, precisely how to realize it is challenging, but what we wanted to do other time is try to understand whether we could tackle the cosmological constant problem related to the late time acceleration of the universe with a better understanding of gravity at large distances. And at the time there was all sorts of work based on extra dimensions"
},
{
"end_time": 716.374,
"index": 31,
"start_time": 693.746,
"text": " Because it was realized from string theory that you could have extra dimensions out there. And in fact, from M theory, one of these extra dimensions could be large in the sense that it could be even millimeter size. So there was all sorts of different ideas in trying to understand what is the representation of gravity from a four-dimensional point of view and whether the leakage"
},
{
"end_time": 744.053,
"index": 32,
"start_time": 716.374,
"text": " of gravity within the extra dimensions could in fact lead to modification of the behavior of gravity on large cosmological distances and this could help us understanding how to tackle the cosmological constant problem. The cosmological constant problem is very much as the interface between quantum particle physics and gravity and it's coming from the fact that we would have expected"
},
{
"end_time": 765.179,
"index": 33,
"start_time": 744.65,
"text": " To have all of the vacuum energy, the quantum vacuum energy of all the particles that we know of to gravitate and to gravitate with an amount that effectively the universe not only should be accelerating, but should be accelerating by many, many orders of magnitude larger as compared to what is being observed."
},
{
"end_time": 790.162,
"index": 34,
"start_time": 765.776,
"text": " And this in fact, this cosmological problem or this quantum vacuum energy problem is also been known since almost a hundred years now since Pauli and even other people before him. At the start of quantum quantum field theory very much so people realize that if you consider the quantum vacuum energy of electrons simply of electrons"
},
{
"end_time": 820.111,
"index": 35,
"start_time": 790.162,
"text": " This should populate space time and lead to an accelerated expansion of the universe, which would mean a space between the earth and the moon would accelerate so fast that we shouldn't be able to see the moon anymore. And this is something that was postulated, that was written down, that was understood as a challenge already since Pauli at the very, very start of the formulation of quantum field theory or even quantum mechanics, in fact. And so faced with this problem,"
},
{
"end_time": 847.415,
"index": 36,
"start_time": 820.384,
"text": " People thought that there was something one could one was missing in how a cosmological constant or how quantum vacuum energy was was gravitating and maybe for a symmetry reason or another reason that evades us as the moment really the universe is not accelerating and so that was the lure actually for almost 80 years until it was realized that"
},
{
"end_time": 874.497,
"index": 37,
"start_time": 847.773,
"text": " The universe is accelerating. The universe is not flat. It is expanding, but this expansion is also accelerating. And this is really the challenge because we would be happier if we would say for a reason or another, I don't know what's happening, but there's no acceleration altogether. So all of this quantum vacuum energy, even though it should lead to an accelerated expansion of the universe, let's just forget about it. And there may be some other phenomenon coming in the game."
},
{
"end_time": 896.067,
"index": 38,
"start_time": 874.497,
"text": " The issues very much when all of a sudden we realize that the expansion of the universe is accelerating but bad really just a ridiculously small amount. So what is it is this is quantum vacuum energy leading to an acceleration of the universe or it's not and then we need to add something else but no formulation is perfect."
},
{
"end_time": 925.452,
"index": 39,
"start_time": 896.63,
"text": " So what we were trying to do at the time is trying to understand whether it is this quantum vacuum energy that leads to an accelerated expansion of the universe but not as much as one would have anticipated according to Einstein's theory of gene relativity because gravity is actually leaking in the extra dimension and so this is something we don't see on short distances in the"
},
{
"end_time": 940.094,
"index": 40,
"start_time": 925.691,
"text": " on solar system scales, on galactic scales, on cluster of galaxy scales, but it's something that we start seeing on very large cosmological distances, on the distances where we really see the accelerated expansion of the universe."
},
{
"end_time": 966.049,
"index": 41,
"start_time": 940.401,
"text": " So that was the idea at the time. Not at all to go back into a theorem led by my great heroes, but much more into trying to tackle these issues. And we thought at the time we knew that it would be challenging to come up with a model which was purely four dimensional because of all those no go theorems. So that's why we were basing ourself on extra dimensions."
},
{
"end_time": 994.599,
"index": 42,
"start_time": 966.305,
"text": " where the effect of the extra dimension may look like non-local from our four-dimensional perspective so may look may be expressed in a slightly different way and yet could lead to effectively an accelerated expansion of the universe. I have a variety of questions about energy and we'll get to what is energy shortly especially what is negative energy but let's talk about dark energy so to be clear dark energy is a placeholder for our ignorance regarding the cosmic acceleration"
},
{
"end_time": 1018.575,
"index": 43,
"start_time": 994.974,
"text": " And then vacuum energy is seen as a natural candidate. But the problem is that it predicts these absurdly high acceleration rates. That's right. So is there another reason other than that the vacuum energy is canceled? So supersymmetry would say that the vacuum energy contributions are canceled. Is there another reason that the vacuum energy shouldn't even factor in to"
},
{
"end_time": 1045.213,
"index": 44,
"start_time": 1018.865,
"text": " I don't usually stop mid-conversation to talk about molecules, but this one's different. I've been taking something called cell being by Verso, and if you're into longevity science like David Sinclair, NAD+, that whole world, then this is exactly that and it's authentic. So why do I care about it?"
},
{
"end_time": 1068.643,
"index": 45,
"start_time": 1045.213,
"text": " Well as i age as we age as you age our levels of something called NAD drop off and precipitously that's not good news and that's because NAD is crucial for repairing DNA damage it's also necessary for improving metabolism and keeping one's energy levels up across the board like your brain your immune system your muscles you name it it needs it."
},
{
"end_time": 1088.268,
"index": 46,
"start_time": 1068.643,
"text": " However i can't just supplement you can't just supplement none of us can with any directly ourselves they won't absorb it and that's why sell being combined and i'm an reservoir troll and t. m. g. these are three molecules the work together to help you boost your own n. a. d. production personally i've been taking it for the past while"
},
{
"end_time": 1102.927,
"index": 47,
"start_time": 1088.268,
"text": " And i've noticed clear focus i've noticed more steady energy and i even started taking it a couple days into the flu and the next day is when i started to feel better now that could be a coincidence but hey i'll take it and in fact i should take my now."
},
{
"end_time": 1132.056,
"index": 48,
"start_time": 1105.06,
"text": " Verso also third-party tests every single batch and publishes the results, so you're not getting any mystery capsules here. If you're curious about aging well or want to feel better or think more clearly, then check it out. Go to Verso, so V-E-R dot S-O slash Toe, T-O-E, and use the code T-O-E to get 15% off your first order. That's V-E-R dot S-O slash T-O-E code Toe."
},
{
"end_time": 1161.544,
"index": 49,
"start_time": 1132.056,
"text": " Thanks to Verso for supporting this episode and supporting my health. And that should have bearing on the cosmological constant. So the answer is we don't know. We don't know for sure. We don't really know. So even, for instance, if we take supersymmetry as an example, it is an amazing symmetry that would cancel the contributions when the symmetry is being satisfied. So it is very possible that the realization"
},
{
"end_time": 1171.34,
"index": 50,
"start_time": 1162.261,
"text": " at high energy is supersymmetric so if we discover new particles at the NHC or next particle collider or anything else,"
},
{
"end_time": 1194.275,
"index": 51,
"start_time": 1171.766,
"text": " We will start seeing some signs of supersymmetry. That is still very much possible and it is still very much possible that supersymmetry is being restored at a given scale. But the world that we experiencing at low energy is clearly not supersymmetric. There's not a clear partner for each, for instance Boson, there's not a clear"
},
{
"end_time": 1220.179,
"index": 52,
"start_time": 1194.275,
"text": " Famine partner so super symmetry the reality it has to be broken below a given scale this is observations this is the reality of the world that we live in so even if they were super symmetry that would cancel all of the high energy contributions the contributions from the particles of the standard model so the contribution from the particles that we know we are made out of electrons the top quarks the Higgs etc."
},
{
"end_time": 1249.599,
"index": 53,
"start_time": 1220.538,
"text": " they should in principle lead to a contribution to the quantum vacuum energy which is not cancelled out by supersymmetry. So there may be another symmetry out there but supersymmetry is doing an amazing job of potentially cancelling out all of the contribution beyond let's say even TeV scale but below that we still need to face the fact that we have a leftover from the standard model which will not cancel by supersymmetry."
},
{
"end_time": 1265.469,
"index": 54,
"start_time": 1250.401,
"text": " It is a little tricky when we say when we say the quantum vacuum energy of for instance loops of electrons lead to contribution to they interact with gravity on a loop lead to quantum"
},
{
"end_time": 1286.323,
"index": 55,
"start_time": 1266.032,
"text": " It is a little bit tricky when we say that loop of the particles of the standard model lead to a contribution to the quantum vacuum energy. In fact, what we're doing there is compute some loops, which technically are infinite. And so we need to do a renormalization procedure. And if we do the most conservative"
},
{
"end_time": 1306.288,
"index": 56,
"start_time": 1286.681,
"text": " I'm regularization if i do friends is what i call dimension regularization so i'm not putting a cutoff at high energy and i'm doing any of this i'm just looking at how the contribution of this bubble diagrams this loops flows with energy i see that for each massive particle."
},
{
"end_time": 1326.903,
"index": 57,
"start_time": 1306.732,
"text": " It leads to contribution which scales like the mass of this particle to the power of four. And this is the most conservative way to do things. So it is still possible that we don't understand everything in this regularization and renormalization procedure. That is very possible."
},
{
"end_time": 1348.49,
"index": 58,
"start_time": 1327.585,
"text": " However, we understand this renormalization procedure extremely well for all sorts of other loops which we then go and compute and compare with scattering processes at the LHC and they give a flow and regularization scales of all sorts of different things which we know, understand extremely, extremely well."
},
{
"end_time": 1371.766,
"index": 59,
"start_time": 1348.49,
"text": " So it is a little bit puzzling to think that we know so well how to compute those things when gravity is not part of the game and all of a sudden now all i do is a sandwich some gravity on external legs i'm not i don't need really to deal with quantum gravity in the sense of looking at an ultimate high energy completion of."
},
{
"end_time": 1396.237,
"index": 60,
"start_time": 1371.766,
"text": " quantum gravity at or beyond the plank scale that's not at all what i'm doing i'm just looking at the quantum effective field description of gravity which we do on a daily basis i do it on the board and we do look for observations of that in the sky we do we think we know very well how to do that and yet as soon as i start"
},
{
"end_time": 1422.637,
"index": 61,
"start_time": 1396.561,
"text": " Putting in some external legs which are gravitons so I want to look at the effect of these loop diagrams of let's say electrons on external legs which are graviton which in effect I'm wanting to see how this loop of electrons loops of virtual electrons for instance lead to an effect to an interaction with space-time that's really what we're doing all of a sudden"
},
{
"end_time": 1448.865,
"index": 62,
"start_time": 1423.814,
"text": " What we get as a result seems to be completely inconsistent with observations. So probably it is true that something is going on there and we don't understand that so well, but it is very puzzling because everything else we understand it so well. Why is it the case that when I think of it in the case of Graviton that stops being so sensible?"
},
{
"end_time": 1477.108,
"index": 63,
"start_time": 1449.258,
"text": " We don't know. The answer is we don't know. You can go into string theory landscape and think of there being a landscape of different possibilities where the leftover cosmological constant, the leftover vacuum energy could take many different values and we just happen to be living in a realization where the leftover is just the right value."
},
{
"end_time": 1505.265,
"index": 64,
"start_time": 1477.363,
"text": " Because if you wasn't that right value, we wouldn't be here to ask ourselves that question. That is always a possibility. But then but then it's a little bit unsatisfying because we don't know how to probe that possibility. We don't know how to probe alternatives to that. We sort of giving up on trying to find a more dynamical, a more fundamental reason as to why the effect of all of the loops is not leading to what we would have expected."
},
{
"end_time": 1531.032,
"index": 65,
"start_time": 1507.278,
"text": " Does philosophy inform your physics research and by philosophy you can count causality and thinking about lawfulness or the foundation of time into your answer? So those questions like causality, like unitarity, like the flow of time, that definitely informs all of our research, all of our results,"
},
{
"end_time": 1548.183,
"index": 66,
"start_time": 1531.271,
"text": " All of the way we think about things in fact causality is really intrinsic to a lot of the question that we asking ourselves and so for instance we are we looking at effective descriptions effective quantum field theory descriptions."
},
{
"end_time": 1578.626,
"index": 67,
"start_time": 1548.643,
"text": " for some phenomenon around us we always want to make sure that they satisfy some basic criteria of basic I would call them basic physics you can call them philosophy if you want to we would like it to be to satisfy some notion of causality this is essential for us and that manifests itself in many different ways we for instance you can think of it the notion of causality at zeroth order you can think of it as saying"
},
{
"end_time": 1602.995,
"index": 68,
"start_time": 1579.343,
"text": " Phenomenology where I'm not able to go backwards in time and kill my grandfather so that I'm not there anymore. That's at the basic level. But in fact when you represent that into a model where you think that Lorentz invariance is a fundamental symmetry then that tells you that you shouldn't be able to have processes that go faster than light."
},
{
"end_time": 1624.94,
"index": 69,
"start_time": 1603.353,
"text": " In fact, it's not really that it's a bit more precise than that, but we can embed those concepts into much more formal, much more rigorous ways to clarify how to move forward. There's no notion of unitarity as well, which in some sense is a very simple concept for us to think about. It's really to say that if"
},
{
"end_time": 1637.551,
"index": 70,
"start_time": 1626.152,
"text": " If I think of the possibilities of a different outcome and so in quantum physics we know that things are not deterministic. I can do an experiment over and over again."
},
{
"end_time": 1661.988,
"index": 71,
"start_time": 1637.773,
"text": " For each time, for each realization, I won't know exactly what the outcome will be, but what I know is what the probability of a given outcome will be. And so we are thinking everything the realization is really very much into probability or amplitude of probabilities of different outcomes. But we want the sum of all of these probabilities to sum up to one."
},
{
"end_time": 1672.978,
"index": 72,
"start_time": 1662.278,
"text": " And we want those probabilities is individual probabilities never to be negative so i never wanted to be a real number and so that seems to be trivial statements."
},
{
"end_time": 1702.039,
"index": 73,
"start_time": 1673.2,
"text": " If i play the lottery i shouldn't have more than 100 chances to win and i shouldn't be able to have a negative chance to win because i can't quite make sense of that this seems like completely trivial statements that guide our everyday life in fact is structural in the way we live our lives if we didn't have this notion then all hell will break loose we'll be able to play the lottery over and over and over again and just take advantage of this so it sort of sets up"
},
{
"end_time": 1730.998,
"index": 74,
"start_time": 1702.432,
"text": " The structure of the reality in which we live in, and in the same way, this notion of unitarity sets up the reality of the physics with which we work, and so the models with which we work. So to put up a counterpoint, last time we touched on ghosts, and there were these good ghosts, which are the fidei of popov ghosts, and then the more problematic one, like desser, and I don't know how to pronounce balware. I would say boulevard deser ghost."
},
{
"end_time": 1753.097,
"index": 75,
"start_time": 1731.101,
"text": " The Klein-Gordon equation initially faced rejection over negative probabilities and I believe Schrodinger came up with it first and just didn't even publish about it because"
},
{
"end_time": 1771.032,
"index": 76,
"start_time": 1753.234,
"text": " Do you see that there's some other point of view where what's seen as a fatal flaw here is no longer?"
},
{
"end_time": 1794.189,
"index": 77,
"start_time": 1771.578,
"text": " For negative probabilities or unitarity or even locality conditions. So as you say, we certainly use ghosts in some formulation, like for the father of ghosts, we use those ghosts almost as a trick. We we when we have when we have some symmetries, for instance, it's easier for us to work with our feminism where we take too much into account."
},
{
"end_time": 1820.282,
"index": 78,
"start_time": 1794.462,
"text": " And then we use those fadif of ghosts or related ghosts to cancel out contribution that we know shouldn't have been there in the first place. And we do that a lot in many different things, but they are under control and you have to think of them as a mathematical trick. You have to think of this as a formulation. We give too much away and then we know how to control what we've given too much away and we know how to remove those things."
},
{
"end_time": 1845.879,
"index": 79,
"start_time": 1820.606,
"text": " So in that sense, it's a negative, it violates unitarity in the sense that it has a negative contribution and negative energy, but of just the right amount to remove the positive contribution that we had added on. And so in that sense, that is completely under control. Now there are other situations like the bullwad as a ghost, where this is not something which has been added to"
},
{
"end_time": 1865.316,
"index": 80,
"start_time": 1846.101,
"text": " Remove another contribution is just something that comes in and it's on and it's on from its own accord and you can see you can see in the case of the ball what is a ghost why starts becoming problematic and it's particularly problematic because you're dealing with modes related to space time."
},
{
"end_time": 1888.029,
"index": 81,
"start_time": 1866.118,
"text": " And so let's just imagine a little bit what you mean by gravitational waves. We have observed gravitational waves and the way we have observed them is them distorting space within our interferometer, distorting the space between two mirrors in our interferometer. And so they make the space between the interferometer evolve in time."
},
{
"end_time": 1909.343,
"index": 82,
"start_time": 1888.592,
"text": " But you can in principle we are dealing with a theory of space time you can in principle sake of having the same thing with time and then if you start having a mode for gravitational waves which allows you to jiggle things in time as well then this is also related to some level of causality violation and so."
},
{
"end_time": 1928.387,
"index": 83,
"start_time": 1909.343,
"text": " This notion of breaking unitarity with some of those ghosts can be linked directly to a violation of causality and as soon as you enable for that possibility to happen then you are opening a whole pandora box of pathologies which are not under control."
},
{
"end_time": 1946.442,
"index": 84,
"start_time": 1928.387,
"text": " Because this is not something that we engineered precisely so as to remove another contribution because we were lazy in some sense in the in the first place it's something that just populate just based on by its own accord is not under control so you may say well it does have."
},
{
"end_time": 1972.363,
"index": 85,
"start_time": 1946.442,
"text": " He's on that does he have its own way of thinking of it you can i mean in some sense from the formalism yes you can you can you can analyze it is a pathology and as a scientist you can analyze it you can try to understand it you can look at the structure and it has some a lot of interesting features in its own right but at the same time you know that this mode it is a pathology you can't have it in"
},
{
"end_time": 1985.776,
"index": 86,
"start_time": 1972.602,
"text": " In your space time as a fully dynamical degree of freedom in its own right that that you can't have and it is a little bit different as compared to saying that you have an instability."
},
{
"end_time": 2015.828,
"index": 87,
"start_time": 1986.34,
"text": " So for instance the Higgs potential is unstable within some range and you may think that this instability may be the sign of a pathology but that is in fact just a time evolution and it's just a transition a transitioning behavior from one point to another and you can think for instance that the whole evolution of the universe is something that signals some level of instability because we are going into a different configuration we are evolving"
},
{
"end_time": 2044.343,
"index": 88,
"start_time": 2015.828,
"text": " in the evolution of the universe those are not they're not pathologies they are just the reality and we may not like the thing is never necessarily pleasant to be in an unstable configuration but we can deal with it and and that may just be the reality the issue with the ghost is that we know that that tells us there's no vacuum there's no ground zero around which we can think about about our theories"
},
{
"end_time": 2074.582,
"index": 89,
"start_time": 2044.599,
"text": " And so we can't even start looking at the model into how to represent anything. As soon as you have this actual negative kinetic energy mode, a genuine degree of freedom that delivers energy when it moves, we know that there's no ground zero in which we can start thinking of our whole quantum field theory framework. So in that sense, we can't even start doing anything."
},
{
"end_time": 2101.357,
"index": 90,
"start_time": 2076.374,
"text": " So speaking of energy, what is energy, especially in general relativity? What is gravitational energy? And what is this criteria or wishlist that you would like a well-defined definition of energy to have, like locality or covariance or what have you? Yeah, okay. So for me, I don't have so much about wishlist for energy because I"
},
{
"end_time": 2113.131,
"index": 91,
"start_time": 2101.749,
"text": " I don't have the need of having this concept as being as fundamental as we may have otherwise have. I think we're very much driven by"
},
{
"end_time": 2141.135,
"index": 92,
"start_time": 2114.155,
"text": " almost a Newtonian perspective of things being static in time and this symmetry in time tells us that there's an associated conserved quantity which we have which we call energy. So it's almost a luxury to have energy as a conserved quantity and as a well defined quantity that we can rely on and we can rely on to predict phenomena and to understand how you can borrow energy from one system"
},
{
"end_time": 2166.527,
"index": 93,
"start_time": 2141.323,
"text": " Give it to another system and that the whole energy within a box, let's say, should be conserved. Now, as you said yourself, when you have gravity in the game, things become much more complicated. There's no local conserved, ordinary conserved notion of energy in the same way that we would think we should have otherwise. And that in our everyday life,"
},
{
"end_time": 2188.66,
"index": 94,
"start_time": 2167.346,
"text": " We follow the rules as if the notion of energy was conserved. This is related to the fact that gravity is in fact a spin to particle so it behaves slightly differently and so the stress energy tensor is no longer conserved, ordinarily conserved. It's covariantly conserved but that means that the conservation"
},
{
"end_time": 2215.452,
"index": 95,
"start_time": 2189.206,
"text": " of the quantities related like energy they're not absolutely conserved there's a borrowing or there's a trade-off between the energy of what we call matter let's say and the energy of space-time. A system can borrow energy from the space-time or just dwell energy into the space-time and that disturbs us a little bit."
},
{
"end_time": 2241.203,
"index": 96,
"start_time": 2216.067,
"text": " And we know this maybe a simple example to think about which helps us a little bit into making the analogy into how we think of energy being conserved in normal system and how different things are with gravity. Let me just imagine that I have two stars. Let me imagine I can start having one star and that star is emitting light. It's emitting electromagnetic waves."
},
{
"end_time": 2269.855,
"index": 97,
"start_time": 2241.544,
"text": " And so that star is losing energy at one point, it will die and that's sad, but that's life. Um, it's losing energy, but this energy has been carried by the electromagnetic waves has been carried by light. And so in principle, if I take that star and then I were to draw a sphere around that star, I can compute the amount of energy lost by that star, but also the flux of energy, uh, carried by light, by electromagnetic waves."
},
{
"end_time": 2296.476,
"index": 98,
"start_time": 2270.145,
"text": " within that sphere around or that box whatever around that star and I have a complete trade-off between the amount of energy being lost by that star and the flux of light going through that surface and so we have this very well understood notion of conservation or trade-off of energy in a normal system. Now if I do the same thing with gravity"
},
{
"end_time": 2311.852,
"index": 99,
"start_time": 2297.073,
"text": " So let me just imagine, instead of having one star, let me just imagine I have two stars. I can do that as well. And so they will lose energy through light. They radiate light, but they also radiate gravitational waves. We actually need two stars rather than one."
},
{
"end_time": 2334.889,
"index": 100,
"start_time": 2312.159,
"text": " For gravitational waves to be radiated and that we know. In fact, there are some systems where they lose more energy through gravitational waves than they lose energy through radiation of light. So it's not something which is simply innocent. It's actually it can be quite substantial. So for some system, they lose most of their energy through the radiation of gravitational waves."
},
{
"end_time": 2363.131,
"index": 101,
"start_time": 2335.35,
"text": " and you could in principle ask yourself if you could do the same thing let me just draw a sphere that encompass those two stars and let me think of the energy lost by that system of two stars so they're losing the they're losing the chemical energy they're losing some energy inside each of the stars but they're also losing some of their potential energy because they're getting closer and closer together"
},
{
"end_time": 2384.889,
"index": 102,
"start_time": 2363.49,
"text": " I can think I'm a little bit further away from these two systems of stars. I drew a sphere around them and I compute the flux of gravitational waves through that surface and the flux of light through that surface and that doesn't work in the same way. There's no such a notion of local at a given finite distance away from these two stars."
},
{
"end_time": 2414.377,
"index": 103,
"start_time": 2384.889,
"text": " Of energy which is concerned for that system i would really need to go to infinity if it's asymptotically flat at infinity if i recover flat space time at infinity and then i'll be able to finally define a whole notion of energy which will be conserved but only because i'm in flat space time asymptotically and only in that case i'm able to define a local standard notion of energy."
},
{
"end_time": 2419.189,
"index": 104,
"start_time": 2414.787,
"text": " And that's because the notion of energy is very much a consequence of"
},
{
"end_time": 2445.094,
"index": 105,
"start_time": 2419.94,
"text": " some symmetries of the space time. You need to have a time like killing vector to have a conserved charge, a conserved quantity related to that. All of this is actually I should say, I want to say because it's important, all of these concepts is actually thanks to Amy Noether that understood very much that she pioneered all of this fundamental connection between"
},
{
"end_time": 2467.705,
"index": 106,
"start_time": 2445.094,
"text": " Symmetry and conserved charges and nowadays we understand the whole world we understand it so this notion of symmetry is that the building blocks of everything that we how we represent reality around us three classification of different symmetries and those different symmetries come in with as a consequence with conserved charges but only one we have."
},
{
"end_time": 2494.77,
"index": 107,
"start_time": 2468.114,
"text": " what I'll call time translation invariance or that flat space time has, or something related to a time like Keeling vector. So this is the same thing, a symmetry in time, if you want, then I can have the luxury as a present to have a conserved charge associated with it, which I can call the energy. But in a normal gravitational setup where I have space time,"
},
{
"end_time": 2522.329,
"index": 108,
"start_time": 2495.179,
"text": " This is not the case and there's not going to be any local gauge environment quantity which is an observable and that directly tells me that there's no such a thing as a local ordinary conserved notion of energy even if integrated within a given volume that doesn't happen. So for those two stars you really need to go to infinity to define this notion of conserved energy."
},
{
"end_time": 2540.52,
"index": 109,
"start_time": 2523.046,
"text": " And that's if you're lucky and you are asymptotically flat in the world in which we live in now. Right. How reasonable is that assumption? No, that's not. You can make it mathematically. You can make it theoretically. But the world we live in is not like that. We know we are living."
},
{
"end_time": 2562.381,
"index": 110,
"start_time": 2540.623,
"text": " in an accelerating expanding universe something which i'll call is close to doceta not minkowski it's a different topology it's a different asymptotics and so that we know there's not going to be such a thing as a conserved notion of energy you know for instance that you can in in an accelerated expanding universe"
},
{
"end_time": 2592.637,
"index": 111,
"start_time": 2562.654,
"text": " just in an expanding universe in fact you can create out of the vacuum some physical particles and so as time goes on you have some particles being created constantly being created and you can think of this as being created with a finite amount of energy which is borrowed from this bath which is space-time you can just borrow energy from from space-time which if it's not flat and if it's curved as it would be the case in a"
},
{
"end_time": 2622.278,
"index": 112,
"start_time": 2592.961,
"text": " accelerated expanding universe. That bothers us a little bit but it doesn't mean that is not right. It just means that the rules of the games are in fact quite different in the presence of gravity and this ability in fact to actually take in energy from the vacuum. So we can still make traction in defining some quantities which are conserved ordinarily and then as you mentioned in your"
},
{
"end_time": 2641.715,
"index": 113,
"start_time": 2622.722,
"text": " Actually, I have a popular article that I wrote on Substack called What is Energy Actually, which goes into technical detail into what general relativity conceptualizes as energy and why it's ill-defined. A link to that article will be in the description. I'm also recording a video version of that, so that link will be in the description as well."
},
{
"end_time": 2666.954,
"index": 114,
"start_time": 2644.326,
"text": " Taking some pseudo stress energy tensor to compensate that but but that you really need to think of it as. Borrowing borrowing what is happening from from from space time itself and that that has slightly different rules of the games it doesn't make them wrong and it's but it's only in some very special limits that was standard notion of energy as you want."
},
{
"end_time": 2696.886,
"index": 115,
"start_time": 2667.381,
"text": " to satisfy with being local, being gauge environment, being conserved, ordinary conserved will be present but typically is not. Perhaps this is one of the reasons why for instance holography ADS-CFT has become so so popular because you are living in ADS, let's say the gravitational theory is in ADS which is a curved"
},
{
"end_time": 2724.599,
"index": 116,
"start_time": 2696.886,
"text": " but the boundary it has a boundary as you can think of its gravity in a box which has a boundary and on the boundary of ads where actually the cft is living on the boundary of ads you have a time like killing vectors so you have a symmetry associated with that along the time direction and so then you have the luxury of having uh conserved quantity which is energy related to this"
},
{
"end_time": 2748.234,
"index": 117,
"start_time": 2724.599,
"text": " I'm sorry in the concept of holography in a DSC FT correspondence you have the CFT been described in flat space and then themselves they have a notion of energy and just like you have on the boundary of ADS you have a time like killing vector and a notion of conserved energy as you would want it in there now if you wanted to do the same thing for not ADS."
},
{
"end_time": 2763.234,
"index": 118,
"start_time": 2748.592,
"text": " cft correspondence not in the same holographic description if you wanted to do it in the setter cft correspondence because we leave in something which is close to the setter within the expanded"
},
{
"end_time": 2789.497,
"index": 119,
"start_time": 2763.541,
"text": " Accelerating universe then in fact the the boundary of the setter wouldn't would would would not be a boundary which has a time like killing vector so you wouldn't have an authority on that boundary and you wouldn't have a conservation of energy on that boundary so this is one of the reasons why it's actually quite the reality of the world we live in the fact again the fact that the universe"
},
{
"end_time": 2814.599,
"index": 120,
"start_time": 2789.906,
"text": " Firstly, you're an exceptional explainer. You're great at being a public science communicator."
},
{
"end_time": 2832.176,
"index": 121,
"start_time": 2815.316,
"text": " And I want to know how did you develop that skill and has that translated to new physics for you? When I say has that translated to new physics, what I mean is have the insights that you've gleaned from simplifying for a general audience led to new research?"
},
{
"end_time": 2860.247,
"index": 122,
"start_time": 2834.462,
"text": " So I don't know that I can answer the first question other than this if this is something that you like doing the more you do it I think the more the easier it become and you learn a lot from the questions that people ask. I think the key thing is being able to relate to the way people are thinking in the different challenges they may have in trying to address"
},
{
"end_time": 2875.35,
"index": 123,
"start_time": 2860.572,
"text": " i'm some of the concepts i think i think this is probably one of the essential things i don't know if it's easy to explain to others but i think the listening part is the most essential part of i think you know when you understand."
},
{
"end_time": 2904.565,
"index": 124,
"start_time": 2876.084,
"text": " How people think about things and why some concept that you may have taken for granted and you may not have questioned them yourself because you don't think of it like that. You realize how other people think about it, how they address it and what are the stumbling blocks for them. I think it's very enriching for everybody. It has been very enriching for me. Sometimes I was, you're in the bus and you talk with someone, just someone next to you on the bus"
},
{
"end_time": 2920.026,
"index": 125,
"start_time": 2904.923,
"text": " first of all being able to see that the things that we are studying sometimes we go so deep in the research and it becomes so technical that you forget where everything comes in and so being able just to explain those concepts"
},
{
"end_time": 2938.456,
"index": 126,
"start_time": 2920.486,
"text": " To someone else who's not at all fluent in that language and go back to what actually was the original passion is really great and seeing that this is something they can connect with because a lot of the questions we asking ourselves people connect without they want to know they want to know what is the origin of space time."
},
{
"end_time": 2966.237,
"index": 127,
"start_time": 2938.797,
"text": " What is a black hole? What is space time? What is gravity? Why are we here? What is going to happen to us? All of those questions that we all have them and we're all excited about it. Everybody I think is excited about looking at the sky and trying to understand the world that surrounds us. But then in trying to connect with those people and seeing what that question means for them and how they would go along addressing some of the questions"
},
{
"end_time": 2994.974,
"index": 128,
"start_time": 2966.647,
"text": " that we all ask ourselves. I think it's very enriching for everybody. So I think this is very much something you can build on. Of course, it's not that the perspective necessarily helps me understanding whether it's a factor of two or pi in my equation, but putting things together in the bigger picture and understanding how things are connected with one another is very enriching. And I think this is really where it comes in."
},
{
"end_time": 3025.333,
"index": 129,
"start_time": 2995.674,
"text": " And so to answer your question, I think yes, it does help a lot in making progress in research. I often describe it a little bit like a chess player where you see this. I don't play chess. My daughter plays chess, but you can see these people playing chess and they don't need the pieces anymore. They don't think about one step at a time. They think about the whole game as a whole. And so being able to embrace enough"
},
{
"end_time": 3040.35,
"index": 130,
"start_time": 3025.333,
"text": " Experience in understanding what is the done long term dynamics of a game knowing how knowing how i started and what are the different possibilities of outcome. I can think of this a little bit in physics as well where."
},
{
"end_time": 3064.633,
"index": 131,
"start_time": 3041.715,
"text": " The math and the logic and all of this formulation they are the basis but if you're able to gain enough intuition you can extrapolate yourself from that and use much more your creativity to understand where things are going without needing to go sit down and do every single step along the way. You'll do that eventually but"
},
{
"end_time": 3094.428,
"index": 132,
"start_time": 3065.094,
"text": " To get the bigger picture you start with having embraced all of this intuition which is coming from all sorts of different people you spoke with in all sorts of different backgrounds and then from that you understand where things are going what does it mean what does it mean if i have two electrons capturing and i have an interaction with a graviton there but also when i push that to higher energy and i include a contribution from other things you have a bigger picture of what will happen and from that what it means"
},
{
"end_time": 3123.166,
"index": 133,
"start_time": 3094.428,
"text": " I think you want to understand what he means and how different things are connected with one another. And so I do think it does help and it does help to gain some intuition and just put aside a little bit all of the formulation if you can and use your creativity to free yourself a little bit and that's how you make progress. You need a bit of both of course you need to have built in from all of this"
},
{
"end_time": 3149.684,
"index": 134,
"start_time": 3123.677,
"text": " I should also state that you have a book called The Beauty of Falling which will be on screen and the link will be in the description."
},
{
"end_time": 3170.776,
"index": 135,
"start_time": 3150.247,
"text": " So while we're on the subject of dark energy, there are the DESI results that hint that dark energy may be dynamical. What does that mean? And what do you make of it? And does it have any bearing on massive gravity? So it's really exciting. Any departure from a cosmological constant would be extremely exciting."
},
{
"end_time": 3192.534,
"index": 136,
"start_time": 3171.476,
"text": " It precisely what he means i would say is a little too early to just to tell i think that there's a lot of signals which are sometimes below three sigma which come and go and so before it's actually very much there and has sufficient significance it's going to be hard to tell whether"
},
{
"end_time": 3211.732,
"index": 137,
"start_time": 3192.824,
"text": " Is going to survive or not but it's true that is going into more and more into this direction so first of all having some dynamical dark energy would be extremely exciting for many different reasons just the fact that is not the vanilla model that one would have expected."
},
{
"end_time": 3229.428,
"index": 138,
"start_time": 3211.732,
"text": " Is telling you that there's some signs from new physics and that is very much what we need we need traction into something new that tells us where to go where to look for more information on what is leading to the expansion of the universe anything which is done i make all is really."
},
{
"end_time": 3246.084,
"index": 139,
"start_time": 3230.111,
"text": " fascinating because it tells us it may uncover the reasoning as to why we have an accelerated expansion of the universe with precisely that amount of magnitude and not a little bit more or not a little bit less if it is dynamical."
},
{
"end_time": 3274.616,
"index": 140,
"start_time": 3246.084,
"text": " Then you can understand that much more dynamically. Having dynamical dark energy would tell you that there's actually other degrees of freedom out there and so there may even be a particle, a field, related to that. That would be really fascinating because it tells us that there's something else to discover there. So having dynamical dark energy to me would be fascinating because it tells you that it's not just a cosmological constant which is kind of boring and we're stuck with that problem as to why it has"
},
{
"end_time": 3300.009,
"index": 141,
"start_time": 3275.196,
"text": " That particular value having dynamical dark energy could tell us that it didn't always have this value. It's something that evolves in time. And so it gives us really different new clues to the to the problem. One thing, though, is that we call it dynamical dark energy. Really what it is is an equation of state parameter, which is not constant in time. This is based on the observations."
},
{
"end_time": 3329.07,
"index": 142,
"start_time": 3300.469,
"text": " But it could be due to many different things. It could either be that the actual source for the accelerator expansion of the universe evolves in time, or it could be that the dictionary between this source, between this dark energy or cosmological constant and its effect on the evolution of the universe is what evolves in time. And that would lead to, for instance, a modification of gravity."
},
{
"end_time": 3356.681,
"index": 143,
"start_time": 3329.07,
"text": " If it's true that there is dynamical dark energy, what it tells us is that there's something new out there precisely where it is. If it's in the source, if it's in the gravitational side, if it's in between that, that will have to be uncovered. What do you mean by the source? So the source would be dark energy itself being not just a cosmological constant, but being something that evolves in time. So that's possibly the simplest possible."
},
{
"end_time": 3385.418,
"index": 144,
"start_time": 3357.227,
"text": " this could be the simplest possibility although you need to understand what this field is and why it evolves in time or what we know is that this is what we observe and if we observe something that appears to be evolving in time it could still be the case that we have a cosmological constant but the effect of this cosmological constant on the evolution of the universe is what evolves in time and so it's in the translation between what"
},
{
"end_time": 3414.019,
"index": 145,
"start_time": 3385.913,
"text": " is present in its effect on the evolution of the universe that's where the time dependence comes in and if that were the case then that would hint towards a model of modified gravity where as time goes on or when the scales involves change then the effect of a particular source for instance a cosmological constant is different and so leads to a slightly different rate of acceleration of the universe."
},
{
"end_time": 3438.933,
"index": 146,
"start_time": 3414.138,
"text": " And that would really be so incredibly fascinating. One thing which is very interesting, it's a little early still, but one thing which is very interesting is that at the moment observations seem to be suggest that it's going towards even smaller than minus one equation of state parameter. And that is quite puzzling because normal matter, normal energy,"
},
{
"end_time": 3456.834,
"index": 147,
"start_time": 3439.616,
"text": " doesn't even need to be matter normal energy as we as we know it even quantum vacuum energy typically is behaving with the opposite behavior so with an equation of state parameter which is slightly larger than minus one."
},
{
"end_time": 3480.862,
"index": 148,
"start_time": 3457.056,
"text": " Having some an equation of state parameter w as it's called being smaller than minus one would mean that the evolution of the acceleration of the expansion of the universe would mean that the accelerated expansion of the universe would even go faster and faster. So the Hubble rate would go even faster and faster in time and so that could lead to a big rip."
},
{
"end_time": 3501.852,
"index": 149,
"start_time": 3480.862,
"text": " universe is not only accelerating but this acceleration is going faster and faster to the point where even if you consider the space between in cosmic voice of space between two two clusters of galaxies will be ripped apart. So we don't know it's too early to tell but definitely"
},
{
"end_time": 3520.077,
"index": 150,
"start_time": 3502.5,
"text": " How do i make a dark energy goes would have incredible consequences for the future of a universe what is the destiny what is the fate of a universe depends on the precise behavior of dark energy and that so it's amazing i think to us being able"
},
{
"end_time": 3545.452,
"index": 151,
"start_time": 3520.418,
"text": " to look in the sky and see those results from daisy and then from that determine what is the fate not of us on earth but the fate of the very structure of space time in the universe is incredible really um we don't know for sure right now but but either way is going to be fascinating i'll put a link on screen to the new desi results there's an article from the economist"
},
{
"end_time": 3563.217,
"index": 152,
"start_time": 3545.811,
"text": " I know you said that your approach is agnostic to whatever the final quantum gravity theory may be. However, one of the initial motivating reasons to go into string theory was that as a side effect it produced a massless spin-to-field."
},
{
"end_time": 3591.408,
"index": 153,
"start_time": 3563.66,
"text": " So it didn't produce a massive one. I don't know if the fervor would have initially been as intense had it produced a massive one. So how do you make sense of the disparity between the string approaches to quantum gravity, which predominantly have massless spin two field and then, and then yours. And if massiveness is up for grabs, then is spin two-ness up for grabs? Like maybe grab a tongue. Like what is up for grabs? Just a moment. Don't go anywhere. Hey, I see you inching away."
},
{
"end_time": 3615.145,
"index": 154,
"start_time": 3591.92,
"text": " Don't be like the economy. Instead, read The Economist. I thought all The Economist was was something that CEOs read to stay up to date on world trends. And that's true, but that's not only true. What I found more than useful for myself, personally, is their coverage of math, physics, philosophy, and AI, especially how something is perceived by other countries and how it may impact markets."
},
{
"end_time": 3639.172,
"index": 155,
"start_time": 3615.145,
"text": " For instance the economist had an interview with some of the people behind deep seek the week deep seek was launched no one else had that another example is the economist has this fantastic article on the recent dark energy data which surpasses even scientific americans coverage in my opinion they also have the charts of everything like the chart version of this channel it's something which is a pleasure to scroll through and learn from."
},
{
"end_time": 3656.988,
"index": 156,
"start_time": 3639.172,
"text": " Links to all of these will be in the description of course. Now the economist commitment to rigorous journalism means that you get a clear picture of the world's most significant developments. I am personally interested in the more scientific ones like this one on extending life via mitochondrial transplants which creates actually a new field of medicine."
},
{
"end_time": 3679.104,
"index": 157,
"start_time": 3656.988,
"text": " Something that would make Michael Levin proud. The Economist also covers culture, finance and economics, business, international affairs, Britain, Europe, the Middle East, Africa, China, Asia, the Americas, and of course the USA. Whether it's the latest in scientific innovation or the shifting landscape of global politics, The Economist provides comprehensive coverage"
},
{
"end_time": 3706.015,
"index": 158,
"start_time": 3679.104,
"text": " and it goes far beyond just headlines. Look, if you're passionate about expanding your knowledge and gaining a new understanding, a deeper one of the forces that shape our world, then I highly recommend subscribing to The Economist. I subscribe to them and it's an investment into my, into your intellectual growth. It's one that you won't regret. As a listener of this podcast, you'll get a special 20% off discount. Now you can enjoy The Economist and all it has to offer."
},
{
"end_time": 3727.312,
"index": 159,
"start_time": 3706.271,
"text": " Thanks for tuning in and now let's get back to the exploration of the mysteries of our universe."
},
{
"end_time": 3752.722,
"index": 160,
"start_time": 3727.79,
"text": " Yeah good good good amazing question let me just start by telling you that in fact the first model of string theory bosonic string theory actually came in with a massive spin-2 field. It was unstable and that was in a supersymmetric version and there was all sorts of different problems but in fact the first model of string theory came up with a massive spin-2 particle."
},
{
"end_time": 3775.213,
"index": 161,
"start_time": 3752.722,
"text": " That doesn't mean that i do believe that a massive spin to grab it on a woodcut would come from strength area i don't i don't i don't think so the moment indication seem to suggest quite the quite the opposite but this is just to say in fact we. We have many different realizations and we never know for sure what is gonna be the final outcome."
},
{
"end_time": 3796.186,
"index": 162,
"start_time": 3775.606,
"text": " Now we have learned a lot from understanding what is possible to come from string theory in fact and what are potential high energy completion of massive gravitons. So I think unlike the approach of remaining quite agnostic in precisely what the high energy completion is,"
},
{
"end_time": 3823.763,
"index": 163,
"start_time": 3796.493,
"text": " so long as it satisfies some basic rules that we discussed about earlier like causality, like unitarity and it doesn't need to be string theory per se but we want however physics manifests itself at very high energy we want it to be so that it satisfies these very simple rules without which I don't think we can even make sense of reality anymore and we don't even need to have a notion of"
},
{
"end_time": 3854.002,
"index": 164,
"start_time": 3824.155,
"text": " I want causality to be satisfied. These are very much the ground rules for what we want to base ourselves on."
},
{
"end_time": 3883.49,
"index": 165,
"start_time": 3854.326,
"text": " And then it can be string theory, or then it can be something quite different. It doesn't matter. From that, you can actually make contact with how physics manifests itself at low energy. And we know that there are some models that I can come up with NASA models that I can write down. And that seems quite consistent at low energy. And I can even convince myself that they could be good representations for what happens in the world that"
},
{
"end_time": 3903.029,
"index": 166,
"start_time": 3883.729,
"text": " That i observe in the experiments that we make and they seem to be self-consistent within the remit in which we want to probe them and yet those models in fact we know they will never be imbeddable they will never have a representation of high energy or they will never come from a high energy"
},
{
"end_time": 3932.654,
"index": 167,
"start_time": 3903.029,
"text": " Representation of physics, which is consistent, which is unitary and which is causal, for instance. And so this good outcomes, because then we can carve out a whole region of models. We have carved out all sorts of different ways to represent the world, which otherwise would have seemed consistent, but we know it's not consistent with having high energy completion, which is unitary or causal or those kind of kind of base rules. Now for massive gravity."
},
{
"end_time": 3956.408,
"index": 168,
"start_time": 3933.78,
"text": " At zero order it is already challenging because of all the modes that come in to be embeddable in a standard high energy completion. If in addition I want the high energy completion to be weakly coupled in the sense that I have a standard perturbative approach all the way up to high energy then we know nowadays that this will not happen."
},
{
"end_time": 3975.35,
"index": 169,
"start_time": 3956.954,
"text": " What is a disaster for a massive gravity some of my colleagues would say that's a disaster for string theory but in the reality is that even in string theory is not the case that it necessarily needs to be weekly coupled we are we have to make a distinction between what is."
},
{
"end_time": 3994.241,
"index": 170,
"start_time": 3975.742,
"text": " easier to keep traction on what is easier to calculate where we can actually make more predictions and make more progress and the realm of all sorts of other possibilities and this is what the distinction is a lot of the time we go much further in directions which are"
},
{
"end_time": 4024.155,
"index": 171,
"start_time": 3994.701,
"text": " easier to calculate, that's the truth of the matter. When things are weakly coupled, when things are more perturbative, it's much easier to make traction in some directions and in those directions we know that we're not going to be able to make contact with massive gravity. The graviton will have to be massless and that's the end of the story. So that is definitely true. And so in all of the string theory realizations that we have at the moment, we can't"
},
{
"end_time": 4041.92,
"index": 172,
"start_time": 4024.36,
"text": " Make space for a massive gravity will have to be a mass less gravity has to be a master's gravity. So they can be massive spin to fields and in fact we do believe in string theory that we believe there will be massive spin to fill but there's never such a case where you have."
},
{
"end_time": 4072.073,
"index": 173,
"start_time": 4042.329,
"text": " What we call a gap, a separation of scales between a small remit where you have massive spin to fields for instance and a large gap and then nothing else so that we can treat those massive spin to fields as being a low energy effective description for the world in which we live in. It's always a continuum of states in between. So that is the nature of it. Does it mean that massive gravity is ruled out?"
},
{
"end_time": 4100.708,
"index": 174,
"start_time": 4072.466,
"text": " Possibly, I don't know. It is in tension with the standard realization of string theory. That is definitely true. I would say, though, that better understanding how you can have a realization which builds on this strong coupling, which is very challenging to keep track of and very challenging to get predictable, observable from is actually interesting in its own right."
},
{
"end_time": 4120.572,
"index": 175,
"start_time": 4100.964,
"text": " I don't know whether this is going to be ultimately realized but I still think that this is an interesting direction to study and it is possible that ultimately even for our standard completion of the world in which we live in, we're going to need to rely on a strongly coupled high energy completion that may just be the reality."
},
{
"end_time": 4141.903,
"index": 176,
"start_time": 4121.152,
"text": " and in that if that's the case then it would be much easier to understand how to make sense of it in sort of a toy model as it is the case in massive gravity as opposed to a fully fledged theory of quantum gravity. That is for the mass of the of the graviton. For the spin"
},
{
"end_time": 4155.657,
"index": 177,
"start_time": 4142.671,
"text": " So long as you follow a standard approach where you think of the spin first of all that's also a consequence of a symmetry which is Lorentz invariance so everything that"
},
{
"end_time": 4182.039,
"index": 178,
"start_time": 4156.22,
"text": " A lot of the things I'm thinking about that people would be thinking about in string theory and in a lot of high energy completion are still within the remit that Lorentz environments is a fundamental symmetry. So the world in which we live in right now is not Lorentz environment, but that's a continuous breaking. And if I were to zoom into a very small region of space time, you'd think that you recover this Lorentz environments."
},
{
"end_time": 4201.357,
"index": 179,
"start_time": 4182.466,
"text": " And so if you have Lorentz invariance you have all sorts of related quantities associated with it and one of them like the notion of mass and another one is a notion of spin which is discretized and you can have a spin zero like a scalar field and in fact there are"
},
{
"end_time": 4224.582,
"index": 180,
"start_time": 4202.039,
"text": " Before general activity there were models for gravity which were based just on a scalar field spin zero gravity. Now we know this is completely incompatible with observation you can't have gravity being just a spin zero particle you would you wouldn't get gravitational waves but you wouldn't even get the right behavior in the solar system so we can't have that."
},
{
"end_time": 4253.712,
"index": 181,
"start_time": 4225.06,
"text": " spin one particle that corresponds in fact to the photon. The photon is a spin one particle. It's massless. You can have massive spin one particles like the W and the Z bosons. We also know that the graviton cannot be a spin one particle. It has to be at least a spin two particle. So really the question is could it be the case that the graviton is not a spin two particle but it's a higher spin particle"
},
{
"end_time": 4267.858,
"index": 182,
"start_time": 4254.036,
"text": " the spin two subspace of a higher spin particle"
},
{
"end_time": 4296.015,
"index": 183,
"start_time": 4268.268,
"text": " In fact it's quite challenging we know just to have a higher spin particle interacting just by itself without having an infinite tower of other higher spin particles being present as well that that we know and in fact string theory is just that it is a spin two and a whole higher spin tower of other particles that that come in along the way that's what that's where string theory is. So in that sense"
},
{
"end_time": 4318.677,
"index": 184,
"start_time": 4296.596,
"text": " Part of string theory is having the spin two as one of the states but a whole tower of higher spin so we in fact embrace this spinness for grab in many of the models of quantum gravity. We know that we can't just stop at one given spin. The thing with spin two"
},
{
"end_time": 4348.268,
"index": 185,
"start_time": 4319.019,
"text": " and higher spin is that as soon as you switch on, as soon as you have a spin to particle, and I'm not talking about a mass here, just in gravity itself, as soon as you have a spin to particle, we know that its behavior as you go to high and high energy, it grows too fast with energy to be consistent at high energy. And so you actually need to have an infinite tower of higher spin states"
},
{
"end_time": 4366.459,
"index": 186,
"start_time": 4348.524,
"text": " Where when you resume everything together that's what's taming down the high energy behavior of him talking about amplitudes of probabilities and things like that but we know. Already in if you take to my activity you have the."
},
{
"end_time": 4381.22,
"index": 187,
"start_time": 4366.732,
"text": " This is the only way to have"
},
{
"end_time": 4411.22,
"index": 188,
"start_time": 4381.681,
"text": " Are you working on a theory that gives mass"
},
{
"end_time": 4439.138,
"index": 189,
"start_time": 4412.5,
"text": " I am actually working on a theory. I can tell you one question I have. It's related. Well, it's lots of questions that I have every day. There are these, let's say, swan plant conjectures or landscape conjectures. One of them is called the weak gravity conjecture."
},
{
"end_time": 4469.087,
"index": 190,
"start_time": 4440.009,
"text": " We would think for many different reasons which are very well founded that in fact gravity should be the weakest force there is and we can think of this around a black hole, we can think of a black hole having a mass but also having a charge with respect to not necessarily electromagnetism but it could be an electric charge but also another kind of charge"
},
{
"end_time": 4494.428,
"index": 191,
"start_time": 4469.65,
"text": " We want to be able for the black hole to evaporate its charge faster than it evaporates its mass because as it evaporates we don't want it to become too charged and become a critical black hole which would lead to a naked singularity. So this is a very very simplified way to explain the weak gravity conjecture in the sense that we would like"
},
{
"end_time": 4506.63,
"index": 192,
"start_time": 4494.718,
"text": " to being able to evaporate into charge more rapidly than evaporate into the mass if you want or we would like the gravity to ultimately be the weakest force around."
},
{
"end_time": 4528.524,
"index": 193,
"start_time": 4507.125,
"text": " So a lot of my work is trying to understand how to think of this weak gravity conjecture and whether we know that from the high energy completion of quantum gravity, whatever it is, the ultimate completion of everything in fact, we can derive this weak gravity conjecture or slightly modified versions of this weak gravity conjecture."
},
{
"end_time": 4556.408,
"index": 194,
"start_time": 4529.565,
"text": " But something else I want to work about related to your question is the long gravity conjecture. So I told you that in I don't know how much I want to go into that. Don't start working. Is it because it's too new? It's too new. Yeah. Now, let me just say, one question I have is if if we if we know that one question I have is,"
},
{
"end_time": 4576.442,
"index": 195,
"start_time": 4556.852,
"text": " If you were the case of gravity on could have a mass and the photon could have a mass in principle. Now I know that I can't embed that in a weekly coupled high energy completion. But let me allow for myself to have a strongly couple high energy completion where some of the bounds that have been derived are not quite as"
},
{
"end_time": 4604.735,
"index": 196,
"start_time": 4576.766,
"text": " So let me enable this possibility and think about whether it could be the case that the graviton could have a mass, in fact the photon could have a mass, in fact every particles have a mass, it may be just very very small. And the bound we have on the photon mass, observationally, that's nothing to do with me, but observationally there's reason to believe that from the coherence of magnetic fields in galaxies"
},
{
"end_time": 4630.469,
"index": 197,
"start_time": 4605.555,
"text": " The bound on the photon mass is of the order of 10 to the minus 20 electron volt. I should say in fact there's some very nice papers by some colleagues of mine, Giyad Vali and Lasha, who've gone through this analysis again and I think they have some very nice results in showing that there's a little bit more leeway into that. Anyways, let me accept that"
},
{
"end_time": 4660.162,
"index": 198,
"start_time": 4630.845,
"text": " In principle the photon could have a mass and if that were the case the bond is not so stringent. In fact the bond is weaker as compared to the bond we have on the graviton mass just from observations. Now I'd like to understand whether from being able to embed these theories in a consistent high energy completion not necessarily weakly couple them but it could be strongly coupled even whether"
},
{
"end_time": 4689.77,
"index": 199,
"start_time": 4660.964,
"text": " It is the case whether it would be possible for the photon to be lighter than the graviton or not. And I think that's an interesting question and it's alright because if we can come up with a way to understand as to why the graviton should always be lighter than the photon, it can be massless but if you had a mass it has to be lighter than the photon and in fact lighter than any of the other particles that exist,"
},
{
"end_time": 4714.94,
"index": 200,
"start_time": 4690.128,
"text": " It would tell you that at long distances, gravity is always the force that survives. So it would be a long gravity phenomenon in some sense. All the other forces in nature will have to be switching off faster than gravity. So that's just one idea I've been trying to think about for breakfast, but there's lots of things that come up every day."
},
{
"end_time": 4738.712,
"index": 201,
"start_time": 4715.674,
"text": " So our audience largely comprises researchers in math, physics and philosophy, but there's also a substantial part, a portion that is lay is not educated in physics at the university level. So I just want to distinguish something here. You said gravity could be lighter than the photon. Someone may think, well, the photon is light. The photon is light as in when you're saying it's lighter, you mean it has less mass."
},
{
"end_time": 4767.466,
"index": 202,
"start_time": 4738.712,
"text": " I don't know if people know who are not physicists how difficult it was what you did in 2010 and how radical this approach is."
},
{
"end_time": 4796.92,
"index": 203,
"start_time": 4767.466,
"text": " Because if I recall correctly from our first conversation, you said diffusomorphism invariance in GR may be approximate, maybe something that emerges. Am I recalling correctly? Yeah, so this is something that I think is quite interesting in that if you take a textbook on general relativity, on Einstein's theory of gravity, or if you teach it or even historically, it's always"
},
{
"end_time": 4824.991,
"index": 204,
"start_time": 4797.483,
"text": " seems to be the case that you have these pillars there you have the equivalence principle you have this sort of even assumptions and we call them sometimes Einstein principles on which Einstein's theory of general relativity is being built and if we phrase it like that it may almost seem like these are for grab and I can just remove them and I have a completely different theory which maybe would be consistent in its own right and"
},
{
"end_time": 4852.637,
"index": 205,
"start_time": 4825.282,
"text": " It may be more historical or it may be because those are actually conceptually very important frameworks. For instance, the notion of covariance, the notion of the fact that every observer is equivalent and I can change my quantum system but you shouldn't change the laws of physics and that's related to a symmetry which we call coordinate diffimorphism invariance, diff invariance."
},
{
"end_time": 4868.746,
"index": 206,
"start_time": 4853.336,
"text": " Now you may think that this is built in and general relativity emerges from that. And in fact, if you take that perspective, you can ask yourself whether you can get rid of this symmetry."
},
{
"end_time": 4885.265,
"index": 207,
"start_time": 4869.172,
"text": " Maybe it's not necessarily comfortable to do that but you can ask yourself whether you can get rid of that symmetry and then you get up with a much more general theory of gravity which is not based on the symmetry but a lot of other possibilities emerge."
},
{
"end_time": 4906.681,
"index": 208,
"start_time": 4885.691,
"text": " And in fact you can go through this and realize that all other possibility for which they're not they're breaking different variants at least in the kinetic term in the way the dynamics of gravity is being built in if you allow yourself you enable yourself to include some"
},
{
"end_time": 4936.8,
"index": 209,
"start_time": 4907.381,
"text": " potential correction, which would break that symmetry. You see that those potential correction automatically lead to pathologies, which are those goals like pathologies that completely rule out that theory. So I think this is quite interesting because it tells us that we don't need to base ourselves necessarily on these principles. We don't need to base ourselves necessarily on those notion of symmetries to build our theories."
},
{
"end_time": 4950.998,
"index": 210,
"start_time": 4937.142,
"text": " We can start with in principle it will be much more complicated but we can start with something which is much more messy much more complicated and much more flexible and then you realize that the only thing that makes sense."
},
{
"end_time": 4977.176,
"index": 211,
"start_time": 4951.425,
"text": " is what is what is the substructure for which a symmetry just pops out and so it in fact gives you a motivation as to why the symmetry has to be there if the symmetry wasn't there the theory would not be stable and it's not so it's not that we simply stubborn and we can't think things in a different way or we just focus on particular framework where it has a given level of symmetry"
},
{
"end_time": 5003.916,
"index": 212,
"start_time": 4977.176,
"text": " is in fact the symmetry is essential to protect the theory against all sorts of pathologies. And if it wasn't there, the world simply would be completely unstable to the point where there wouldn't be any structure of reality. So the only possibility is for this symmetry to emerge. Now, if diffeomorphism invariance emerges,"
},
{
"end_time": 5034.087,
"index": 213,
"start_time": 5004.241,
"text": " then, and if theomorphism invariance is analogous in Yang-Mills to gauge automorphism invariance, then is gauge invariance approximate? Is there room for that? So I would say the same thing that in Yang-Mills, for instance, you know that the symmetry is there to preserve the stability of the theory. And that's the same thing in electromagnetism as well, where you have some notion of gauge invariance there as well."
},
{
"end_time": 5063.097,
"index": 214,
"start_time": 5034.087,
"text": " You can break that gauge invariance in electromagnetism by adding not a change in the kinetic structure, because you know that this will lead to pathologies. You can break it for other terms, some other what I call irrelevant operators, a mass term. So in principle you can add a mass to the photon that breaks the gauge invariance that you have for electromagnetism. But even if you do break it softly at the level of the mass,"
},
{
"end_time": 5082.381,
"index": 215,
"start_time": 5063.2,
"text": " You can't break it at the level of the structure. Sorry, you can't break it at the level of the kinetics. So even in models that consider the photon to be massive, the dynamics of the photon themselves through the Maxwell structure has to be preserved exactly in the way it is."
},
{
"end_time": 5109.087,
"index": 216,
"start_time": 5082.381,
"text": " And so even if you enable yourself in the same way to start with something which even softly break the gauge invariance in electromagnetism, you'll restore this gauge invariance by stability for the standard kinetics of the photon. So there's a conceptual clash between quantum theories, external and absolute time, and then general relativity's dynamical spacetime."
},
{
"end_time": 5133.268,
"index": 217,
"start_time": 5109.36,
"text": " You mentioned that massive gravity needs to be embedded in QFT. So does constructing a quantum theory of massive gravity give you some clue about time? Like maybe it's due to the inherent scale introduced by the graviton mass. Do you have an answer to the problem of time? I don't have an answer to the problem of time, but it does give you a framework where indeed you"
},
{
"end_time": 5153.2,
"index": 218,
"start_time": 5133.831,
"text": " Because you set up the scene much more clearly or you are forced to set up some parts of the scene from the outset, it's a curse but also it's an ability to work with those things from the beginning. So there's a lot of things that were"
},
{
"end_time": 5181.715,
"index": 219,
"start_time": 5153.78,
"text": " On the face of it, it is much more complicated in massive gravity, but possibly embracing those things and understanding how to make sense of those. So the scale of the mass and indeed the breaking of the time different invariance may enable you to then understand how to make sense of it at the quantum level in a way that would otherwise have appeared much more challenging in a fully fledged theory of quantum gravity."
},
{
"end_time": 5212.705,
"index": 220,
"start_time": 5183.814,
"text": " Einstein had a whole argument, H-O-L-E argument, and that led him to say that diffeomorphism, I believe that may be among some other factors, but that was one of the principal factors that led him to diffeomorphism invariance because he wanted to retain determinism in GR. So does removing diffeomorphism invariance then at the fundamental scale reintroduce indeterminism into GR?"
},
{
"end_time": 5236.749,
"index": 221,
"start_time": 5214.326,
"text": " I think it's hard to tell at this stage. I think we're not really there because I mean perturbatively we would get the same thing that is okay. We understand how to, we can restore that symmetry if you want and you can think of other degrees of freedom there that will restore that symmetry. I think that really the question"
},
{
"end_time": 5267.312,
"index": 222,
"start_time": 5237.329,
"text": " Is what happens when you are in a regime where things are no longer perturbative and are so strongly coupled that the potential outcome of that is quite different as compared to what you had started with. But that is also very complicated to look into. So I honestly, I can't tell you at the moment. I don't know. What are gravitational rainbows? It's like rainbows. What are rainbows? What are rainbows? Rainbows?"
},
{
"end_time": 5296.749,
"index": 223,
"start_time": 5267.961,
"text": " Just the fact that light as it travels through a medium, let's say through water, through glass, will be affected by the medium slightly differently depending on its frequency and we understand that because as light goes through a medium it will interact with whatever matter is in that medium in a way which is"
},
{
"end_time": 5322.875,
"index": 224,
"start_time": 5296.937,
"text": " If the wavelength of the light the color of the light is quite similar to the relevant scale in that medium it will interact strongly with that and it will be slowed down by matter by the atoms in that medium and if it's very high frequency it will just zoom through completely unaffected and so the speed of light in water is in fact dependent on its color"
},
{
"end_time": 5345.947,
"index": 225,
"start_time": 5323.387,
"text": " And because of that, as we shine light through water, through a droplet of water, when it just rain in the sky, we see that light comes out of this droplet of water in a way which is different depending on the different frequency, the different colors of light. So we see this pattern in the sky."
},
{
"end_time": 5364.787,
"index": 226,
"start_time": 5346.34,
"text": " Now you can do exactly the same thing for gravitational waves. Gravitation waves are traveling through the universe and most of the universe we think is empty but still we think that most of the universe is filled with dark energy. That's what leads to the accelerated expansion of the universe."
},
{
"end_time": 5391.323,
"index": 227,
"start_time": 5365.367,
"text": " What is dark energy precisely I don't know and we know more or less how it interacts roughly with gravity but we don't know precisely how it interacts with gravity in a frequency dependent way at very very low frequencies. So it's possible that as gravitational waves are just traveling through the universe they are interacting with dark energy in a way which is frequency dependent."
},
{
"end_time": 5407.056,
"index": 228,
"start_time": 5391.323,
"text": " And so that's the case we will see that gravitational waves with different colors or different frequencies will have been affected every so slightly by dark energy all the things along the way in a way which depends in the in the colors."
},
{
"end_time": 5436.852,
"index": 229,
"start_time": 5407.449,
"text": " Of course, we're not going to look in the sky and see a beautiful rainbow in the same way as we see it for light, because we can't see gravitational waves with our eyes. So it's not going to look so pretty just like that. But in principle, the same type of phenomena can happen. And so we know, for instance, that there's different systems that emit gravitational waves, and they do so within a range of frequencies."
},
{
"end_time": 5454.326,
"index": 230,
"start_time": 5437.312,
"text": " The system that we have observed for the merging of black holes or neutron stars that we have observed so far, the gravitational waves emitted a relatively high frequency within that spectrum and so they zoomed through the universe completely unaffected by dark energy or anything else."
},
{
"end_time": 5476.203,
"index": 231,
"start_time": 5454.735,
"text": " But if we were looking at system, which are supermassive black holes starting their journey much further away, the frequency they met to start with will be much lower. So more towards the red of the spectrum in comparison. And so they can start being much more affected by the medium of the universe, for instance, by dark energy."
},
{
"end_time": 5504.684,
"index": 232,
"start_time": 5476.596,
"text": " And then you could observe that the speed of very low frequency gravitational waves, we're talking very, very low of the order of 10 to the minus 30 electron volt. So 10 or so orders of magnitude below what we have observed so far. But potentially we can observe that those would propagate at a speed ever so slightly smaller than those are very high frequency. And so that would distort the signal that we observe."
},
{
"end_time": 5531.817,
"index": 233,
"start_time": 5505.111,
"text": " That would be a gravitational window. Whether they exist or not, I don't know. That depends a little bit on what dark energy is. It depends how gravity interacts with dark energy. It depends on lots of different things. But it is something that we should keep our mind open for because this is a way to distinguish between different models. This is a new way to observe the universe. It's a new way to interrogate an environment and ask ourselves, is this happening or not?"
},
{
"end_time": 5554.241,
"index": 234,
"start_time": 5533.814,
"text": " Suppose we could do a double slit experiment in ideal conditions with gravitons. Would we expect an interference pattern? Yes, we are dealing with gravitational waves. So yes, in principle, you would expect the same thing for gravitational waves as you do for light. Yeah, there are waves, so you would expect that."
},
{
"end_time": 5582.125,
"index": 235,
"start_time": 5556.084,
"text": " So is there something different about gravity that acts as an observation or measurement in the measurement problem sense? So one thing which is different with gravity as compared to the other things is the fact that it's so weak. The strength of gravity is making it quite unique and especially"
},
{
"end_time": 5596.852,
"index": 236,
"start_time": 5582.705,
"text": " Possibly the reason why we actually can be here and ask ourselves that question, but gravity is much weaker as a force as compared to everything else. So this has a direct impact in ability to in fact"
},
{
"end_time": 5627.329,
"index": 237,
"start_time": 5598.029,
"text": " detect the fundamental particle of gravity in the same way as we have been able to detect the fundamental particle of light we know how to make sense of a single electron we know how to make sense of a single photon we can do experiments with that and we can look at the effect of a single photon that we can do but for gravity because it's so so weak the effect of gravitational waves is already the way we observe on earth they've been so weak"
},
{
"end_time": 5652.773,
"index": 238,
"start_time": 5627.5,
"text": " We're just observing gravitational waves. We see light all the time. We're sensitive to light and it drops energy in our retina. We can see light all the time. We interact with it quite strongly in some sense. With gravity, we interact with it very, very weakly. And so it's only when we have a coherent state on so many gravitons all together"
},
{
"end_time": 5678.848,
"index": 239,
"start_time": 5652.995,
"text": " that the effect is sufficiently large to being able to observe a gravitational waves passing through. Now if you were just to think of the effect of a single graviton in the same way as you think of the effect of a single photon, it's not only challenging at the moment to observe a single graviton with interferometers, that would go below Heisenberg uncertainty principle. So you can ask"
},
{
"end_time": 5707.978,
"index": 240,
"start_time": 5679.189,
"text": " yourself if I have a single graviton going through our interferometers, a single one of those with a given momentum which is associated with the length of the interferometer will lead to a displacement of space, an effective displacement of the mirrors in an interferometer which is too small to be observable. It's not just a technical engineering challenge"
},
{
"end_time": 5727.312,
"index": 241,
"start_time": 5708.234,
"text": " It goes below Heisenberg uncertainty principles that is quite different as compared to everything else that we know so we know that to prove the quantum nature of gravity observationally is going to be challenging so there's one side of that but then there's another side which makes it even"
},
{
"end_time": 5755.486,
"index": 242,
"start_time": 5727.961,
"text": " more problematic is that if you try really to probe gravity in a way which becomes stronger and stronger you have this sort of protection mechanism where it creates a black hole and so it sort of protect itself from even being able to being observed in stronger and stronger environments. So probing the quantum nature of gravity and being able to observe it in interesting regions"
},
{
"end_time": 5773.473,
"index": 243,
"start_time": 5755.708,
"text": " We do know it's going to be very, very challenging. I'd like to get to some of your latest research. So you've been working on positivity bounds derived from the S matrix theory and how they constrain massive gravity. So can you please talk about that and explain what positive bounds are?"
},
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"text": " Hi everyone, hope you're enjoying today's episode. If you're hungry for deeper dives into physics, AI, consciousness, philosophy, along with my personal reflections, you'll find it all on my sub stack. Subscribers get first access to new episodes, new posts as well, behind the scenes insights, and the chance to be a part of a thriving community of like-minded pilgrimers."
},
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"text": " By joining you'll directly be supporting my work and helping keep these conversations at the cutting edge. So click the link on screen here, hit subscribe and let's keep pushing the boundaries of knowledge together. Thank you and enjoy the show. Just so you know, if you're listening, it's C-U-R-T-J-A-I-M-U-N-G-A-L.org."
},
{
"end_time": 5846.886,
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"text": " So positivity bounds are in fact something quite intuitive I would say. If you think of having ultimate high energy completion of whatever it is. I don't know exactly what physics looks like at high energy. I may not have any fields there to describe reality. I may need to have"
},
{
"end_time": 5867.278,
"index": 247,
"start_time": 5847.176,
"text": " Use a different tool, I may need to use strings, I may need to use something else yet I haven't even thought about. I don't know but it doesn't matter too much because what I'm thinking about is amplitude of probabilities of given outcomes and I don't really need to understand what the other fundamental blocks of nature at very high energy."
},
{
"end_time": 5896.51,
"index": 248,
"start_time": 5868.131,
"text": " but what i do know is when i make a link between high energy and i go down to low and low energy i can sum up probabilities and so for instance if i if i am at low energy and i take two electrons let's say i take two particles and i scatter them together at a given energy they're gonna interact and lots of different things can happen and what can happen depends a"
},
{
"end_time": 5915.776,
"index": 249,
"start_time": 5897.176,
"text": " high energy physics but all other additional contribution should adopt positively to some quantities related to the amplitude of probability so whatever if i have all the particles that come in there that come and play along in the game"
},
{
"end_time": 5943.712,
"index": 250,
"start_time": 5916.135,
"text": " All they can do is add up for a new outcome which will give an additional positive contribution to the realm of possibilities. So this is really what the positivity bounds are in some sense. It's embedded in this notion of unitarity but you don't need to go into the details. It's very much into thinking that when you have"
},
{
"end_time": 5970.384,
"index": 251,
"start_time": 5944.531,
"text": " When i scatter things so the scattering this is what is encoded in this as matrix and that's why we're talking about the s metrics i can look at the different possible outcomes and if i have more and more physics coming in at high energy that opens more and more possibilities or it happens some more and more contributions to the potential outcomes but they will bring in positive contribution i don't want anything"
},
{
"end_time": 5986.254,
"index": 252,
"start_time": 5971.049,
"text": " which may lead me to negative contributions because otherwise I could simply focus on this and end up with a probability which is doesn't make sense which is negative let's say. So these are what the positivity bounds are."
},
{
"end_time": 6006.22,
"index": 253,
"start_time": 5987.381,
"text": " Conceptually, you can think they're quite simple. They're quite simple to understand that things should add up constructively and positively. Of course, it's a bit more mathematical than that. What I'm saying is a little bit simplified. It's not entirely correct, I should say, but it's just to give you the gist of it, a little bit of the taste of it."
},
{
"end_time": 6029.036,
"index": 254,
"start_time": 6007.295,
"text": " But the beauty of this is that it enables you to make a connection between an unknown high energy completion. I don't know what it is. All I know is possibilities, contribution to an amplitude of probability at high energy and then some potential outcome at low energy and some realization, some models at low energy."
},
{
"end_time": 6052.961,
"index": 255,
"start_time": 6029.48,
"text": " And so I can from that have a model at low energy, which I'll call it an effective description. It's a effective quantum field description for the world at low energy. For instance, the standard model of particle physics, I can think of it as a low energy, effective quantum field theory. It's valid up to a given energy scale."
},
{
"end_time": 6079.48,
"index": 256,
"start_time": 6053.217,
"text": " And even general relativity, I can think of it as an effective quantum field description. It's a quantum field theory and an effective one, which makes sense. It makes complete sense. It's consistent. Everything goes well. There's absolutely no problem up to a given energy scale. And it's only when I start looking at things at a high energy scale and I can think of doing scattering processes,"
},
{
"end_time": 6103.575,
"index": 257,
"start_time": 6079.821,
"text": " That involves gravity. When I start doing this at energy scales, which are comparable to the Planck scale, then I start producing black holes and all sorts of funny things happen. And if I were just to take general relativity with nothing else at high energy, I would seem to break this outcome of unitarity, break this notion that the probability should sum up to one."
},
{
"end_time": 6133.456,
"index": 258,
"start_time": 6103.575,
"text": " So this is really the issue and this is why we know that something else has to come up to compensate for that. But now I can just take effective descriptions at low energy the quantum field theories and just consider amplitudes of probability at low energy and ask myself whether their behavior and their behavior as a function of energy and different parameters which are related"
},
{
"end_time": 6154.258,
"index": 259,
"start_time": 6133.78,
"text": " To some extent to energy is consistent with what I would have expected had it come from a consistent high energy theory. And so, as I mentioned before, for some of those models, we already know that they will not be consistent. An interesting thing is that sometimes you can look at it at low energy."
},
{
"end_time": 6169.155,
"index": 260,
"start_time": 6154.582,
"text": " And nothing wrong seem to happen in principle they could be an ok description as an effective perturbative quantum field theory they may be consistent but then we know that in fact they're never gonna be linked."
},
{
"end_time": 6194.241,
"index": 261,
"start_time": 6169.599,
"text": " To link them to a high-energy completion something bad has to happen somewhere along the way there needs to be some negative contribution somewhere along the way and that can't happen otherwise we could just focus on this negative contribution and everything will be unstable everything will be bad. So now you can do that for all sorts of theories that you have out there including for massive gravity."
},
{
"end_time": 6212.91,
"index": 262,
"start_time": 6195.247,
"text": " Now for Massive Gravity, there's a very nice paper actually by Chang and Roman from 2015 or 2016, maybe it was 2016. It's called Positive Science in Massive Gravity. So Massive Gravity comes up with different parameters."
},
{
"end_time": 6235.06,
"index": 263,
"start_time": 6213.234,
"text": " for interactions is a different parameters that come in and then they show that there's an island of possibility among this parameter space where those positivity bounds are satisfied. So for the theory to be consistent and to be embeddable with a high energy completion, you need to be within a region of parameter space. And that was quite nice because before"
},
{
"end_time": 6251.152,
"index": 264,
"start_time": 6235.52,
"text": " In fact we anticipated that there would be no region of parameter space where it would ever be embeddable in a standard high energy completion and you always needed something which is quite different. So even the possibility for this to happen is quite interesting in its own right."
},
{
"end_time": 6269.445,
"index": 265,
"start_time": 6251.613,
"text": " And then there's been a series of other papers since then that show that if you make further assumption and you push those bounds further and further in particular if you make some assumption which are stronger based on weekly couple high energy completion then you can't have the theory being."
},
{
"end_time": 6299.838,
"index": 266,
"start_time": 6269.855,
"text": " embedded massive gravity being embeddable in a standard high energy completion so that we know so for massive gravity to have a high energy completion it can't be just a weakly coupled more let me say perturbative approach I have something more in mind when I say that but it can't be just a weakly coupled high energy completion it will have to be something quite different which may be interesting but makes it also quite challenging so this is the the statue of that"
},
{
"end_time": 6329.804,
"index": 267,
"start_time": 6299.838,
"text": " I think to my mind this is really"
},
{
"end_time": 6357.363,
"index": 268,
"start_time": 6330.657,
"text": " Very interesting, but it's also very challenging. So what we know is that you have to redress some of the coupling constants that come in in the situation and the roles of the games become quite different, but also very challenging to keep track of. So very little progress has been made in those directions for massive gravity. For other things, a lot of progress has been made, but not for massive gravity."
},
{
"end_time": 6383.507,
"index": 269,
"start_time": 6358.558,
"text": " But another completely different direction is simply to use those positivity bounds not for massive gravity but all sorts of different effective descriptions that we have out there. And for instance for particle physics we understand now that we have the standard model of particle physics that includes the Higgs but if you were to ask the community 10 years ago even 13 years ago they would have told you that"
},
{
"end_time": 6410.811,
"index": 270,
"start_time": 6384.104,
"text": " One would have hoped to observe something beyond the standard model, which is based on particular models coming from high-energy realizations. So either some signs of supersymmetry or some particular models that would have come in. And the reality is nothing has emerged. We haven't seen anything beyond the standard of particle physics, but we know that it will be hard for it to be just the standard of particle physics. We would have expected something else to come in."
},
{
"end_time": 6427.961,
"index": 271,
"start_time": 6411.169,
"text": " At the very least we know that we have to couple it with gravity at some point that the neutrinos have masses maybe that's not really the big issue but at some point of this before the plan scale something has to come in and we believe that something will have to come in even at a much lower energy scale than that."
},
{
"end_time": 6445.93,
"index": 272,
"start_time": 6428.558,
"text": " But before we were driven much more by beautiful, very well thought out, specific realizations at high energy, some specific models which come out with their specific signatures at low energy. And unfortunately nothing has been found along those realms."
},
{
"end_time": 6469.224,
"index": 273,
"start_time": 6446.254,
"text": " So nowadays quite a different approach has been taken where people are looking at what we call the SMEFT, the standard model effective field theory, where instead of looking for specific model dependent signatures, they're looking for all possibilities. So they parameterize the corrections that you can have"
},
{
"end_time": 6495.128,
"index": 274,
"start_time": 6469.582,
"text": " Beyond the standard model of particle physics, it's the SMEFT, so you're looking at corrections which will become more and more important than high energy that go beyond the standard model of particle physics. But there's thousands of those and so those positivity bounds can enable us to see where in this big region of parameter space you have, you can be"
},
{
"end_time": 6524.121,
"index": 275,
"start_time": 6495.35,
"text": " connected with a sensible high energy completion and which regions you are not and so that allows us to make tractions and focus in sensible regions in parameter space for physics beyond the standard model without being focused on specific model dependent on a focusing on a consistent high energy completion and this consistency is just a notion of causality and unitarity."
},
{
"end_time": 6554.701,
"index": 276,
"start_time": 6526.476,
"text": " When people hear the terms high energy realization, UV completion, high energy completion, are those all synonyms? And then what would be a synonym for the viewer or listener so that they can understand it more? Is it final theory? Is it a more final theory? What does that mean? Yeah, so it means slightly different things depending on the context. For this discussion, when I talk about high energy completion, I really mean"
},
{
"end_time": 6582.807,
"index": 277,
"start_time": 6555.401,
"text": " Something that in principle could be probed at infinitely high energy. You know that general relativity is an extremely good description of the world we live in up to some given energy scale. But we know that if I were to probe Einstein's theory of general relativity at too high energy, things go wrong. It's not longer consistent. It's no longer consistent as a quantum field theory."
},
{
"end_time": 6609.735,
"index": 278,
"start_time": 6583.097,
"text": " And so some new physics has to come in. It could be that there's never really gonna be a finite end of the story. It could be that we understand what is the next layer of physics beyond general relativity. We have let's say string theory and then things go on and then we realize there's something beyond that and there's something beyond that etc. But what we want to know is what at the very least what happens"
},
{
"end_time": 6627.142,
"index": 279,
"start_time": 6610.469,
"text": " within a consistent quantum theory of gravity at energy scales beyond the Planck scale. But in some sense it doesn't matter too much whether it's the final word or whether it continues like a fractal"
},
{
"end_time": 6647.312,
"index": 280,
"start_time": 6627.995,
"text": " Realization because all we asking ourselves is for physics have a manifest itself to be consistent in the sense that we want causality there and we want some notion of unitarity the probabilities some up to one and so it doesn't matter if it's an infinite."
},
{
"end_time": 6677.159,
"index": 281,
"start_time": 6647.756,
"text": " infinity of models that we need to go deeper and deeper and deeper or if it stops and we'll get to a point where we understood everything and that's it it's string theory everything stops there and we have all the tools at our disposal to compute anything you want I don't know probably I will never know within my lifetime and probably in the next generation will also find it quite challenging to know and that's why we don't want to be too committed into"
},
{
"end_time": 6695.06,
"index": 282,
"start_time": 6677.739,
"text": " Add that being a finite mess in our knowledge or whether we gonna keep pursuing knowledge deeper and deeper levels to get more and more precise into what makes a structure of reality and it doesn't matter all that matters is that we know."
},
{
"end_time": 6723.404,
"index": 283,
"start_time": 6698.012,
"text": " That what we have access to right now is not the final story and there have to be something else out there for which we don't have direct contact with at the moment because we don't have the tools to fully describe what's going on there. Now, the last time we spoke, you discussed longitudinal modes in the context of Einstein screening, if I'm not mistaken, and how that overcomes the VDVZ issue."
},
{
"end_time": 6747.193,
"index": 284,
"start_time": 6723.933,
"text": " So does the presence of this mode in Massive Gravity leave imprints on the CMB that are different than standard cosmology? That's an excellent question and the answer is probably, although we don't know yet. So what is quite likely is that"
},
{
"end_time": 6775.845,
"index": 285,
"start_time": 6748.183,
"text": " The presence of this mode means that depending on the scale you're looking at, you change every so slightly how easy or challenging it is for structures to form. So for the structure we see in a universe, the clusters of galaxies and the filament of dark matter, they got seeded by original quantum fluctuations in the very beginning of the universe and then there's been gravitational collapse"
},
{
"end_time": 6802.619,
"index": 286,
"start_time": 6776.084,
"text": " around them and things being patched around those seeds and those structure. But if you change every so slightly the strength of gravity because of this longitudinal mode that will affect the spectrum of those structures and it affects every so slightly differently depending on the size of the structure and depending as well on when they got formed in"
},
{
"end_time": 6830.162,
"index": 287,
"start_time": 6802.619,
"text": " Devolution of the universe whether it was early on or later on so we would expect a slightly different realization of this and in fact there's some very nice work by Mark Wyman and Justin Corey where they look in at the different ways structure get form depending on how strongly this longitudinal mode start kicking in through the history of our universe now for the CMB"
},
{
"end_time": 6851.476,
"index": 288,
"start_time": 6831.63,
"text": " One would believe, one would think that at the time of the imprint on the CNB, this is coming from quantum fluctuations at the very beginning of the universe, the energy scales involved at that time are so high that the longitudinal mode would be completely screened."
},
{
"end_time": 6875.196,
"index": 289,
"start_time": 6851.766,
"text": " Because it's we're dealing with very high energy scale so that probably is not where one would expect to see the best signatures for the longitudinal mode but really being able to come up with a precise calculation requires us to being able to follow the whole evolution of the universe in a fear of massive gravity which is very challenging."
},
{
"end_time": 6899.957,
"index": 290,
"start_time": 6875.879,
"text": " But there's been some other work being done where just from the fact that not only you have a longitudinal mode but just the standard tensor mode, the standard what you call gravitational waves are massive, that would change the spectrum of gravitational waves fluctuations at the beginning of the universe. And if we did observe primordial gravitational waves,"
},
{
"end_time": 6921.8,
"index": 291,
"start_time": 6900.162,
"text": " which could be imprinted on the cosmic micro background through polarization of the CMB. This would come in with a particular spectrum, which depends on the alley, depends on the angular momentum and angular distance, depends on the frequency if you want, and that will"
},
{
"end_time": 6952.602,
"index": 292,
"start_time": 6923.08,
"text": " be affected by the scale, the mass of the graviton. In particular, if you observe primordial gravitational waves, so for instance, if you observe a polarization in the cosmic microwave background that you can trace down directly to primordial gravitational waves as opposed to anything else like dust along the way or anything else. And if those came in at very, very low, very large distances, let's say very, very large angular distances,"
},
{
"end_time": 6981.305,
"index": 293,
"start_time": 6952.927,
"text": " then that would tell you that the graviton has to be effectively massless at the time of emission and therefore that could put a constraint on the graviton mass. So the spectrum of the polarization of the CMB may enable us to put some constraints on the graviton mass and there's some very nice papers being done in the focus just on the effect of the mass on the standard tensor mode of gravitational waves."
},
{
"end_time": 7009.241,
"index": 294,
"start_time": 6982.517,
"text": " What about the spectrum of Hawking radiation or the temperature? Is there any introduction of decays into the massive gravitons? Yeah, so that's an excellent question. In principle, yeah, you can start looking at those things. In fact, yes, it's a very nice paper by Rachel Rosen, which has looked at the effect of the thermodynamics of the massive graviton and the correction. So the reality is"
},
{
"end_time": 7016.305,
"index": 295,
"start_time": 7009.787,
"text": " What happens is that you introduce a new scale, which is the graviton mass, in the spectrum."
},
{
"end_time": 7042.005,
"index": 296,
"start_time": 7016.715,
"text": " And so she has followed through the differences that comes in in the thermodynamics lows in a theory of massive gravity. In fact, in normal processes, the mass is so small as compared to the other scales involved, it makes a very little difference. But it's still very interesting to see how you recover the standard smooth massless limit in the limit where the mass becomes very small."
},
{
"end_time": 7066.357,
"index": 297,
"start_time": 7044.104,
"text": " So Claudia, thank you for spending two hours with me. I appreciate that. Yeah, thank you. Thanks. So it's great talking to you. I want to know before I talk about what is it that you're currently working on and where people can find out more about you. And by the way, there's the beauty of falling, which will be on screen and link in the description as well. What's your current assessment of emergent gravity proposals?"
},
{
"end_time": 7090.196,
"index": 298,
"start_time": 7068.609,
"text": " You know I really like to stay agnostic. There's so many good ideas out there but at the moment my work is very much making connection between those and low energy physics in terms of observables in a way where I don't want to commit too much into what is emerging gravity, what is the realization because to me I mean it"
},
{
"end_time": 7111.476,
"index": 299,
"start_time": 7090.759,
"text": " Ideally a lot of those ideas are jeweled to one another and I would love it if in fact it's not just one realization or another is if we see a correspondence between these different ways to think about it. So I'm going to be speaking with Ted Jacobson soon and I'm curious if you have any questions for him."
},
{
"end_time": 7139.002,
"index": 300,
"start_time": 7111.834,
"text": " What do you think he's doing that's wrong or what questions come up to you? Don't put me on the spot for that. No, I don't want to go into that. Okay. I see him every so often, so I'll talk to him offline. You'll talk to him yourself. All right. All right. Great. Yeah."
},
{
"end_time": 7165.828,
"index": 301,
"start_time": 7139.36,
"text": " Okay, so what are you most excited about now that you're pursuing? Yeah, every day I have a new idea and I like to pursue. So one thing I'm quite excited about is to try to understand whether again moving into this notion of symmetries where they emerge from more fundamental principle. So in a lot of the way we're thinking about things, we think of symmetries as a guiding principle because it helps us to"
},
{
"end_time": 7191.442,
"index": 302,
"start_time": 7166.357,
"text": " Put an order into things and to keep things under control but sometimes it's almost like a way to simplify our life and in a lot of the work we're starting to see we realize that it's not up for grab actually they have to be there those symmetries emerging from all sorts of different requirements which we thought"
},
{
"end_time": 7220.674,
"index": 303,
"start_time": 7192.824,
"text": " we're just there to make our life simpler but in fact it may be that high energy completion actually requires a level of symmetry which from a low energy perspective we didn't think we needed to but the high energy world is becoming more and more symmetric so symmetries just emerge as you go to high and higher energy and that's just based not only on stability if it were"
},
{
"end_time": 7249.275,
"index": 304,
"start_time": 7220.674,
"text": " but an even more fundamental principle like again unitarity. So that's one of the things I'm quite excited to look into into it and what type of symmetries are actually emerging is an interesting question in itself. Are there any experiments that you're looking forward to? So I love the daisy experiment to be pushed further but I mean the next decade is just going to be incredible in terms of observations from"
},
{
"end_time": 7266.783,
"index": 305,
"start_time": 7249.684,
"text": " I'm"
},
{
"end_time": 7296.852,
"index": 306,
"start_time": 7267.176,
"text": " all of those things it's really gonna enable us to not only see the universe to the different structure but also get a whole spectrum of gravitational waves ideally going all the way up to nanohertz all the way up to a hundred hertz and connecting between these different frequencies of gravitational waves is gonna give us such a handle on gravity to me that's so exciting it's no it's really it's incredible the wealth of data we're gonna have"
},
{
"end_time": 7325.776,
"index": 307,
"start_time": 7297.278,
"text": " I've received several messages, emails and comments from professors saying that they recommend theories of everything to their students and that's fantastic. If you're a professor or a lecturer and there's a particular standout episode that your students can benefit from, please do share and as always feel free to contact me."
},
{
"end_time": 7353.422,
"index": 308,
"start_time": 7326.203,
"text": " Hey Kurt, you've spoken to so many people in the fields of theoretical physics, philosophy, and consciousness. What are your thoughts?"
},
{
"end_time": 7365.503,
"index": 309,
"start_time": 7353.66,
"text": " While I remain impartial in interviews, this substack is a way to peer into my present deliberations on these topics. Also, thank you to our partner, The Economist."
},
{
"end_time": 7390.111,
"index": 310,
"start_time": 7367.722,
"text": " Firstly, thank you for watching, thank you for listening. If you haven't subscribed or clicked that like button, now is the time to do so. Why? Because each subscribe, each like helps YouTube push this content to more people like yourself, plus it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm,"
},
{
"end_time": 7416.152,
"index": 311,
"start_time": 7390.162,
"text": " Which means that whenever you share on Twitter, say on Facebook or even on Reddit, et cetera, it shows YouTube. Hey, people are talking about this content outside of YouTube, which in turn greatly aids the distribution on YouTube. Thirdly, you should know this podcast is on iTunes. It's on Spotify. It's on all of the audio platforms. All you have to do is type in theories of everything and you'll find it. Personally, I gained from rewatching lectures and podcasts."
},
{
"end_time": 7436.084,
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"text": " I also read in the comments"
},
{
"end_time": 7459.565,
"index": 313,
"start_time": 7436.084,
"text": " and donating with whatever you like there's also paypal there's also crypto there's also just joining on youtube again keep in mind it's support from the sponsors and you that allow me to work on toe full time you also get early access to ad free episodes whether it's audio or video it's audio in the case of patreon video in the case of youtube for instance this episode that you're listening to right now was released a few days earlier"
},
{
"end_time": 7466.152,
"index": 314,
"start_time": 7459.565,
"text": " Every dollar helps far more than you think either way your viewership is generosity enough. Thank you so much"
}
]
}No transcript available.