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Gabriele Carcassi: "We Have Physics Completely Backwards!"
October 11, 2024
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When did we first get in contact? Oh jeez, I don't remember.
It must have been more more than a year ago. Yeah. OK, well, I've been following your channel for approximately one year. I believe I contacted you shortly afterward. OK. Yeah. And you have a fantastic channel people should know about. So it's called the Assumptions of Physics, or at least that's the project name. And Gabriel is going to take it over at some point and give the elevator pitch the five minute version. So a long elevator at CN Tower or in Toronto, that sort of elevator. What makes your channel different?
is that you focus on the equations and the rigor and many people who are into demonstrating that some conventional aspect of physics is incorrect. If they're in the academy, they do so from the philosophy of physics angle. So maybe some interpretation of quantum mechanics, but you don't focus on that. You're much more about demonstrating with line by line proofs. In that vein, you remind me of Jacob Berandes and he's from Harvard and you're based in Michigan.
Well, I'll list some examples for people who, if you just want a teaser of what's to come, why is it that Heisenberg's uncertainty or some analog of it is already in classical mechanics under the proviso that you have to assume that thermodynamics is true? Another is that the action principle, which the way that I thought of it is, it's a compression mechanism. So it encodes several different equations inside and then you unpack it with Euler-Lagrange's equations.
You show the action principle itself has a geometric meaning and the idea that you can translate between Newtonian mechanics and Hamiltonian mechanics and Lagrangian mechanics is false. You can't. There are some systems that are only describable in some or not translatable to the other. There's not a one-to-one bijection between these guys. Correct. Okay. We'll also talk about what defines quantum mechanics. So many people think that it's commuting variables or non-commuting observables.
Is that actually what defines quantum mechanics that makes it separate from classical mechanics and why reductionism is incorrect? You have a video on, you shouldn't think physics is reductionistic because at some point you get down to atomic facts. At the fundamental level, to justify the mathematical structure, you can't just say, oh, there is another mathematical structure that I used to justify this because how would you justify the first? And another way of saying that is that people think of physics as a mechanistic science that you're always looking for mechanisms.
But also that's another false view. I believe you say that because you can't look for a mechanism is something that's irreducible. Right, because it's more that if you are at the fundamental level, you can't invoke a deeper level to justify the fundamental level that you have. There is no mechanism after that. That's a bit of a teaser. Some of those are technical. But why don't you go over the assumptions of physics project? Right.
The project that I, the goal of the project that I work on is essentially to find a minimal set of assumptions, of physical assumptions, from which we can re-derive the laws. And we have essentially two approaches. One we call reverse physics, where we start with the current laws of classical mechanics, quantum mechanics, and so on, which there
modern theories are just presented as sort of a mathematical structure. And the idea is to go backwards from that mathematical structures and find physical conditions that are equivalent to that mathematical structure. And that's why it's called reverse physics, a little bit because it's like reverse engineering. You're taking the thing, breaking apart, finding what pieces go together, what pieces are independent. And another reason is because in the foundations of mathematics, there is an approach called reverse mathematics.
Now just a moment. So in reverse mathematics, I've always wondered, so just for people who are tuning in, there's a theorem and then you usually use assumptions to prove a theorem. And the way that I understand reverse mathematics is instead of starting from your axioms and moving forward to derive a theorem, you start with what could be true and then you think about what needs to be true in order for that to be true.
Well, you're looking for a subsystem. So, to prove a simple theorem, you might not need, let's say, all of mathematics. You might need just a smaller subset of starting points, let's say. And you sort of, by doing that, you sort of learn more of what is the structure of mathematics itself. Now, I'm not an expert in this, but I actually had a chance to talk to one of the people that work there.
And so what I do, what we do in assumptions of physics in the reverse physics is slightly different because we're more interested at the conceptual structure, like what is the minimal conceptual structure that I need to get to some parts of the mathematics of the physical laws. But like the spirit is the same. You're taking what you think is physics, what you think is mathematics, and trying to find what pieces are there, like the structure of
of physics itself and mathematics itself.
And one of the things that then we saw while doing this work is that you can have these, you know, physical assumptions that are equivalent to the different laws, but that sort of gives you only the higher level mathematical structure. And what we realized is that you really can't say that you understand the higher level mathematical structure if you really don't understand all the nuts and bolts of the more fundamental mathematical structures.
And so we started another approach, which is called physical mathematics. And there the goal is really to start from scratch and layering each axiom and definition and each axiom and definition has to have a physical justification. So it's not enough to say I have a mathematical structure. I have to say these are the things that I have to model in the real world. And this is why I will use this particular mathematical structure to model this thing. Why don't you give an example right now?
So, for example, the basic constituents that we use in physical mathematics, because we need a basic building block for everything, is the idea of an experimentally verifiable statement. A statement for which you have a test, and the test succeeds in finite time if and only if the statement is true. So, for example, you say the sky is blue, you can look, it's blue, finite time, verify.
Something like the mass of the electron is less than 10 to the minus 13 electron volt. That's something where we can go and verify. But a massless photon. As another example, you can say the mass of the photon is less than 10 to the minus 13 electron volt. And that's something that we can verify experimentally. But if you said the mass of the photon is exactly zero, that's not something that we can verify experimentally because we always are bound to finite precision.
And so these are the things that we want to have as a fundamental thing. We want to say a physical theory has to give us statements about the world and a physical theory has to be fully explorable by testable statements. And so those are the things that we axiomatize. We say these things exist.
And they have a particular way to be composed.
But if you have infinitely many, you're not going to be able to be guaranteed because it would take you an infinite time to do it. So for a verifiable statement, you're only guaranteed that the finite conjunction is actually verifiable. You're not guaranteed the infinite conjunction. So the infinite conjunction is still a statement, but it's not a verifiable statement.
And again, we have in the justification, we have somewhat proofs that would have been accepted as proof probably in the 1700, but they don't follow the current standard mathematical rigor, because mathematical rigor now starts with essentially elements that where the meaning is being stripped out is just symbols that you manipulate and so on.
And when we are trying to reason on the physical objects, well, the physical objects are not meaningless marks of paper. And so we need to be able to reason what these things are such that then we can find these definitions and say, OK, these things can be. And so all of these process we call physical mathematics, because at the end of the day, we will come from mathematics. We will have all the theorems and we want to recover the mathematical structure that we already have. We don't want to create crazy mathematical structure that we
We don't know what they are. You want to justify the use of the mathematical structures that we already use? Correct. And find whether those are 100% appropriate for the type of physics that we're trying to describe. And what is the realm of applicability in those mathematical structures? So something like the real numbers or even the complex numbers. Correct. Which are a continuum. Do they have a place in physical mathematics?
Yes, for example, we have a complete derivation or we have a set of necessary and sufficient physical assumption they have to make such that a set of variable statements are going to be identifying with identifying essentially open sets of the real numbers. And so we know when we can take those things to be valid or not.
And again, the idea is really to construct things that are a modelization of what we do in a sort of operational settings. So how do we define numbers? Well, we're going to have a reference and then we say something is before the reference or after the reference. So, for example, we have a clock ticks and then we say something happened before the third ticks and after the second.
Or you have rulers and you have notches on the rulers and you can say before this notch and after this notch. Or you have a balance scales and you have weights that you put on one side. It always works with this. You have references and the way that these references work is that essentially they give you three statements. Whatever you're measuring is before the reference, after the reference or on the reference in the sense that it overlaps.
And the before and after are assumed to be verifiable. It's something that you can check. And now the question becomes, how many references do you need? And what is the logical relationship needs to be such that all these references are going to tell you, aha, you're measuring something on a continuum of the real number.
And what is most interesting in doing this work, apparently that is fascinating because you really understand exactly how these things work. What we find is that there are three conditions that you need to have that are the most important and they
It's like the biggest difficulty is not getting the real numbers. The biggest difficulty is to find a linear order. So a set of points that you always have something either before or after. That's really where all the sort of a harder assumption that you need to put are there. Once you have the linear order,
Whether you have the real numbers or the integer is just a matter of saying, oh, I have two references. Can I put one in the middle of the two? Okay. Now, why is it difficult to have an order on the real numbers? Because they already are ordered. Right. No, it's justifying an order with just saying, oh, I have these references where things can be before or after. Right.
References don't need to be ordered. You have references in space and you don't have a linear order there, right? And so the idea is that all the references have to be able to be arrangeable in some way, such that, for example, if I put a reference and another reference, you know, having something that is before this implies that something is before the other.
Right, because the point is that you're starting from scratch. You just say, I have a bunch of statements. What are the minimal conditions that I have on those statements such that an order emerges from these statements? And that's the hard bit. So what are you working on now? What I'm working on right now, it's a sort of a
The piece that I need in between physical mathematics and reference physics, I need physical mathematics and reference physics and reverse physics, reverse physics. Right. So I speak to everything that sort of merges together.
So from the reverse physics side, I have a lot of conditions that allow me to recover fully classical mechanics and quantum mechanics in a hodgy podgy way that a physicist might like, but not a mathematician.
And I need a place where I can run these arguments in a more precise way. And so I need sort of a general theory of the states and processes that it's more abstract than the two theories, such as I can say, these are things that you always need to have if you're doing physics. You need to be able to define states and states have to have these characteristics. And then if I have a classical system, I'm making this additional assumption.
And if I have a quantum system, I'm making these other additional assumption. So I basically want to be able to push as much as I can. The theorems that are true, both in classical mechanics and quantum mechanics, push them up to a single theory, right? To a more general theory so that I can see these two other theories as instantiation of the two.
And so, again, this is part more of physical mathematics because I need to identify actions that I have to assume to be able to do physics in the same way that I say, well, physics is about experimental evidence. So I have I need to have statements of other words that are testable. What I want to say is that physical theory has to be testable in a repeatable way. Right. I need to be able to set up experiments and test them.
And so the basic objects that I have to describe a system must be at the level of ensemble, because when I go and prepare things in a lab, that's what I prepare, prepare ensembles, I prepare statistical things that then I make statistical measurement and it's on these statistical measurement that we have the interest. So this sounds extremely practical, like everything that comes from physics has to be some experiment or some
a statement about an experiment or an observable. Would the theorem, if you have a vector outside the light cone, then you act on it with the Lorentz group, you can rotate it to any other vector outside the light cone. Would that be okay under yours or would that not even be considered physical mathematics? Because it's not making some specific experimental statement. In other words, if you have a space like vector, it will always be space like under any Lorentz transformation.
Right, that's going to be if you have set up things correctly, right, that's going to be something that comes out from the math. So that's an OK statement.
Yeah, it's probably come. So that's going to be true when we are doing even reverse physics in classical mechanics. You do find that when you set up your assumptions for classical mechanics, by the way, are not very difficult. You need three things to get to classical mechanics. One is that what we call the assumption of infinitesimal reducibility.
You have a system and the system is made of parts and the parts are made of parts, the parts are made of parts, and giving the state of the whole is equivalent to giving the state of these infinitesimal parts. And so the infinitesimal parts are essentially what we think of the classical particles, right?
and the whole system is giving is a distribution over the space of the particle. You're going to be able to say, you need to be able to say 10% of the system is within this part, this 10% of the system is within these states, 90% of the system is in the other states. So it's really a distribution over all the possible configuration of the infinitesimal parts.
And because you want these distribution, the count of states, the densities and the entropy to be the same for different observers, right? So if you have a set of units and you're there and I have a set of units and I'm here,
we want still to be able to count states in the same way and we want to be able to define entropy in the same way because otherwise you know entropy would be increasing for you and not for me and that would make sense because i would see something that is deterministic and reversible you see something that is not deterministic and reversible that that would not make sense so even this constraint
Basically, it's what gives you the structure of the classical phase space is what gives you the idea of conjugate variables. And mathematically is what gives you the idea of a symplectic structure, which is sort of the geometrical way that we describe phase space. So with that assumption, infinitesimal redistributed, we get all this stuff.
And then you say, now I want the system to be deterministic and reversible, meaning that for each initial configuration, I have a final configuration and the number of states are mapped to each other, right? Then that's what's going to give you Hamiltonian mechanics. It's this preservation of volume. This basically gives you the preservation of the number of states.
The other thing that you need that I sort of didn't say before to make all this work is the assumption that you're describing a system that is made of independent degrees of freedom so that the total number of states can be understood as the count of states on one degree of freedom multiplied by the count of states on another degree of freedom. If you have these three conditions you get classical Hamiltonian mechanics and that's it.
Then if you allow an extra assumption that basically says all that I'm studying are actually trajectories, meaning that I can go from the kinematics to the dynamics. So from position and velocity to position and momentum. And the this transition is invertible. If you say that it's invertible, that's what gives you Lagrangian mechanics.
And then if you go one step forward and say, look, both momentum and velocity are linear structure, and I need that linear structure to be preserved, then the map between position from momentum to velocity has to be linear.
And if you do just a couple of integrals, you find that you're constraining yourself to massive particles under a scalar and vector potentials. So you basically find the laws of charged particles in an electromagnetic field. And this was a surprise to me, right? Like when I set up to do all these things, we said, I just want to understand these things a little bit better. And I had no sense that
from just four simple assumptions. Four simple assumptions? Yes. Okay. Right. It's infinitesimal reducibility, independence of degrees of freedom, determinism of reversibility, and what I call kinematic equivalence, the fact that you can go from position and velocity to position and momentum, that looking at the trajectory is enough to understand what's going on at the dynamical level to reconstruct the energy, the momentum and all that.
And that sort of gave me a different insight in physics, right? Because I don't need anything below to justify this mathematical structure. I don't need a mechanism for how we get an Hamiltonian or how we get a Lagrangian. It's just the definition. I have a system in front of me. I can assume that this system satisfies these assumptions in these particular circumstances, and you get the laws.
And so I never think that philosopher ask themselves, could we have a universe that have different laws? Well, if we have objects that can be infinitesimal, reducible, independent degrees of freedom and all this, you're going to get the same laws. Interesting. That's a question that many philosophers, as you mentioned, ask. What would the universe look like under different physical laws? And then there's also the thought experiment that proves that you can demonstrate to yourself just without
Going to the Leaning Tower of Pisa that a bowling ball and a feather will fall at the same rate if you remove air resistance. Do you know that? Yeah, that's actually in Galileo's dialogues. So this is another myth that people always think Galileo didn't know whether objects fell at the same rate or not, went to the Tower of Pisa and dropped that.
No, in his dialogue, he creates this simple experiment. They say, okay, let's suppose that I have two rocks and one is heavier than the other, and let's suppose that these fall faster than this. Now you put them together, you tie them up, right?
What is the velocity of this? Well, you say, well, the faster object is going to be slowed down by the slower object. So the velocity should be in the middle of the faster object and the smaller object. But now you have put them together and now it's a more massive object. So it should go faster than the faster object than we were before.
Right. And also here is the configuration is how much, how tight do you have to bind these things such that you are going to consider these two separate objects with different mass and how, you know, when you tie them together, they're actually one object of different message, like how tight you have to bind them. Right. And there's, of course, it makes no sense. And then that's how in the dialogue he,
He concludes that all objects have to fall at the same rate. So the type of things that I'm trying to do is exactly this type of things on steroids, right? To really go and find all these sort of reasoning that you can from simple things and build as much as possible. And that's kind of the game that I've been painting a lot of the time. Some arguments when I start, I'm really just trying to find an argument and I try to find many, right?
And at the beginning, they all seem impossible because you're not used to it. Like any argument, even false one, as long as you think about them enough times, they're going to seem plausible to you. And the reverse is true. Even if an argument is false, it's true, but you are not used to thinking in that way, you still think that it's false. There is something weird about it. So you need to sort of get comfortable with them a little bit. They say, OK, well, this argument that I just made for fun,
Actually has some merit. And then you find that there is a correlation with something else and actually two different argument becomes the same one. And you say, oh, then I must have something. In fact, the first time where I said I have something is where I was able to read arrive Hamiltonian mechanics from deterministic and reverse stability in four different ways. Because I could say I have determines because I map states one to one.
I could have determined is because I preserve the information or the information that I know at the beginning is the same amount that I have at the end. So it's an information theoretic argument, or I have something that conserves thermodynamic entropy. So it's reversible, not in the sense that that I do a one to one map with the state is reversible because the entropy does not increase.
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And so these are all the uncertainties, right? You know, you think of determinism as points in math, but we never really measure points. We really measure some statistical distribution and some uncertainty around it. And so if you say, I want something to be deterministic and reversible, then you're going to say, well, the measurement uncertainty has to be preserved because I need to sort of describe the system at the same level of accuracy.
Yes i saw that however i made the the case in those four different case i would get to the same results. Okay now i have something stable right because you just have one type of argument that you can always fool yourself but now i have four of them that are starting from the same point and at reaching the same conclusion.
I must not be fooling myself. Now, are those four equivalent to one another? Yes. Okay. And mathematically, they're basically just assuming that the Jacobian of transformation is unitary, that the volumes preserve the same. And in our book, we show we have all these different ways. And then you see that they're all equivalent. It's quite fascinating. I think 10 years ago or so I learned about the thought experiment of Galileo. And then I wondered,
How much more of physics can we derive from purely, well, you're thinking in terms of assumptions, but I was thinking in terms of thought experiments. And there's also the Newton's bucket thought experiment. Have you thought much about that? I'm not familiar with that one. Then don't worry about that because I'm not familiar enough with it to be able to describe it with confidence. But I believe it's an argument for absolute space.
It has to do with you have water in a bucket and then you start rotating it and then the water creeps up the sides of the bucket, making a U shape. So you're able to tell that this is being rotated. And somehow that's an argument for absolute space that Newton gave. And then Mach takes that and says actually Newton, if you examine that, that's an argument for relational space. You probably have to talk to Julian Barbour for Mach and stuff. He is the expert. Now for the Hamiltonian mechanics, do you recover that
Momentum is a covector? Yes. And the reason is quite simple. And it has to do with units. And this is one of the problems that in physics, we follow the math too much. And the math does not care about units. But a lot of geometrical structures that we have there are actually there to keep track of the units. So the setup is basically this. You want to be able to count states.
and the count of states have to have a unit that is independent of anything else. Then you're going to have the units that you use to identify the state, which could be meters, angle, and so on, to start defining the configuration. What you need now is if you only had the variable that defines the units and let's call that q,
Then you would have a problem because now there would be special reference system for which the counter state would actually be the unit and all the others would not be the same. So you start having special coordinate systems that are sort of privileged because you're using the exact units to kind of say. So what you really want to do
Is to be
such that when I make an area between the two, well, this is units of Q. This is units of inverse Q. When I multiply with each other, now I have an invariant. And then invariant is the count of states. Is that the volume in the phase space? And that's the volume in the phase space. So you have Q that defines the units. You have K that is the inverse units. And then you say, I want to measure states with H bar.
And so you just multiply K by H bar and you get P. Why are we talking about H bar when we're speaking about Hamiltonian mechanics or classical mechanics right now? Because that's what we use for for the unit that we use to count states is the units of actions. Is that what we use? And we the reason that we use that, because in mechanics, the units turn out to be, you know, position times kinetic momentum and the square, right?
And that's then what we use to define units. But you still need a unit to be able to measure these things.
And when you calculate an entropy, even in classical mechanics, that you have a distribution on phase space, you need, you know, you're going to have a logarithm of the distribution, but the distribution is going to be, you know, let's say probability over volume. And if the volume is in unit of phase space, you are in a log, you have to take that out. So you need the sum, you know, some constant so that you can define where your zero entropy is, and you get the correct end. Right.
It turns out that you still need to fix some of these constants even in classical mechanics. And again, it's one of those things that... It's quite bizarre. Right. It's one of those things that if you just take all the units down, and that's what mathematicians do, you're not going to see. And unfortunately, this is what we do in theoretical physics. We have all the units, we throw them out. What do you mean we throw them out? Like set C equal to one, is that what you're referring to?
Yeah, but it's not just setting it to one. It's setting it to one pure number. But if you set it to one, but you still have some units of space over some units of time, then you're still preserving the physical content of what you're going to measure. Because when we measure distances in space, we use different instruments than when we measure distances in time.
But that's what we do. We just set everything to one and we forget about the units and then we lose the structure because you don't see you can't appreciate what is it that the physics that the thing is described. So what would be an example of something where they set C equal to one or H bar equal to one or what have you and it turns out it's incorrect under what you've investigated?
It's not incorrect. You see, this is, if you do the calculation correctly and do everything correctly, it's not the problem. You just lose the physical meaning. So for example, you know, the Dirac equation. Yes. What does it tell you? What is it saying? So if you, if in that, instead of the gamma, right, the gamma is these matrices that sort of sum to one, put a C in front. Now that C gamma is actually a velocity that comes from the booster of the spin part.
So the gamma is telling you what is velocity of the spin going. And then you have a partial derivative, you know, put the h bar, that's momentum. So it's velocity contracted with the momentum of the particle equal MC square. So it's basically telling you all these things is telling you that the V times P equal
It's going to give you MC square because you have the momentum which is MV and then you have the velocity is MV but you're contracting together those those vector the norm of V square is going to be C. So you're just saying you know something that you already have in in
Classical particle mechanics in a relativistic setting that the the inner product between the momentum and velocity is equal to MC square. That's it is just that you're saying in the context of field theory so of course you're going to use a language of that it's a lot more complicated but the physics that you're describing what the equation is telling you is just that this is nothing there is nothing more.
so what i feel that we've done by essentially stripping all these things away and just following blinded mathematics and looking for mathematical structure for new thing we think we're just losing all the physics they still there and if we did it in the way that we used to the physics right because
These assumptions are just a new version, maybe like more rigorous version of Newton's laws and the laws of thermodynamics. We used to do physics like that. You start, you figure out what are the, you boil the world into these assumptions that you're making or these starting points.
And then get everything from there. And you keep track of what it is that you're doing. You check your, you know, when you're doing undergrad problems in physics, you do the dimensional checking where, you know, to make sure that your masses are masses and that suddenly didn't become velocity and so on. So why are we not doing it in the more complicated theories where we can even get, you know, more confused because it's all abstract math and so on.
Well, I understand that you want to make sure at the end that the units match up on both sides of the equation, but I don't see what would be an example of something in mathematical physics. Say the standard model, we set C equals to one and H bar equal to one and so on. And it's the most predictive of all the models that we have. You're just choosing a specific type of units in which you're doing the calculation because they're more convenient. So that's what you're doing. Okay. What I mean is,
I don't know if you saw the iceberg in string theory that I did. They understood more about string theory by looking at that than talking to actual string theorists. Okay. Well, can you give me an overview that it was better than what other people give? So thank you. Thank you. At any rate, at some point you get n equals four super Yang-Mills theory in four dimensions and so on, and they're different results. So what I'm saying is in those results, is there something that they're doing that is incorrect now outside of
The complaint that there is no supersymmetry that we find and this is assuming strings at a base, even though what I just said was not assuming strings, the Yang-Mills case, but you get the idea. So what's something that is quite advanced in mathematical sophistication that is incorrect? I understand that for us to gain insight into what this is saying, what this means, reintroducing units is useful. Correct. But is there something wrong at the mathematical level? Like, is there something that
We've gotten incorrect. I get you. So there becomes a little tricky because that's not my job. So to be able to make the claim, I would have to know string theory enough to be able to say that or any other physical theory. And I don't have the level of knowledge that, you know, that I need that. But I can tell you this. Remember when I was talking about the real numbers, the assumption that we have to put there are very idealized, right?
And there is no way that those all those assumptions are going to hold if we are looking at something at Planck scale. And if you remember before, I said that the hard part was getting the ordering right was not getting the real numbers is getting the order right. And so what needs to happen is that when you go at Planck scale, you are going to lose completely the notion of ordering, which also means you're not going to be able to
define real numbers for things that you go and measure, because you're not going to have ordered quantities. So I don't know what structure we're going to have, because I don't have enough constraints to know what needs to happen. I don't know what are the things that I can assume to be valid at that scale. But I know that at that scale, the assumptions that you need for the real numbers are going to implode. And therefore,
i if i have a theory that says oh yes this is going to be going to work at plant scales and i see that they're still using real numbers for quantities they're using integration right because how can you have a differentiable structure if you don't have the structure of the real numbers underneath right so all these pieces that assume underneath the real numbers and i i'm pretty sure all those pieces are going to go so
If you have a theory, whatever it is, that the claims, oh, this is going to work at plan scale and it's still using differential geometry, real numbers and so on. From what I know, I would be extremely skeptical. Right. But I can't tell you any specific theory because I would have to go and look at it. I can't. And what about Dirac's equation? Does it not assume the real numbers? It's a differential equation. And that is also about the quantum. So how does that work?
If it's easier to go to Klein Gordon, feel free to go to Klein Gordon, any of them. It doesn't matter. So the issue there is that you are doing, even in quantum mechanics, you're still using real numbers, right? So you're still making this assumption that you have references and you can put them up and you have a scale that it's perfect and you know what number is greater and below. And so, yes, these structure, I would think that they have to fail as well.
They fail at what point? Like, what does it mean that they have to fail experimentally? That they do not. So here's how I think of physical theories, which is at this point very different from what people think about. For me is I have a system in front of me and I assume that I can that some things are valid for this system. So, for example,
Let's say in electromagnetism, we have the charge distribution, right? And you think that as a charge field, there is a charge density, okay? Well, that's not what we measure in practice, right? What we measure is finite charge and the finite volume. And then we measure the size of the finite volume.
And then we can make the ratio of the charge within the size of the volume. And then we make these, you know, things smaller and smaller and smaller. Right. And on the assumption that both quantities are additive, that is, if I take a volume, I divide it into two. Right. Then the total charge is the charge of this plus the charge of this. And the total volume is the size of this plus the size of this.
If I have that assumption and I make this limit, I can define a charge density, right? But if I can't do that, because I can't make this limit or the additivity does not hold, I'm not going to be able to use this assumption. Therefore, I'm not going to be able to say, oh, yes, there is a charge density. Because you see, the charge density is not the thing that physically exists. The thing that physically exists is the finite charge in finite volume.
And this is
In a lab we start with a finite thing and then we say oh yeah I'm gonna make this thing smaller and smaller and and then that's where you get the points and so on but the points and all those things exist because you're assuming you can make the limit yes so now if you start with the math and you assume the points you already assume that you can make the limits.
But if you can't make that limit because at some point you get to plant scale or because, for example, the mass is not really additive into volume because you have something that goes on the surface between them. So it is not true that the sum or the total of the math is just the sum of the mass in the volume. Same thing for entropy. Entropy sums only if you're assuming that things are are independent. If they're not independent, that assumption, right?
And so this is, again, this is my game. I need to understand what are the things that I'm assuming at the top level such that I can make those limits and I can define the points and the mathematical objects. Right. And so what does it mean that a theory is applicable in a specific case or is just whether the system that I have in front of me happens to satisfy those assumptions that I'm making?
So, do I have a classical system in front of me? Well, does it satisfy infinitesimal reducibility, independence of degree of freedom, deterministic reversibility and kinematic equivalence? Yes, I can model it as a classical system. No, I cannot model it as a classical system. I have to use something else. So, the fact that you can infinitely divide a classical system doesn't imply points still?
In the theory, yes, but it doesn't mean that we have points in the reality. So this would be a great time to talk about what defines quantum mechanics. So go over the litany of what people usually say separates a quantum system from a classical system and then show why that is false. You have a set of videos, by the way, which I'll put on screen about this. I have never seen and this was my problem. That's why I started all these businesses that I never
found somebody that told me, oh, for this system, you use classical mechanics and for the system use quantum mechanics. I mean, you have examples or, you know, if you have a proton, a double-slit experiment, then you have to use these things. But physics at the end of the day,
If you think about it, it's not like mathematics that you have like one overarching theory and say, okay, these are things that are valid for everything, right? Set theory and, and logic or category theory, if you like category theory, because I don't say that people from category theory.
And then you say okay these are the things that are that we always need to assume and then you're gonna have topological spaces and then we're gonna have groups and then you have we have things that are both groups and topological spaces and we call them topological group so you have a whole hierarchy of sort of things that you assume in a sort of well-defined sort of uniform way of looking at things.
In physics, you have classical mechanics. And when do you use it? Oh, where I have bees on a wire, where I have planets and stuff like that. And then you have thermodynamics. Oh, I use that, you know, when I have the volumes and the gas and the heat. And then I have relativistic mechanics. Oh, I guess I use that when things are really fast and then I have gravity. So it's basically you learn with a physics degree, you learn a bunch of problems and you learn to recognize patterns.
And then, you know, I have a problem of this problem is closest to this one. And so I'm going to use those things. Right. And and this is what I find completely unsatisfying. So when I was a summer student at CERN in 1999, that I was sort of asking myself where I met my wife there, my future wife, it wasn't my wife at the time. But the point was that, OK, I, you know,
I was studying engineering at the time. I wasn't doing physics and I just, you know, wanted to know, like, what are these things? I wasn't really going to read, you know, to do another thing. So I said, okay, I'm in a search. There's a big library. And what I'm sure I'm sure that what there is going to be a book, a textbook that in the first chapter is going to tell me, oh, this is what quantum systems are.
And this is why you should use this thing. And of course, I went through 20, 30 books and I found so no such. Why don't you ask someone? I asked somebody. I got no answers. Yeah. And you got no answers or you got unsatisfactory answers? I got the answers. Well, I don't know. I can tell you. I just burb. It obviously wasn't a great enough answer that it stuck with you. Oh, there was no answer.
Most professors that, all the professors that I talked to, they admitted not having an answer and they just point me somewhere else. Oh, Bell did some stuff. Go read that. I have no idea. And actually the turning point for me was when a PhD student at the time told me, look, you're never going to find these answers. The only thing that we have is the math. I can teach you the math. And so he told me the math and I learned the math badly like all physicists.
And he then stayed there for me. Okay, why do I have that math? Right. And, and then, okay, that's reverse engineer, the math, that's sort of how physical mathematics, how reverse physics started, and then realize, well, I need to actually understand the math a lot better. And that's why. But anyway, we're talking about quantum mechanics. So let me tell you what I think quantum mechanics is.
And the short story is this, is that classical mechanics assumes that you can take something divided, divided, divided, divided, divided, and you can still talk about what things are. And studying the part, all the parts is equivalent to studying the whole. So if you have a ball, you can throw the ball, look how the ball evolves and describe the ball, or you can take a red marker and put a red dot on the ball and study the motion of the red dot on the ball.
Right. And so starting the motion of the whole ball is equivalent to starting all the possible red dot that you could put on the ball, all possible finite sizes. Okay. Right. Because the infinitesimal is just the limit of all the possible finite sizes. And so when you have all the possible finite sizes, although dimension, that's, that's how you know the reason I keep having this as a sticking point is because infinitesimal doesn't mean point. It means
It's as close as you get to a point without being a point. Right. So this opens a whole another world is how do we define calculus? Because I don't think when I'm doing physical mathematics, I will need to define calculus at some point. And I don't think the starting points that we have for calculus can be physically motivated. I want to have a notion infinitesimal that it's similar to what we Newton used to think.
And right now, if you look at the books of how differential geometry is defined, you really don't have those things. You have completely different definition that even when I talk to other mathematicians that do topology, for example, like I was at a conference, a topology conference talking to one of the students and asked, you know, why are you in topology? And one of the reasons that he said was because the definition of differential geometry were too abstract for him and made no sense.
to a mathematician, to somebody who has a PhD. So if they're too abstract for him, you can imagine for somebody that has a physics or engineering background. So I'm trying to understand how we can actually define things in a way that are sort of similar to this idea of pieces that become smaller, but we can do it with modern math. So we would define it in a way that
Okay, so getting to the bowling ball and you can mark it with all these different points or it's market with a finite
find it, but but whatever size you want. So it's arbitrarily small as you can. So at that point, it means essentially describing all the points and so on. Okay, so this is classical mechanics. And in one way or another, in all that you're doing quite in classical mechanics, you are going to have this thing
So just a moment is this classical mechanics in conjunction with thermodynamics yet or is this just pure classical mechanics pure classical mechanics okay so we need to distinguish those two is that do you in your head call that pure classical mechanics where's the other one where there's the heisenberg uncertainty analog is something more cn plus t thermodynamics. Yes of the thermodynamics enters so.
This is where I cannot give you a straight answer because in my mind the distinction is yet not clear. Because you can understand one physical thing and one mathematical thing. Physically you can understand if I say that what I'm really studying are objects and I'm looking at these parts and so on. There is already a sense that
Well, I'm kind of doing some statistics there. So exactly what is it that I'm doing? I don't know. Is it enough to get I see? I don't know. Okay. And but what I can tell you is this is that this is another thing that I think, you know,
We look at it backwards. We think as statistical mechanics and thermodynamics as something that you add on top of both classical mechanics and quantum mechanics, right? So there is mechanics, which is the real thing, and you do statistical mechanics, thermodynamics, it's all sort of derived, the derivative thing. It's not really fundamental. But here's the thing.
As I said, remember that count of states that we need to define to have classical mechanics, classical home internal mechanics. Well, that's the geometrical structure of classical mechanics. It's the symplectic forms that allows essentially to count the configuration, to count to the states. OK, so that thing is what you use then to calculate thermodynamic entropy. So you use that structure to calculate the entropy.
Now, if I gave you all possible distributions, probability distribution in phase space, and I told you what was the entropy of all those distributions, like the Shannon entropy, Gibbs entropy, you would be able to recover the symplectic structure. So the symplectic structure and the entropy are equivalent because either I give you one and you can calculate the other, or I give you the other and you can calculate the first one.
Interesting. So the geometrical structure of quantum classical mechanics is exactly the structure that you need to be able to do thermodynamics and statistical mechanics. So how can you say that one is built on top of the other? They're really one unit. The same applies for quantum mechanics. The geometrical part of quantum mechanics is given by the Born rule. The inner product tells you what is the probability from going from one state to another state during measurement. Okay.
You use the Born rule to calculate the von Neumann entropy, the entropy of distribution. Now, if you take all distribution, in fact, if you take in particular the uniform distribution over two pure states and you look at that entropy, from that entropy you can recover the probability of transition from one to the other.
So again, I could give you the geometric inner product structure of quantum mechanics and you can recover the entropy, or I can give you the entropy and you can recover the inner product. They are equivalent. So again, how can you tell me, oh, quantum statistical mechanics is something that we sprinkle on top of quantum mechanics. They're really much more tied in. So that's why, you know, I can't make these arguments fully because again,
This is where I said I need this theory of ensembles. I need something that is more foundational to be able to say why I have these things, how exactly they are related. So what's interesting to me is classical mechanics seems more objective than notions of entropy. Entropy is subjective to me because it depends on macro states. So you can define macro states in any which way. You can say, what are all the different arrangements of chairs in this room?
But you could also say, what are all the different arrangements of the lights or not even arrangements? You could have something else. So there's something that seems quite subjective about entropy. It's never set right with me, but then there seems to be something ideal and objective about classical mechanics. Now I could just be incorrect about entropy. Keep in mind that for me, statistical mechanics was an easier course than thermodynamics.
And I don't like this liquid notion of entropy and heat, the whole fluid mechanics analogies. But when I got to statistical mechanics, it made much more sense to me. So one of the important pieces that thermodynamics really pushes you in your face is that you need to define the boundary of the system. So even if you have the same physical system,
But you have a different way that you interact with that physical system. You have a different physical system. So entropy, like thermodynamic entropy, the one that is important for us physically, depends on the way that you can interact with the system. Because if you think it like this, that the whole idea of thermodynamics is figuring out how much work you can extract or put in in the system.
Well, it will depend by how you can interact with the system. So James is the one that really sort of made this clear. James James. He had an example in one of these articles that basically says, you know, he was talking about salt crystals. You can say I have a can have a salt crystal and I would have a certain number of thermodynamic variables backing. I can put a polarization on the on the salt Christian.
And now the states that I'm going to have, the macro states that I'm going to have will depend on the polarization. So before I had unpolarized states and I have polarized states, which are more because then you can say I can do the next, you know, instead of linear polarization, you can make, I don't remember the quadruple. There you go.
And now you have a different set of systems. You have more. Right. You have more and more systems. And the entropy associated with those states is going to be different than the entropy that you have. So this, I think, where you have a feeling that it's some sort of subjective. Yeah, because it depends on how you coarse grain, no? It's not coarse graining. It's how you have defined the boundary of the system. And once you define the boundary of the system, you say, I'm going to interact with the system in this way.
That's the definition of the system. But this is true for all systems. Okay. So if I say I have a classical mechanics, I have a cannonball and I studied the motion of the cannonball, everything seems so objective. Yes. Right. But because we are on earth, if I put the cannonball on the surface of the sun, you're not going to be able to talk about the motion of the cannonball.
So even when you define the classical system you you have a notion I have a boundary somewhere why wouldn't I be able to talk about the motion of the cannonball in the sun because we just vaporize you have no kind of okay okay. Right and so we've just saying I have a cannonball you're putting a constraint on the environment that you have.
You're gonna have a certain temperature pressure you're gonna have some sort of equilibrium with the environment that allows you to be able to talk about a cannonball. Interesting. And this is true for classical mechanics and quantum mechanics as well. If I say oh I have an electron and it's polarized the spin up.
Well, it means that at some level, I'm going to have some magnetic trap where my electron is with the external magnetic field oriented vertically so that my spin can be up. Right? If I have it oriented in the other way, I wouldn't think Verizon, the best 5G network is expensive. Think again, bring in your AT&T or T-Mobile bill to a Verizon store
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So that's the idea. And I think that's what it's actually missing from the rest of physics. You see, it's not that thermodynamic is weird because you have to talk about the boundaries. No, it's on the other system, you're already making some outrageously simplifying assumptions, and then you don't think about it. I see. And then you say, oh,
Firmware Dynamics is so weird. No, it's like you've put yourself in the simplest case possible. The case where isolated, right? Hamiltonian mechanics where you're completely isolated, which means there is no interaction with the assignment. Your system is completely closed. That's the harder assumption that you would have in practice because nothing is really ever
Properly isolated. What happens on the surface of Jupiter will have an influence of what we are, you know, on your system. But you're going to say, well, you know what? It's small enough. I'm going to ignore it. But you are ignoring it. And the problem is that is that if you don't take these assumptions out and you think about it, you don't even know what you ignore. And then you're going to generalize both your mathematical structure, your physics and so on.
Okay, so we've gallivanted around the cannonball. Let's go back to what distinguishes quantum mechanics from classical mechanics. Yes. Okay. So we said the classical mechanics is the thing that I can think of made of small pieces and everything works and I can study these pieces as small as I want. I have absolutely no problem. And then you say, okay,
But now I have an election. I have an election, I want to start the election. I can't take a red marker and say, oh, I'll put this dot on the electron, right? You can't say, you know, how do we measure electrons? I don't know. You have electrons, you scatter some photons off of it. These are the type of experiments that you do. You can't just say, oh, I'm going to scatter the electron, but off only of this person, right? No, either you interact with the whole of the electron or none of the electrons. And is that actually what defines a particle?
I would think yes. And again, it depends on the circumstance. So if I'm talking about a proton at a certain skin, at a certain level of energy,
The photon comes in, interacts with the whole thing and is not going to tell me anything about the substructure. So in those particular settings, I would say, aha, my proton is irreducible. Meaning, not that there is no substructure, is that I can't probe it. So anything that I can describe is only at the level of the whole object.
And there is no physical process that depends on the substructure. If I am in those conditions, I can say my objects is irreducible. But then I say, OK, now I take photons and I probe the same object at higher energy. Now I can probe the substructure.
And now the thing is not a single particle. It's not a single quantum system because I can probe the inside. So I can't just use a single wave function. The proton is not a single particle at that point, but the substructures, they are single particles. Right now it's a mess. It's a little bit of a mess to tell you who are the proton. My wife actually studies the
The structure of the product, especially on the on the spin side and the host, there is a whole problem of the spin crisis there. It's a it's very complicated, but you can't describe the product as a single particle. And so now you have an electron, right? An electron. We haven't found any scale, any energy level at which
We can see an internal structure so we can always assume at least so far that the electron is a single irreducible thing because there is not nothing that that we decided but maybe in a hundred years somebody very clever will find a way rings on any whatever and that is not going to be a single no no in the example of strings you don't say the electron is made of multiple strings.
You would say that one string in some vibrational mode is the electron. So would that be a substructure? Would that technically be a substructure? No. Okay. Forget about strings. What I mean is let's say there's something else that a mini electron inside the electron in order for you to be reducible, do you have to have more than one sub part or can you just have a smaller part? Well, the whole is to be the sum of the parts. So as long as you have one part, you're going to have another part that you have to put together.
But then you're also assuming that in classical mechanics, you're assuming that you can give a state to each part independently from the other, because you're saying the sum of the parts is studying the parts independently is the same as studying the whole thing. And this is not true in quantum mechanics. Right. So if I have two particles that are entangled,
That system is irreducible. Even if there are two particles, that system is irreducible. I can't describe the system as, oh, there are two parts and I can interact one part and study the motion of one part. No, you can't do it. So quantum mechanics has a way to compose things and still be irreducible. Right. And so if you have something inside, what's going to happen is that you're going to have multiple parts and then you're going to have a quantum. So
Here the assumption, what I'm, I still have to prove again, as I said before, we get to quantum mechanics is sort of a physicsy hodgy podgy way. I'd like to do it very precisely because I want to be assured that there is only one way to create this quantized object. And right now I don't know that there is only one way.
And this is why you don't believe reductionism, even though it's associated with physics, is ultimately, ultimately should be associated with physics. Maybe it shouldn't. Same with mechanisms. No, it's fine to have reduction, but you have to assume that your physics description at some point will stop because either we'll assume I have a fundamental structure or in the case of quantum mechanics,
I can't observe below this threshold. This is the level at which I can manipulate the system. Yeah. What I mean is ultimately fundamental physics should be about what's at the fundament. So what is irreducible? And if it's what's irreducible, then it can't be reduced and it can't be described with reductionism. Right. Yes. Yeah. So the point is that either I have a system that is reusable, which I would
Think it's just quantum mechanics, right? Or I do not. But then what you're doing is just putting the level of the reducible system below it. Tell me about the early 2000s now. You said in 1999, you started to think about these problems as to what classifies a quantum system versus a classical or a thermodynamic system, et cetera. And now it's a couple of years later. Take us through your academic journey and where you are in your mental framework.
Oh, so I got my degree in engineering. I was a software engineer just because I started doing software when I was eight or nine. And when I was the choice to do physics engineering, I said engineering first. I have much more of a stable job there. And then I had the intuition, which turned out to be correct, that I will learn more things. I'm a generalist at heart. So in engineering, I
I studied control theory, information theory, system theory, a lot of different things and a lot of the ideas that I got from there actually stuck.
I basically used every intuition from every, I really like seeing the things from multiple angles. And that's why in the reverse physics, I never like to have just one condition. I like to have like, so for classical Hamiltonian mechanics for one degree of freedom, I have 12 conditions that I can say, oh, this is equivalent to this and this is equivalent to this. I really like from what are some of those 12?
Well, the four physical one we already discussed determines the irreversibility in terms of counting states, conservation information entropy, conservation of thermodynamic entropy, which means reversibility in the thermodynamic level, and conservation of uncertainty for peak distribution.
Those are the physical ones. For the mathematical ones, there are the set of equations that you have. You have the fact that the volumes are conserved, the fact that densities are conserved, the fact that the flow is incompressible. If you look at a phase space, how the flow goes around, you take an area, this flow is incompressible. And then the symplectic structure is preserved, the Poisson brackets are preserved.
And then if you take the flow, rotate it 90 degrees in phase space, the curl of that flow is zero. I think they should be all that. But anyway, so that's, that's what I like doing. Because the more hats you have, the more intuition you get and you can tie things together. Because now I know
Take us through some more of those insights that you've had where you've examined something, it could be physics related, but it could also be math or computer science related, or even artist, even you're a musician as well, even music related, where you thought you understood something, you realize you didn't, and then you observed it from multiple angles and gained
Yeah. So the most beautiful thing it's where it's when you don't even think that there is an explanation and then you find it because that's totally surprised. So when we do physics, we are taught that the math is the stuff for mathematicians. Right. And we know discrete continuous what I said, the topology. What is this? It's
And again, because I wanted to really understand these things, I said, OK, I need to understand what topology is. And what I found was that there is this link between, as I said, verifiable statements to open sets in topology. For somebody who does not know what a topology is, a topology is essentially a collection of sets for which you can do a finite intersection
and an arbitrary union. So you have two sets, you can do the finite intersection, three sets you can do further, but you can't do it. Now there is this translation between set theory and logic where an intersection becomes the end. And as we said before, if I have two verifiable statements, I can make the finite conjunction, the finite end, which becomes the finite intersection in the topology.
Or, if I have verified the statement, I can also test the OR, because as long as I have an end statement, the one terminates successfully, I can say, oh, the disjunction is true. And you can test an infinite amount of ORs? And that's the issue. How many ORs can I test? Because the thing is that I need to find one element of the OR, and then I can drop out.
So if I have countably many ores, I can go and find the one that terminates and stop. But if I have more than countably many, I'm not going to be able to do it. So the verifiable statements are closed under the countable or right. And now that you see, oh, there is a little bit of a difference between the topology because the topology tells you arbitrary or like arbitrary union. But then you think, okay, but I want my theory
To be physically explorable with with tests. Yes. And even if I give you an unlimited amount of time, the most that you're going to be able to do is test countably many. Now, if you truly wanted it to be physical, wouldn't you say that it has to you put some bound like some Bekenstein bound or some informational bound because we only have this universe. And so there'll be the heat depth at some point. And so you put Graham's number as the ultimate large number. Yeah, but
Remember, we're creating models. When we create physical theories, we create models that are valid under certain assumptions, right? So why are you going to worry about that when at the end of the day, I'm going to worry that I'm going to say that I have a system that is isolated? So in other words, we currently think that the universe will end in a heat death. We don't know because that's already assuming some physical model. So let's just say finite and not think about all the interactions and
What I mean is that when people want to say some large number, they'll usually say that's 10 to the 600 and that's larger than the amount of atoms there are in the universe. They'll usually use the number of atoms. Maybe it should be the number of interactions between atoms, which is a much larger number, but it doesn't matter. There exists some finite bound. I believe it could be Graham's number.
You're saying even to calculate Graham's number as the largest finite bound, assume some other physical theory, and we're trying to not assume that, so we're just going to say finite, not a particular number that's finite. No, I'm saying that I'm perfectly fine to assume that there are infinitely many things because it's in the model. And in the model, I can assume that there are infinitely many things, even it's like the thermodynamic limit. You make the thermodynamic limit, you say you have infinitely many particles. What do you mean? I really mean a large amount of particles.
But still in the math, you're going to do the limit with infinity. What is the problem? You do it. You know that you're making a model. So the model doesn't have to be factually correct. The model has to be a good approximation of what you do. Then in science you also have another problem is that you assume reproducibility.
If you assume reproducibility, you're already saying, I can do it one more time. Yeah. And if you assume I can do it one more time, you're already getting infinity. I see. Can we ever do something one more time? Technically speaking, technically speaking, I know I'm going to die. No.
But in the model, you assume that. You assume, well, OK, I'm not going to be able to do it with somebody else. Really, we want to put the physical theory that the sun is going to expand and destroy. It's a model. So I don't see the problem. The problem is that, again, you need the justification to say that this model, you need to know when the model holds.
And so you're basically your model is, okay, I'm going to have an infinite amount of time. I will have all these tests. It's not even infinite. You see, it's arbitrary or large, which is not infinite. And if I have a procedure that has to cope for an arbitrary large amount of time, because I can always do something one more time, you still need to give me an algorithm that have, you know, countably many possible tests that it can run.
Even if you're not going to run all of them, but the whole thing, defined on arbitrary time, is defined uncountably many. So at this point in your journey, it's 2010? Oh no, this I figured out in 2000. How was it? I don't know, 17. Okay, so this is quite recent.
The whole thing worked like this. Up until 2012, which is when I moved to Michigan, I was sort of fuzzing around by myself reading books, auditing classes on quantum field theory, reading books. I had absolutely no
Will interest to do any of this i was happy to do essentially. Engineering within a big computer so i i i wanted certain and then i remain the in a sort of big particle accelerator and i was doing.
databases, wide area network data distribution, cybersecurity, a lot of different things, control systems. I did a lot of these things in 2012. So it wasn't actually particle physics?
Well, I was in support of particle physics. What I mean is, look, we can work on creating a TV show or we could work on ensuring that the HDMI cables are plugged into the right place. They're both working on the TV show. I'm working within the experiment, working on the software infrastructure that they have. Or I'm working at a facility that provides the acceleration, for example, in I don't remember when it was 2008, 2009, something like that.
I was a broken natural lab they were creating a new light source light source is basically something where you accelerate a bunch of electrons and then you shake the electrons to generate photos and then those are very high energy photos event people use to do crystallography all sorts of things.
So it's a facility that you go, you are a researcher somewhere, you have your experiment, you book your beam line for two weeks, you come here, there, your things, you attach it, you gather your data, and then you disappear. And I was there sort of at the moment of construction, working on the control systems, working on the UI parts of the control system, working on the protocol of communication. And you were studying physics and the
I'm a spare time in your spare time. Yes. Okay. Stealing books from all these other people and that's all. And also I was auditing a quantum field theory in a Stony Brook, which is the university closer to there. And so at some point I started attending the classes to see, learn.
Then I moved, but again, it was just a hobby for me. I had no interest or inclination. I didn't think it was my job anyway, so I don't have the background for doing these things. Then what happened in 2012, we moved to Michigan and that's where some of the things about the four different ways of thinking about Hamiltonian mechanics clicked. Okay, but you had to have been doing research in that.
So you were doing research in your spare time or you were paid to do this research? No, in my spare time. I was just reading a book and trying to figure things out. That's it. And it's kind of my mind was doing that by itself. It's like having a background process that kept going. I would
My mind would think about these things while dreaming and then you wake up to say, oh, I figured out this stuff. It's all like this, completely not driven by me. It was like the curiosity of my brain. And OK, I'll give you some stuff. And yeah. And that's around the complete then doesn't tell the where was where I sort of some things started to click on the classical mechanics side before. I mean, before that, I was really more interested in quantum.
and then at some point it dawned on me
right? That what I really wanted was essentially have this dictionary between the math and the physics, right? What is the physics represent? And I realized that to really be sure that the dictionary was working, I would have to go from the physics to the math. Because if I, that's the only way that I know that the dictionary is complete. If from the physics, I'm able to recover the math. Because if I'm not able to do that, or I don't know whether I can do that, I don't know whether I figured out all the physical concepts.
And then at that point, it dawned on me, I can't do this for classical mechanics either. So it's not that I don't understand quantum mechanics is I don't understand classical mechanics. I don't understand thermodynamics and anything. And so sort of that was the first aha moment that I paid more attention to classical mechanics. In 2012 was where I started putting some something to maybe even more. I don't know. I would have to go and read them. But at some point, those things clicked.
on the classical mechanics side. And at that moment, I was still of the idea, you know, this is not my job. This is my my field. I just need to find somebody who who understands this and they can write a paper and I don't care. And I couldn't find anybody to be interested in lots of strange things. But anyway, I couldn't find anybody could be bothered to to understand or to care about the physical motivation of classical mechanics.
And that's the moment that basically said, okay, you know, I have this thing. Clearly, you know, if I want to do something with it, I have to do it myself.
I'm never gonna be able to find somebody who takes it and does something and so I started the auditing classes and doing this more but still in my spare time and in a more structured way and with my wife also who is a professor in physics so she is really more academic than me and the first thing that I did was a proof of concept
We got some seed money from the university, and we also involved a person in the physics department, in the math department, and a person in the physics department. And there for me was really, can we make like a proof of concept that we can go from scratch and get to classical and particle mechanics? A proof of concept of the assumptions of physics project? Basically, yes. Before it was even titled assumptions of physics? Correct. And this is again my
I guess by engineering thinking, you know, before doing something, you do an MVP. Yes. Right. And so I did that. And that's where, you know, I drilled it through topology and science. I said, OK, this starts making sense. I can actually like I know it can be done. And then from there, I shifted and shifted more work towards this. And now I'm basically doing it full time.
And the reason that I'm doing it for town also today is because last summer we got a grant from the John Templeton Foundations that allowed me, it's actually the first grant that we were able to do for this because there is really no money for this type of thing. And they're funding a small part into this whole enterprise.
It sounds like what you're doing is similar to foundations of quantum mechanics and there's money for that, not much. What would be the classification of what you do? Foundations of physics? It's really a foundation of physics and there are some tie-in with also foundations of math and philosophy of science. It's really the thing that is in the middle. Because the game is figuring out when I have a problem,
First, I need to understand is it a philosophical problem, mathematical problem, or physical problem? At the beginning, you said, oh, you don't just go and look at the philosophy. That's because, first of all, I need to identify where the problem is. So, for example, there is a lot of literature in philosophy that takes for face value what the physicists say that
Newtonian mechanics, Lagrangian mechanics, and Hamiltonian mechanics are equivalent. Because of course, you're a philosopher, you read this in almost every textbook, you're going to say, okay, this is what the physicists conclude, I'll go and do my thing. But then I look at it and say, okay, wait a minute, wait a minute. Lagrangian and Hamiltonian mechanics are fully identified by one function on the state. While
Newtonian mechanics is identified by the forces, which is one force for H degree of freedom. And I can't have a diffeomorphism. These things are not equivalent if I have n functions. I can't just go to one function in a continuous way and come back. So there's something fishy there.
And again, that's the math that is telling me and then the math is informing me that so you go in on the physics and you figure out, oh, wait a second. When you go and derive Lagrangian mechanics and Hamilton mechanics in the book, there is always an assumption of conservative forces. Are we ever able to relax that condition? And of course not.
Entering out that the assumption of conservative forces is so strong that you take essentially that say and and the dimensional problem into a one dimensional problem. So you discarded a lot of stuff there right so and and again.
Then you know what the physics is. And then you want to go back to the math and say, can I get from these different physical assumption? Can I go and we get the different math? And then it turns out you can. And so if you're not well informed on all three subjects, I don't mean so well informed. If you don't have a general sense, you can't put your head as a mathematician and think like a mathematician, put yourself as a philosopher and think like a philosopher. You're never going to be able to solve this because you don't know where the problem is.
It's like I have a software problem and I try to fix it in the hardware. You're never going to solve it because it's a software problem. So here is the same. If I have the math that is wrong, you're not going to be able to fix the physics. Or if you have the philosophy that is wrong, the math and the physics, you're interpreted incorrectly. They can do whatever they want, but you're never going to get to the right answer. Yeah, you and I both share this generalist mindset. So you mentioned you had difficulty publishing.
Yes. Explain. Because the stuff that I'm interested in is not what most people are interested in. I'm interested in it. I know. That's why I have the YouTube channel because I find that the YouTube channel is actually what keeps me sane.
because I see that there are people that have exactly the same question as me. And from these simple comments, I always suspected that these things were different. I can feel the frustration of these people that went through classes like I did.
the professor who is in a hurry who doesn't have the time to think about all these things deeply and quite frankly he has his own research he has to get the grant and stuff is going to tell you some answer and you kind of feel that that answer doesn't satisfy you is there something fishy but you have to take your exam and you have to move on and get a job and you never have the time to sit there and think and basically the idiot that stayed there on the time and sit there and think right
And I know that there are people that are interested in this thing, but it's not what you get grants for. And if you don't get grants for it, then you don't have people that work in the field. So it's not that people aren't interested in it or that researchers aren't interested in it because this podcast has a large platform of researchers who are interested in similar subjects as you and myself. Hopefully it's that the grant agencies aren't interested in it.
Yes, and it has been happening for so long that the people that were interested in these topics, either they didn't get an academic job or they had to switch their topic. You know, follow the money, right? So what can be done? Find people that give me lots of money. No, like seriously, I don't know. I really don't know.
What I'm trying to do is, again, through the channel, through the activity, I'm just trying to find a community of people that sort of can help me push and work on the project because, as I said, the ambition is, oh, we have to go from scratch, we derive all the math from scratch, all the physics. It's an outrageously large amount of
work. I can't do it all by myself. Do you analogize what you're doing to what Bertrand Russell did with math, trying to find the foundations, the axiomatic foundations? As I said, it has a similar feel to a foundation of mathematics and foundation of computer science. They both have a foundation where the foundation is not find the theorem of everything or the algorithm of everything,
But it's to find, okay, what is math? How do we do proofs? Right. And what can we do with a proof? Right. Or what is a computer? What is a computation device? What can we do with those things? What classes of problems are there? It's a different sort of axiomatization than say, axiomatic quantum field theory. Correct. Yes. Because I'm asking, okay, in the same way, what is a math proof? What is a computation? What is a physical theory?
What are the minimum requirements that physical theory must have? Therefore, what is the space of physical theory?
And what physical theory can we possibly have and not? And within this context, we put there all the theories that we have. So they are classified and categorized and re-systematized in the same way that mathematics is systematized and computer science is systematized. Yeah. Now suppose someone with funding was watching this and was saying, okay, is this more than just a theoretical interest?
Is there something that you see that is practical that can come from this, such as, for instance, when people were funding research more fundamental than quantum mechanics to QFT to whatever may come beyond their thinking in terms of an analogy to to World War Two, where they invented the bomb because of investigations into physics. Okay, so they're thinking, can some new technology emerge from understanding what general relativity would be like combined with the standard model, something like that?
I have no idea. That's the first honest answer. What I know is that first, it's going to make teaching physics a lot better because, again, you're going to know what you're talking about. And usually, knowing what you're talking about helps communicate more effectively. And the other thing, and this is my feeling, is that
I can't see a way for us to go past the current theory and do the theories that people want to do that unify things and so on without doing this work. And I'll tell you like this. So imagine that you are
In the late 1800s, you study classical mechanics and therefore you, well, I know if you knew manifold per se, because that maybe the concept wasn't so crystal clear, but you have, you know, that's how you thought about things with points and so on. Could you imagine knowing that, could you predict the Hilbert spaces of quantum mechanics, the projections postulate all of this?
No, because the mathematics is so different. The approach to the theory is so different. Like the jump from classical mechanics of two quantum mechanics is too far for you to be able to say, oh yeah, I want to quantize things. I'm going to need this thing. And there at least we had
The experiments that we could do both in statistical mechanics and then, you know, with this, that tells you, okay, well, we need something different and there are some hints and so on. And then it was, you know, just cram some math together. Oh, it's kind of working. Then it evolved. Now, let's say that, okay, now we want to have a theory for Planck scale or whatever those everything. To me, I expect the same jump that we had for classical mechanics or quantum mechanics.
And so I'm expecting the math that we need to do be completely different. Lord knows what it is. As I said, the no differential geometry topology. I don't know what time we're going to have a topology because that's we need to connect to experimental verification better. And so I can't imagine that we just get to the math that we have right now.
Generalized by mathematicians to solve their math problems, not for the for the physics problem. So it's not generalized with an intent. Oh, we are relaxing some physical assumption. We're putting others right. And I think it's going to be very likely that we're just going to have this magnitude of experimental data that we had for quantum mechanics.
So from my perspective, if we don't go back and re understand everything, we understand exactly what's happening from classical to quantum such that we can have an idea principle idea what needs to happen next. I don't see it happen. And again, it's not a direct thing like because I can't work on that first. First, I need I need to it's like really, you want to build a
A building that is taller, right, that allows you to see farther. That's what the ultimate theory, the theory of everything, is not at the foundation. It's the top floor. You want the top floor very high so you can see everything and do everything very good. You need the sturdier foundation on top to build higher.
And this is the work that I'm doing. I'm trying to re-understand when you're doing the foundation, you're not going to redo the foundation only for the top floor. You need to redo the foundation for all the floors in between. So all the floors are more stable so that you can build on top. So that's what I'm interested in, in reorganizing all of these things, get the math
Right. So that all the math that we have is physical and all the physics that we have is in the math. We understand we have we can read all the proofs. Right. As a mathematical as a physical argument, not just as a mathematical thing that you're doing. No, no. Every step. Right. Once you know, once you have a perfect dictionary, you can read the proof and say, oh, this is what I'm doing physically. I'm making the limit by making verifiable statement that are finer and finer and finer. And that's what I'm doing. That's what a limit is. And therefore I can do these things.
What's the latest project that's in your mind that has this unrelenting, scintillating pull to you, much like when you were in 2012 thinking about classical mechanics and you couldn't stop, you would even dream about it?
Once I've started doing this all my time, the mind hasn't been so pesky. But what I'm interested right now, it's really this general theory of ensemble space and basically the ensemble spaces. Yeah. And it really figuring out the basic axioms. And again, right now, for me, the interest is to be able to do the argument of classical mechanics and quantum mechanics well.
Basically, here's what I want to be able to prove. And let's do it like this. So we said before, right, that areas in volumes in phase space count the number of states, right? And
And they have a measure, they don't count the points, right? If I have discrete elements, you just count the points, then that's fine. But areas in phase space, right, when you are a continuum, you have infinitely many points. So you can't just say, oh, I have infinitely many states, because then if you double the space, like if you double the volume, you would have the same number of states, which makes no sense.
So you put mathematically a measure, and the measure is going to be additive. So if you take two volumes that are disjoint, and you double it, you're going to have double the size. Perfect. Now imagine that you have these volumes and you divide them in half and half and half and half. At some point, your count of states will become less than one. What does it mean to have a region with less than one state? It means nothing.
Not only, remember, if you have a uniform distribution on a certain amount of states, the entropy is the logarithm of that number, right? If I have less than one state, it would mean that I have logarithm of a number less than one, which is negative number. What does it mean to have negative entropy? Nothing. So this is where in another way to say, OK, classical mechanics does not work because it tells me that there are regions with less than one state.
What happens is that if you do this analog, if you try to construct an analog of this, and I can't understand why nobody has ever done it. I've never seen it in the literature. If you do the same analog in quantum mechanics, you look at the entropy how it goes. Well, the entropy of pure state is exactly zero. And the exponential of zero is one. So every pure state count as one. And you can't have something smaller.
But the state space of quantum mechanics is still a continuous, like if you take the block ball, which is the two degrees, the surface is still continuous. So what happens if you take the surface of the full ball and you say how many states there are there? There are two.
Because the
And there are basically these three conditions. You want to be able to count things, right? You want to be able to count states. And there are three things that you would imagine. One is that every state counts as one. And if you have a finite region of phase space, of your state space, that should have a finitely many states. And you want the measure to be additive.
What you can't have all three, because once you have infinitely many points and you say everyone is one, well, the count of the region is going to go to infinity. And so you can you have to relax one of this. And what happens is that if you are in a classical discrete space,
You relax that the finite region are going to have finite entropy, finite count of states. So everything is out of it and every state is counted one. On a Lebesgue measure, what you do in phase space, you say, well, points are zero, but then I still have finite volumes and I have additivity. And in quantum mechanics, you say, well, I remove the additivity. And there are a lot of things that you can see that the weirdness of quantum mechanics
comes from that activity. But then you see, okay, why do I want to lose that activity? Well, because I need to be able to count states. Every state must be one and a finite patch with infinitely many states on top of it. If I make a mixture of that, I still need the final 10 to be final to many states. And so this is what I like to say that there is only one way to create the ensembles that have an entropy and account of states.
such that I have a measure defined on a continuum that counts a state, but it has a lower limit. And so the quantization in my mind is really putting this lower limit to the count of states. Classical mechanics does not have, because you can make things smaller and smaller and smaller. So you take one state, choppy, choppy, choppy, choppy. In quantum mechanics, the quantization is, I can't have less than one state.
And so when you go up, things are going to look additive, things that are going to look classical. But when you go smaller, I know that you have this lower bound. And just to tell you, this is what I'd like to have in this ensemble of spaces, I'd like to be able to run that argument. But I want to be able to create this structure in a way that I'll be able to use for field theory as well. And that's a challenge because it's the whole problem of infinity. And I want to
Try to see if I have a path for quantizing space-time as well, and leave it as a possibility. Because in space-time you're going to have the same problem. You say, I have a field theory. Now, I count the number of states in each field, but then I have to count the number of degrees of freedom. And in particle mechanics, it's fine at the content one, two, three, right? But in a field theory, you have a field for each point of physical space.
So now you have, you know, sort of continuously many degrees of freedom. You can't say that they're infinite. That wouldn't make sense, because if you double the region of space, now you would have the same number of degrees of freedom. So what's going to happen is that you need to put a volume measure on space. And you say, if I double the volume, I have doubly many, twice as many degrees of freedom. Right. Well, why don't you just use the, I mentioned this before, the Bekenstein bound.
I need things to go smoothly to zero. I can't just say at some point things become discrete because that's not what's happening. What's happening is that I have something where I still have, you know, all these dense states. Quite frankly, it doesn't even matter if it's real or rational. The important thing is that you have dense sets and you need to count the elements in the dense set.
All right, Gabriel, so we talked about philosophy, math and physics. Let's talk about math and physics. Where does that line lay? Okay.
Yeah, so the line between math and physics is something that I, you know, had to think a lot about because since I want to have this sort of rigorous axiomatization approach, I need to understand how do they do in math and whether the way that they do in math is actually good for physics if it's enough.
And one of the things that we have sort of a wrong impression in physics or in engineering is that math, it seems also elegant or pristine and so precise. And it feels like everything is there and we should imitate math in some way.
But this is never going to work because the way that math is able to be rigorous, like the way that they did it is essentially to remove all the parts that are difficult or impossible to make precise and remain only with the formal structure, the syntactic structure that you can actually be precise about. So there are sort of a lot of things like
There's the largest number that can't be described. There's the smallest number that can't be described in so-and-so amount of characters. Exactly. That's something that if you have meaning, meaning is attached, meaning is always these very fuzzy things and it always allows you to create some things like that.
And so what, I guess, the formalists decided, Hilbert, I think, was the one that pushes for this, is, okay, we'll forget what the meanings are. We just have some symbols. They have some rules. And that's it. That's all that we're going to describe in mathematics. And a lot of mathematics is now thought in that way, in one way or another. And in a sense, that's sort of where the power of math comes from.
because if you talk about, I don't know, a boule and lattice, for example, well, that same structure could be representing sets of statements. So a logical structure or sets of sets, or it could have like physically could even describe the systems and subsystem relationship. So you can study the mathematical structure. You can study the equations regardless of where they come from.
So in the end of the day, to the mathematician, it has an advantage to just drop the meaning because then their tools are more powerful because they can apply regardless of the meaning.
And in physics, we can't do that because we have that pesky connection with experiments. And so we can't just manipulate the symbols in any way, whatever. We need to know that that symbol corresponds to a specific system prepared in a specific way with things that we measure a specific thing. So we always have an informal system in physics. You can't just get rid of it. And so what the challenge is,
is not saying we're going to put everything in the formal system because it's never going to happen. The experiments are not going to suddenly become symbols. You need to define what is advantageous to put in the formal system and what is not.
And that's the hard part. So it's not a question of whether you can do it, but it becomes, you know, sort of a technical problem, sort of an engineeristic problem in how can you do it efficiently? Essentially, the game is to find the again, the minimal set of axioms that you want, that you need, actually, in the form that it's as easily justifiable from the physics.
Because that surface, that line in between when you take physical informal things and you put them in the formal things, that's where the things can go wrong. Once you are in the formal system, you have the math to help you. And so those parts, and that's the part that I'm interested in physical mathematics, getting those definitions and justification right, it's the part that is the most difficult. And it's most difficult because
I have a feeling, and I'd like to be able to have a proof for this, but again, you can't because it ties in things in the informal system, so it's difficult to create a proof for that. I'd like to have a tight argument that shows that whenever you're taking something from the informal system to the formal system, that is my feeling, you are always going to make some kind of simplification.
And so even a simple concept like, you know, whether something is an orange or not, right, you go to a supermarket, you can easily identify what is an orange or not an orange. So it seems natural that Oh, that's a true false statement. Very easy. But even think how an orange develops starts with a flower gets pollinated. And there is no point that you can say, Oh, this is the instance where he actually became an orange. Right. So all these concepts that we have are fuzzy.
And you're going to have to make a cut. And so if you're talking about objects in a supermarket, yeah, perfectly fine, because we're not having, we're not going to have these in between. And so it's going to be either true or false. But if you're studying your biology, you're not going to, that statement is going to be defined. So even defining this property, even defining the statements themselves, I don't think there is a way to define statements that are universally applicable in all circumstances. It's always a matter of
I have a realm of applicability, a domain, and in that domain, in that context, that statement makes sense. Okay, you just mentioned the word cut, which makes me think of Heisenberg cut, which makes me think of the measurement problem. So I'm curious what you think of the measurement problem. What have you found out? What are your current thoughts?
I don't understand what the measurement problem is, because when I talk to a lot of people, they seem to have a different interpretation. How would you formulate the measurement problem? What counts as a measurement? That I don't have an answer for. It's, again, one of those things that for me lives in the informal system.
And so I don't even know if I can formulate something precise. Right. So you see, this is exactly why I asked because there is another part that is why do we have two different laws of evolution, one for measurement and one for processes that I think can be understood. Oh, okay. But what counts as a measurement that
What separates a measure from a measured? Well, yes. So what I want to say is that in this realm, what counts as a measurement, what counts as a measurement, and all of these problems are connected to the problem that I was saying before of defining boundaries between system and environment. Because when you're saying I have a system and make a measurement, you're basically saying, okay, there is a system,
There is a boundary. Well, let me predict a problem with this is that if we're saying that, then there's necessarily something subjective because we're going to be the ones that are dictating the boundary. There's then the meta measurement problem of who is defining the system. Right. So defining the system is not subjective. It's objective, but it's contextual. Like you need it again.
In this context, these are the things that can happen. This is what happens at the boundary. So it's not an arbitrary. When I say I have a system and I define a boundary, I'm also defining what is happening at the boundary.
Right. So it's not just saying, oh, I'm grouping these things together, but I'm grouping this together. There is this interaction between the boundary and the system. Like I need to give you the boundary conditions, not just to solve the to find the problem of the equation, but we need to be able to define the system. Right. And so part of the problem of defining what a measurement is and how it works and all of this is because you are trying to model something that goes across the boundary, which is
Even just the information that passes from one thing to the other, and then information has to be encoded in some physical system. So something needs to happen. And then in quantum mechanics, there is a thing that actually happens during the measurement. And this is how I think about it. So imagine that you have your block ball for the two state system, right? You pick an observable, right? Which means you're picking an axis in some direction.
and the points at the axis are going to be your eigenstates and all the points in the middle are mixtures of those of those two states right so now imagine that you start at any other points right and you want to say oh i'm going to make a measurement right like none of these what you're going to be predicting after the measurement
Is going to be that you're going to be either in this state or this state. So you're going to be in this after the measurement. What you predict is that you're going to be at a point on the axis. So what the measurement process needs to do in one way or the another, whether it's through whatever mechanism, it doesn't really matter. What needs to happen is that that point that is here needs to be projected on that axis. That process is a process that increases entry. Right.
And so that's something that needs to happen. And there are a lot of people that from other places argue that measurement devices are things that increase entropy. You have a metastable state that gets perturbed and then falls into two equilibria, right? There is this sense that you have something and you fall into two equilibria. And there are some people that have argued that there is literature in that that it shows that.
But I'm trying to argue it more from a sort of more conceptual, you know, again, from what I need to have to be able to make this make sense. And there's something else that, yes. So I understand that this measurement process is a process that actually increases entropy. It has given me sort of a way to think about these changes of context.
Add along the lines of what happens in thermodynamics. So since you started the statistical mechanics and you are happy with that, you know that there are different types of the sample. There is the grand canonical ensemble, there is canonical ensemble and so on. And in each of those ensembles, some quantities are the ones used to actually define the ensemble. So if I have a cup of water,
And it's just sitting there and I ask you how many molecules are there in the cup of water? Well, it's a problem because molecules keep going out and coming in. So the molecules are fluctuating, right? And this is the overall macrostate is not defined by the number of molecules. It's a grand canonical ensemble is going to be defined by temperature, volume and chemical potential.
But now you want to really see and say, I really want to know how many molecules are there. And so you need a way first to stop these molecules from fluctuating, because otherwise you can't even know which one you can't resolve. So what you do, you close the glass. And when you close the glass, you transition from a grand canonical ensemble to a canonical ensemble. And now the canonical ensemble has volume, temperature and number of particles well defined.
And the chemical potential is no longer well defined. Now, of course, when you close that you can predict exactly how many molecules are there because the molecules were fluctuating.
So the final state is going to be a probability distribution over all the possible canonical ensembles of all the different number of molecules with the distribution exactly matching the fluctuation that you had before. Wait, why can't you just say if you have a cup you say how many molecules are in this cup at 2 p.m.
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I see. You switch the thing, the number of molecules are no longer fluctuating. In a way, you can think of measurements in quantum mechanics doing exactly that. So you have your spin system, right? But wouldn't that have some hidden variable associated with it? The hidden variables, you can only define them
If you're able to prepare ensembles that are at a finer resolution of what you were able to do. Right. So you are able to talk about the actual number of particles and so on in those ensembles because you can isolate the molecule and talk about the parts.
But now when I have a single system, how can I talk about the fluctuations of the spin in terms of hidden variables without at least being able to talk about ensembles that are better specified than just a single spin state? To put it like this, imagine that you have a probability distribution.
You could have that probability distribution because you have a single point that is jingling around, or because you have an actual statistical distribution, something that is actually smeared, and that thing is jiggling around, or I really have something smeared and I'm just taking a piece of it, right? The ability for you to distinguish between these three cases means that you're able to resolve the system at a finer level.
But if you say, oh, my system is irreducible, I don't have a finer level, you can distinguish between these three things.
So whether there is really like a spin that is jiggling around or something that is more complicated that is jingling around or some kind of uniform distribution that then collapses into something like this, to be able to distinguish those cases, you would need to, again, have a finer level of description, which assuming irreducibility tells you that you can't have.
So there are a lot of things that once you assume irreducibility, you can get a conceptual level at quantum mechanics without. So if you say, OK, my system is irreducible, right? It means I cannot have a perfect value for positional momentum. I need to have this finite entropy that smears things out, because if everything was at a single point, I would be able to tell you what all the parts were doing. All the parts were exactly there with the same exact fraction of momentum.
So you can say that so you need some kind of smearing you need some uncertainty principle.
which actually in Italian and other languages is more an indetermination principle than uncertainty principle. And I think it capture really more what's going on. So you need to have this system to be a little bit undetermined so that so that you can say, I know everything of what's going on. But once you say that I have a distribution in space that I can't tell what the parts of the distribution are doing. Well, that thing is non-local by definition.
Because I have something that is distributed in space, but I can't say, oh, I can follow one part in space and what it's doing. And so you can only follow the whole thing. The object is no lockout because it's irreducible.
But you're not going to be able to have communication from one side to the other, like superluminar communication or those things. Because if you were able to detect it, you would be able to go at a resolution that it's below this uncertainty and be able to make a correlation between parts. But you can't because the system is irreducible.
So you see, a lot of these weirdness that once you swallow the bullet, like it's like in relativity, you say, okay, I will concede that the speed of light is constant. And then you're, oh, energy is equal, mass is equal to energy and all these things. But it's all from here, from there. And so I think this is sort of the same idea. The system is you can't know what's going on inside.
Okay then i'm gonna have a new principle i'm gonna have that the thing is you know no i mean that we could have some bizarre laws that are just inaccessible to us yes including retro causality or superluminal speeds if they're not accessible to us you can't even say whether they are retro causal or superluminal interesting you can only say that because you set up an experiment every time that you do this
You know, this happens before that. So we've talked about what's directly next for you. You're hoping to solve this problem. I'm working on this ensemble space and trying to get that math to work out. What's something you hope to achieve in the next 10 years? I hope to find other people to help me clear up and fix both the mathematics and also the philosophy of this.
What I really love, because you see, I'm okay enough to scope some of these problems, but I don't know that I will ever be able to achieve the technical competence in all the sub fields that I need to be able to carry the project through. I mean, it's just a matter of time. So the thing that I'm
I've been trained myself to do is to be a translator so that I can talk to the guy who does philosophy of. Yeah, that's something else that unites us is that I think of theories of everything as a Rosetta Stone or it's I hope it to be a Rosetta Stone because academia is designed to instead of creating the silos.
Add that don't really know how to talk each other to each other. I really had some problems and philosophy. I think in some sense is the worst offender because they still have this idea in mind that the philosopher is the one that thinks by himself in a room and then comes up with this great idea. And then this price, the single author paper, which
Right. That is true. So that for people who don't know who are watching who aren't researchers in physics, it's quite common and computer science and math to have multiple co-authors. But in philosophy, it's quite rare. And I have had this problem that I did find some PhD students that from that were instruments working and I wrote a paper with one. We have another one that sort of PhD student in philosophy.
And, and one of them clearly said, you know, I can't put so much time in this because I need to have my single author literature. Otherwise, they're not gonna take up and not gonna get a position and all that. And, and to me is bizarre because
You know, you start writing the single author paper, I guess, you know, when you're 20 something, there is so much stuff that I had to learn on both math and physics and everything before I had even something remotely interesting to say, you know, I said it before, I didn't start doing this when I was
I
Yes. What are you going to be able to say? The hard bit right now is putting all these pieces together because it's like we have most of the pieces scrambled around in silos that don't know how to talk to each other.
and nobody's ever even able to see that they go together. And sometimes they're not designed to go together because the math is designed by the mathematician who doesn't know the physics and the physicist is thinking about their things without knowing that there is some other math over there.
And so what I'm trying to put is like a framework where I said, okay, the mathematician says that, okay, that party has to be there. But the physicist says that so that that thing can't be said like that. It needs to be and then the philosopher says the other thing. And I guess his perspective needs to fit like you need to put all these things in a way that they all fit together. And but the training that they all they have, right is only from there.
Viewpoint and so a mathematician might look at my thing and says, oh, but why did find things like that in mathematics? Yeah, I know that in mathematics you do that, but I need to justify that the accent from the physical and you're not interested in the fun and perfectly fine. I'm going to reach your structures, but it can't be the foundation of physics, a mathematical structure that you put there.
What I really like to have in 10 years is to find other people like me that are interested in getting this piece.
specific technical or one thing without having the general thing. That's not a problem. I can keep the general thing. I can keep all the things together. Right. But the other person. You're the manager hiring a front end developer and then a back end developer. They don't need to know. They don't need to know the detail of all that. Yes, it's exactly. It's an engineering project. It's not a research. This is the other problem. In academia, they always think that you need a grand new idea and so
If you're an engineer you know the most of the time you want the simplest idea that works and that creates the list and these are the things that i like find it's not all the new you know grassman compacting fiction of the whatever whatever like it.
No, the simplest math that works, and we already have a lot of math that works, and it must be a reason why it works. There must be a physical justification for where it works, so we need to uncover important things. So if I had other people to help me do this, maybe we could finish the project before I die, and that would make me happy.
There are some researchers who are watching right now who are probably interested. Where can they find out more about you? How can they contact you? So I have a YouTube channel, but that's mainly for popularizing the research. So my YouTube channel is called Gabriella Carcassi. Gabriella Carcassi is my name and last name. There is another YouTube channel called Assumptions of Physics the Research. It's where I try to put every month sort of me talking for an hour, an hour and a half of open problems that I have.
And even there I did this June, I had a sort of an online summer school on the assumptions of physics, which again, it's something that we promoted through the internet. And all of that is recorded. So you hear me rambling for, I don't know, nine hours, you know, these things that saying these are the pieces that we have. These are the pieces that we don't have. These are the pieces and how
So there is a lot of content there and then of course we have the website the assumptions of physics dot org that has all the research we have an open access open source book which is to me it's the thing
that is the output of the research. So whenever pieces are figured out, they become an extra chapter in the book. So there is a reverse physics part that has all of the classical mechanics, all with the details, all these conditions and how their equivalents are or they're not. And then there is the physical mathematics where we get topologies, we get continuous functions and we get the real numbers. All of that is there. So if somebody wants to look at how actually things are done are there.
And that's the idea. I'd like to run this as an open source project. Who knows whether we're going to be able to do it or not, but I'm trying to set up the structure more and more like that. And I'll try to
try to push some of my work more online because again since there might be other people but I don't have salary to give them but maybe they have another position somewhere else and then we can collaborate well if you can structure it in a manner similar to how open source projects are structured
People contribute little bits here and there. That would be the idea. I don't know how to do it because I don't have a template for that, but all the software development that I did before within physics was all open source. So that's sort of my nature. I think that may be more impactful than any given one of the outputs of this project is the entire
Templating of an open-sourced physics project because that can then be used. I understand and I have to figure that out. I would be extremely interested because I want to know.
What are the limitations of academia so their academia has pros and cons and what they're pro at they're fantastic at some don't touch that but what are the cons and how can they be filled not to supplant academia but to supplement we could have a whole other to our discussion just on that topic and there is a lot of things
From my perspective, that the type of things that I do, academia is insulated by design, but I wouldn't even want to change academia because you don't change the structure of a whole field for the project that it's like, it wouldn't even make sense. So yeah, the way that I'm trying to set up,
This year, we are having the first PhD student coming to work with us at the university. And he learned about the project years ago through the YouTube channel. Okay, the first PhD student for this project for that's not for your university. No, no, no, quite a new university. Yes. But that's why I started becoming more active on YouTube, because I've seen that I have much more impact
Also, thank you to our partner, The Economist.
Firstly, thank you for watching. Thank you for listening. There's now a website, curtjymongle.org, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon, they can disable you for whatever reason, whenever they like. That's just part of the terms of service.
Now a direct mailing list ensures that I have an untrammeled communication with you. Plus, soon I'll be releasing a one-page PDF of my top 10 toes. It's not as Quentin Tarantino as it sounds like. Secondly, 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, which means that whenever you share on Twitter, say on Facebook or even on Reddit, etc., it shows YouTube, hey, people are talking about this content outside of YouTube, which in turn
Thirdly, there's a remarkably active Discord and subreddit for theories of everything where people explicate toes, they disagree respectfully about theories, and build as a community our own toe. Links to both are in the description. Fourthly, you should know this podcast is on iTunes, it's on Spotify, it's on all of the audio platforms,
All you have
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▶ View Full JSON Data (Word-Level Timestamps)
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"text": " The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science, they analyze culture, they analyze finance, economics, business, international affairs across every region."
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"text": " I'm particularly liking their new insider feature was just launched this month it gives you gives me a front row access to the economist internal editorial debates where senior editors argue through the news with world leaders and policy makers and twice weekly long format shows basically an extremely high quality podcast whether it's scientific innovation or shifting global politics the economist provides comprehensive coverage beyond headlines."
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"text": " As a Toe Listener, you get a special discount. Head over to Economist.com slash TOE to subscribe. That's Economist.com slash TOE for your discount. Close your eyes. Exhale. Feel your body relax."
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"text": " And let go of whatever you're carrying today. Well, I'm letting go of the worry that I wouldn't get my new contacts in time for this class. I got them delivered free from 1-800-CONTACTS. Oh my gosh, they're so fast! And breathe. Oh, sorry. I almost couldn't breathe when I saw the discount they gave me on my first order. Oh, sorry. Namaste. Visit 1-800-CONTACTS.COM today to save on your first order. 1-800-CONTACTS!"
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"text": " When did we first get in contact? Oh jeez, I don't remember."
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"text": " It must have been more more than a year ago. Yeah. OK, well, I've been following your channel for approximately one year. I believe I contacted you shortly afterward. OK. Yeah. And you have a fantastic channel people should know about. So it's called the Assumptions of Physics, or at least that's the project name. And Gabriel is going to take it over at some point and give the elevator pitch the five minute version. So a long elevator at CN Tower or in Toronto, that sort of elevator. What makes your channel different?"
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"text": " is that you focus on the equations and the rigor and many people who are into demonstrating that some conventional aspect of physics is incorrect. If they're in the academy, they do so from the philosophy of physics angle. So maybe some interpretation of quantum mechanics, but you don't focus on that. You're much more about demonstrating with line by line proofs. In that vein, you remind me of Jacob Berandes and he's from Harvard and you're based in Michigan."
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"text": " Well, I'll list some examples for people who, if you just want a teaser of what's to come, why is it that Heisenberg's uncertainty or some analog of it is already in classical mechanics under the proviso that you have to assume that thermodynamics is true? Another is that the action principle, which the way that I thought of it is, it's a compression mechanism. So it encodes several different equations inside and then you unpack it with Euler-Lagrange's equations."
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"text": " You show the action principle itself has a geometric meaning and the idea that you can translate between Newtonian mechanics and Hamiltonian mechanics and Lagrangian mechanics is false. You can't. There are some systems that are only describable in some or not translatable to the other. There's not a one-to-one bijection between these guys. Correct. Okay. We'll also talk about what defines quantum mechanics. So many people think that it's commuting variables or non-commuting observables."
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"text": " Is that actually what defines quantum mechanics that makes it separate from classical mechanics and why reductionism is incorrect? You have a video on, you shouldn't think physics is reductionistic because at some point you get down to atomic facts. At the fundamental level, to justify the mathematical structure, you can't just say, oh, there is another mathematical structure that I used to justify this because how would you justify the first? And another way of saying that is that people think of physics as a mechanistic science that you're always looking for mechanisms."
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"text": " But also that's another false view. I believe you say that because you can't look for a mechanism is something that's irreducible. Right, because it's more that if you are at the fundamental level, you can't invoke a deeper level to justify the fundamental level that you have. There is no mechanism after that. That's a bit of a teaser. Some of those are technical. But why don't you go over the assumptions of physics project? Right."
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"text": " The project that I, the goal of the project that I work on is essentially to find a minimal set of assumptions, of physical assumptions, from which we can re-derive the laws. And we have essentially two approaches. One we call reverse physics, where we start with the current laws of classical mechanics, quantum mechanics, and so on, which there"
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"text": " modern theories are just presented as sort of a mathematical structure. And the idea is to go backwards from that mathematical structures and find physical conditions that are equivalent to that mathematical structure. And that's why it's called reverse physics, a little bit because it's like reverse engineering. You're taking the thing, breaking apart, finding what pieces go together, what pieces are independent. And another reason is because in the foundations of mathematics, there is an approach called reverse mathematics."
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"text": " Now just a moment. So in reverse mathematics, I've always wondered, so just for people who are tuning in, there's a theorem and then you usually use assumptions to prove a theorem. And the way that I understand reverse mathematics is instead of starting from your axioms and moving forward to derive a theorem, you start with what could be true and then you think about what needs to be true in order for that to be true."
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"text": " Well, you're looking for a subsystem. So, to prove a simple theorem, you might not need, let's say, all of mathematics. You might need just a smaller subset of starting points, let's say. And you sort of, by doing that, you sort of learn more of what is the structure of mathematics itself. Now, I'm not an expert in this, but I actually had a chance to talk to one of the people that work there."
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"text": " And so what I do, what we do in assumptions of physics in the reverse physics is slightly different because we're more interested at the conceptual structure, like what is the minimal conceptual structure that I need to get to some parts of the mathematics of the physical laws. But like the spirit is the same. You're taking what you think is physics, what you think is mathematics, and trying to find what pieces are there, like the structure of"
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"text": " of physics itself and mathematics itself."
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"text": " And one of the things that then we saw while doing this work is that you can have these, you know, physical assumptions that are equivalent to the different laws, but that sort of gives you only the higher level mathematical structure. And what we realized is that you really can't say that you understand the higher level mathematical structure if you really don't understand all the nuts and bolts of the more fundamental mathematical structures."
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"text": " And so we started another approach, which is called physical mathematics. And there the goal is really to start from scratch and layering each axiom and definition and each axiom and definition has to have a physical justification. So it's not enough to say I have a mathematical structure. I have to say these are the things that I have to model in the real world. And this is why I will use this particular mathematical structure to model this thing. Why don't you give an example right now?"
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"text": " So, for example, the basic constituents that we use in physical mathematics, because we need a basic building block for everything, is the idea of an experimentally verifiable statement. A statement for which you have a test, and the test succeeds in finite time if and only if the statement is true. So, for example, you say the sky is blue, you can look, it's blue, finite time, verify."
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"text": " Something like the mass of the electron is less than 10 to the minus 13 electron volt. That's something where we can go and verify. But a massless photon. As another example, you can say the mass of the photon is less than 10 to the minus 13 electron volt. And that's something that we can verify experimentally. But if you said the mass of the photon is exactly zero, that's not something that we can verify experimentally because we always are bound to finite precision."
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"text": " And so these are the things that we want to have as a fundamental thing. We want to say a physical theory has to give us statements about the world and a physical theory has to be fully explorable by testable statements. And so those are the things that we axiomatize. We say these things exist."
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"text": " And they have a particular way to be composed."
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"text": " But if you have infinitely many, you're not going to be able to be guaranteed because it would take you an infinite time to do it. So for a verifiable statement, you're only guaranteed that the finite conjunction is actually verifiable. You're not guaranteed the infinite conjunction. So the infinite conjunction is still a statement, but it's not a verifiable statement."
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"text": " And again, we have in the justification, we have somewhat proofs that would have been accepted as proof probably in the 1700, but they don't follow the current standard mathematical rigor, because mathematical rigor now starts with essentially elements that where the meaning is being stripped out is just symbols that you manipulate and so on."
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"text": " And when we are trying to reason on the physical objects, well, the physical objects are not meaningless marks of paper. And so we need to be able to reason what these things are such that then we can find these definitions and say, OK, these things can be. And so all of these process we call physical mathematics, because at the end of the day, we will come from mathematics. We will have all the theorems and we want to recover the mathematical structure that we already have. We don't want to create crazy mathematical structure that we"
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"text": " We don't know what they are. You want to justify the use of the mathematical structures that we already use? Correct. And find whether those are 100% appropriate for the type of physics that we're trying to describe. And what is the realm of applicability in those mathematical structures? So something like the real numbers or even the complex numbers. Correct. Which are a continuum. Do they have a place in physical mathematics?"
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"text": " Yes, for example, we have a complete derivation or we have a set of necessary and sufficient physical assumption they have to make such that a set of variable statements are going to be identifying with identifying essentially open sets of the real numbers. And so we know when we can take those things to be valid or not."
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"text": " And again, the idea is really to construct things that are a modelization of what we do in a sort of operational settings. So how do we define numbers? Well, we're going to have a reference and then we say something is before the reference or after the reference. So, for example, we have a clock ticks and then we say something happened before the third ticks and after the second."
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"text": " Or you have rulers and you have notches on the rulers and you can say before this notch and after this notch. Or you have a balance scales and you have weights that you put on one side. It always works with this. You have references and the way that these references work is that essentially they give you three statements. Whatever you're measuring is before the reference, after the reference or on the reference in the sense that it overlaps."
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"text": " And the before and after are assumed to be verifiable. It's something that you can check. And now the question becomes, how many references do you need? And what is the logical relationship needs to be such that all these references are going to tell you, aha, you're measuring something on a continuum of the real number."
},
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"text": " And what is most interesting in doing this work, apparently that is fascinating because you really understand exactly how these things work. What we find is that there are three conditions that you need to have that are the most important and they"
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"text": " It's like the biggest difficulty is not getting the real numbers. The biggest difficulty is to find a linear order. So a set of points that you always have something either before or after. That's really where all the sort of a harder assumption that you need to put are there. Once you have the linear order,"
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"text": " Whether you have the real numbers or the integer is just a matter of saying, oh, I have two references. Can I put one in the middle of the two? Okay. Now, why is it difficult to have an order on the real numbers? Because they already are ordered. Right. No, it's justifying an order with just saying, oh, I have these references where things can be before or after. Right."
},
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"text": " References don't need to be ordered. You have references in space and you don't have a linear order there, right? And so the idea is that all the references have to be able to be arrangeable in some way, such that, for example, if I put a reference and another reference, you know, having something that is before this implies that something is before the other."
},
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"text": " Right, because the point is that you're starting from scratch. You just say, I have a bunch of statements. What are the minimal conditions that I have on those statements such that an order emerges from these statements? And that's the hard bit. So what are you working on now? What I'm working on right now, it's a sort of a"
},
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"text": " The piece that I need in between physical mathematics and reference physics, I need physical mathematics and reference physics and reverse physics, reverse physics. Right. So I speak to everything that sort of merges together."
},
{
"end_time": 922.176,
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"start_time": 902.295,
"text": " So from the reverse physics side, I have a lot of conditions that allow me to recover fully classical mechanics and quantum mechanics in a hodgy podgy way that a physicist might like, but not a mathematician."
},
{
"end_time": 951.937,
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"start_time": 922.602,
"text": " And I need a place where I can run these arguments in a more precise way. And so I need sort of a general theory of the states and processes that it's more abstract than the two theories, such as I can say, these are things that you always need to have if you're doing physics. You need to be able to define states and states have to have these characteristics. And then if I have a classical system, I'm making this additional assumption."
},
{
"end_time": 973.012,
"index": 39,
"start_time": 952.142,
"text": " And if I have a quantum system, I'm making these other additional assumption. So I basically want to be able to push as much as I can. The theorems that are true, both in classical mechanics and quantum mechanics, push them up to a single theory, right? To a more general theory so that I can see these two other theories as instantiation of the two."
},
{
"end_time": 1002.944,
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"start_time": 973.012,
"text": " And so, again, this is part more of physical mathematics because I need to identify actions that I have to assume to be able to do physics in the same way that I say, well, physics is about experimental evidence. So I have I need to have statements of other words that are testable. What I want to say is that physical theory has to be testable in a repeatable way. Right. I need to be able to set up experiments and test them."
},
{
"end_time": 1032.807,
"index": 41,
"start_time": 1003.336,
"text": " And so the basic objects that I have to describe a system must be at the level of ensemble, because when I go and prepare things in a lab, that's what I prepare, prepare ensembles, I prepare statistical things that then I make statistical measurement and it's on these statistical measurement that we have the interest. So this sounds extremely practical, like everything that comes from physics has to be some experiment or some"
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"index": 42,
"start_time": 1033.097,
"text": " a statement about an experiment or an observable. Would the theorem, if you have a vector outside the light cone, then you act on it with the Lorentz group, you can rotate it to any other vector outside the light cone. Would that be okay under yours or would that not even be considered physical mathematics? Because it's not making some specific experimental statement. In other words, if you have a space like vector, it will always be space like under any Lorentz transformation."
},
{
"end_time": 1072.688,
"index": 43,
"start_time": 1063.183,
"text": " Right, that's going to be if you have set up things correctly, right, that's going to be something that comes out from the math. So that's an OK statement."
},
{
"end_time": 1097.142,
"index": 44,
"start_time": 1073.251,
"text": " Yeah, it's probably come. So that's going to be true when we are doing even reverse physics in classical mechanics. You do find that when you set up your assumptions for classical mechanics, by the way, are not very difficult. You need three things to get to classical mechanics. One is that what we call the assumption of infinitesimal reducibility."
},
{
"end_time": 1115.913,
"index": 45,
"start_time": 1097.585,
"text": " You have a system and the system is made of parts and the parts are made of parts, the parts are made of parts, and giving the state of the whole is equivalent to giving the state of these infinitesimal parts. And so the infinitesimal parts are essentially what we think of the classical particles, right?"
},
{
"end_time": 1141.766,
"index": 46,
"start_time": 1115.913,
"text": " and the whole system is giving is a distribution over the space of the particle. You're going to be able to say, you need to be able to say 10% of the system is within this part, this 10% of the system is within these states, 90% of the system is in the other states. So it's really a distribution over all the possible configuration of the infinitesimal parts."
},
{
"end_time": 1160.964,
"index": 47,
"start_time": 1142.261,
"text": " And because you want these distribution, the count of states, the densities and the entropy to be the same for different observers, right? So if you have a set of units and you're there and I have a set of units and I'm here,"
},
{
"end_time": 1181.288,
"index": 48,
"start_time": 1160.964,
"text": " we want still to be able to count states in the same way and we want to be able to define entropy in the same way because otherwise you know entropy would be increasing for you and not for me and that would make sense because i would see something that is deterministic and reversible you see something that is not deterministic and reversible that that would not make sense so even this constraint"
},
{
"end_time": 1199.923,
"index": 49,
"start_time": 1181.288,
"text": " Basically, it's what gives you the structure of the classical phase space is what gives you the idea of conjugate variables. And mathematically is what gives you the idea of a symplectic structure, which is sort of the geometrical way that we describe phase space. So with that assumption, infinitesimal redistributed, we get all this stuff."
},
{
"end_time": 1224.36,
"index": 50,
"start_time": 1200.35,
"text": " And then you say, now I want the system to be deterministic and reversible, meaning that for each initial configuration, I have a final configuration and the number of states are mapped to each other, right? Then that's what's going to give you Hamiltonian mechanics. It's this preservation of volume. This basically gives you the preservation of the number of states."
},
{
"end_time": 1254.019,
"index": 51,
"start_time": 1224.718,
"text": " The other thing that you need that I sort of didn't say before to make all this work is the assumption that you're describing a system that is made of independent degrees of freedom so that the total number of states can be understood as the count of states on one degree of freedom multiplied by the count of states on another degree of freedom. If you have these three conditions you get classical Hamiltonian mechanics and that's it."
},
{
"end_time": 1279.633,
"index": 52,
"start_time": 1254.292,
"text": " Then if you allow an extra assumption that basically says all that I'm studying are actually trajectories, meaning that I can go from the kinematics to the dynamics. So from position and velocity to position and momentum. And the this transition is invertible. If you say that it's invertible, that's what gives you Lagrangian mechanics."
},
{
"end_time": 1297.466,
"index": 53,
"start_time": 1280.418,
"text": " And then if you go one step forward and say, look, both momentum and velocity are linear structure, and I need that linear structure to be preserved, then the map between position from momentum to velocity has to be linear."
},
{
"end_time": 1325.384,
"index": 54,
"start_time": 1298.353,
"text": " And if you do just a couple of integrals, you find that you're constraining yourself to massive particles under a scalar and vector potentials. So you basically find the laws of charged particles in an electromagnetic field. And this was a surprise to me, right? Like when I set up to do all these things, we said, I just want to understand these things a little bit better. And I had no sense that"
},
{
"end_time": 1351.084,
"index": 55,
"start_time": 1325.93,
"text": " from just four simple assumptions. Four simple assumptions? Yes. Okay. Right. It's infinitesimal reducibility, independence of degrees of freedom, determinism of reversibility, and what I call kinematic equivalence, the fact that you can go from position and velocity to position and momentum, that looking at the trajectory is enough to understand what's going on at the dynamical level to reconstruct the energy, the momentum and all that."
},
{
"end_time": 1377.91,
"index": 56,
"start_time": 1351.732,
"text": " And that sort of gave me a different insight in physics, right? Because I don't need anything below to justify this mathematical structure. I don't need a mechanism for how we get an Hamiltonian or how we get a Lagrangian. It's just the definition. I have a system in front of me. I can assume that this system satisfies these assumptions in these particular circumstances, and you get the laws."
},
{
"end_time": 1406.186,
"index": 57,
"start_time": 1378.404,
"text": " And so I never think that philosopher ask themselves, could we have a universe that have different laws? Well, if we have objects that can be infinitesimal, reducible, independent degrees of freedom and all this, you're going to get the same laws. Interesting. That's a question that many philosophers, as you mentioned, ask. What would the universe look like under different physical laws? And then there's also the thought experiment that proves that you can demonstrate to yourself just without"
},
{
"end_time": 1427.483,
"index": 58,
"start_time": 1407.244,
"text": " Going to the Leaning Tower of Pisa that a bowling ball and a feather will fall at the same rate if you remove air resistance. Do you know that? Yeah, that's actually in Galileo's dialogues. So this is another myth that people always think Galileo didn't know whether objects fell at the same rate or not, went to the Tower of Pisa and dropped that."
},
{
"end_time": 1444.701,
"index": 59,
"start_time": 1427.483,
"text": " No, in his dialogue, he creates this simple experiment. They say, okay, let's suppose that I have two rocks and one is heavier than the other, and let's suppose that these fall faster than this. Now you put them together, you tie them up, right?"
},
{
"end_time": 1465.401,
"index": 60,
"start_time": 1445.452,
"text": " What is the velocity of this? Well, you say, well, the faster object is going to be slowed down by the slower object. So the velocity should be in the middle of the faster object and the smaller object. But now you have put them together and now it's a more massive object. So it should go faster than the faster object than we were before."
},
{
"end_time": 1486.613,
"index": 61,
"start_time": 1465.623,
"text": " Right. And also here is the configuration is how much, how tight do you have to bind these things such that you are going to consider these two separate objects with different mass and how, you know, when you tie them together, they're actually one object of different message, like how tight you have to bind them. Right. And there's, of course, it makes no sense. And then that's how in the dialogue he,"
},
{
"end_time": 1514.94,
"index": 62,
"start_time": 1486.613,
"text": " He concludes that all objects have to fall at the same rate. So the type of things that I'm trying to do is exactly this type of things on steroids, right? To really go and find all these sort of reasoning that you can from simple things and build as much as possible. And that's kind of the game that I've been painting a lot of the time. Some arguments when I start, I'm really just trying to find an argument and I try to find many, right?"
},
{
"end_time": 1545.111,
"index": 63,
"start_time": 1515.247,
"text": " And at the beginning, they all seem impossible because you're not used to it. Like any argument, even false one, as long as you think about them enough times, they're going to seem plausible to you. And the reverse is true. Even if an argument is false, it's true, but you are not used to thinking in that way, you still think that it's false. There is something weird about it. So you need to sort of get comfortable with them a little bit. They say, OK, well, this argument that I just made for fun,"
},
{
"end_time": 1569.326,
"index": 64,
"start_time": 1545.111,
"text": " Actually has some merit. And then you find that there is a correlation with something else and actually two different argument becomes the same one. And you say, oh, then I must have something. In fact, the first time where I said I have something is where I was able to read arrive Hamiltonian mechanics from deterministic and reverse stability in four different ways. Because I could say I have determines because I map states one to one."
},
{
"end_time": 1591.578,
"index": 65,
"start_time": 1569.872,
"text": " I could have determined is because I preserve the information or the information that I know at the beginning is the same amount that I have at the end. So it's an information theoretic argument, or I have something that conserves thermodynamic entropy. So it's reversible, not in the sense that that I do a one to one map with the state is reversible because the entropy does not increase."
},
{
"end_time": 1618.968,
"index": 66,
"start_time": 1592.415,
"text": " Hola, Miami! When's the last time you've been in Burlington? We've updated, organized, and added fresh fashion. See for yourself Friday, November 14th to Sunday, November 16th at our Big Deal event. You can enter for a chance to win free wawa gas for a year, plus more surprises in your Burlington. Miami, that means so many ways and days to save. Burlington. Deals. Brands. Wow! No purchase necessary. Visit BigDealEvent.com for more details."
},
{
"end_time": 1634.804,
"index": 67,
"start_time": 1619.991,
"text": " Extra value meals are back. That means 10 tender juicy McNuggets and medium fries and a drink are just $8. Only at McDonald's. For limited time only. Prices and participation may vary. Prices may be higher in Hawaii, Alaska and California and for delivery."
},
{
"end_time": 1663.831,
"index": 68,
"start_time": 1635.128,
"text": " And so these are all the uncertainties, right? You know, you think of determinism as points in math, but we never really measure points. We really measure some statistical distribution and some uncertainty around it. And so if you say, I want something to be deterministic and reversible, then you're going to say, well, the measurement uncertainty has to be preserved because I need to sort of describe the system at the same level of accuracy."
},
{
"end_time": 1682.244,
"index": 69,
"start_time": 1664.07,
"text": " Yes i saw that however i made the the case in those four different case i would get to the same results. Okay now i have something stable right because you just have one type of argument that you can always fool yourself but now i have four of them that are starting from the same point and at reaching the same conclusion."
},
{
"end_time": 1709.497,
"index": 70,
"start_time": 1682.568,
"text": " I must not be fooling myself. Now, are those four equivalent to one another? Yes. Okay. And mathematically, they're basically just assuming that the Jacobian of transformation is unitary, that the volumes preserve the same. And in our book, we show we have all these different ways. And then you see that they're all equivalent. It's quite fascinating. I think 10 years ago or so I learned about the thought experiment of Galileo. And then I wondered,"
},
{
"end_time": 1732.329,
"index": 71,
"start_time": 1709.923,
"text": " How much more of physics can we derive from purely, well, you're thinking in terms of assumptions, but I was thinking in terms of thought experiments. And there's also the Newton's bucket thought experiment. Have you thought much about that? I'm not familiar with that one. Then don't worry about that because I'm not familiar enough with it to be able to describe it with confidence. But I believe it's an argument for absolute space."
},
{
"end_time": 1760.998,
"index": 72,
"start_time": 1732.585,
"text": " It has to do with you have water in a bucket and then you start rotating it and then the water creeps up the sides of the bucket, making a U shape. So you're able to tell that this is being rotated. And somehow that's an argument for absolute space that Newton gave. And then Mach takes that and says actually Newton, if you examine that, that's an argument for relational space. You probably have to talk to Julian Barbour for Mach and stuff. He is the expert. Now for the Hamiltonian mechanics, do you recover that"
},
{
"end_time": 1789.633,
"index": 73,
"start_time": 1761.613,
"text": " Momentum is a covector? Yes. And the reason is quite simple. And it has to do with units. And this is one of the problems that in physics, we follow the math too much. And the math does not care about units. But a lot of geometrical structures that we have there are actually there to keep track of the units. So the setup is basically this. You want to be able to count states."
},
{
"end_time": 1815.794,
"index": 74,
"start_time": 1790.128,
"text": " and the count of states have to have a unit that is independent of anything else. Then you're going to have the units that you use to identify the state, which could be meters, angle, and so on, to start defining the configuration. What you need now is if you only had the variable that defines the units and let's call that q,"
},
{
"end_time": 1839.872,
"index": 75,
"start_time": 1815.964,
"text": " Then you would have a problem because now there would be special reference system for which the counter state would actually be the unit and all the others would not be the same. So you start having special coordinate systems that are sort of privileged because you're using the exact units to kind of say. So what you really want to do"
},
{
"end_time": 1863.08,
"index": 76,
"start_time": 1840.179,
"text": " Is to be"
},
{
"end_time": 1888.985,
"index": 77,
"start_time": 1863.439,
"text": " such that when I make an area between the two, well, this is units of Q. This is units of inverse Q. When I multiply with each other, now I have an invariant. And then invariant is the count of states. Is that the volume in the phase space? And that's the volume in the phase space. So you have Q that defines the units. You have K that is the inverse units. And then you say, I want to measure states with H bar."
},
{
"end_time": 1919.189,
"index": 78,
"start_time": 1889.428,
"text": " And so you just multiply K by H bar and you get P. Why are we talking about H bar when we're speaking about Hamiltonian mechanics or classical mechanics right now? Because that's what we use for for the unit that we use to count states is the units of actions. Is that what we use? And we the reason that we use that, because in mechanics, the units turn out to be, you know, position times kinetic momentum and the square, right?"
},
{
"end_time": 1927.858,
"index": 79,
"start_time": 1919.599,
"text": " And that's then what we use to define units. But you still need a unit to be able to measure these things."
},
{
"end_time": 1957.005,
"index": 80,
"start_time": 1928.302,
"text": " And when you calculate an entropy, even in classical mechanics, that you have a distribution on phase space, you need, you know, you're going to have a logarithm of the distribution, but the distribution is going to be, you know, let's say probability over volume. And if the volume is in unit of phase space, you are in a log, you have to take that out. So you need the sum, you know, some constant so that you can define where your zero entropy is, and you get the correct end. Right."
},
{
"end_time": 1985.265,
"index": 81,
"start_time": 1957.005,
"text": " It turns out that you still need to fix some of these constants even in classical mechanics. And again, it's one of those things that... It's quite bizarre. Right. It's one of those things that if you just take all the units down, and that's what mathematicians do, you're not going to see. And unfortunately, this is what we do in theoretical physics. We have all the units, we throw them out. What do you mean we throw them out? Like set C equal to one, is that what you're referring to?"
},
{
"end_time": 2008.951,
"index": 82,
"start_time": 1985.879,
"text": " Yeah, but it's not just setting it to one. It's setting it to one pure number. But if you set it to one, but you still have some units of space over some units of time, then you're still preserving the physical content of what you're going to measure. Because when we measure distances in space, we use different instruments than when we measure distances in time."
},
{
"end_time": 2031.34,
"index": 83,
"start_time": 2009.462,
"text": " But that's what we do. We just set everything to one and we forget about the units and then we lose the structure because you don't see you can't appreciate what is it that the physics that the thing is described. So what would be an example of something where they set C equal to one or H bar equal to one or what have you and it turns out it's incorrect under what you've investigated?"
},
{
"end_time": 2060.486,
"index": 84,
"start_time": 2031.664,
"text": " It's not incorrect. You see, this is, if you do the calculation correctly and do everything correctly, it's not the problem. You just lose the physical meaning. So for example, you know, the Dirac equation. Yes. What does it tell you? What is it saying? So if you, if in that, instead of the gamma, right, the gamma is these matrices that sort of sum to one, put a C in front. Now that C gamma is actually a velocity that comes from the booster of the spin part."
},
{
"end_time": 2083.916,
"index": 85,
"start_time": 2061.049,
"text": " So the gamma is telling you what is velocity of the spin going. And then you have a partial derivative, you know, put the h bar, that's momentum. So it's velocity contracted with the momentum of the particle equal MC square. So it's basically telling you all these things is telling you that the V times P equal"
},
{
"end_time": 2104.957,
"index": 86,
"start_time": 2084.462,
"text": " It's going to give you MC square because you have the momentum which is MV and then you have the velocity is MV but you're contracting together those those vector the norm of V square is going to be C. So you're just saying you know something that you already have in in"
},
{
"end_time": 2128.899,
"index": 87,
"start_time": 2104.957,
"text": " Classical particle mechanics in a relativistic setting that the the inner product between the momentum and velocity is equal to MC square. That's it is just that you're saying in the context of field theory so of course you're going to use a language of that it's a lot more complicated but the physics that you're describing what the equation is telling you is just that this is nothing there is nothing more."
},
{
"end_time": 2147.79,
"index": 88,
"start_time": 2129.462,
"text": " so what i feel that we've done by essentially stripping all these things away and just following blinded mathematics and looking for mathematical structure for new thing we think we're just losing all the physics they still there and if we did it in the way that we used to the physics right because"
},
{
"end_time": 2169.667,
"index": 89,
"start_time": 2147.79,
"text": " These assumptions are just a new version, maybe like more rigorous version of Newton's laws and the laws of thermodynamics. We used to do physics like that. You start, you figure out what are the, you boil the world into these assumptions that you're making or these starting points."
},
{
"end_time": 2198.831,
"index": 90,
"start_time": 2169.667,
"text": " And then get everything from there. And you keep track of what it is that you're doing. You check your, you know, when you're doing undergrad problems in physics, you do the dimensional checking where, you know, to make sure that your masses are masses and that suddenly didn't become velocity and so on. So why are we not doing it in the more complicated theories where we can even get, you know, more confused because it's all abstract math and so on."
},
{
"end_time": 2228.831,
"index": 91,
"start_time": 2199.531,
"text": " Well, I understand that you want to make sure at the end that the units match up on both sides of the equation, but I don't see what would be an example of something in mathematical physics. Say the standard model, we set C equals to one and H bar equal to one and so on. And it's the most predictive of all the models that we have. You're just choosing a specific type of units in which you're doing the calculation because they're more convenient. So that's what you're doing. Okay. What I mean is,"
},
{
"end_time": 2258.131,
"index": 92,
"start_time": 2229.428,
"text": " I don't know if you saw the iceberg in string theory that I did. They understood more about string theory by looking at that than talking to actual string theorists. Okay. Well, can you give me an overview that it was better than what other people give? So thank you. Thank you. At any rate, at some point you get n equals four super Yang-Mills theory in four dimensions and so on, and they're different results. So what I'm saying is in those results, is there something that they're doing that is incorrect now outside of"
},
{
"end_time": 2287.278,
"index": 93,
"start_time": 2258.524,
"text": " The complaint that there is no supersymmetry that we find and this is assuming strings at a base, even though what I just said was not assuming strings, the Yang-Mills case, but you get the idea. So what's something that is quite advanced in mathematical sophistication that is incorrect? I understand that for us to gain insight into what this is saying, what this means, reintroducing units is useful. Correct. But is there something wrong at the mathematical level? Like, is there something that"
},
{
"end_time": 2316.015,
"index": 94,
"start_time": 2287.756,
"text": " We've gotten incorrect. I get you. So there becomes a little tricky because that's not my job. So to be able to make the claim, I would have to know string theory enough to be able to say that or any other physical theory. And I don't have the level of knowledge that, you know, that I need that. But I can tell you this. Remember when I was talking about the real numbers, the assumption that we have to put there are very idealized, right?"
},
{
"end_time": 2344.343,
"index": 95,
"start_time": 2316.408,
"text": " And there is no way that those all those assumptions are going to hold if we are looking at something at Planck scale. And if you remember before, I said that the hard part was getting the ordering right was not getting the real numbers is getting the order right. And so what needs to happen is that when you go at Planck scale, you are going to lose completely the notion of ordering, which also means you're not going to be able to"
},
{
"end_time": 2372.875,
"index": 96,
"start_time": 2344.718,
"text": " define real numbers for things that you go and measure, because you're not going to have ordered quantities. So I don't know what structure we're going to have, because I don't have enough constraints to know what needs to happen. I don't know what are the things that I can assume to be valid at that scale. But I know that at that scale, the assumptions that you need for the real numbers are going to implode. And therefore,"
},
{
"end_time": 2401.305,
"index": 97,
"start_time": 2373.507,
"text": " i if i have a theory that says oh yes this is going to be going to work at plant scales and i see that they're still using real numbers for quantities they're using integration right because how can you have a differentiable structure if you don't have the structure of the real numbers underneath right so all these pieces that assume underneath the real numbers and i i'm pretty sure all those pieces are going to go so"
},
{
"end_time": 2430.64,
"index": 98,
"start_time": 2401.613,
"text": " If you have a theory, whatever it is, that the claims, oh, this is going to work at plan scale and it's still using differential geometry, real numbers and so on. From what I know, I would be extremely skeptical. Right. But I can't tell you any specific theory because I would have to go and look at it. I can't. And what about Dirac's equation? Does it not assume the real numbers? It's a differential equation. And that is also about the quantum. So how does that work?"
},
{
"end_time": 2462.125,
"index": 99,
"start_time": 2432.585,
"text": " If it's easier to go to Klein Gordon, feel free to go to Klein Gordon, any of them. It doesn't matter. So the issue there is that you are doing, even in quantum mechanics, you're still using real numbers, right? So you're still making this assumption that you have references and you can put them up and you have a scale that it's perfect and you know what number is greater and below. And so, yes, these structure, I would think that they have to fail as well."
},
{
"end_time": 2486.476,
"index": 100,
"start_time": 2462.961,
"text": " They fail at what point? Like, what does it mean that they have to fail experimentally? That they do not. So here's how I think of physical theories, which is at this point very different from what people think about. For me is I have a system in front of me and I assume that I can that some things are valid for this system. So, for example,"
},
{
"end_time": 2509.206,
"index": 101,
"start_time": 2487.654,
"text": " Let's say in electromagnetism, we have the charge distribution, right? And you think that as a charge field, there is a charge density, okay? Well, that's not what we measure in practice, right? What we measure is finite charge and the finite volume. And then we measure the size of the finite volume."
},
{
"end_time": 2536.288,
"index": 102,
"start_time": 2509.633,
"text": " And then we can make the ratio of the charge within the size of the volume. And then we make these, you know, things smaller and smaller and smaller. Right. And on the assumption that both quantities are additive, that is, if I take a volume, I divide it into two. Right. Then the total charge is the charge of this plus the charge of this. And the total volume is the size of this plus the size of this."
},
{
"end_time": 2566.169,
"index": 103,
"start_time": 2536.937,
"text": " If I have that assumption and I make this limit, I can define a charge density, right? But if I can't do that, because I can't make this limit or the additivity does not hold, I'm not going to be able to use this assumption. Therefore, I'm not going to be able to say, oh, yes, there is a charge density. Because you see, the charge density is not the thing that physically exists. The thing that physically exists is the finite charge in finite volume."
},
{
"end_time": 2588.217,
"index": 104,
"start_time": 2566.766,
"text": " And this is"
},
{
"end_time": 2607.073,
"index": 105,
"start_time": 2588.439,
"text": " In a lab we start with a finite thing and then we say oh yeah I'm gonna make this thing smaller and smaller and and then that's where you get the points and so on but the points and all those things exist because you're assuming you can make the limit yes so now if you start with the math and you assume the points you already assume that you can make the limits."
},
{
"end_time": 2634.906,
"index": 106,
"start_time": 2607.5,
"text": " But if you can't make that limit because at some point you get to plant scale or because, for example, the mass is not really additive into volume because you have something that goes on the surface between them. So it is not true that the sum or the total of the math is just the sum of the mass in the volume. Same thing for entropy. Entropy sums only if you're assuming that things are are independent. If they're not independent, that assumption, right?"
},
{
"end_time": 2662.637,
"index": 107,
"start_time": 2634.906,
"text": " And so this is, again, this is my game. I need to understand what are the things that I'm assuming at the top level such that I can make those limits and I can define the points and the mathematical objects. Right. And so what does it mean that a theory is applicable in a specific case or is just whether the system that I have in front of me happens to satisfy those assumptions that I'm making?"
},
{
"end_time": 2686.203,
"index": 108,
"start_time": 2662.807,
"text": " So, do I have a classical system in front of me? Well, does it satisfy infinitesimal reducibility, independence of degree of freedom, deterministic reversibility and kinematic equivalence? Yes, I can model it as a classical system. No, I cannot model it as a classical system. I have to use something else. So, the fact that you can infinitely divide a classical system doesn't imply points still?"
},
{
"end_time": 2713.763,
"index": 109,
"start_time": 2687.022,
"text": " In the theory, yes, but it doesn't mean that we have points in the reality. So this would be a great time to talk about what defines quantum mechanics. So go over the litany of what people usually say separates a quantum system from a classical system and then show why that is false. You have a set of videos, by the way, which I'll put on screen about this. I have never seen and this was my problem. That's why I started all these businesses that I never"
},
{
"end_time": 2729.411,
"index": 110,
"start_time": 2714.548,
"text": " found somebody that told me, oh, for this system, you use classical mechanics and for the system use quantum mechanics. I mean, you have examples or, you know, if you have a proton, a double-slit experiment, then you have to use these things. But physics at the end of the day,"
},
{
"end_time": 2744.77,
"index": 111,
"start_time": 2729.616,
"text": " If you think about it, it's not like mathematics that you have like one overarching theory and say, okay, these are things that are valid for everything, right? Set theory and, and logic or category theory, if you like category theory, because I don't say that people from category theory."
},
{
"end_time": 2768.746,
"index": 112,
"start_time": 2744.974,
"text": " And then you say okay these are the things that are that we always need to assume and then you're gonna have topological spaces and then we're gonna have groups and then you have we have things that are both groups and topological spaces and we call them topological group so you have a whole hierarchy of sort of things that you assume in a sort of well-defined sort of uniform way of looking at things."
},
{
"end_time": 2797.125,
"index": 113,
"start_time": 2769.48,
"text": " In physics, you have classical mechanics. And when do you use it? Oh, where I have bees on a wire, where I have planets and stuff like that. And then you have thermodynamics. Oh, I use that, you know, when I have the volumes and the gas and the heat. And then I have relativistic mechanics. Oh, I guess I use that when things are really fast and then I have gravity. So it's basically you learn with a physics degree, you learn a bunch of problems and you learn to recognize patterns."
},
{
"end_time": 2822.944,
"index": 114,
"start_time": 2797.125,
"text": " And then, you know, I have a problem of this problem is closest to this one. And so I'm going to use those things. Right. And and this is what I find completely unsatisfying. So when I was a summer student at CERN in 1999, that I was sort of asking myself where I met my wife there, my future wife, it wasn't my wife at the time. But the point was that, OK, I, you know,"
},
{
"end_time": 2846.493,
"index": 115,
"start_time": 2823.268,
"text": " I was studying engineering at the time. I wasn't doing physics and I just, you know, wanted to know, like, what are these things? I wasn't really going to read, you know, to do another thing. So I said, okay, I'm in a search. There's a big library. And what I'm sure I'm sure that what there is going to be a book, a textbook that in the first chapter is going to tell me, oh, this is what quantum systems are."
},
{
"end_time": 2872.824,
"index": 116,
"start_time": 2846.493,
"text": " And this is why you should use this thing. And of course, I went through 20, 30 books and I found so no such. Why don't you ask someone? I asked somebody. I got no answers. Yeah. And you got no answers or you got unsatisfactory answers? I got the answers. Well, I don't know. I can tell you. I just burb. It obviously wasn't a great enough answer that it stuck with you. Oh, there was no answer."
},
{
"end_time": 2902.346,
"index": 117,
"start_time": 2873.217,
"text": " Most professors that, all the professors that I talked to, they admitted not having an answer and they just point me somewhere else. Oh, Bell did some stuff. Go read that. I have no idea. And actually the turning point for me was when a PhD student at the time told me, look, you're never going to find these answers. The only thing that we have is the math. I can teach you the math. And so he told me the math and I learned the math badly like all physicists."
},
{
"end_time": 2925.401,
"index": 118,
"start_time": 2903.012,
"text": " And he then stayed there for me. Okay, why do I have that math? Right. And, and then, okay, that's reverse engineer, the math, that's sort of how physical mathematics, how reverse physics started, and then realize, well, I need to actually understand the math a lot better. And that's why. But anyway, we're talking about quantum mechanics. So let me tell you what I think quantum mechanics is."
},
{
"end_time": 2955.043,
"index": 119,
"start_time": 2926.049,
"text": " And the short story is this, is that classical mechanics assumes that you can take something divided, divided, divided, divided, divided, and you can still talk about what things are. And studying the part, all the parts is equivalent to studying the whole. So if you have a ball, you can throw the ball, look how the ball evolves and describe the ball, or you can take a red marker and put a red dot on the ball and study the motion of the red dot on the ball."
},
{
"end_time": 2981.63,
"index": 120,
"start_time": 2955.674,
"text": " Right. And so starting the motion of the whole ball is equivalent to starting all the possible red dot that you could put on the ball, all possible finite sizes. Okay. Right. Because the infinitesimal is just the limit of all the possible finite sizes. And so when you have all the possible finite sizes, although dimension, that's, that's how you know the reason I keep having this as a sticking point is because infinitesimal doesn't mean point. It means"
},
{
"end_time": 3009.411,
"index": 121,
"start_time": 2981.63,
"text": " It's as close as you get to a point without being a point. Right. So this opens a whole another world is how do we define calculus? Because I don't think when I'm doing physical mathematics, I will need to define calculus at some point. And I don't think the starting points that we have for calculus can be physically motivated. I want to have a notion infinitesimal that it's similar to what we Newton used to think."
},
{
"end_time": 3039.377,
"index": 122,
"start_time": 3010.162,
"text": " And right now, if you look at the books of how differential geometry is defined, you really don't have those things. You have completely different definition that even when I talk to other mathematicians that do topology, for example, like I was at a conference, a topology conference talking to one of the students and asked, you know, why are you in topology? And one of the reasons that he said was because the definition of differential geometry were too abstract for him and made no sense."
},
{
"end_time": 3065.23,
"index": 123,
"start_time": 3039.94,
"text": " to a mathematician, to somebody who has a PhD. So if they're too abstract for him, you can imagine for somebody that has a physics or engineering background. So I'm trying to understand how we can actually define things in a way that are sort of similar to this idea of pieces that become smaller, but we can do it with modern math. So we would define it in a way that"
},
{
"end_time": 3092.892,
"index": 124,
"start_time": 3065.23,
"text": " Okay, so getting to the bowling ball and you can mark it with all these different points or it's market with a finite"
},
{
"end_time": 3108.404,
"index": 125,
"start_time": 3093.217,
"text": " find it, but but whatever size you want. So it's arbitrarily small as you can. So at that point, it means essentially describing all the points and so on. Okay, so this is classical mechanics. And in one way or another, in all that you're doing quite in classical mechanics, you are going to have this thing"
},
{
"end_time": 3132.21,
"index": 126,
"start_time": 3108.404,
"text": " So just a moment is this classical mechanics in conjunction with thermodynamics yet or is this just pure classical mechanics pure classical mechanics okay so we need to distinguish those two is that do you in your head call that pure classical mechanics where's the other one where there's the heisenberg uncertainty analog is something more cn plus t thermodynamics. Yes of the thermodynamics enters so."
},
{
"end_time": 3155.384,
"index": 127,
"start_time": 3132.858,
"text": " This is where I cannot give you a straight answer because in my mind the distinction is yet not clear. Because you can understand one physical thing and one mathematical thing. Physically you can understand if I say that what I'm really studying are objects and I'm looking at these parts and so on. There is already a sense that"
},
{
"end_time": 3170.196,
"index": 128,
"start_time": 3155.742,
"text": " Well, I'm kind of doing some statistics there. So exactly what is it that I'm doing? I don't know. Is it enough to get I see? I don't know. Okay. And but what I can tell you is this is that this is another thing that I think, you know,"
},
{
"end_time": 3190.094,
"index": 129,
"start_time": 3170.947,
"text": " We look at it backwards. We think as statistical mechanics and thermodynamics as something that you add on top of both classical mechanics and quantum mechanics, right? So there is mechanics, which is the real thing, and you do statistical mechanics, thermodynamics, it's all sort of derived, the derivative thing. It's not really fundamental. But here's the thing."
},
{
"end_time": 3215.811,
"index": 130,
"start_time": 3190.93,
"text": " As I said, remember that count of states that we need to define to have classical mechanics, classical home internal mechanics. Well, that's the geometrical structure of classical mechanics. It's the symplectic forms that allows essentially to count the configuration, to count to the states. OK, so that thing is what you use then to calculate thermodynamic entropy. So you use that structure to calculate the entropy."
},
{
"end_time": 3242.517,
"index": 131,
"start_time": 3216.63,
"text": " Now, if I gave you all possible distributions, probability distribution in phase space, and I told you what was the entropy of all those distributions, like the Shannon entropy, Gibbs entropy, you would be able to recover the symplectic structure. So the symplectic structure and the entropy are equivalent because either I give you one and you can calculate the other, or I give you the other and you can calculate the first one."
},
{
"end_time": 3269.974,
"index": 132,
"start_time": 3243.097,
"text": " Interesting. So the geometrical structure of quantum classical mechanics is exactly the structure that you need to be able to do thermodynamics and statistical mechanics. So how can you say that one is built on top of the other? They're really one unit. The same applies for quantum mechanics. The geometrical part of quantum mechanics is given by the Born rule. The inner product tells you what is the probability from going from one state to another state during measurement. Okay."
},
{
"end_time": 3294.514,
"index": 133,
"start_time": 3270.572,
"text": " You use the Born rule to calculate the von Neumann entropy, the entropy of distribution. Now, if you take all distribution, in fact, if you take in particular the uniform distribution over two pure states and you look at that entropy, from that entropy you can recover the probability of transition from one to the other."
},
{
"end_time": 3324.531,
"index": 134,
"start_time": 3296.067,
"text": " So again, I could give you the geometric inner product structure of quantum mechanics and you can recover the entropy, or I can give you the entropy and you can recover the inner product. They are equivalent. So again, how can you tell me, oh, quantum statistical mechanics is something that we sprinkle on top of quantum mechanics. They're really much more tied in. So that's why, you know, I can't make these arguments fully because again,"
},
{
"end_time": 3352.892,
"index": 135,
"start_time": 3325.026,
"text": " This is where I said I need this theory of ensembles. I need something that is more foundational to be able to say why I have these things, how exactly they are related. So what's interesting to me is classical mechanics seems more objective than notions of entropy. Entropy is subjective to me because it depends on macro states. So you can define macro states in any which way. You can say, what are all the different arrangements of chairs in this room?"
},
{
"end_time": 3378.78,
"index": 136,
"start_time": 3353.319,
"text": " But you could also say, what are all the different arrangements of the lights or not even arrangements? You could have something else. So there's something that seems quite subjective about entropy. It's never set right with me, but then there seems to be something ideal and objective about classical mechanics. Now I could just be incorrect about entropy. Keep in mind that for me, statistical mechanics was an easier course than thermodynamics."
},
{
"end_time": 3406.271,
"index": 137,
"start_time": 3379.07,
"text": " And I don't like this liquid notion of entropy and heat, the whole fluid mechanics analogies. But when I got to statistical mechanics, it made much more sense to me. So one of the important pieces that thermodynamics really pushes you in your face is that you need to define the boundary of the system. So even if you have the same physical system,"
},
{
"end_time": 3435.452,
"index": 138,
"start_time": 3406.817,
"text": " But you have a different way that you interact with that physical system. You have a different physical system. So entropy, like thermodynamic entropy, the one that is important for us physically, depends on the way that you can interact with the system. Because if you think it like this, that the whole idea of thermodynamics is figuring out how much work you can extract or put in in the system."
},
{
"end_time": 3465.691,
"index": 139,
"start_time": 3435.964,
"text": " Well, it will depend by how you can interact with the system. So James is the one that really sort of made this clear. James James. He had an example in one of these articles that basically says, you know, he was talking about salt crystals. You can say I have a can have a salt crystal and I would have a certain number of thermodynamic variables backing. I can put a polarization on the on the salt Christian."
},
{
"end_time": 3486.681,
"index": 140,
"start_time": 3465.981,
"text": " And now the states that I'm going to have, the macro states that I'm going to have will depend on the polarization. So before I had unpolarized states and I have polarized states, which are more because then you can say I can do the next, you know, instead of linear polarization, you can make, I don't remember the quadruple. There you go."
},
{
"end_time": 3517.159,
"index": 141,
"start_time": 3487.21,
"text": " And now you have a different set of systems. You have more. Right. You have more and more systems. And the entropy associated with those states is going to be different than the entropy that you have. So this, I think, where you have a feeling that it's some sort of subjective. Yeah, because it depends on how you coarse grain, no? It's not coarse graining. It's how you have defined the boundary of the system. And once you define the boundary of the system, you say, I'm going to interact with the system in this way."
},
{
"end_time": 3539.974,
"index": 142,
"start_time": 3517.568,
"text": " That's the definition of the system. But this is true for all systems. Okay. So if I say I have a classical mechanics, I have a cannonball and I studied the motion of the cannonball, everything seems so objective. Yes. Right. But because we are on earth, if I put the cannonball on the surface of the sun, you're not going to be able to talk about the motion of the cannonball."
},
{
"end_time": 3563.268,
"index": 143,
"start_time": 3540.469,
"text": " So even when you define the classical system you you have a notion I have a boundary somewhere why wouldn't I be able to talk about the motion of the cannonball in the sun because we just vaporize you have no kind of okay okay. Right and so we've just saying I have a cannonball you're putting a constraint on the environment that you have."
},
{
"end_time": 3584.65,
"index": 144,
"start_time": 3563.626,
"text": " You're gonna have a certain temperature pressure you're gonna have some sort of equilibrium with the environment that allows you to be able to talk about a cannonball. Interesting. And this is true for classical mechanics and quantum mechanics as well. If I say oh I have an electron and it's polarized the spin up."
},
{
"end_time": 3610.52,
"index": 145,
"start_time": 3585.299,
"text": " Well, it means that at some level, I'm going to have some magnetic trap where my electron is with the external magnetic field oriented vertically so that my spin can be up. Right? If I have it oriented in the other way, I wouldn't think Verizon, the best 5G network is expensive. Think again, bring in your AT&T or T-Mobile bill to a Verizon store"
},
{
"end_time": 3642.892,
"index": 146,
"start_time": 3615.026,
"text": " It's the season for all your holiday favorites. Like a very Jonas Christmas movie and Home Alone on Disney Plus. Can I burn down the joint? I don't think so."
},
{
"end_time": 3665.623,
"index": 147,
"start_time": 3643.422,
"text": " Then Hulu has National Lampoon's Christmas Vacation. We're all in for a very big Christmas treat. All of these and more streaming this holiday season. And right now, stay big with our special Black Friday offer. Bundle Disney Plus and Hulu for just $4.99 a month for one year. Savings compared to current regular monthly price. Ends 12-one. Offer for ad-supported Disney Plus Hulu bundle only. Then $12.99 a month or then current regular monthly price. 18 Plus terms apply."
},
{
"end_time": 3688.404,
"index": 148,
"start_time": 3666.135,
"text": " So that's the idea. And I think that's what it's actually missing from the rest of physics. You see, it's not that thermodynamic is weird because you have to talk about the boundaries. No, it's on the other system, you're already making some outrageously simplifying assumptions, and then you don't think about it. I see. And then you say, oh,"
},
{
"end_time": 3709.445,
"index": 149,
"start_time": 3688.985,
"text": " Firmware Dynamics is so weird. No, it's like you've put yourself in the simplest case possible. The case where isolated, right? Hamiltonian mechanics where you're completely isolated, which means there is no interaction with the assignment. Your system is completely closed. That's the harder assumption that you would have in practice because nothing is really ever"
},
{
"end_time": 3735.145,
"index": 150,
"start_time": 3709.957,
"text": " Properly isolated. What happens on the surface of Jupiter will have an influence of what we are, you know, on your system. But you're going to say, well, you know what? It's small enough. I'm going to ignore it. But you are ignoring it. And the problem is that is that if you don't take these assumptions out and you think about it, you don't even know what you ignore. And then you're going to generalize both your mathematical structure, your physics and so on."
},
{
"end_time": 3764.684,
"index": 151,
"start_time": 3735.981,
"text": " Okay, so we've gallivanted around the cannonball. Let's go back to what distinguishes quantum mechanics from classical mechanics. Yes. Okay. So we said the classical mechanics is the thing that I can think of made of small pieces and everything works and I can study these pieces as small as I want. I have absolutely no problem. And then you say, okay,"
},
{
"end_time": 3792.688,
"index": 152,
"start_time": 3765.145,
"text": " But now I have an election. I have an election, I want to start the election. I can't take a red marker and say, oh, I'll put this dot on the electron, right? You can't say, you know, how do we measure electrons? I don't know. You have electrons, you scatter some photons off of it. These are the type of experiments that you do. You can't just say, oh, I'm going to scatter the electron, but off only of this person, right? No, either you interact with the whole of the electron or none of the electrons. And is that actually what defines a particle?"
},
{
"end_time": 3810.52,
"index": 153,
"start_time": 3794.275,
"text": " I would think yes. And again, it depends on the circumstance. So if I'm talking about a proton at a certain skin, at a certain level of energy,"
},
{
"end_time": 3837.705,
"index": 154,
"start_time": 3811.323,
"text": " The photon comes in, interacts with the whole thing and is not going to tell me anything about the substructure. So in those particular settings, I would say, aha, my proton is irreducible. Meaning, not that there is no substructure, is that I can't probe it. So anything that I can describe is only at the level of the whole object."
},
{
"end_time": 3860.555,
"index": 155,
"start_time": 3838.234,
"text": " And there is no physical process that depends on the substructure. If I am in those conditions, I can say my objects is irreducible. But then I say, OK, now I take photons and I probe the same object at higher energy. Now I can probe the substructure."
},
{
"end_time": 3883.251,
"index": 156,
"start_time": 3860.862,
"text": " And now the thing is not a single particle. It's not a single quantum system because I can probe the inside. So I can't just use a single wave function. The proton is not a single particle at that point, but the substructures, they are single particles. Right now it's a mess. It's a little bit of a mess to tell you who are the proton. My wife actually studies the"
},
{
"end_time": 3906.34,
"index": 157,
"start_time": 3883.677,
"text": " The structure of the product, especially on the on the spin side and the host, there is a whole problem of the spin crisis there. It's a it's very complicated, but you can't describe the product as a single particle. And so now you have an electron, right? An electron. We haven't found any scale, any energy level at which"
},
{
"end_time": 3934.002,
"index": 158,
"start_time": 3906.766,
"text": " We can see an internal structure so we can always assume at least so far that the electron is a single irreducible thing because there is not nothing that that we decided but maybe in a hundred years somebody very clever will find a way rings on any whatever and that is not going to be a single no no in the example of strings you don't say the electron is made of multiple strings."
},
{
"end_time": 3964.258,
"index": 159,
"start_time": 3934.377,
"text": " You would say that one string in some vibrational mode is the electron. So would that be a substructure? Would that technically be a substructure? No. Okay. Forget about strings. What I mean is let's say there's something else that a mini electron inside the electron in order for you to be reducible, do you have to have more than one sub part or can you just have a smaller part? Well, the whole is to be the sum of the parts. So as long as you have one part, you're going to have another part that you have to put together."
},
{
"end_time": 3985.009,
"index": 160,
"start_time": 3964.684,
"text": " But then you're also assuming that in classical mechanics, you're assuming that you can give a state to each part independently from the other, because you're saying the sum of the parts is studying the parts independently is the same as studying the whole thing. And this is not true in quantum mechanics. Right. So if I have two particles that are entangled,"
},
{
"end_time": 4011.459,
"index": 161,
"start_time": 3985.316,
"text": " That system is irreducible. Even if there are two particles, that system is irreducible. I can't describe the system as, oh, there are two parts and I can interact one part and study the motion of one part. No, you can't do it. So quantum mechanics has a way to compose things and still be irreducible. Right. And so if you have something inside, what's going to happen is that you're going to have multiple parts and then you're going to have a quantum. So"
},
{
"end_time": 4033.916,
"index": 162,
"start_time": 4011.852,
"text": " Here the assumption, what I'm, I still have to prove again, as I said before, we get to quantum mechanics is sort of a physicsy hodgy podgy way. I'd like to do it very precisely because I want to be assured that there is only one way to create this quantized object. And right now I don't know that there is only one way."
},
{
"end_time": 4058.234,
"index": 163,
"start_time": 4034.548,
"text": " And this is why you don't believe reductionism, even though it's associated with physics, is ultimately, ultimately should be associated with physics. Maybe it shouldn't. Same with mechanisms. No, it's fine to have reduction, but you have to assume that your physics description at some point will stop because either we'll assume I have a fundamental structure or in the case of quantum mechanics,"
},
{
"end_time": 4086.51,
"index": 164,
"start_time": 4058.575,
"text": " I can't observe below this threshold. This is the level at which I can manipulate the system. Yeah. What I mean is ultimately fundamental physics should be about what's at the fundament. So what is irreducible? And if it's what's irreducible, then it can't be reduced and it can't be described with reductionism. Right. Yes. Yeah. So the point is that either I have a system that is reusable, which I would"
},
{
"end_time": 4114.65,
"index": 165,
"start_time": 4086.937,
"text": " Think it's just quantum mechanics, right? Or I do not. But then what you're doing is just putting the level of the reducible system below it. Tell me about the early 2000s now. You said in 1999, you started to think about these problems as to what classifies a quantum system versus a classical or a thermodynamic system, et cetera. And now it's a couple of years later. Take us through your academic journey and where you are in your mental framework."
},
{
"end_time": 4144.036,
"index": 166,
"start_time": 4116.049,
"text": " Oh, so I got my degree in engineering. I was a software engineer just because I started doing software when I was eight or nine. And when I was the choice to do physics engineering, I said engineering first. I have much more of a stable job there. And then I had the intuition, which turned out to be correct, that I will learn more things. I'm a generalist at heart. So in engineering, I"
},
{
"end_time": 4156.971,
"index": 167,
"start_time": 4144.411,
"text": " I studied control theory, information theory, system theory, a lot of different things and a lot of the ideas that I got from there actually stuck."
},
{
"end_time": 4179.326,
"index": 168,
"start_time": 4157.517,
"text": " I basically used every intuition from every, I really like seeing the things from multiple angles. And that's why in the reverse physics, I never like to have just one condition. I like to have like, so for classical Hamiltonian mechanics for one degree of freedom, I have 12 conditions that I can say, oh, this is equivalent to this and this is equivalent to this. I really like from what are some of those 12?"
},
{
"end_time": 4198.507,
"index": 169,
"start_time": 4179.599,
"text": " Well, the four physical one we already discussed determines the irreversibility in terms of counting states, conservation information entropy, conservation of thermodynamic entropy, which means reversibility in the thermodynamic level, and conservation of uncertainty for peak distribution."
},
{
"end_time": 4227.363,
"index": 170,
"start_time": 4198.507,
"text": " Those are the physical ones. For the mathematical ones, there are the set of equations that you have. You have the fact that the volumes are conserved, the fact that densities are conserved, the fact that the flow is incompressible. If you look at a phase space, how the flow goes around, you take an area, this flow is incompressible. And then the symplectic structure is preserved, the Poisson brackets are preserved."
},
{
"end_time": 4250.981,
"index": 171,
"start_time": 4227.363,
"text": " And then if you take the flow, rotate it 90 degrees in phase space, the curl of that flow is zero. I think they should be all that. But anyway, so that's, that's what I like doing. Because the more hats you have, the more intuition you get and you can tie things together. Because now I know"
},
{
"end_time": 4278.148,
"index": 172,
"start_time": 4251.152,
"text": " Take us through some more of those insights that you've had where you've examined something, it could be physics related, but it could also be math or computer science related, or even artist, even you're a musician as well, even music related, where you thought you understood something, you realize you didn't, and then you observed it from multiple angles and gained"
},
{
"end_time": 4302.773,
"index": 173,
"start_time": 4278.933,
"text": " Yeah. So the most beautiful thing it's where it's when you don't even think that there is an explanation and then you find it because that's totally surprised. So when we do physics, we are taught that the math is the stuff for mathematicians. Right. And we know discrete continuous what I said, the topology. What is this? It's"
},
{
"end_time": 4333.08,
"index": 174,
"start_time": 4303.319,
"text": " And again, because I wanted to really understand these things, I said, OK, I need to understand what topology is. And what I found was that there is this link between, as I said, verifiable statements to open sets in topology. For somebody who does not know what a topology is, a topology is essentially a collection of sets for which you can do a finite intersection"
},
{
"end_time": 4358.985,
"index": 175,
"start_time": 4333.626,
"text": " and an arbitrary union. So you have two sets, you can do the finite intersection, three sets you can do further, but you can't do it. Now there is this translation between set theory and logic where an intersection becomes the end. And as we said before, if I have two verifiable statements, I can make the finite conjunction, the finite end, which becomes the finite intersection in the topology."
},
{
"end_time": 4384.923,
"index": 176,
"start_time": 4360.009,
"text": " Or, if I have verified the statement, I can also test the OR, because as long as I have an end statement, the one terminates successfully, I can say, oh, the disjunction is true. And you can test an infinite amount of ORs? And that's the issue. How many ORs can I test? Because the thing is that I need to find one element of the OR, and then I can drop out."
},
{
"end_time": 4410.503,
"index": 177,
"start_time": 4385.316,
"text": " So if I have countably many ores, I can go and find the one that terminates and stop. But if I have more than countably many, I'm not going to be able to do it. So the verifiable statements are closed under the countable or right. And now that you see, oh, there is a little bit of a difference between the topology because the topology tells you arbitrary or like arbitrary union. But then you think, okay, but I want my theory"
},
{
"end_time": 4440.077,
"index": 178,
"start_time": 4410.896,
"text": " To be physically explorable with with tests. Yes. And even if I give you an unlimited amount of time, the most that you're going to be able to do is test countably many. Now, if you truly wanted it to be physical, wouldn't you say that it has to you put some bound like some Bekenstein bound or some informational bound because we only have this universe. And so there'll be the heat depth at some point. And so you put Graham's number as the ultimate large number. Yeah, but"
},
{
"end_time": 4466.869,
"index": 179,
"start_time": 4440.606,
"text": " Remember, we're creating models. When we create physical theories, we create models that are valid under certain assumptions, right? So why are you going to worry about that when at the end of the day, I'm going to worry that I'm going to say that I have a system that is isolated? So in other words, we currently think that the universe will end in a heat death. We don't know because that's already assuming some physical model. So let's just say finite and not think about all the interactions and"
},
{
"end_time": 4485.93,
"index": 180,
"start_time": 4466.869,
"text": " What I mean is that when people want to say some large number, they'll usually say that's 10 to the 600 and that's larger than the amount of atoms there are in the universe. They'll usually use the number of atoms. Maybe it should be the number of interactions between atoms, which is a much larger number, but it doesn't matter. There exists some finite bound. I believe it could be Graham's number."
},
{
"end_time": 4515.589,
"index": 181,
"start_time": 4486.305,
"text": " You're saying even to calculate Graham's number as the largest finite bound, assume some other physical theory, and we're trying to not assume that, so we're just going to say finite, not a particular number that's finite. No, I'm saying that I'm perfectly fine to assume that there are infinitely many things because it's in the model. And in the model, I can assume that there are infinitely many things, even it's like the thermodynamic limit. You make the thermodynamic limit, you say you have infinitely many particles. What do you mean? I really mean a large amount of particles."
},
{
"end_time": 4538.524,
"index": 182,
"start_time": 4515.896,
"text": " But still in the math, you're going to do the limit with infinity. What is the problem? You do it. You know that you're making a model. So the model doesn't have to be factually correct. The model has to be a good approximation of what you do. Then in science you also have another problem is that you assume reproducibility."
},
{
"end_time": 4557.739,
"index": 183,
"start_time": 4539.121,
"text": " If you assume reproducibility, you're already saying, I can do it one more time. Yeah. And if you assume I can do it one more time, you're already getting infinity. I see. Can we ever do something one more time? Technically speaking, technically speaking, I know I'm going to die. No."
},
{
"end_time": 4582.619,
"index": 184,
"start_time": 4558.097,
"text": " But in the model, you assume that. You assume, well, OK, I'm not going to be able to do it with somebody else. Really, we want to put the physical theory that the sun is going to expand and destroy. It's a model. So I don't see the problem. The problem is that, again, you need the justification to say that this model, you need to know when the model holds."
},
{
"end_time": 4609.497,
"index": 185,
"start_time": 4582.961,
"text": " And so you're basically your model is, okay, I'm going to have an infinite amount of time. I will have all these tests. It's not even infinite. You see, it's arbitrary or large, which is not infinite. And if I have a procedure that has to cope for an arbitrary large amount of time, because I can always do something one more time, you still need to give me an algorithm that have, you know, countably many possible tests that it can run."
},
{
"end_time": 4629.889,
"index": 186,
"start_time": 4610.094,
"text": " Even if you're not going to run all of them, but the whole thing, defined on arbitrary time, is defined uncountably many. So at this point in your journey, it's 2010? Oh no, this I figured out in 2000. How was it? I don't know, 17. Okay, so this is quite recent."
},
{
"end_time": 4652.346,
"index": 187,
"start_time": 4630.401,
"text": " The whole thing worked like this. Up until 2012, which is when I moved to Michigan, I was sort of fuzzing around by myself reading books, auditing classes on quantum field theory, reading books. I had absolutely no"
},
{
"end_time": 4672.5,
"index": 188,
"start_time": 4652.705,
"text": " Will interest to do any of this i was happy to do essentially. Engineering within a big computer so i i i wanted certain and then i remain the in a sort of big particle accelerator and i was doing."
},
{
"end_time": 4692.517,
"index": 189,
"start_time": 4673.251,
"text": " databases, wide area network data distribution, cybersecurity, a lot of different things, control systems. I did a lot of these things in 2012. So it wasn't actually particle physics?"
},
{
"end_time": 4721.51,
"index": 190,
"start_time": 4693.029,
"text": " Well, I was in support of particle physics. What I mean is, look, we can work on creating a TV show or we could work on ensuring that the HDMI cables are plugged into the right place. They're both working on the TV show. I'm working within the experiment, working on the software infrastructure that they have. Or I'm working at a facility that provides the acceleration, for example, in I don't remember when it was 2008, 2009, something like that."
},
{
"end_time": 4741.032,
"index": 191,
"start_time": 4721.937,
"text": " I was a broken natural lab they were creating a new light source light source is basically something where you accelerate a bunch of electrons and then you shake the electrons to generate photos and then those are very high energy photos event people use to do crystallography all sorts of things."
},
{
"end_time": 4770.947,
"index": 192,
"start_time": 4741.032,
"text": " So it's a facility that you go, you are a researcher somewhere, you have your experiment, you book your beam line for two weeks, you come here, there, your things, you attach it, you gather your data, and then you disappear. And I was there sort of at the moment of construction, working on the control systems, working on the UI parts of the control system, working on the protocol of communication. And you were studying physics and the"
},
{
"end_time": 4792.005,
"index": 193,
"start_time": 4770.947,
"text": " I'm a spare time in your spare time. Yes. Okay. Stealing books from all these other people and that's all. And also I was auditing a quantum field theory in a Stony Brook, which is the university closer to there. And so at some point I started attending the classes to see, learn."
},
{
"end_time": 4819.275,
"index": 194,
"start_time": 4792.551,
"text": " Then I moved, but again, it was just a hobby for me. I had no interest or inclination. I didn't think it was my job anyway, so I don't have the background for doing these things. Then what happened in 2012, we moved to Michigan and that's where some of the things about the four different ways of thinking about Hamiltonian mechanics clicked. Okay, but you had to have been doing research in that."
},
{
"end_time": 4842.244,
"index": 195,
"start_time": 4819.923,
"text": " So you were doing research in your spare time or you were paid to do this research? No, in my spare time. I was just reading a book and trying to figure things out. That's it. And it's kind of my mind was doing that by itself. It's like having a background process that kept going. I would"
},
{
"end_time": 4869.821,
"index": 196,
"start_time": 4842.739,
"text": " My mind would think about these things while dreaming and then you wake up to say, oh, I figured out this stuff. It's all like this, completely not driven by me. It was like the curiosity of my brain. And OK, I'll give you some stuff. And yeah. And that's around the complete then doesn't tell the where was where I sort of some things started to click on the classical mechanics side before. I mean, before that, I was really more interested in quantum."
},
{
"end_time": 4873.268,
"index": 197,
"start_time": 4870.145,
"text": " and then at some point it dawned on me"
},
{
"end_time": 4902.637,
"index": 198,
"start_time": 4874.104,
"text": " right? That what I really wanted was essentially have this dictionary between the math and the physics, right? What is the physics represent? And I realized that to really be sure that the dictionary was working, I would have to go from the physics to the math. Because if I, that's the only way that I know that the dictionary is complete. If from the physics, I'm able to recover the math. Because if I'm not able to do that, or I don't know whether I can do that, I don't know whether I figured out all the physical concepts."
},
{
"end_time": 4930.725,
"index": 199,
"start_time": 4903.08,
"text": " And then at that point, it dawned on me, I can't do this for classical mechanics either. So it's not that I don't understand quantum mechanics is I don't understand classical mechanics. I don't understand thermodynamics and anything. And so sort of that was the first aha moment that I paid more attention to classical mechanics. In 2012 was where I started putting some something to maybe even more. I don't know. I would have to go and read them. But at some point, those things clicked."
},
{
"end_time": 4959.633,
"index": 200,
"start_time": 4931.357,
"text": " on the classical mechanics side. And at that moment, I was still of the idea, you know, this is not my job. This is my my field. I just need to find somebody who who understands this and they can write a paper and I don't care. And I couldn't find anybody to be interested in lots of strange things. But anyway, I couldn't find anybody could be bothered to to understand or to care about the physical motivation of classical mechanics."
},
{
"end_time": 4988.353,
"index": 201,
"start_time": 4960.452,
"text": " And that's the moment that basically said, okay, you know, I have this thing. Clearly, you know, if I want to do something with it, I have to do it myself."
},
{
"end_time": 5013.234,
"index": 202,
"start_time": 4988.609,
"text": " I'm never gonna be able to find somebody who takes it and does something and so I started the auditing classes and doing this more but still in my spare time and in a more structured way and with my wife also who is a professor in physics so she is really more academic than me and the first thing that I did was a proof of concept"
},
{
"end_time": 5043.592,
"index": 203,
"start_time": 5013.626,
"text": " We got some seed money from the university, and we also involved a person in the physics department, in the math department, and a person in the physics department. And there for me was really, can we make like a proof of concept that we can go from scratch and get to classical and particle mechanics? A proof of concept of the assumptions of physics project? Basically, yes. Before it was even titled assumptions of physics? Correct. And this is again my"
},
{
"end_time": 5066.169,
"index": 204,
"start_time": 5044.155,
"text": " I guess by engineering thinking, you know, before doing something, you do an MVP. Yes. Right. And so I did that. And that's where, you know, I drilled it through topology and science. I said, OK, this starts making sense. I can actually like I know it can be done. And then from there, I shifted and shifted more work towards this. And now I'm basically doing it full time."
},
{
"end_time": 5093.985,
"index": 205,
"start_time": 5067.671,
"text": " And the reason that I'm doing it for town also today is because last summer we got a grant from the John Templeton Foundations that allowed me, it's actually the first grant that we were able to do for this because there is really no money for this type of thing. And they're funding a small part into this whole enterprise."
},
{
"end_time": 5120.947,
"index": 206,
"start_time": 5094.428,
"text": " It sounds like what you're doing is similar to foundations of quantum mechanics and there's money for that, not much. What would be the classification of what you do? Foundations of physics? It's really a foundation of physics and there are some tie-in with also foundations of math and philosophy of science. It's really the thing that is in the middle. Because the game is figuring out when I have a problem,"
},
{
"end_time": 5146.152,
"index": 207,
"start_time": 5121.442,
"text": " First, I need to understand is it a philosophical problem, mathematical problem, or physical problem? At the beginning, you said, oh, you don't just go and look at the philosophy. That's because, first of all, I need to identify where the problem is. So, for example, there is a lot of literature in philosophy that takes for face value what the physicists say that"
},
{
"end_time": 5173.78,
"index": 208,
"start_time": 5146.152,
"text": " Newtonian mechanics, Lagrangian mechanics, and Hamiltonian mechanics are equivalent. Because of course, you're a philosopher, you read this in almost every textbook, you're going to say, okay, this is what the physicists conclude, I'll go and do my thing. But then I look at it and say, okay, wait a minute, wait a minute. Lagrangian and Hamiltonian mechanics are fully identified by one function on the state. While"
},
{
"end_time": 5193.729,
"index": 209,
"start_time": 5175.367,
"text": " Newtonian mechanics is identified by the forces, which is one force for H degree of freedom. And I can't have a diffeomorphism. These things are not equivalent if I have n functions. I can't just go to one function in a continuous way and come back. So there's something fishy there."
},
{
"end_time": 5214.77,
"index": 210,
"start_time": 5194.326,
"text": " And again, that's the math that is telling me and then the math is informing me that so you go in on the physics and you figure out, oh, wait a second. When you go and derive Lagrangian mechanics and Hamilton mechanics in the book, there is always an assumption of conservative forces. Are we ever able to relax that condition? And of course not."
},
{
"end_time": 5231.732,
"index": 211,
"start_time": 5215.145,
"text": " Entering out that the assumption of conservative forces is so strong that you take essentially that say and and the dimensional problem into a one dimensional problem. So you discarded a lot of stuff there right so and and again."
},
{
"end_time": 5261.084,
"index": 212,
"start_time": 5232.568,
"text": " Then you know what the physics is. And then you want to go back to the math and say, can I get from these different physical assumption? Can I go and we get the different math? And then it turns out you can. And so if you're not well informed on all three subjects, I don't mean so well informed. If you don't have a general sense, you can't put your head as a mathematician and think like a mathematician, put yourself as a philosopher and think like a philosopher. You're never going to be able to solve this because you don't know where the problem is."
},
{
"end_time": 5290.913,
"index": 213,
"start_time": 5261.51,
"text": " It's like I have a software problem and I try to fix it in the hardware. You're never going to solve it because it's a software problem. So here is the same. If I have the math that is wrong, you're not going to be able to fix the physics. Or if you have the philosophy that is wrong, the math and the physics, you're interpreted incorrectly. They can do whatever they want, but you're never going to get to the right answer. Yeah, you and I both share this generalist mindset. So you mentioned you had difficulty publishing."
},
{
"end_time": 5307.619,
"index": 214,
"start_time": 5291.254,
"text": " Yes. Explain. Because the stuff that I'm interested in is not what most people are interested in. I'm interested in it. I know. That's why I have the YouTube channel because I find that the YouTube channel is actually what keeps me sane."
},
{
"end_time": 5323.063,
"index": 215,
"start_time": 5308.046,
"text": " because I see that there are people that have exactly the same question as me. And from these simple comments, I always suspected that these things were different. I can feel the frustration of these people that went through classes like I did."
},
{
"end_time": 5348.387,
"index": 216,
"start_time": 5323.063,
"text": " the professor who is in a hurry who doesn't have the time to think about all these things deeply and quite frankly he has his own research he has to get the grant and stuff is going to tell you some answer and you kind of feel that that answer doesn't satisfy you is there something fishy but you have to take your exam and you have to move on and get a job and you never have the time to sit there and think and basically the idiot that stayed there on the time and sit there and think right"
},
{
"end_time": 5373.387,
"index": 217,
"start_time": 5348.387,
"text": " And I know that there are people that are interested in this thing, but it's not what you get grants for. And if you don't get grants for it, then you don't have people that work in the field. So it's not that people aren't interested in it or that researchers aren't interested in it because this podcast has a large platform of researchers who are interested in similar subjects as you and myself. Hopefully it's that the grant agencies aren't interested in it."
},
{
"end_time": 5400.725,
"index": 218,
"start_time": 5374.309,
"text": " Yes, and it has been happening for so long that the people that were interested in these topics, either they didn't get an academic job or they had to switch their topic. You know, follow the money, right? So what can be done? Find people that give me lots of money. No, like seriously, I don't know. I really don't know."
},
{
"end_time": 5423.797,
"index": 219,
"start_time": 5401.203,
"text": " What I'm trying to do is, again, through the channel, through the activity, I'm just trying to find a community of people that sort of can help me push and work on the project because, as I said, the ambition is, oh, we have to go from scratch, we derive all the math from scratch, all the physics. It's an outrageously large amount of"
},
{
"end_time": 5452.21,
"index": 220,
"start_time": 5424.019,
"text": " work. I can't do it all by myself. Do you analogize what you're doing to what Bertrand Russell did with math, trying to find the foundations, the axiomatic foundations? As I said, it has a similar feel to a foundation of mathematics and foundation of computer science. They both have a foundation where the foundation is not find the theorem of everything or the algorithm of everything,"
},
{
"end_time": 5482.517,
"index": 221,
"start_time": 5452.517,
"text": " But it's to find, okay, what is math? How do we do proofs? Right. And what can we do with a proof? Right. Or what is a computer? What is a computation device? What can we do with those things? What classes of problems are there? It's a different sort of axiomatization than say, axiomatic quantum field theory. Correct. Yes. Because I'm asking, okay, in the same way, what is a math proof? What is a computation? What is a physical theory?"
},
{
"end_time": 5490.043,
"index": 222,
"start_time": 5483.131,
"text": " What are the minimum requirements that physical theory must have? Therefore, what is the space of physical theory?"
},
{
"end_time": 5515.111,
"index": 223,
"start_time": 5490.555,
"text": " And what physical theory can we possibly have and not? And within this context, we put there all the theories that we have. So they are classified and categorized and re-systematized in the same way that mathematics is systematized and computer science is systematized. Yeah. Now suppose someone with funding was watching this and was saying, okay, is this more than just a theoretical interest?"
},
{
"end_time": 5545.094,
"index": 224,
"start_time": 5515.367,
"text": " Is there something that you see that is practical that can come from this, such as, for instance, when people were funding research more fundamental than quantum mechanics to QFT to whatever may come beyond their thinking in terms of an analogy to to World War Two, where they invented the bomb because of investigations into physics. Okay, so they're thinking, can some new technology emerge from understanding what general relativity would be like combined with the standard model, something like that?"
},
{
"end_time": 5573.763,
"index": 225,
"start_time": 5545.708,
"text": " I have no idea. That's the first honest answer. What I know is that first, it's going to make teaching physics a lot better because, again, you're going to know what you're talking about. And usually, knowing what you're talking about helps communicate more effectively. And the other thing, and this is my feeling, is that"
},
{
"end_time": 5592.159,
"index": 226,
"start_time": 5574.616,
"text": " I can't see a way for us to go past the current theory and do the theories that people want to do that unify things and so on without doing this work. And I'll tell you like this. So imagine that you are"
},
{
"end_time": 5616.869,
"index": 227,
"start_time": 5592.637,
"text": " In the late 1800s, you study classical mechanics and therefore you, well, I know if you knew manifold per se, because that maybe the concept wasn't so crystal clear, but you have, you know, that's how you thought about things with points and so on. Could you imagine knowing that, could you predict the Hilbert spaces of quantum mechanics, the projections postulate all of this?"
},
{
"end_time": 5635.691,
"index": 228,
"start_time": 5618.063,
"text": " No, because the mathematics is so different. The approach to the theory is so different. Like the jump from classical mechanics of two quantum mechanics is too far for you to be able to say, oh yeah, I want to quantize things. I'm going to need this thing. And there at least we had"
},
{
"end_time": 5665.111,
"index": 229,
"start_time": 5636.049,
"text": " The experiments that we could do both in statistical mechanics and then, you know, with this, that tells you, okay, well, we need something different and there are some hints and so on. And then it was, you know, just cram some math together. Oh, it's kind of working. Then it evolved. Now, let's say that, okay, now we want to have a theory for Planck scale or whatever those everything. To me, I expect the same jump that we had for classical mechanics or quantum mechanics."
},
{
"end_time": 5687.807,
"index": 230,
"start_time": 5665.794,
"text": " And so I'm expecting the math that we need to do be completely different. Lord knows what it is. As I said, the no differential geometry topology. I don't know what time we're going to have a topology because that's we need to connect to experimental verification better. And so I can't imagine that we just get to the math that we have right now."
},
{
"end_time": 5709.821,
"index": 231,
"start_time": 5688.285,
"text": " Generalized by mathematicians to solve their math problems, not for the for the physics problem. So it's not generalized with an intent. Oh, we are relaxing some physical assumption. We're putting others right. And I think it's going to be very likely that we're just going to have this magnitude of experimental data that we had for quantum mechanics."
},
{
"end_time": 5735.384,
"index": 232,
"start_time": 5710.657,
"text": " So from my perspective, if we don't go back and re understand everything, we understand exactly what's happening from classical to quantum such that we can have an idea principle idea what needs to happen next. I don't see it happen. And again, it's not a direct thing like because I can't work on that first. First, I need I need to it's like really, you want to build a"
},
{
"end_time": 5753.166,
"index": 233,
"start_time": 5735.879,
"text": " A building that is taller, right, that allows you to see farther. That's what the ultimate theory, the theory of everything, is not at the foundation. It's the top floor. You want the top floor very high so you can see everything and do everything very good. You need the sturdier foundation on top to build higher."
},
{
"end_time": 5772.056,
"index": 234,
"start_time": 5753.541,
"text": " And this is the work that I'm doing. I'm trying to re-understand when you're doing the foundation, you're not going to redo the foundation only for the top floor. You need to redo the foundation for all the floors in between. So all the floors are more stable so that you can build on top. So that's what I'm interested in, in reorganizing all of these things, get the math"
},
{
"end_time": 5801.596,
"index": 235,
"start_time": 5772.432,
"text": " Right. So that all the math that we have is physical and all the physics that we have is in the math. We understand we have we can read all the proofs. Right. As a mathematical as a physical argument, not just as a mathematical thing that you're doing. No, no. Every step. Right. Once you know, once you have a perfect dictionary, you can read the proof and say, oh, this is what I'm doing physically. I'm making the limit by making verifiable statement that are finer and finer and finer. And that's what I'm doing. That's what a limit is. And therefore I can do these things."
},
{
"end_time": 5818.046,
"index": 236,
"start_time": 5802.585,
"text": " What's the latest project that's in your mind that has this unrelenting, scintillating pull to you, much like when you were in 2012 thinking about classical mechanics and you couldn't stop, you would even dream about it?"
},
{
"end_time": 5847.363,
"index": 237,
"start_time": 5818.695,
"text": " Once I've started doing this all my time, the mind hasn't been so pesky. But what I'm interested right now, it's really this general theory of ensemble space and basically the ensemble spaces. Yeah. And it really figuring out the basic axioms. And again, right now, for me, the interest is to be able to do the argument of classical mechanics and quantum mechanics well."
},
{
"end_time": 5863.166,
"index": 238,
"start_time": 5847.807,
"text": " Basically, here's what I want to be able to prove. And let's do it like this. So we said before, right, that areas in volumes in phase space count the number of states, right? And"
},
{
"end_time": 5884.65,
"index": 239,
"start_time": 5863.353,
"text": " And they have a measure, they don't count the points, right? If I have discrete elements, you just count the points, then that's fine. But areas in phase space, right, when you are a continuum, you have infinitely many points. So you can't just say, oh, I have infinitely many states, because then if you double the space, like if you double the volume, you would have the same number of states, which makes no sense."
},
{
"end_time": 5913.541,
"index": 240,
"start_time": 5884.65,
"text": " So you put mathematically a measure, and the measure is going to be additive. So if you take two volumes that are disjoint, and you double it, you're going to have double the size. Perfect. Now imagine that you have these volumes and you divide them in half and half and half and half. At some point, your count of states will become less than one. What does it mean to have a region with less than one state? It means nothing."
},
{
"end_time": 5943.626,
"index": 241,
"start_time": 5914.616,
"text": " Not only, remember, if you have a uniform distribution on a certain amount of states, the entropy is the logarithm of that number, right? If I have less than one state, it would mean that I have logarithm of a number less than one, which is negative number. What does it mean to have negative entropy? Nothing. So this is where in another way to say, OK, classical mechanics does not work because it tells me that there are regions with less than one state."
},
{
"end_time": 5969.155,
"index": 242,
"start_time": 5944.735,
"text": " What happens is that if you do this analog, if you try to construct an analog of this, and I can't understand why nobody has ever done it. I've never seen it in the literature. If you do the same analog in quantum mechanics, you look at the entropy how it goes. Well, the entropy of pure state is exactly zero. And the exponential of zero is one. So every pure state count as one. And you can't have something smaller."
},
{
"end_time": 5984.326,
"index": 243,
"start_time": 5969.974,
"text": " But the state space of quantum mechanics is still a continuous, like if you take the block ball, which is the two degrees, the surface is still continuous. So what happens if you take the surface of the full ball and you say how many states there are there? There are two."
},
{
"end_time": 6006.118,
"index": 244,
"start_time": 5985.043,
"text": " Because the"
},
{
"end_time": 6028.643,
"index": 245,
"start_time": 6006.476,
"text": " And there are basically these three conditions. You want to be able to count things, right? You want to be able to count states. And there are three things that you would imagine. One is that every state counts as one. And if you have a finite region of phase space, of your state space, that should have a finitely many states. And you want the measure to be additive."
},
{
"end_time": 6047.5,
"index": 246,
"start_time": 6029.804,
"text": " What you can't have all three, because once you have infinitely many points and you say everyone is one, well, the count of the region is going to go to infinity. And so you can you have to relax one of this. And what happens is that if you are in a classical discrete space,"
},
{
"end_time": 6075.896,
"index": 247,
"start_time": 6047.841,
"text": " You relax that the finite region are going to have finite entropy, finite count of states. So everything is out of it and every state is counted one. On a Lebesgue measure, what you do in phase space, you say, well, points are zero, but then I still have finite volumes and I have additivity. And in quantum mechanics, you say, well, I remove the additivity. And there are a lot of things that you can see that the weirdness of quantum mechanics"
},
{
"end_time": 6106.357,
"index": 248,
"start_time": 6076.544,
"text": " comes from that activity. But then you see, okay, why do I want to lose that activity? Well, because I need to be able to count states. Every state must be one and a finite patch with infinitely many states on top of it. If I make a mixture of that, I still need the final 10 to be final to many states. And so this is what I like to say that there is only one way to create the ensembles that have an entropy and account of states."
},
{
"end_time": 6133.183,
"index": 249,
"start_time": 6106.664,
"text": " such that I have a measure defined on a continuum that counts a state, but it has a lower limit. And so the quantization in my mind is really putting this lower limit to the count of states. Classical mechanics does not have, because you can make things smaller and smaller and smaller. So you take one state, choppy, choppy, choppy, choppy. In quantum mechanics, the quantization is, I can't have less than one state."
},
{
"end_time": 6161.271,
"index": 250,
"start_time": 6133.541,
"text": " And so when you go up, things are going to look additive, things that are going to look classical. But when you go smaller, I know that you have this lower bound. And just to tell you, this is what I'd like to have in this ensemble of spaces, I'd like to be able to run that argument. But I want to be able to create this structure in a way that I'll be able to use for field theory as well. And that's a challenge because it's the whole problem of infinity. And I want to"
},
{
"end_time": 6191.596,
"index": 251,
"start_time": 6161.698,
"text": " Try to see if I have a path for quantizing space-time as well, and leave it as a possibility. Because in space-time you're going to have the same problem. You say, I have a field theory. Now, I count the number of states in each field, but then I have to count the number of degrees of freedom. And in particle mechanics, it's fine at the content one, two, three, right? But in a field theory, you have a field for each point of physical space."
},
{
"end_time": 6220.265,
"index": 252,
"start_time": 6192.449,
"text": " So now you have, you know, sort of continuously many degrees of freedom. You can't say that they're infinite. That wouldn't make sense, because if you double the region of space, now you would have the same number of degrees of freedom. So what's going to happen is that you need to put a volume measure on space. And you say, if I double the volume, I have doubly many, twice as many degrees of freedom. Right. Well, why don't you just use the, I mentioned this before, the Bekenstein bound."
},
{
"end_time": 6250.486,
"index": 253,
"start_time": 6221.817,
"text": " I need things to go smoothly to zero. I can't just say at some point things become discrete because that's not what's happening. What's happening is that I have something where I still have, you know, all these dense states. Quite frankly, it doesn't even matter if it's real or rational. The important thing is that you have dense sets and you need to count the elements in the dense set."
},
{
"end_time": 6262.005,
"index": 254,
"start_time": 6251.101,
"text": " All right, Gabriel, so we talked about philosophy, math and physics. Let's talk about math and physics. Where does that line lay? Okay."
},
{
"end_time": 6282.841,
"index": 255,
"start_time": 6263.302,
"text": " Yeah, so the line between math and physics is something that I, you know, had to think a lot about because since I want to have this sort of rigorous axiomatization approach, I need to understand how do they do in math and whether the way that they do in math is actually good for physics if it's enough."
},
{
"end_time": 6300.725,
"index": 256,
"start_time": 6283.49,
"text": " And one of the things that we have sort of a wrong impression in physics or in engineering is that math, it seems also elegant or pristine and so precise. And it feels like everything is there and we should imitate math in some way."
},
{
"end_time": 6327.654,
"index": 257,
"start_time": 6301.118,
"text": " But this is never going to work because the way that math is able to be rigorous, like the way that they did it is essentially to remove all the parts that are difficult or impossible to make precise and remain only with the formal structure, the syntactic structure that you can actually be precise about. So there are sort of a lot of things like"
},
{
"end_time": 6351.374,
"index": 258,
"start_time": 6327.756,
"text": " There's the largest number that can't be described. There's the smallest number that can't be described in so-and-so amount of characters. Exactly. That's something that if you have meaning, meaning is attached, meaning is always these very fuzzy things and it always allows you to create some things like that."
},
{
"end_time": 6374.172,
"index": 259,
"start_time": 6351.561,
"text": " And so what, I guess, the formalists decided, Hilbert, I think, was the one that pushes for this, is, okay, we'll forget what the meanings are. We just have some symbols. They have some rules. And that's it. That's all that we're going to describe in mathematics. And a lot of mathematics is now thought in that way, in one way or another. And in a sense, that's sort of where the power of math comes from."
},
{
"end_time": 6401.288,
"index": 260,
"start_time": 6374.172,
"text": " because if you talk about, I don't know, a boule and lattice, for example, well, that same structure could be representing sets of statements. So a logical structure or sets of sets, or it could have like physically could even describe the systems and subsystem relationship. So you can study the mathematical structure. You can study the equations regardless of where they come from."
},
{
"end_time": 6414.889,
"index": 261,
"start_time": 6401.288,
"text": " So in the end of the day, to the mathematician, it has an advantage to just drop the meaning because then their tools are more powerful because they can apply regardless of the meaning."
},
{
"end_time": 6442.688,
"index": 262,
"start_time": 6415.606,
"text": " And in physics, we can't do that because we have that pesky connection with experiments. And so we can't just manipulate the symbols in any way, whatever. We need to know that that symbol corresponds to a specific system prepared in a specific way with things that we measure a specific thing. So we always have an informal system in physics. You can't just get rid of it. And so what the challenge is,"
},
{
"end_time": 6458.37,
"index": 263,
"start_time": 6443.046,
"text": " is not saying we're going to put everything in the formal system because it's never going to happen. The experiments are not going to suddenly become symbols. You need to define what is advantageous to put in the formal system and what is not."
},
{
"end_time": 6488.046,
"index": 264,
"start_time": 6459.07,
"text": " And that's the hard part. So it's not a question of whether you can do it, but it becomes, you know, sort of a technical problem, sort of an engineeristic problem in how can you do it efficiently? Essentially, the game is to find the again, the minimal set of axioms that you want, that you need, actually, in the form that it's as easily justifiable from the physics."
},
{
"end_time": 6512.722,
"index": 265,
"start_time": 6488.524,
"text": " Because that surface, that line in between when you take physical informal things and you put them in the formal things, that's where the things can go wrong. Once you are in the formal system, you have the math to help you. And so those parts, and that's the part that I'm interested in physical mathematics, getting those definitions and justification right, it's the part that is the most difficult. And it's most difficult because"
},
{
"end_time": 6536.237,
"index": 266,
"start_time": 6513.422,
"text": " I have a feeling, and I'd like to be able to have a proof for this, but again, you can't because it ties in things in the informal system, so it's difficult to create a proof for that. I'd like to have a tight argument that shows that whenever you're taking something from the informal system to the formal system, that is my feeling, you are always going to make some kind of simplification."
},
{
"end_time": 6564.377,
"index": 267,
"start_time": 6537.056,
"text": " And so even a simple concept like, you know, whether something is an orange or not, right, you go to a supermarket, you can easily identify what is an orange or not an orange. So it seems natural that Oh, that's a true false statement. Very easy. But even think how an orange develops starts with a flower gets pollinated. And there is no point that you can say, Oh, this is the instance where he actually became an orange. Right. So all these concepts that we have are fuzzy."
},
{
"end_time": 6593.677,
"index": 268,
"start_time": 6564.633,
"text": " And you're going to have to make a cut. And so if you're talking about objects in a supermarket, yeah, perfectly fine, because we're not having, we're not going to have these in between. And so it's going to be either true or false. But if you're studying your biology, you're not going to, that statement is going to be defined. So even defining this property, even defining the statements themselves, I don't think there is a way to define statements that are universally applicable in all circumstances. It's always a matter of"
},
{
"end_time": 6615.435,
"index": 269,
"start_time": 6594.104,
"text": " I have a realm of applicability, a domain, and in that domain, in that context, that statement makes sense. Okay, you just mentioned the word cut, which makes me think of Heisenberg cut, which makes me think of the measurement problem. So I'm curious what you think of the measurement problem. What have you found out? What are your current thoughts?"
},
{
"end_time": 6642.159,
"index": 270,
"start_time": 6616.8,
"text": " I don't understand what the measurement problem is, because when I talk to a lot of people, they seem to have a different interpretation. How would you formulate the measurement problem? What counts as a measurement? That I don't have an answer for. It's, again, one of those things that for me lives in the informal system."
},
{
"end_time": 6670.043,
"index": 271,
"start_time": 6642.756,
"text": " And so I don't even know if I can formulate something precise. Right. So you see, this is exactly why I asked because there is another part that is why do we have two different laws of evolution, one for measurement and one for processes that I think can be understood. Oh, okay. But what counts as a measurement that"
},
{
"end_time": 6695.64,
"index": 272,
"start_time": 6670.384,
"text": " What separates a measure from a measured? Well, yes. So what I want to say is that in this realm, what counts as a measurement, what counts as a measurement, and all of these problems are connected to the problem that I was saying before of defining boundaries between system and environment. Because when you're saying I have a system and make a measurement, you're basically saying, okay, there is a system,"
},
{
"end_time": 6720.879,
"index": 273,
"start_time": 6696.101,
"text": " There is a boundary. Well, let me predict a problem with this is that if we're saying that, then there's necessarily something subjective because we're going to be the ones that are dictating the boundary. There's then the meta measurement problem of who is defining the system. Right. So defining the system is not subjective. It's objective, but it's contextual. Like you need it again."
},
{
"end_time": 6735.896,
"index": 274,
"start_time": 6722.108,
"text": " In this context, these are the things that can happen. This is what happens at the boundary. So it's not an arbitrary. When I say I have a system and I define a boundary, I'm also defining what is happening at the boundary."
},
{
"end_time": 6765.691,
"index": 275,
"start_time": 6736.596,
"text": " Right. So it's not just saying, oh, I'm grouping these things together, but I'm grouping this together. There is this interaction between the boundary and the system. Like I need to give you the boundary conditions, not just to solve the to find the problem of the equation, but we need to be able to define the system. Right. And so part of the problem of defining what a measurement is and how it works and all of this is because you are trying to model something that goes across the boundary, which is"
},
{
"end_time": 6792.91,
"index": 276,
"start_time": 6765.998,
"text": " Even just the information that passes from one thing to the other, and then information has to be encoded in some physical system. So something needs to happen. And then in quantum mechanics, there is a thing that actually happens during the measurement. And this is how I think about it. So imagine that you have your block ball for the two state system, right? You pick an observable, right? Which means you're picking an axis in some direction."
},
{
"end_time": 6817.449,
"index": 277,
"start_time": 6793.387,
"text": " and the points at the axis are going to be your eigenstates and all the points in the middle are mixtures of those of those two states right so now imagine that you start at any other points right and you want to say oh i'm going to make a measurement right like none of these what you're going to be predicting after the measurement"
},
{
"end_time": 6846.954,
"index": 278,
"start_time": 6817.841,
"text": " Is going to be that you're going to be either in this state or this state. So you're going to be in this after the measurement. What you predict is that you're going to be at a point on the axis. So what the measurement process needs to do in one way or the another, whether it's through whatever mechanism, it doesn't really matter. What needs to happen is that that point that is here needs to be projected on that axis. That process is a process that increases entry. Right."
},
{
"end_time": 6871.305,
"index": 279,
"start_time": 6847.329,
"text": " And so that's something that needs to happen. And there are a lot of people that from other places argue that measurement devices are things that increase entropy. You have a metastable state that gets perturbed and then falls into two equilibria, right? There is this sense that you have something and you fall into two equilibria. And there are some people that have argued that there is literature in that that it shows that."
},
{
"end_time": 6900.418,
"index": 280,
"start_time": 6871.305,
"text": " But I'm trying to argue it more from a sort of more conceptual, you know, again, from what I need to have to be able to make this make sense. And there's something else that, yes. So I understand that this measurement process is a process that actually increases entropy. It has given me sort of a way to think about these changes of context."
},
{
"end_time": 6924.309,
"index": 281,
"start_time": 6900.759,
"text": " Add along the lines of what happens in thermodynamics. So since you started the statistical mechanics and you are happy with that, you know that there are different types of the sample. There is the grand canonical ensemble, there is canonical ensemble and so on. And in each of those ensembles, some quantities are the ones used to actually define the ensemble. So if I have a cup of water,"
},
{
"end_time": 6949.582,
"index": 282,
"start_time": 6925.265,
"text": " And it's just sitting there and I ask you how many molecules are there in the cup of water? Well, it's a problem because molecules keep going out and coming in. So the molecules are fluctuating, right? And this is the overall macrostate is not defined by the number of molecules. It's a grand canonical ensemble is going to be defined by temperature, volume and chemical potential."
},
{
"end_time": 6977.483,
"index": 283,
"start_time": 6950.435,
"text": " But now you want to really see and say, I really want to know how many molecules are there. And so you need a way first to stop these molecules from fluctuating, because otherwise you can't even know which one you can't resolve. So what you do, you close the glass. And when you close the glass, you transition from a grand canonical ensemble to a canonical ensemble. And now the canonical ensemble has volume, temperature and number of particles well defined."
},
{
"end_time": 6989.394,
"index": 284,
"start_time": 6978.456,
"text": " And the chemical potential is no longer well defined. Now, of course, when you close that you can predict exactly how many molecules are there because the molecules were fluctuating."
},
{
"end_time": 7011.527,
"index": 285,
"start_time": 6989.855,
"text": " So the final state is going to be a probability distribution over all the possible canonical ensembles of all the different number of molecules with the distribution exactly matching the fluctuation that you had before. Wait, why can't you just say if you have a cup you say how many molecules are in this cup at 2 p.m."
},
{
"end_time": 7041.357,
"index": 286,
"start_time": 7011.664,
"text": " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ."
},
{
"end_time": 7063.148,
"index": 287,
"start_time": 7041.544,
"text": " I see. You switch the thing, the number of molecules are no longer fluctuating. In a way, you can think of measurements in quantum mechanics doing exactly that. So you have your spin system, right? But wouldn't that have some hidden variable associated with it? The hidden variables, you can only define them"
},
{
"end_time": 7086.954,
"index": 288,
"start_time": 7063.473,
"text": " If you're able to prepare ensembles that are at a finer resolution of what you were able to do. Right. So you are able to talk about the actual number of particles and so on in those ensembles because you can isolate the molecule and talk about the parts."
},
{
"end_time": 7117.346,
"index": 289,
"start_time": 7087.807,
"text": " But now when I have a single system, how can I talk about the fluctuations of the spin in terms of hidden variables without at least being able to talk about ensembles that are better specified than just a single spin state? To put it like this, imagine that you have a probability distribution."
},
{
"end_time": 7146.561,
"index": 290,
"start_time": 7117.944,
"text": " You could have that probability distribution because you have a single point that is jingling around, or because you have an actual statistical distribution, something that is actually smeared, and that thing is jiggling around, or I really have something smeared and I'm just taking a piece of it, right? The ability for you to distinguish between these three cases means that you're able to resolve the system at a finer level."
},
{
"end_time": 7153.848,
"index": 291,
"start_time": 7147.346,
"text": " But if you say, oh, my system is irreducible, I don't have a finer level, you can distinguish between these three things."
},
{
"end_time": 7178.524,
"index": 292,
"start_time": 7154.804,
"text": " So whether there is really like a spin that is jiggling around or something that is more complicated that is jingling around or some kind of uniform distribution that then collapses into something like this, to be able to distinguish those cases, you would need to, again, have a finer level of description, which assuming irreducibility tells you that you can't have."
},
{
"end_time": 7208.387,
"index": 293,
"start_time": 7180.213,
"text": " So there are a lot of things that once you assume irreducibility, you can get a conceptual level at quantum mechanics without. So if you say, OK, my system is irreducible, right? It means I cannot have a perfect value for positional momentum. I need to have this finite entropy that smears things out, because if everything was at a single point, I would be able to tell you what all the parts were doing. All the parts were exactly there with the same exact fraction of momentum."
},
{
"end_time": 7213.319,
"index": 294,
"start_time": 7208.677,
"text": " So you can say that so you need some kind of smearing you need some uncertainty principle."
},
{
"end_time": 7241.305,
"index": 295,
"start_time": 7213.712,
"text": " which actually in Italian and other languages is more an indetermination principle than uncertainty principle. And I think it capture really more what's going on. So you need to have this system to be a little bit undetermined so that so that you can say, I know everything of what's going on. But once you say that I have a distribution in space that I can't tell what the parts of the distribution are doing. Well, that thing is non-local by definition."
},
{
"end_time": 7254.582,
"index": 296,
"start_time": 7241.647,
"text": " Because I have something that is distributed in space, but I can't say, oh, I can follow one part in space and what it's doing. And so you can only follow the whole thing. The object is no lockout because it's irreducible."
},
{
"end_time": 7276.664,
"index": 297,
"start_time": 7255.469,
"text": " But you're not going to be able to have communication from one side to the other, like superluminar communication or those things. Because if you were able to detect it, you would be able to go at a resolution that it's below this uncertainty and be able to make a correlation between parts. But you can't because the system is irreducible."
},
{
"end_time": 7303.677,
"index": 298,
"start_time": 7277.534,
"text": " So you see, a lot of these weirdness that once you swallow the bullet, like it's like in relativity, you say, okay, I will concede that the speed of light is constant. And then you're, oh, energy is equal, mass is equal to energy and all these things. But it's all from here, from there. And so I think this is sort of the same idea. The system is you can't know what's going on inside."
},
{
"end_time": 7332.466,
"index": 299,
"start_time": 7303.677,
"text": " Okay then i'm gonna have a new principle i'm gonna have that the thing is you know no i mean that we could have some bizarre laws that are just inaccessible to us yes including retro causality or superluminal speeds if they're not accessible to us you can't even say whether they are retro causal or superluminal interesting you can only say that because you set up an experiment every time that you do this"
},
{
"end_time": 7362.705,
"index": 300,
"start_time": 7333.063,
"text": " You know, this happens before that. So we've talked about what's directly next for you. You're hoping to solve this problem. I'm working on this ensemble space and trying to get that math to work out. What's something you hope to achieve in the next 10 years? I hope to find other people to help me clear up and fix both the mathematics and also the philosophy of this."
},
{
"end_time": 7384.804,
"index": 301,
"start_time": 7363.387,
"text": " What I really love, because you see, I'm okay enough to scope some of these problems, but I don't know that I will ever be able to achieve the technical competence in all the sub fields that I need to be able to carry the project through. I mean, it's just a matter of time. So the thing that I'm"
},
{
"end_time": 7408.575,
"index": 302,
"start_time": 7385.964,
"text": " I've been trained myself to do is to be a translator so that I can talk to the guy who does philosophy of. Yeah, that's something else that unites us is that I think of theories of everything as a Rosetta Stone or it's I hope it to be a Rosetta Stone because academia is designed to instead of creating the silos."
},
{
"end_time": 7434.002,
"index": 303,
"start_time": 7408.746,
"text": " Add that don't really know how to talk each other to each other. I really had some problems and philosophy. I think in some sense is the worst offender because they still have this idea in mind that the philosopher is the one that thinks by himself in a room and then comes up with this great idea. And then this price, the single author paper, which"
},
{
"end_time": 7464.36,
"index": 304,
"start_time": 7435.009,
"text": " Right. That is true. So that for people who don't know who are watching who aren't researchers in physics, it's quite common and computer science and math to have multiple co-authors. But in philosophy, it's quite rare. And I have had this problem that I did find some PhD students that from that were instruments working and I wrote a paper with one. We have another one that sort of PhD student in philosophy."
},
{
"end_time": 7480.657,
"index": 305,
"start_time": 7464.77,
"text": " And, and one of them clearly said, you know, I can't put so much time in this because I need to have my single author literature. Otherwise, they're not gonna take up and not gonna get a position and all that. And, and to me is bizarre because"
},
{
"end_time": 7504.497,
"index": 306,
"start_time": 7482.705,
"text": " You know, you start writing the single author paper, I guess, you know, when you're 20 something, there is so much stuff that I had to learn on both math and physics and everything before I had even something remotely interesting to say, you know, I said it before, I didn't start doing this when I was"
},
{
"end_time": 7525.043,
"index": 307,
"start_time": 7504.497,
"text": " I"
},
{
"end_time": 7544.65,
"index": 308,
"start_time": 7525.708,
"text": " Yes. What are you going to be able to say? The hard bit right now is putting all these pieces together because it's like we have most of the pieces scrambled around in silos that don't know how to talk to each other."
},
{
"end_time": 7560.879,
"index": 309,
"start_time": 7545.333,
"text": " and nobody's ever even able to see that they go together. And sometimes they're not designed to go together because the math is designed by the mathematician who doesn't know the physics and the physicist is thinking about their things without knowing that there is some other math over there."
},
{
"end_time": 7585.998,
"index": 310,
"start_time": 7561.305,
"text": " And so what I'm trying to put is like a framework where I said, okay, the mathematician says that, okay, that party has to be there. But the physicist says that so that that thing can't be said like that. It needs to be and then the philosopher says the other thing. And I guess his perspective needs to fit like you need to put all these things in a way that they all fit together. And but the training that they all they have, right is only from there."
},
{
"end_time": 7607.125,
"index": 311,
"start_time": 7586.459,
"text": " Viewpoint and so a mathematician might look at my thing and says, oh, but why did find things like that in mathematics? Yeah, I know that in mathematics you do that, but I need to justify that the accent from the physical and you're not interested in the fun and perfectly fine. I'm going to reach your structures, but it can't be the foundation of physics, a mathematical structure that you put there."
},
{
"end_time": 7617.688,
"index": 312,
"start_time": 7607.125,
"text": " What I really like to have in 10 years is to find other people like me that are interested in getting this piece."
},
{
"end_time": 7644.002,
"index": 313,
"start_time": 7618.183,
"text": " specific technical or one thing without having the general thing. That's not a problem. I can keep the general thing. I can keep all the things together. Right. But the other person. You're the manager hiring a front end developer and then a back end developer. They don't need to know. They don't need to know the detail of all that. Yes, it's exactly. It's an engineering project. It's not a research. This is the other problem. In academia, they always think that you need a grand new idea and so"
},
{
"end_time": 7660.213,
"index": 314,
"start_time": 7644.002,
"text": " If you're an engineer you know the most of the time you want the simplest idea that works and that creates the list and these are the things that i like find it's not all the new you know grassman compacting fiction of the whatever whatever like it."
},
{
"end_time": 7678.268,
"index": 315,
"start_time": 7660.691,
"text": " No, the simplest math that works, and we already have a lot of math that works, and it must be a reason why it works. There must be a physical justification for where it works, so we need to uncover important things. So if I had other people to help me do this, maybe we could finish the project before I die, and that would make me happy."
},
{
"end_time": 7707.09,
"index": 316,
"start_time": 7678.268,
"text": " There are some researchers who are watching right now who are probably interested. Where can they find out more about you? How can they contact you? So I have a YouTube channel, but that's mainly for popularizing the research. So my YouTube channel is called Gabriella Carcassi. Gabriella Carcassi is my name and last name. There is another YouTube channel called Assumptions of Physics the Research. It's where I try to put every month sort of me talking for an hour, an hour and a half of open problems that I have."
},
{
"end_time": 7732.534,
"index": 317,
"start_time": 7707.517,
"text": " And even there I did this June, I had a sort of an online summer school on the assumptions of physics, which again, it's something that we promoted through the internet. And all of that is recorded. So you hear me rambling for, I don't know, nine hours, you know, these things that saying these are the pieces that we have. These are the pieces that we don't have. These are the pieces and how"
},
{
"end_time": 7748.643,
"index": 318,
"start_time": 7732.534,
"text": " So there is a lot of content there and then of course we have the website the assumptions of physics dot org that has all the research we have an open access open source book which is to me it's the thing"
},
{
"end_time": 7776.254,
"index": 319,
"start_time": 7748.643,
"text": " that is the output of the research. So whenever pieces are figured out, they become an extra chapter in the book. So there is a reverse physics part that has all of the classical mechanics, all with the details, all these conditions and how their equivalents are or they're not. And then there is the physical mathematics where we get topologies, we get continuous functions and we get the real numbers. All of that is there. So if somebody wants to look at how actually things are done are there."
},
{
"end_time": 7789.531,
"index": 320,
"start_time": 7776.578,
"text": " And that's the idea. I'd like to run this as an open source project. Who knows whether we're going to be able to do it or not, but I'm trying to set up the structure more and more like that. And I'll try to"
},
{
"end_time": 7810.128,
"index": 321,
"start_time": 7790.367,
"text": " try to push some of my work more online because again since there might be other people but I don't have salary to give them but maybe they have another position somewhere else and then we can collaborate well if you can structure it in a manner similar to how open source projects are structured"
},
{
"end_time": 7830.555,
"index": 322,
"start_time": 7810.606,
"text": " People contribute little bits here and there. That would be the idea. I don't know how to do it because I don't have a template for that, but all the software development that I did before within physics was all open source. So that's sort of my nature. I think that may be more impactful than any given one of the outputs of this project is the entire"
},
{
"end_time": 7842.91,
"index": 323,
"start_time": 7830.555,
"text": " Templating of an open-sourced physics project because that can then be used. I understand and I have to figure that out. I would be extremely interested because I want to know."
},
{
"end_time": 7861.391,
"index": 324,
"start_time": 7843.268,
"text": " What are the limitations of academia so their academia has pros and cons and what they're pro at they're fantastic at some don't touch that but what are the cons and how can they be filled not to supplant academia but to supplement we could have a whole other to our discussion just on that topic and there is a lot of things"
},
{
"end_time": 7879.923,
"index": 325,
"start_time": 7861.391,
"text": " From my perspective, that the type of things that I do, academia is insulated by design, but I wouldn't even want to change academia because you don't change the structure of a whole field for the project that it's like, it wouldn't even make sense. So yeah, the way that I'm trying to set up,"
},
{
"end_time": 7906.237,
"index": 326,
"start_time": 7880.299,
"text": " This year, we are having the first PhD student coming to work with us at the university. And he learned about the project years ago through the YouTube channel. Okay, the first PhD student for this project for that's not for your university. No, no, no, quite a new university. Yes. But that's why I started becoming more active on YouTube, because I've seen that I have much more impact"
},
{
"end_time": 7934.036,
"index": 327,
"start_time": 7907.227,
"text": " Also, thank you to our partner, The Economist."
},
{
"end_time": 7953.319,
"index": 328,
"start_time": 7936.271,
"text": " Firstly, thank you for watching. Thank you for listening. There's now a website, curtjymongle.org, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon, they can disable you for whatever reason, whenever they like. That's just part of the terms of service."
},
{
"end_time": 7977.722,
"index": 329,
"start_time": 7953.575,
"text": " Now a direct mailing list ensures that I have an untrammeled communication with you. Plus, soon I'll be releasing a one-page PDF of my top 10 toes. It's not as Quentin Tarantino as it sounds like. Secondly, 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"
},
{
"end_time": 7996.22,
"index": 330,
"start_time": 7977.722,
"text": " Plus, it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm, which means that whenever you share on Twitter, say on Facebook or even on Reddit, etc., it shows YouTube, hey, people are talking about this content outside of YouTube, which in turn"
},
{
"end_time": 8018.183,
"index": 331,
"start_time": 7996.408,
"text": " Thirdly, there's a remarkably active Discord and subreddit for theories of everything where people explicate toes, they disagree respectfully about theories, and build as a community our own toe. Links to both are in the description. Fourthly, you should know this podcast is on iTunes, it's on Spotify, it's on all of the audio platforms,"
},
{
"end_time": 8033.456,
"index": 332,
"start_time": 8018.404,
"text": " All you have"
},
{
"end_time": 8056.852,
"index": 333,
"start_time": 8033.456,
"text": " I'm"
},
{
"end_time": 8074.445,
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"start_time": 8056.852,
"text": " 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. Every dollar helps far more than you think. Either way, your viewership is generosity enough. Thank you so much."
}
]
}No transcript available.