Theories of Everything with Curt Jaimungal - "We Have Physics Completely Backwards!" | Gabriele Carcassi

Episode Date: October 11, 2024

Gabriele Carcassi is a dedicated physicist and software engineer based in Michigan, leading the innovative "Assumptions of Physics" project to redefine the foundational principles of physics. By bridging mathematics, physics, and philosophy, Gabriele advocates for an open-source, interdisciplinary approach to advance our understanding of the universe. SPONSOR (THE ECONOMIST): As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe LINKED MENTIONED: - Assumptions of Physics (website): https://assumptionsofphysics.org/ - Assumptions of Physics (book): https://www.fulcrum.org/concern/monographs/tx31qm110 - Assumptions of Physics YouTube channel: https://www.youtube.com/@AssumptionsofPhysicsResearch - Gabriele Carcassi’s personal YouTube channel: https://www.youtube.com/@gcarcassi/videos - Seven misconceptions in the foundations of physics (video): https://www.youtube.com/watch?v=vbv0Fij1-38 - TOE’s String Theory Iceberg: https://www.youtube.com/watch?v=X4PdPnQuwjY - Gabriele’s ‘Quantum Essentials’ playlist: https://www.youtube.com/playlist?list=PLmNMSMaNjnDd-viRHQRzrYvEeCWb7Ruef TOE'S TOP LINKS: - Support TOE on Patreon: https://patreon.com/curtjaimungal (ad-free audio episodes!) - Listen to TOE on Spotify: http://tinyurl.com/TOESpotify - Become a YouTube Member: https://tinyurl.com/TOEmember - Join TOE's Newsletter 'TOEmail' at https://www.curtjaimungal.org TIMESTAMPS: 00:00 - Intro 00:22 - Gabriele's Channel 03:13 - Assumptions Project 06:06 - Physical Mathematics 09:38 - Real Numbers 13:06 - Ensemble Space 16:38 - Classical Mechanics 19:00 - Additional Assumptions 21:26 - Classical vs Quantum 23:19 - Entropy & Symplectic 25:07 - Jaynes & Thermodynamics 30:25 - Units in Physics 33:21 - Math vs Physics 37:07 - Planck Scale Structures 41:51 - Theory Applicability 1:16:25 - Engineering Background 1:18:04 - Physics-Math Bridge 1:19:01 - Assumptions Project 1:21:08 - Grant Funding 1:23:05 - Mechanics Critique 1:24:25 - Problem Identification 1:25:03 - Publishing Challenges 1:27:03 - Engineering Approach 1:29:03 - Practical Implications 1:33:28 - Measurement Problem 1:37:05 - Classical vs Quantum 1:43:04 - Integrating Math Physics 1:55:07 - Current Projects 2:04:43 - Future Goals 2:07:03 - Open-Source Framework 2:10:57 - Support TOE SPONSORS (please check them out to support TOE): - THE ECONOMIST: As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe - INDEED: Get your jobs more visibility at https://indeed.com/theories - HELLOFRESH: https://www.HelloFresh.com/freetheoriesofeverything - PLANET WILD: https://planetwild.com/r/theoriesofeverything/join or use my code EVERYTHING9. Other Links: - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything #science #physics #sciencepodcast #theoreticalphysics #podcast Learn more about your ad choices. Visit megaphone.fm/adchoices

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iGaming Ontario. What does possible sound like for your business? It's more cash on hand to grow with up to 55 interest-free days. Redefine possible with Business Platinum. That's the powerful backing of American Express. Terms and conditions apply. Visit amex.ca slash Business Platinum. Just following the mathematics and I think we're just losing all the physics. We have for physics backwards as what it should be. Because all the math that we do are point set topology, are differential geometries, all that.

You start with points, and then you define infinitesimal things on points, and then you integrate. But that's not what we do in a lab. When did we first get in contact? Oh, jeez. I don't remember. It must have been more than a year ago, yeah. Okay, well, I've been following your channel for approximately one year. I believe I contacted you shortly afterward. Okay, 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's going to take it over at some point and give the elevator pitch the five minute version so a long elevator it's 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 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. 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 use to justify this because how would you justify the first term? 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 in 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 mechanisms 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 goal of the project that I work on is essentially to

find a minimal set of assumptions, a physical assumptions for which we can re-derive the laws. We have essentially two approaches. One we call reverse physics. We start with the current laws of classical mechanics, quantum mechanics, and so on, which in modern theories are just presented as sort of a mathematical structure. And the idea is to go backwards from that mathematical structure and find physical conditions that are equivalent to that mathematical structure.

That's why it's called reverse physics, a little bit because it's like reverse engineering. You're taking the thing, breaking it apart, finding what pieces go together, what pieces are independent. Another reason is because in the foundations of mathematics, there is an approach called reverse mathematics that takes theorems and asks what is the minimal subsystem of mathematics, then I need to express that theorem and prove it. 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, all 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 physics itself and mathematics itself. And one of the things that then we saw while doing this work is that you can have these 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 balls 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 layer in 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. So 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, 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. So for example, if you take two verifiable statements, you can verify the end of the conjunction,

because you test one, you test the other, they both finish infinite time, then you know that the end finishes infinite time and it's verifiable. 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 1700s, 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, okay, these things can be. And so all of these processes 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 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, 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 gonna 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 sort of operational settings. So how do we define numbers? Well, we're gonna 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 or after the reference. So for example, we have clock ticks, and then we say something happened before the third tick 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 balance scales and you have weights that you put on one side. It always works like 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 their logical relationship needs to be, such that all these references are going to tell you, aha, you are 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 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? Cause 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. So references don't need to be ordered. You have references in space, and you don't have a linear order there. And so the idea is that all the references have to be able to be arranged in some way, such that, for example, if I put a reference and I have a reference, having something

that is before this implies that something is before the other. 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 sort is the piece that I need in between physical mathematics and reference physics. Physical mathematics and reference physics. And reverse physics. Reverse physics, right. Sorry, I speak too fast and then everything 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, that's in a hojy-pohjy 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 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 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 assumptions. So I basically want to be able to push as much as I can, 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 axioms

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 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. 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 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'll 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, that 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 a distribution over the space of the particle. You're gonna 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 distributions, 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 wouldn't make sense, because I would see something that is deterministic and reversible. You see something that is not deterministic and reversible, that would not make sense. So even this constraint, basically, is what gives you the structure of the classical phase space, is what gives you the structure of the classical phase space. It's what gives you the idea of conjugate variables. And mathematically, it's what gives you the idea of a symplectic structure, which is the

geometrical way that we describe phase space. So with that, with assumption, infinitesimal redistributity, 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 gonna 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 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 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 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 difference in physics, 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 satisfied 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 infinitesimally usable, in dependence 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, yeah. That's actually in Galileo's dialogues. So this is another myth that people always

think, oh, Galileo, you know, didn't know whether objects fell at the same rate or not, went to the Tower of Pisa and dropped that. And no, in his dialogue, he creates this simple thought 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. 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. And also here is the configuration is,

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, when you tie them together, they're actually one object of different mass. So how tight you have to bind them, right? And this, of course, makes no sense. And then that's how in the dialogue 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 these 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 playing. And 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.

Then you say, okay, 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 arguments 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 Hamiltonian mechanics from deterministic and reverse stability in four different ways. Because I could say, I have determinists because I map states one-to-one. I could have determinists because I preserve the information. All 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 I do a one-to-one map with the state. It's reversible because the entropy does not increase.

And so these are all the uncertainties. 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. As I saw that, however I made the case in those four different cases, I would get

to the same result. And I say, okay, now I have something stable, right? Because if you just have one type of argument, you can always fool yourself. But now I have four of them that are starting from the same point and reach the same conclusion. And that tells me, oh, I must not be fooling myself. Now are those four equivalent to one another? Mm-hmm. Yes. Okay.

And mathematically, they're basically just assuming that the Jacobian of the 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 familiar with that one? And 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 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 Machian stuff. He is the expert. Now for the Hamiltonian mechanics, do you recover that momentum as 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 unit. 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.

And then you're gonna have the units that you use to identify the state, which could be meters, angle, and so on, to start defining the configuration. And so 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 units, 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 using units to kind of say. So what you really want to do is to be able to change that unit

and still preserve the structure such that the units that you use for the states is independent of the units. So you're going to say, OK, I'm going to have multiple variables. In fact, what happens is that I'm going to have another variable of which the units are the inverse of the first, 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 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 have an invariant

Uh-huh, and then invariant is the count of states. Is that the volume in the phase space? and that's the following the first in phase space so you have a Q that defines the units you have K That is the inverse units and then you, I want to measure states with h bar. And so you just multiply k by h bar and you get p. Wait, 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 the unit that we use to count states is the units of actions.

Is that what we use? And the reason that we use that because in mechanics, the units turn out to be position times kinetic momentum, mv squared. And that's then what we use to define units. But you still need a unit to be able to measure these things. When you calculate an entropy, even in classical mechanics that you have a distribution on phase space, you're going to have a logarithm of the distribution, but the distribution is going to be probability over volume. If the volume is in unit of phase space,

you are in a log, but you have to take that out. So you need some constants so that you can define where your zero entropy is and you get the correct entropy. And so it turns out that these, 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... It's quite bizarre. Right. It's one of those things that if you just take all the units out, and that's what mathematicians do, you're not going to see. And unfortunately, this is what we do in theoretical physics. So we have all the units, so we throw them out. What do you mean we throw them out? Like set C equal to 1? Is that what you're referring to?

Yeah, but it's not just setting it to 1. It's setting it to 1 pure number. But if you set it to 1, 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 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 of the thing is describing. 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 the machinery 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 you're that instead of the gamma right the gamma is these matrices that sort of sum to one.

Put a c in front. Now the c gamma is actually a velocity that comes from the boost of the spin part. So the gamma is telling you what is the 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, it's telling you that the v times p equal, it's going to give you mc squared because you have the momentum, which is mv, and then you have the velocity is mv, but you're contracting together those vectors. The norm of v squared is going to be c.

So you're just saying, you know, something that you already have in classical particle mechanics in a relativistic setting, that the inner product between the momentum and velocity is equal to MC squared. That's it. It's just that you're saying in the context of field theory, so of course you're gonna use a language that is a lot more complicated, but the physics that you're describing,

what the equation is telling you, is just that. There is nothing more. And so what I feel that we have done by essentially stripping all these things away and just following blinded mathematics and looking for mathematical structure for new things, I think we're just losing all the physics. They're still there. And if we did it in the way that we used to do 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 are 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 it becomes velocity and so on. So why are we not doing it in the more complicated theories where we can even get 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. That's what you're doing. Okay, what I mean is, I don't know if you saw the 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 and four dimensions and so on and there are 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.

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. I don't have the level of knowledge that I need that. But I can tell you this. Remember when I was talking about the real numbers?

The assumptions that we have to put there are very idealized, right? And there is no way that all those assumptions are gonna hold if we are looking at something at blank scale. And if you remember, before I said that the hard part was getting the ordering right. Was not getting said that the hard part was getting the ordering right, was not getting the real numbers, it's getting the order right. And

so what needs to happen is that when you go at plan scale that you are gonna lose completely the notion of ordering, which also means you're not gonna 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, if I have a theory that says, oh, yes, this is going to be going to work at plan 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? 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'm pretty sure all those pieces are going to go. So if you have a theory, whatever it is, that claims, oh, this is going to work at plan scale, and it's still using, 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. But I can't tell you any specific theory because I would have to go and look at the difference. I can't. And what about Dirac's equation? Does it not assume the real numbers? It's a differential

equation. Yeah, of course. 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 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 structures, I would think that they have to fail as well. They fail at what points?

Like, what does it mean that they have to fail? Experimentally? That they do not... fail at what point? What does it mean that they have to fail experimentally? Here's how I think of physical theories, which is at this point very different from what people think about the different things. For me, I have a system in front of me and I assume that some things are valid for this system. For example, let's say in electromagnetism, we have the charge distribution, right? And you think that as a charge, a field that 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 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 things smaller and smaller and smaller, right? And on the assumption that both quantices 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.

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 where we have all the math that we have for physics backwards as what it should be. Because all the math that we do are point set topology,

our differential geometry, all that. You start with points, and then you define infinitesimal things on points, and then you integrate. But that's not what we do in a lab. In lab we start with a finite thing, and then we say, oh yeah, yeah, I'm gonna make this thing smaller and smaller, 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. 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's not true that the sum, the total of the math is just the sum of the mass in the

volume. Same thing for entropy. Your entropy sums only if you're assuming that things 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? Oh, it's 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 tells me, oh, for this system, you use classical mechanics, and for this system, you use quantum mechanics. I mean, you have examples, oh, 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 one overarching theory and say, okay, these are things that are valid for everything, set theory and logic, or category theory, if you like category theory, because I don't say that, there's people from category theory. And then you say, okay, these are the things that we always need to assume, and then you're going to have topological spaces, and then we're going to have groups, and then you have things that are both groups and topological spaces, and we call them topological groups. 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. When do you use it? Where I have bees on a wire, where I have planets and stuff like that. Then you have thermodynamics. I use that when I have the volumes and the gas and the heat. Then I have relativistic mechanics. I guess I use that when things are really fast. Then I have gravity. Basically, you guess I use that when things are really fast and then I have gravity.

So it's basically, you learn, when you do a physics degree, you learn a bunch of problems and you learn to recognize patterns. And then you know, oh, I have a new problem or this problem is closest to this one. And so I'm gonna use those things, right? And this is what I find completely unsatisfying.

So when I was a summer student at CERN in 1999, then I was sort of asking myself. In 1999. Yes. I was summer student in CERN. That's also where I met my wife there. Well, future wife. It wasn't my wife at the time.

But the point was that, OK, I was studying engineering at the time. I wasn't doing physics. And I just wanted to know, like, what are these things? I wasn't really going to read to another theory. So I said, OK, I'm in a cert. There's a big library. And I'm sure that 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 no such thing. Why didn't you ask someone? I asked somebody. I got no answers. Yeah, yeah, 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 got the answers, well, I don't know, I can't tell you. I just burb with me. 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 to 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 gonna find these answers, the only thing that we have is the math.

I can teach you the math. And so he taught 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? And then, OK, that's reverse engineer the math. That's sort of how reverse physics started. And then I realized, well, I need

to actually understand the math a lot better. 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, 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. And so studying the motion of the whole ball is equivalent to studying all the possible red dots that you could put on the ball. OK, red dot? Of all possible size. Of finite size? could put on the wall. OK, red dots of finite size? Of all possible finite sizes. OK.

Because infinitesimal is just the limit of all the possible finite sizes. And so when you have all the possible finite sizes of all dimensions, that's how you define them. Now, the reason I keep having this as a sticking point is because infinitesimal doesn't mean point. It's as close as you get to a point without being a point. Right. So this opens a whole other world is how do we define calculus because I don't think,

you know, 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 Newton used to think. 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 interested 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 and made no sense. To a mathematician, to somebody who has a PhD student. 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 a modern mathematician

would look and say, okay, yeah, this is rigorous. This actually works, right? But this is a whole other problem. So we're in physics right now. We don't care exactly what the infinitesimal means, but it's this intuition that you have. It's something smaller, but it's not zero. Because if it's zero and

then we have all points that are zero dimension, how do we get the whole again? Okay, so getting to the bowling ball and you can mark it with all these different points or mark it with a finite point? Finite, 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 do in classical mechanics, you are going to have this thing. So, oh, just a moment. Is this classical mechanics in conjunction with thermodynamics yet?

Or is this just pure classical mechanics? It's pure classical mechanics. Okay, so we need to distinguish those two. Is that, do you in your head call that pure classical mechanics, whereas the other one where there's the Heisenberg uncertainty analog is something more CM plus T, thermodynamics? Yeah, so 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. 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 use 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 the count of states that we need to define to have classical mechanics, classical home-entertainment mechanics. Well that's the geometrical structure of classical mechanics.

It's the symplectic forms that allows essentially to count the configuration, to count the states. Okay. 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 create the first one. Interesting. So the geometrical structure of quantum of 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 of going from one state to another state during measurement.

You use the Born rule to calculate the phenomenon 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 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 macrostates. So you can define macrostates 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. 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 Janes is the one that really sort of made this clear. Jains. Jains.

He had an example, one of his articles, that basically says, you know, he was talking about salt crystals. And you can say, I can have a salt crystal, and I would have a certain number of thermodynamic variables. But I can put a polarization on the salt crystal. And now the states that I'm going to have, the micro-states

that I'm going to have, will depend on the polarization. So before I had unpolarized states and now I have polarized states, which are more because... Then you can say I can do the next... Instead of linear polarization, you can make, I don't remember, the quadrupole, there you go. And now you have a different set of systems. You have more. Right, you have more systems, and the entropy associated with those states

is gonna be different than the entropy that he has. So this, I think, where you have a feeling that it's some sort of subjective. Yeah, because it depends on how you coarse-grained, 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. So if I say I have a classical mechanics, I have a cannonball and I study the motion of the cannonball, everything seems so objective. 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 have a notion, I have a boundary somewhere. Wait, why wouldn't I be able to talk about the motion of the cannonball in the sun? Because it would just vaporize and you have no cannonball.

Okay. Right? And so we've just seen I have a cannonball, you're putting a constraint on the environment that you have. You're going to have a certain temperature, pressure, you're going to have some sort of equilibria with the environment that allows you to be able to talk about a cannonball. Interesting. Right?

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 be able to. 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, thermodynamics 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 assign, 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 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 to realm of applicabilities that don't work anymore because you

don't know what your realm of applicability was in the first place. 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, OK, but now I have an electron. I have an electron. I want to study the electron. I can't take a red marker and say, oh, I'll put this dot on the electron. You can't say, 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 gonna scatter the electron but off only of this person, right? No, either you interact with the whole of the electron or none of the electron. And is that actually what defines a particle? I would think yes. Yes.

And again, it's, I can say, it depends on the circumstance. So if I'm talking about a proton, right, 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 object is irreducible. But then I say, okay, 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 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. 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 structure of the proton, especially on the spin side. And there is a whole problem of the spin crisis there. It's very complicated. But you can't describe the proton 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 singularly reducible thing because there is nothing that we can study. But maybe in 100 years somebody very clever will find a way. Strings underneath. Whatever. And then it's not going to be a single.

Now 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 subpart? 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. 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 physicsyy, 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 a reaction, 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 reducible, 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 etc. And now it's a couple 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, I'll do 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 studied control theory, information theory, system theory, a lot of different things. And a lot of the idea that I got from there actually stuck. And 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. Det terms are reversibility in terms of counting states, conservation of information entropy, conservation of thermodynamic entropy, which means reversibility in 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, that's what I like doing. Because the more hats you have, the more intuition you get and you can tie things a lot together. Because now I know that the curl of the flow is somehow related to the conservation of

information entropy. Why is that? And then you look, oh, that's what's happening. 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. You're a musician as well.

Even music related, where you thought you understood something, you realized you didn't, and then you observed it from multiple angles and gained. Yeah, yeah, 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 surprising. So when we do physics, we are taught that the math is the stuff for mathematicians.

And we know discrete, continuous, whatever. It's the topology. What is this? And again, because I wanted to really understand these things, I said, okay, 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 sites in topology. For somebody who does not know what topology is, 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 the finite intersection, 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 statement, I can make the finite conjunction, the finite end, which becomes the finite intersection in the topology.

Or if I have a verifiable 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 ORs, 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. And now 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, OK, but I want my theory to be physically explorable with tests. 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 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. 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. Yes.

Well, 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 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. 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 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, so no. But in the model, you assume that. You assume, well, okay, I'm not going to be able to do it with somebody else. Like, really, we want to put the physical theory that, you know, the sun is going to expand and destroy the... It's a model. So I don't see the problem of... The problem is that, again, you need the justification to say that this model...

Like, you need to know when the model holds and And so you're basically your model is okay. I'm gonna have an infinite amount of time I will have all these tests. We started 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 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 on countably 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. Okay, that you were thinking about the... 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 book, auditing classes on quantum field theory, reading book, quantum mechanics. I had absolutely no real interest to do any of this. I was happy to do essentially engineering within a big computer. So I went at CERN and then I remained in sort of big particle accelerator and I was doing

databases, wide area network data distribution, security, cyber security. There's 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. It was a Brookhaven National Lab. They were creating a new light source. A light source is basically something where you accelerate a bunch of electrons and then you shake the electrons to generate photons.

And then those are very high energy photons that then 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 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 with the... And you were studying physics in the...

On my spare time. On your spare time? Yes. Okay. Stealing books from all these other people and that's all. And also I was auditing quantum field theory at Stony Brook, which is the university closer to there. And so at some point I started attending classes to see, learn.

Then I moved in. 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 and so on. 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 book and trying to figure things out. That's it. And kind of my mind was doing that by itself. It's like having a background process that kept going. My mind would think about these things while dreaming and then you wake up and 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 okay, I'll give you some stuff. And yeah, and I'm passing around completely. Then in 2012 was where I sort of, uh, uh, 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, uh, it dawned on me, right, uh, that what I really wanted was, was essentially have this dictionary between the math and the physics, right, what is the, the, 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 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. It's I don't understand classical mechanics. I don't understand thermodynamics. I don't understand anything. And so that was the first aha moment that I paid more attention to classical mechanics.

In 2012 was when I started putting 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 not my field, I just need to find somebody 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 understand or to care about the physical motivation of classical mechanics, which is confirmed later by the difficulty of publishing this type of stuff. But that's another story. So I did that. Then at some point, sort of the work

that I was doing as a contractor on the control system of the Breuker-Nescherer-Maschaller fizzled. And that's the moment that basically I said, okay, I have this thing. Clearly, you know, if I want to do something with it, I have to do it myself. I'll never going to 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. With my wife also, who is a professor in physics, so she is really more academic than me.

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, 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, before doing something, you do the- Yes, an MVP. Yes, right.

And so I did that, and that's where I drilled it through topology and so on. I said, oh, okay, this starts making sense. I can actually, 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 full time 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 are 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, OK, 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. E. de Guérillard-Freedon. 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 is something fishy there. And again, that's the math that is telling me. And then the math is informing me of that. So you go on the physics and you figure out, oh, wait a second, when you go and derive Lagrangian mechanics and Hamiltonian mechanics in the book, there is always an assumption of conservative forces. Are we ever able to relax that condition? And of course not.

And turns out that the assumption of conservative forces is so strong that you take essentially, let's say, an n-dimensional problem into a one-dimensional problem. So you discarded a lot of stuff there, right? 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 assumptions, can I go and re-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 interpreting incorrectly. They can do whatever they want, but you're never gonna get to the right answer. Yeah, you and I both share this generalist mindset. Yeah, exactly, yeah.

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,

sits 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. 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.

Like 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? Yeah, yeah. 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 a proof? 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 a 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 that 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, they're thinking in terms of an analogy to World War II, 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, you need, it's going to have, it's going to make teaching physics a lot better because again, you're going to know what you're talking about. And usually, 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 don't know if you knew manifold per se because 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.

The jump from classical mechanics to 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 with the same 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 are with it.

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, 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. But anyway, and so I can't imagine that we just get the math that we have right now generalized by mathematicians to solve their math problems, not 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 unlikely 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 re-understand exactly what's happening from classical to quantum such that we can have an idea, a principal idea what needs to happen next. I don't see it happen. And again, it's not a direct thing,

because I can't work on that first. First, I need to, it's like really, you want to build 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 can read all the proofs right as a mathematical as a physical Argument not just as a mathematical thing that you're touring no no every step right once You know once you have a perfect dictionary you can read read the proof and say oh, this is what I'm doing physically I'm making the limit by making verifiable state a 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 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? So 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. 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 is what I want to be able to prove. And let's do it like this. So we said before that areas in volumes and phase space count a number of states.

And they have a measure. They don't count the points. If I have discrete elements, you just count the points. Then that's fine. But areas in phase space, 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 space 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 and that are disjoint to what and you know, you you you double it You're gonna have double the size Perfect. Now imagine that you have these volume though and you divide them in half and half and half and half At some point your count of states Will become less than one volume though, 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? 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. If I have less than one state, it would mean 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, okay, classical mechanics does not work because it tells me that there are regions with less than one state. Now 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 a 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 whole ball, and you say how many states there are there? There are two. Because the entropy is one, two to the one is two. And if you take smaller and smaller region, you're going to have entropy that is less than two. Sorry, entropy less than one, but more than zero, which means counts of states less than

two and more than one. And you're going to go to one, right? But that clearly cannot be additive, right? 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 count 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. Well, you can't have all three, because once you have infinitely many points, and you say every one is one, well, the count of the region with additive is going to go to infinity. And so you have to relax one of these. And what happens is that if you are in a classical discrete space, you relax that the finite region are going to have a finite entropy,

finite count of states. So everything is added with and every state is counted with. 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 additivity. But then you see, OK, why do I want to lose that additivity? Well, because I need to be able to lose that additivity? 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 finite length to be finite to many states. So this is what I like to say, that there is only one way to create ensembles that have an entropy and a count of states such that I have a measure defined on a continuum that

counts a state, but it has a lower limit. 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 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 will be able to use for field theory as well. And that's a challenge because it's a whole problem of infinity. And I want to try to see if I have a path for quantizing spacetime as well and leave

it as a possibility. Because in spacetime 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 finite, the content 1, 2, 3, right? But in a field theory, you have a field for each point of physical space. So now you have 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 as always. 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. 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 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 sets. And you can't just say that they're infinite. 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 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. One of the things that we have sort of a wrong impression in physics or in engineering is that math seems all so elegant or pristine and so precise. It feels like everything is there and we should imitate math in some way. But this is kind of 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 a lot of things like what are called semantic paradoxes, like something 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. Right. So that's something that if you have meaning, right, 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 say, 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 Boolean 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 relationships.

So you can study the mathematical structure, you can study the equations regardless of where they come from, physics, biology, economics. 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 as specific things.

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 sort of a technical problem,

sort of an engineeristic problem in how can you do it efficiently. Essentially, the game is to find, 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 where 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. So those parts, and that's the part that I'm interested in physical mathematics, getting those definitions and justifications right, it's the part that is the most difficult. And it's most difficult because I have a feeling, and I can't... I'd like to be able to have 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 whether something is an orange or not. You go to a supermarket, you can easily identify what 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 truthful statement,

very easy. But if you think how an orange develops, starts with a flower, gets pollinated, and that, right? And there is no point that you can say, oh, this is the instant where it actually became an orange. 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 this 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 undefined. 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. So how would you formulate the measurement problem? What counts as a measurement? Uh-huh. That I don't have an answer for. And 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.

So you see, this is exactly why I ask, 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 measurer from a measured?

Well, yes. So what I wanted 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, I 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. You need, it's 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 really 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. You pick an observable, 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 two states. So now imagine that you start at any other points. And you want to say, oh, I'm going to make a measurement. 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 gonna be in this After the measurement what you predict is that you're gonna 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 it needs to happen. Is that that point that it is here needs to be projected on that axis. That process is a process that increases entropy. 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. 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 that issues 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... Oh, 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 along the lines of what happens in thermodynamics. So since you studied statistical mechanics and you are happy with that, you know that

there are different types of ensembles. 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 and so on. 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't 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., 201 p.m. on the dot? Exactly. You close it at that time. Yes. And now you go count. Yeah. Is that well defined what I just said? Yeah, you're closing it. Do we still need to do some averaging even for a question like that, where we give a specific time.

At specific time, you are going to have the problem that, again, things are going to be fluctuating. How do you go and measure it at that time? Can you not just close it at that exact instant? Exactly. So when you're closing it, you went from a grand canonical ensemble to a canonical ensemble. I see. Like 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. So you are able to talk about the actual number of particles and so on in those type of 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. So to put it like this, so imagine that you have a probability distribution, right? 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.

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't 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 something that is more complicated that is jiggling 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 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 at a conceptual level at quantum mechanics without... So if you say, okay, 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't 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 captures really more what's going on. So you need to have this system to be a little bit undetermined so that you can't say I know everything about 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 in what it's doing.

And so you can only follow the whole thing. The object is non-local 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 is 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 this weirdness, once you swallow the bullet, it's like in relativity.

You say, OK, I will concede that the speed of light is constant. And then you're, oh, mass is equal to energy and all these things. But it's all from here, from there. So I think this is sort of the same idea. The system is unresolved. You can't know what's going on inside. Okay, then I'm going to have an uncertainty principle. I'm going to have that the thing is, you know, no local.

Does that 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 retrocausal or superluminal. Interesting. You can only say that because you've set up an experiment every time that you do this. You know, this happens before that or 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'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 I hope it to be a Rosetta Stone. Because academia is designed to instead of creating the silos that don't really know

how to talk to each other. I really had some problems. And philosophy, I think in some sense is a worse 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 writes this 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, 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 were instruments working. And I wrote a paper with one. We have another one that are's sort of PhD student philosophy. 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 I'm not going to get a position and all that. And to me it's bizarre because, you know, you start writing the single author paper, I guess, 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. I said it before. I didn't start doing this when I was, I had no expectation that I had anything so interesting to say to go and start a research. It was only after the fact when I had the proof, oh, oh, I'm actually doing something that I said, okay, it's worth to me doing this.

Otherwise, I'd probably go make a lot more money doing other things. And so you're new. 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. 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. What I'm trying to put is like a framework where I said, okay, the mathematician says that, okay, that part has to be there, but the physicist says that, so 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. You need to put all these things in a way that they all fit together.

But the training that they all have is only from their viewpoint. So a mathematician might look at my thing and say, oh, but why did you define things like that in mathematics? Yeah, I know that in mathematics you do that, but I need to justify the axioms from the physical. And you're not interested in that, fine, and perfectly fine. I'm going to reach your structures, but it can't be the foundation of physics, of mathematical structure that you put there without knowing. So what I'd really like to have in 10 years

is to find other people like me that are interested in getting these things. And they can be specific, technical, or one thing without having the general thing. That's not a problem. I can keep 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...

Yeah, you're the manager hiring a front-end developer and then a back-end developer. They don't need to know... Exactly. They don't need to know the detail of all the... 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 that most of the time you want the simplest idea that works and that creates the least. And these are the things that I like finding. It's not all the new, you know, grassman compactification of the whatever, whatever. 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 it. 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 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 in all these things, 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, assumptionsofphysics.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 of 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 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 for 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. It can be used, yeah. I understand. You can figure that out. Well, I would be extremely interested because I want to know what are the limitations of academia? So the academia has pros and cons and what they're pro at, they're fantastic at.

So 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 two hour 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 ill-suited 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 the Science Shoes of Physics. Not for your university. No, no, no, no, no, no. That would be 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 through popularizing the research that I do on YouTube than all the papers that I have published.

So Gabriel, it's been fantastic. Thank you for coming all the way down. Thank you for having me. Thank you for coming to my hometown Yes, seriously if you want to have another conversation on the other thing on academia, that's I would love that Also, thank you to our partner the economist Firstly thank you for watching. Thank you for listening There's now a website Kurt Jai Mungle org and, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon,

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