Theories of Everything with Curt Jaimungal - The Physicist Who Proved Entropy = Gravity

Episode Date: May 1, 2025

What if gravity is not fundamental but emerges from quantum entanglement? In this episode, physicist Ted Jacobson reveals how Einstein’s equations can be derived from thermodynamic principles of the quantum vacuum, reshaping our understanding of space, time, and gravity itself. 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 Join My New Substack (Personal Writings): https://curtjaimungal.substack.com Listen on Spotify: https://tinyurl.com/SpotifyTOE Become a YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join Timestamps: 00:00 Introduction 01:11 The Journey into Physics 04:26 Spirituality and Physics 06:29 Connecting Gravity and Thermodynamics 09:22 The Concept of Rindler Horizons 13:12 The Nature of Quantum Vacuum 20:53 The Duality of Quantum Fields 32:59 Understanding the Equation of State 35:05 Exploring Local Rindler Horizons 47:15 Holographic Duality and Space-Time Emergence 58:19 The Metric and Quantum Fields 59:58 Extensions and Comparisons in Gravity 1:26:26 The Nature of Black Hole Physics 1:31:04 Comparing Theories Links Mentioned:: •⁠ ⁠Ted’s published papers: https://scholar.google.com/citations?user=QyHAXo8AAAAJ&hl=en •⁠ ⁠Claudia de Rham on TOE: https://www.youtube.com/watch?v=Ve_Mpd6dGv8 •⁠ ⁠Neil Turok on TOE: https://www.youtube.com/watch?v=zNZCa1pVE20 •⁠ ⁠Bisognano–Wichmann theorem: https://ncatlab.org/nlab/show/Bisognano-Wichmann+theorem •⁠ ⁠Scott Aaronson and Jacob Barandes on TOE: https://www.youtube.com/watch?v=5rbC3XZr9-c •⁠ ⁠Stephen Wolfram on TOE: https://www.youtube.com/watch?v=0YRlQQw0d-4 •⁠ ⁠Ruth Kastner on TOE: https://www.youtube.com/watch?v=-BsHh3_vCMQ •⁠ ⁠Jacob Barandes on TOE: https://www.youtube.com/watch?v=YaS1usLeXQM •⁠ ⁠Leonard Susskind on TOE: https://www.youtube.com/watch?v=2p_Hlm6aCok •⁠ ⁠Ted’s talk on black holes: https://www.youtube.com/watch?v=aYt2Rm_dXf4 •⁠ ⁠Ted Jacobson: Diffeomorphism invariance and the black hole information paradox: https://www.youtube.com/watch?v=r6kdHge-NNY •⁠ ⁠Bose–Einstein condensate: https://en.wikipedia.org/wiki/Bose–Einstein_condensate •⁠ ⁠Holographic Thought Experiments (paper): https://arxiv.org/pdf/0808.2845 •⁠ ⁠Peter Woit and Joseph Conlon on TOE: https://www.youtube.com/watch?v=fAaXk_WoQqQ •⁠ ⁠Chiara Marletto on TOE: https://www.youtube.com/watch?v=Uey_mUy1vN0 •⁠ ⁠Entanglement Equilibrium and the Einstein Equation (paper): https://arxiv.org/pdf/1505.04753 •⁠ ⁠Ivette Fuentes on TOE: https://www.youtube.com/watch?v=cUj2TcZSlZc •⁠ ⁠Unitarity and Holography in Gravitational Physics (paper): https://arxiv.org/pdf/0808.2842 •⁠ ⁠The dominant model of the universe is cracking (Economist article): https://www.economist.com/science-and-technology/2024/06/19/the-dominant-model-of-the-universe-is-creaking •⁠ ⁠Suvrat Raju’s published papers: https://www.suvratraju.net/publications •⁠ ⁠Mark Van Raamsdonk’s published papers: https://scholar.google.ca/citations?user=k8LsA4YAAAAJ&hl=en •⁠ ⁠Ryu–Takayanagi conjecture: https://en.wikipedia.org/wiki/Ryu–Takayanagi_conjecture Support TOE on Patreon: https://patreon.com/curtjaimungal Twitter: https://twitter.com/TOEwithCurt Discord Invite: https://discord.com/invite/kBcnfNVwqs #science Learn more about your ad choices. Visit megaphone.fm/adchoices

I want to take a moment to thank today's sponsor, Huel, specifically their black edition ready to drink. So if you're like me, you juggle interviews or researching or work or editing, whatever else life throws at you, then you've probably had days where you just forget to eat or you eat something quickly and then you regret it a couple hours later. That's where Huel has been extremely useful to myself. It's basically fuel. It's a full nutritionally complete meal in a single bottle. 35 grams of protein, 27 essential vitamins and minerals, and it's low in sugar. I found it especially helpful on recording days so I don't have to think about prepping for food or stepping away to cook. I can just grab something in between conversations and keep going. It's convenient, it's consistent, it doesn't throw off my rhythm.

You may know me, I go with the chocolate flavor. It's simple and it doesn't taste artificial. That's extremely important to me. I was skeptical at first but it's good enough that I keep coming back to it, especially after the gym. Hey, by the way, if it's good enough for Idris Elba, it's good enough for me. New customers visit huel.com slash theoriesofeverything today and use my code theoriesofeverything to get 15% off your first order plus a free gift.

That's huel, H-U-E's Huell.com slash theories of everything, all one word. Thanks again to Huell for supporting the show, Become a Huell Again, by visiting the link in the description. But that's crazy. That means that gravity somehow already knows about thermodynamics. Ordinary physics treats gravity as the curvature of space-time, something described by Einstein's field equations. In 1995, Professor Ted Jacobson uncovered a bizarre connection that explains, or upends, this view depending on your perspective. Jacobson demonstrated that Einstein's equations are actually related to quantum vacuum entanglement.

My name is Kurt J. Mungle and on this channel I explore theories of everything primarily from a theoretical physics perspective, as well as a philosophical one and a mathematical one. However, today is not a theory, it's actually a derivational result, where seemingly separate phenomena of black hole thermodynamics, quantum entanglement, and spacetime geometry are linked. Today, we talk about Corvino gluing, which is about how identical exterior measurements hide different interior realities. This actually questions determinism. We also talk about information paradoxes. So is information ever truly lost, and what is information? Of course, we talk about entropy and we talk about quantum entanglements role privileging quantum correlations

rather than geometric structures. Professor, why don't you tell us about how you got started into physics? Did you think you were going to specialize in something else like math or perhaps something other than gravity? Yeah, I started as a kid, I liked math. I didn't know anything about physics

until I got to my last year of high school. In fact, math was the homework I liked doing. As a kid, I would come home and do my math homework and not do the rest of my homework. I'm similar. I was lucky to get a great physics teacher in my senior year, but before that, I had a chance to take physics and I asked my older sister, should I do it? What's physics? And she said, I think it's something about balls rolling down inclined planes.

And I thought that didn't sound very interesting, so I didn't take it. But later on, I ended up taking it. I had a fantastic teacher. When I learned about quantum mechanics in that class, it seemed shocking, particularly the fact that something like angular momentum is quantized, but angular momentum is made up of mass, velocity, and distance. How could angular momentum be quantized if

mass, velocity, and distance are not quantized? A very naive thought I had. But it stuck with me that, what is really quantization about and does it apply to space and time? So I went to college with that question in mind. I was a physics major and a math major. I thought math was still easier for me in college than physics was, more natural for me in college than physics was, more natural for

me to do math, but I felt physics was far more profound in its significance. So I decided to give physics a try in graduate school and figured if I couldn't hack it, I would switch to math maybe. So I ended up in physics grad school and still hadn't worked on gravity. I did take a class in general relativity. Maybe actually I just audited it even, I didn't even take it.

John Archibald Wheeler was a professor at UT Austin when I was there. I sat in one of his classes and had friends that were in that field. I worked on something in mathematical physics, involving path integrals and spinning particles, like that obey the Dirac equation. But luckily I had met somebody at UC Santa Barbara

when I was at a research program there at the Institute for Theoretical Physics, who hired me as a postdoc. Back in those days, you didn't have to be so specialized. So you could be hired as a postdoc just for a general interest researcher, not in a programmatic way. So, but when I got there, I really learned general relativity effectively because

my hosts were specialists in that area. And I ended up like segueing into that particular field. I really learned general relativity effectively because my hosts were specialists in that area. And I ended up like segueing into that particular field. It's obviously a very natural field if your question is, what's the fundamental nature of space and time and how does quantum mechanics apply to them? So that's kind of how I got into gravity and physics together. Yeah, we're both similar in that we enjoyed math in high school and elementary school maybe for me as well. Then when I went to university,

I did math and physics as a specialist joint degree. I'm more skilled mathematically, but I'm more interested in physics. Yeah. For me, physics, honestly, it's a spiritual thing. I'm not a religious person, but I sort of, but I'm a spiritual person. I feel like my connection with the universe gets deeper the more physics I learn. My appreciation for the mystery of the universe just gets enriched by the physics perspective.

Huh. So it just, it felt like a meaningful life path. Whereas mathematics felt like a really great game, but a kind of sterile structure. I didn't know that you were a spiritual person. Well, I mean, not in any way that's related to an organized religion, but I don't see how you can't be spiritual when you stop and think about, I mean, what is the universe?

What is life? What is consciousness? Did it come from somewhere? Will it go to somewhere? I mean, the huge cosmic questions leave you with a, I don't see how we could not relate to that on some kind of a spiritual level. My whole concept of the world and what the world is made of and what the world is and what it means for the world to exist versus not exist, you know, I mean, it's just the narrow confines of the language and conception of reality that we walk around with every day and talk to each other about it, it's just a very narrow perspective on the cosmos.

And I like to try to open my eyes beyond that perspective. Thinking about the mysteries of physics and cosmology is a good way to do that. Did you set out to connect the laws of gravity with thermodynamics, or did that just occur serendipitously or on the route to something else? Not at all. No, I didn't. I guess like everybody in my generation that came after black hole thermodynamics was discovered and Hawking radiation was discovered and the Unruh effect. It seemed quite striking and surprising

and demanding of explanation of why is there this relationship between gravity, which was just a classical phenomenon of curvature of space and time, nothing to do with quantum mechanics, nothing to do with thermodynamics, seem to be so intricately enmeshed with thermodynamics to work perfectly in concert with it as if it knew. It's almost as if classical gravity knew that it had to be prepared for Hawking radiation because let me, let me explain to you what I mean by that.

Is a very specific thing. Like when a black hole evaporates, you know, the horizon area shrinks. Bekenstein had proposed and supported with good arguments that the area of a horizon of black hole horizon is a measure of entropy and yet the second law of thermodynamics says entropy can't decrease. So if a black hole is shrinking, then it must be that the entropy of everything else is growing by enough to counterbalance that. The Hawking radiation is carrying entropy away. But if you look at that balance sheet in the accounting, like how is it that enough entropy comes out

compared to the shrinking of the horizon so that overall the total entropy goes up? That involves the Einstein equation because you have like the outflux of Hawking radiation is accompanied by an influx of negative energy across the horizon. And the relation between the energy flux across the horizon and the change in the black hole area is governed by Einstein's equation. Only if Einstein's equation works the way it does would the second law of thermodynamics be upheld. But that's crazy, it seems. That means that gravity somehow already knows about thermodynamics. Otherwise, why should it have even worked out that way? So that's what got me thinking about maybe the reason it

knows about it is that it already is part of thermodynamics. But to realize that idea, I had to go from the thermodynamics of black holes, which are just special things out there. Everyone said, there's a black hole somewhere that formed. Right. But gravity is everywhere. So it had to be that everywhere could be like a black hole.

Uh-huh. So I invented this idea of a local Rindler horizon. Basically, it's a perspective by which you can, at any point in space-time, you have the light cone that governs the limits of causality, and you have light-like surfaces that look like little pieces of event horizons of black holes. So, I constructed a framework where I could view any point in space-time as if it were sitting on the horizon of a black hole, and then apply the same relation between entropy and energy that works for black hole thermodynamics and require that it works for this point,

and that point, and that point, and every possible horizon. Because that way I could see if indeed the Einstein equations were a consequence of the thermodynamic relation and that worked. It worked, you know, I wish I don't know how much you want to get into my reservations about it working, but it worked modulo some, let's say, interpretive fuzziness, I think, and foundations of what exactly I was doing with that. We can talk about that more.

Sure. I want to talk about the Rindler horizon. In order for you to have a Rindler horizon, don't you need to be accelerating uniformly? Not really. So Rindler, let's see how to approach the explanation of this. What is it that's accelerating when you ask that question? You're thinking about a particular observer or a particular world line in space-time, but I'm actually talking about a region of space-time bounded by a horizon.

So if you just take flat space-time with no gravity, Minkowski space, and you pick a point, let's reduce to one dimension of space and one of time, the other two dimensions of space are perpendicular, and they play no role in what I'm saying right now. So then at this point in space time, we've got light rays going that way and light rays going that way. And they form a kind of cross like this, which is the light cone intersecting this plane. Okay. The region, this carves up the space-time into four regions, wedges. One of those wedges has a symmetry that is a subgroup of the Lorentz group, which is boosts.

that is a subgroup of the Lorentz group, which is boosts. Lorentz boosts take you from, let's see, here's that wedge. They rotate in the wedge, they're hyperbolic rotations. So that's really what the, if you pick one particular world line and you apply that boost to it, it'll form a uniformly accelerated world line. If you pick a different point further away, it'll also make a uniformly accelerated world line,

but it'll be a lower acceleration. And if you go really close to the corner, again, it will be a uniformly accelerated world line with a very high acceleration. But all of that collection of accelerated world lines with different accelerations all get packaged together into just a flow, a symmetry flow of this wedge of space-time.

That's called a killing flow or the boost killing flow to be specific, boost referring to Lorentz boost. The key facts, let's see, this is a good time to mention this maybe. There's a link. So where does thermodynamics come into the whole story? Why is the vacuum thermodynamical in some sense? It sounds kind of paradoxical because the vacuum of a quantum system or the ground state of

a quantum system is the lowest energy state. Just a moment. It's important that the vacuum is a quantum vacuum and not just an Einsteinian regular space-time vacuum. Yeah, well, right. So let's see, I kind of, I threw in a concept. Let's back up a second. Okay. So there's two sides to this Hawking radiation black hole thermodynamic space-time coin. One is the gravity side. That's described thermodynamic space-time coin. One is the gravity side.

That's described by the space-time metric, which can be curved, can have a black hole, etc. The other side of the coin is quantum fields. The thing that gets radiated in Hawking radiation is quanta of a quantum field. Space-time in the vacuum is filled with two independent things, which I find very pregnant comment. So the metric of space-time exists everywhere in space and time, and the vacuum of quantum fields exists everywhere in space and time, and there's an intimate connection between them.

So right now I started talking about where does the thermal nature of the vacuum come from, and I'm referring to the quantum field side of the coin. But it has to be somehow compatible with the metric side of the coin. So the quantum field side of the coin has the following amazing property. This is related to the Unruh effect and what's called the Bisignano-Vikman theorem in quantum field theory. If you just take the ground state of a quantum field, relativistic quantum field theory,

and you restrict it to that wedge here between the two light cones, you restrict it to a part of space bounded by a boundary, then that state is no longer looks like a ground state, it looks like a thermal state. A thermal state was discovered in the 19th century, I think it's called a Gibbs state now because Gibbs formalized it in terms of the Hamiltonian.

Also Boltzmann was involved in that. So it's a state in which different, it's an uncertain state, in terms of the Hamiltonian. Also Boltzmann was involved in that. So it's a state in which different, it's an uncertain state. Different levels of energy are occupied with different probabilities. And the probability is exponential, it's equal to e to the minus energy divided by temperature.

But what is energy? Energy in physics is the conserved quantity that comes about because of time translation symmetry. But this is a different kind of energy that we're talking about because the symmetry here is not time translation, which would go, time translation would go like this, up straight. But this boost symmetry, it's like a hyperbolic rotation. It's also a symmetry. And it also has conserved quantity associated with it. And that's called the boost energy. And the Hamiltonian that is the generator of the boost symmetry is the Hamiltonian with respect to which the vacuum is thermal inside this wedge.

So let me try to say that in a simple way in summary. You take any plane in space and you chop space in half in the vacuum state of quantum fields. And you just look at observables restricted to one side of that plane. That state can be described as a thermal state. Now, what does that have to do with the Unruh effect? You asked me about acceleration. Well, it's true that if in this wedge I'm localized to a particular worldline and I follow that symmetry flow on my own uniformly accelerated hyperbola, then I will perceive a

particular temperature that's proportional to my acceleration. But I'll see a different temperature if I have a different acceleration follow a different symmetry flow. Right. But there's a way to combine all of those viewpoints into one global statement, which is that the whole state is a thermal state with respect to not a Hamiltonian that generates a time flow like along my world line, but that generates this hyperbolic angle flow, this boost flow in space-time. This is a

little bit non-intuitive for somebody who's not used to thinking about hyperbolic angle as a form of time, but you can see that it would be because if time is going this way and space is going that way, and I'm looking at rotating a surface like that, well, if I sit at, let's say, this midpoint of that surface, and I go on that trajectory, actually that's not a good way to show it. If I follow an orbit, a symmetry orbit of that hyperbolic rotation, I'll be following a time-like world line. And the time on my world line will be proportional to the hyperbolic angle. The proportionality factor being one over at the

acceleration. So there's an intimate connection between the temperature that a particular accelerated observances and the global structure of the state. And I think it's a better way to think of it, to think about the latter, because it doesn't depend on choosing one particular observer. So, do the quantum field virtual particles have anything to do with this thermal state? They have everything to do with it. Yeah. So, does that mean virtual is a misnomer and they should be considered as real? Just a moment.

Don't go anywhere. Hey, I see you inching away. Don't be like the economy. Instead, read The Economist. I thought All The Economist Was was something that CEOs read to stay up to date on world trends. And that's true, but that's not only true. What I found more than useful for myself personally is their coverage of math, physics,

philosophy, and AI. Especially how something is perceived by other countries and how it may impact markets. For instance, the Economist had an interview with some of the people behind DeepSeq the week DeepSeq was launched. No one else had that. Another example is The Economist has this fantastic article on the recent dark energy data, which surpasses even scientific Americans coverage, in my opinion. They also have the chart of everything. It's like the chart version of this channel. It's something which is a pleasure to scroll through and learn from.

Links to all of these will be in the description, of course. Now, The Economist's commitment to rigorous journalism means that you get a clear picture of the world's most significant developments. I am personally interested in the more scientific ones like this one on extending life via mitochondrial transplants which creates actually a new field of medicine. Something that would make Michael Levin proud. The economist also covers culture, finance and economics, business, international affairs, Britain, Europe, the Middle East, Africa, China, Asia, the Americas, and of course,

the USA. Whether it's the latest in scientific innovation or the shifting landscape of global politics, The Economist provides comprehensive coverage and it goes far beyond just headlines. Look, if you're passionate about expanding your knowledge and gaining a new understanding, a deeper one, of the forces that shape our world, then I highly recommend subscribing to The Economist. I subscribe to them and it's an investment into my, into your, intellectual growth. It's one that you won't regret. As a listener of this podcast, you'll get a special 20% off discount. Now you can enjoy The Economist and all it has to offer for less.

Head over to their website www.economist.com slash toe, T-O-E, to get started. Thanks for tuning in and now let's get back to the exploration of the mysteries of our universe. Again, that's economist.com slash toe. So does that mean virtual is a misnomer and they should be considered as real? Again, that's economist.com slash toe. So does that mean virtual is a misnomer and they should be considered as real? Let's see. Well, the fluctuations, you have to remember we're talking about quantum mechanics here. So what is real in quantum mechanics? If you have a quantum state that's a superposition of many possibilities, do you call those possibilities

virtual or real? The system could manifest itself in any one of those possibilities. So I would say that makes it real. On the other hand, before it actually manifests itself in one particular way, you may want to call it virtual. Call all the rest of them virtual, let's say. See what I'm saying? There's a language problem, I think. Uh-huh. There's a particular connection with quantum mechanics

in this thermal statement. Let me also emphasize that. The quantum vacuum of fields is a pure quantum state. That means it's a single vector. It's described by a single vector in Hilbert space. The state is definite in the sense of being a single vector in Hilbert space. The state is definite in the sense of being a single vector in Hilbert space. But the degrees of freedom on different sides of my imaginary wall are entangled with each other.

So if I have access only to one side of my wall, then those entangled degrees of freedom are no longer in a pure state taken by themselves. They become in a mixed state. And that mixed state has a thermal character. A thermal state is a state with some randomness in it, right? As opposed to being a pure state, which is a definite state. Now it's important here that this wall is not a physical wall. It's an artifact of your coordinates or what?

Yeah, an artifact of my choice to carve up space into two halves. So then, like to the lay person who's listening or watching, does that mean that they think of carving up space in a certain way? They just imagine it and then all of a sudden they see a thermal bath? Because that doesn't seem right. It's right. If they restrict their... Yeah, right. So if they restrict their observations, its causality is another key element here. So once again, here's our wedge.

If I restrict observations to this part of space-time, I can't see it. I can't be influenced by something on the other side of this horizon. So I could just choose to leave across the horizon, but if I don't, and I just restrict attention to observables in this wedge, then they are described by a thermal state. So it has to do with restricting attention to a subset of all the possible observables. Let me give you another simple example that's often brought up to explain the key idea of entanglement, which is a spin state of two spins that's a singlet state. It's a completely rotationally invariant state of two spin one half degrees of freedom. And they're opposite to each other completely in the singlet state.

But which direction each one of them is in by itself is completely indeterminate. And if I can only observe this spin and I measure it, I'll find it completely random what direction its spin is. And if I measure only this spin, I'll find it completely random what direction it is. But if I measure both of them, or if somebody else measures, we'll find that they're always exactly opposite to each other. So if we measure along the same axis. So they're correlated in an inextricable way in a pure state, but when we restrict attention

to one of them, that has a random state. That's a good analogy. So let's say you measure it and one is spin up, then it must be that the other is spin down. Okay, now for the virtual particle pairs, what property is it that's entangled? Like what you just gave was the spin properties entangled.

Oh, that's a great question. It's the occupation number of the mode. Can I explain that? Sure. Let's see. So, right. So in quantum field theory, we can break up all the field. The field is a function of space,

so it's a continuous function, right? But we can decompose it into modes, which are like waves of a definite wavelength, let's say. Okay? But in quantum mechanics, each mode is like a harmonic oscillator. It's a quantum system, which can be in its ground state, first excited state, second, third, fourth, et cetera.

And in this thermal state, what we find is that there's a certain probability of it being in each level. The probability goes down as the level goes up, in a way determined by the temperature. But on the other side of my imaginary wall that we just carved space into two halves of, I have a partner oscillator mode. Okay, now this one by itself could be any one of its levels. This could be in any one of its levels. But there's a correlation between which level this is in and which level this is in.

And that's the nature of the entanglement. Now in that case, it wouldn't be an anti-correlation because then you'd have negative energy? Yeah, let's see. It is an anti-correlation in terms of a globally defined boost Hamiltonian. Yeah. So what would it mean then? Let's say you're in your first excited state outside the area. If there's the ground state, what's lower than the ground state?

Can't be below it. Yeah. No, I think that's the question is are taking the time flow to be up on both sides of the wall or up on one side and down on the other side. So because we take it down on one side, we count this as negative energy, but it's actually locally measured as positive. So this is that Wheeler interpretation that it's an antiparticle, like when you go backward in time, then it's an antiparticle? Like when you go backward in time, then it's an antiparticle.

Yeah, I would say it's related to that because it's the thing that, like say we're talking about an electron positron field, the thing an electron here is correlated to across the other side of the horizon is a positron. So if you think of a positron as an electron going backwards in time, then it's correlated to an electron going backwards in time. But I think that's a confusing perspective to try to take. So let's see if I got this correct. Quantum fields are constantly popping in and out of existence these pairs, these particle-antiparticle pairs in this example.

Now these pairs are entangled as you mentioned, and you can imagine a boundary where the pair is straddling it. And so you have one partner on each side. And if you only observe one side, then you've lost information about the other partner. Exactly. Now, it makes it appear random and thermal, like it has temperature. And this lost information, entropy, depends on the boundary area.

We haven't gotten to that point, but... Yeah, right. I've gone through your work, so I'm summarizing a bit further. But why don't you get to the boundary area now? Right. So how much, it has to do with how much entanglement there is and what does that have to do with entropy. So going back to the example of just the two spins one half, which is the simplest example we can construct in quantum mechanics.

How much entropy is there in this singlet state, this perfectly correlated state that looks totally random when you restrict to one of them? It's exactly one bit of entropy. This is an information theoretic interpretation of entropy. So log logarithm of two, because there are two alternatives and they're both equally probable. So if you want to know, well, how much entropy is there associated with this quantum field randomness that we just described. So every mode of the field has some amount of entropy associated with it.

But there are an infinite number of modes of the field and they're packed into the infinite, like the divergence in the density of modes that we have to count up if we're trying to account for all of this entanglement entropy, it's called, is packed up very close to the corner of that wedge, right up next to the horizon. In the context of a black hole, that has to do with the infinite redshift at the horizon of the black hole. But in standard quantum field theory,

there's no shortest wavelength of modes. The field can fluctuate on any scale, no matter how small. And that's required by Lorentz symmetry as far as we know, by relativistic symmetry. So because there's an infinite number of them, it looks like there's an infinite entanglement entropy. Infinite. That is like a problem if you're thinking the entanglement entropy has something to do with the Bekenstein-Hawking entropy because the Bekenstein-Hawking entropy is finite. It's the area divided by four times the Planck length squared.

So that's finite. But the idea physically is that, okay, we're missing some physics. If we just try to use quantum field theory to count up this entropy and ignore gravity when we're doing the counting, we're gonna get infinity, which is the wrong answer. If we take into account the effect of gravity,

how is that going to change the story I just told? Well, remember, you just mentioned the energy of these fluctuations. That's crucial. So the ones that are leading to the infinite entropy have higher and higher and higher energy because they're localized at smaller and smaller and smaller distances from each other and from the horizon.

And according to quantum mechanics, if you localize something smaller and smaller, it has a bigger and bigger uncertainty in its energy. Now, if we turn on gravity, we take into account the fact that everything is affected by gravity. That energy is a source of gravity, and gravity causes the space time to be curved. So the picture I was just using for counting up the entropy initially was just a nice smooth space time.

We plunked our quantum fields into it, and they're doing their fluctuating virtual thing. But now we have to take into account, if you're going down to the shortest distance scale, you better take into account that gravity is acting very strongly at that scale on these fluctuations. And you can actually anticipate that once the fluctuation and its partner get so close together that the gravitational fluctuation they create engulfs them both in like a miniature horizon,

then it's not any more possible to separate them. So this picture of the imaginary wall that I described initially, at the very shortest scale it becomes fuzzy in a way that we can't control like who's on which side of the wall. It just becomes meaningless. So it has to cut itself off because of gravity. And the place it cuts itself off is, you can argue in a hand-waving way, is at the right scale to match the Bekenstein-Hawking entropy. I heard you say that the Einstein field equations were the equation of state of a quantum vacuum, and I wasn't sure if you meant the equation of state or a equation of state.

Is there just a single equation of state that emerges and it's the Einstein field equations? What conditions are you placing on it in order to call it the? Or was that just a verbal error? I might say it's the equation of state, but of what? So an equation of state describes the state parameters of a thermodynamic system and how they relate to each other and to the temperature. Example being the ideal gas law. The pressure, the volume, and temperature, a number of particles, and a gas are all related

by an equation. That's the equation of state. So you have to say what system you're talking about before you can say you're talking about the equation of state of that system. So in my case, what I meant was I'm referring to that system on one side of my imaginary wall. And then the entropy of that system is governed by the horizon area, or at least that's the main contribution to it. And the equation of state is the relation between that horizon area and the energy that's in the space-time flowing across, for example, the horizon, flowing across that boundary. So the equation of state governs how the gravitational field is related to the boost energy flux across the boundary of the system and the area of the horizon. In that sense, it seems

analogous. The ingredients that go into deriving an equation of state for the ideal gas, I can point to you how they're analogous in the gravity case. So for the gas, I would need to know, okay, how does the entropy of the gas depend on the total amount of energy in the gas and the volume of the gas, let's say. Then I also need to know that energy is conserved, it's part of the derivation. And I need to know what's called theerved, it's part of the derivation, and I need to know what's called the Clausius relation, which says how much does the entropy change by if a given amount of heat energy goes into the system or comes out of the system at a given

temperature. And putting those pieces together, you can derive the ideal gas law PV equals nKT. So I was emulating that by saying, okay, my system is the world on one side of this local Rindler horizon. The entropy is the area times some fundamental constant. I'm going to apply energy conservation by demanding that the stress energy tensor is divergence free, which is an expression of local conservation of energy, of matter, energy and momentum. And I'm going to apply the Clausius relation that relates the amount of heat that goes into the system to the amount of entropy change.

Now, I use the word heat. What did I mean by heat? I meant the energy, not what we normally mean by energy, but the boost energy that we just talked about earlier. It's the energy that is relevant. It's the energy in terms of which the system on one side of the horizon is thermal. It's the energy that whose states are populated according to the Boltzmann distribution. So just putting the pieces together in parallel to how you would have done it to derive the

ideal gas law, I found that the area of the horizon must evolve in a way consistent with or determined by Einstein's equation. When we started this conversation, you said you went into graduate school because you wanted to understand the quantization of maybe space-time itself. Like how far does this quantization principle go? It doesn't sound like anything here implies space-time is not continuous. It doesn't sound like space-time is discrete. It still sounds like you're assuming a continuum. Yes, you're right. Initially when I first confronted the finiteness of black hole entropy,

why isn't it infinite given that there seems to be an infinite entanglement? I thought perhaps the answer was that there's some discreteness and there's some shortest cutoff. But I just gave you a different way of trying to answer that, which was that no, no, no, it's because at very short scales, the gravitational interaction is so strong that space-time is very curved and I can't even distinguish which side of my imaginary boundary my degrees of freedom are living on. And that doesn't require discreteness, it looks like. So I think, yeah, this line of thinking led me away from the idea of discrete space and time,

at least for the moment. I think in the long run, it will lead back to that. But this relates to some other questions that you teed up to ask me, which is about like, what is the relation between emergent gravity and space time and the problem of quantum gravity? Right. Like, where are we on the path?

What is the role that thermodynamic reasoning and accounting of the Einstein equation as an equation of a state could play in leading us to better understanding of quantum gravity. And I do have an answer I'll give you for that. I think of it as analogous to the role that thermodynamics played in the history of physics so far. So think about when Carnot initially was trying to account for a theory of the efficiency

of heat engines, right? He had the concept of caloric, which turned out to be an incorrect version of the concept of heat, right? But it was sort of right, and he actually got a correct thing. That's why we call it a Carnot cycle. He inferred that there's a maximum possible efficiency of a heat engine, which is attained by a reversible heat engine. But then other physicists came along after him like Clausius and Kelvin and refined it and said, no, actually that was a good idea, but actually there's no such thing as caloric. Caloric is really just a form of microscopic energy of the degrees of freedom like kinetic energy and potential energy.

Moreover, unlike what Carnot thought caloric is not conserved because it's heat and heat is not conserved. Heat can do work, for example, and you can lose the heat and turn it into work partly. Or you can create heat when you didn't have it to begin with, like by friction or something. So, but nevertheless, the process of figuring out, well, why was Carnot getting something right but not everything right, led physicists to a better understanding of what is the nature

of heat. And that led into also what is the nature of heat. And that led into also what is the nature of statistical mechanics. Like what is, how do we account for the gases in a heat engine from a microscopic viewpoint using statistical mechanics? So, and then another example is with quantum mechanics. Late in the 19th century, Max Planck is trying to understand how can we apply this thermodynamics, which seems to work great for gases, to electromagnetic radiation? What if I have an oven in thermal equilibrium full of radiation? Let me try to count its entropy and account for the distribution of energy among its frequencies or wavelengths. And that was actually impossible to do with the physics that he had at the time.

But he found a formula that worked perfectly, the Planck distribution. Then he tried to account for, okay, I better find a theoretical explanation. Why is this the right formula? And he tried to do it with the physics he had, and he couldn't, because physics needed a new idea, which is quantum mechanics in order for that to make any sense. So the effort. See, here's the deal. Thermodynamics is a very, I call it fault tolerant theory. It can get some things right without actually having the correct foundational microscopic picture. And in fact, you can even have fundamental mistakes,

like Carnot had the mistake he thought that caloric was fundamental and that it was conserved, and it wasn't. But he still got the right answer for the maximum efficiency of a heat engine. Interesting. And that it's a universal maximal efficiency determined by the temperature of operation and the temperature of the reservoir that it flows to, that the heat flows to. That's amazing. So similarly, I think of what I'm doing in that kind of a way. I'm using robust thermodynamic concepts that are probably going to be correct no matter

what the right microscopic picture of space-time and quantum gravity is. And some of what I'm trying to do is probably nonsense the way Carnot, some of what he was doing was nonsense. But it's pushing us into the right place, asking the right questions, confronting us against the right problems that hopefully can lead to a refined understanding. Now whether that refined understanding will require space and time to be discrete, ultimately, I don't know.

I suspect it will, but that's pretty much purely a bias based on almost philosophy. You know, if you ask what is non-discrete space-time? What is the continuum? What is a real number? Right, you say that I was treating space, general relativity and all of physics today uses real numbers to coordinate space and time. What is a real number?

If you think about it, it's a very idealized extrapolation of a notion of counting. And I think it's most likely that it's not an idealization upon which the world is built, if you see what I mean, at its fundamental level. It's just a convenient idealization so far in physics. But that's a side question of whether we'll ever get there to a discrete understanding. Well, what sort of discretization of space-time do you imagine? Because it can't be, well, I don't imagine it could be a naive one where you just discretize space because then you would break

some of the other symmetries that are important. Exactly. Absolutely. And you also can't, for similar reasons, you can't discretize time, just naively. It can't be like a lattice. Moreover, it actually has to be non-local in some sense. I actually thought about this in relation to another question that you sent me, which is if space-time emerges, what does it emerge from? Right.

So this is related to the question we're talking about. So there's a very interesting observation by Don Marolf of UCSB about a constraint on possible emergence of gravity. He made a pretty cogent argument that gravity cannot emerge, gravity I would say in space-time also, from a system which has locally defined observables that can be simultaneously precise at space-like separation. So technically what he's saying is that it can't be described by commuting operators. Sometimes people try to make up an analogy between space-time and condensed matter systems. And there's even papers about emergent gravity and condensed matter systems. And it is possible to actually have emergent spin-2 effective field theories,

but they are not gravitational. Merrill made the observation that if something really behaves like general relativity, emerges that way. The Hamiltonian that governs its time translation has to be a flux integral at the boundary, let's say a large spatial boundary. And then he inferred from that that no system with that property can emerge if its starting point is based on local kinematics with observables that commute with each other at space like separation. This is a bunch of technical words, but the concept of it is that there must be a non-locality built into the very structure from which space, time and gravity are emerging. So like you said, it can't be something naive or simple minded.

It's not just discretizing. I don't know what it is, frankly. I think it's sort of beyond my conceptual horizon at this point to be able to do it. Although I must admit, I play around with ideas sometimes on the side. Yes. Like sort of what if, what would be the simplest discreet thing I could build a universe out of?

And I try things out. On the side, but not published. No, although I'm thinking of publishing something soon on an idea. But I don't see a direct connection between that idea and the physics we know well. So it's really a kind of a flaky idea and that's respect. In one of your talks you had mentioned that Lorentz and Poincaré, they were trying to make sense of the infinite energy of the electron, the self-energy, and so they said okay maybe the electron has some extent but then they need to study the structure of the electron.

And then Einstein came about and said, just forget about all of that and just start to study and stipulate the Lorentz symmetry. And we'll concern ourselves with the structure of the electron later. And that turned out to be the correct move and a question that shouldn't be tackled right now? that direction, which goes by the name of holographic duality or gauge-gravity duality, ADS-CFT. So we've learned from, it actually emerged from string theory, although the idea doesn't really require string theory to be part of the story, that there is a pretty concrete framework in terms of which we account for physics in space and time by using a space-time of one less dimension with no gravity. And that's the AdS-CFT duality.

And in that context, space-time in the bulk emerges in a kind of fuzzy way from a sharp space-time on the boundary. So that's a pretty significant, I think, insight and step forward in our path towards understanding quantum gravity. It's a kind of strange step that bothers me because in that framework one has reduced everything to what's called a conformal field theory on a fixed conformal geometry with no gravity. Gravity is just an effective thing that emerges from higher level description of phenomena of that. But then you have to ask, okay, well, wait a minute, where did this conformal geometry on which this lower dimensional theory lives come from? And why is it just

sitting there rigid? It's like, you know, we made a big step in going from Newtonian gravity and non-relativistic physics to general relativity when Einstein realized that the inertial structure of space-time is not fixed, once and for all laid down by God or whatever, but it's part of the dynamics of everything that's going on. But in ADS-C-CFT duality, the conformal geometry on which this conformal field theory lives is just fixed at the beginning. So I think probably most people have the idea that that feature of this duality is probably not fundamental.

If the duality is leading us to something that's truly fundamental about the nature of space, time and gravity, that picture is just a stepping stone towards it. Because it still relies on a sharply defined rigid conformal geometry. Two quick questions about this. So some people say that you could start with the bulk and recover the CFT and you can go from the CFT to the bulk. So they're dual to one another. If that's the case, why would we say that gravity emerges from CFT, not the other way

around? If they're dual, it doesn't sound like you can privilege one over the other. Right. I think they're not really dual. I think the relationship is not really symmetrical in the sense of a duality of two completely equivalent things. One side of this duality is very sharply defined, in fact, completely understood from the viewpoint of contemporary mathematical physics and quantum field theory.

The other side is kind of fuzzy and its full nature is not understood. And the concepts we use to describe it are approximate. And the concepts we use to describe it are approximate. So in that sense, I think it's not a symmetrical duality. I mean, to be more concrete, like, you know, what is it? What is it that's dual to the CFT? Is it just certain quantum fields and gravity? No, we have to include strings. Okay. Is it just strings, quantum fields and gravity? No, we actually to include strings. Okay, is it just strings, quantum fields, and gravity? No, we actually have to include D-brains. Okay, so is it just D-brains, strings, and quantum fields? Well, then which D-brains, and in which topology, and which, you know, it's just complete.

There's a kind of, I think the answer to all those is, well, it depends on the state of the conformal field theory. There isn't like a single bulk description and there isn't a sharp bulk description. That's my interpretation of it. So it's not CFT-ADS duality. It's CFT-ADS plus strings plus D-brains plus so-and-so plus dot dot dot unknown question mark duality. That's good. In my opinion, then my other question was going to be if you want the dynamics on the CFT to not be fixed in terms of the space time, then wouldn't that just be saying CFT

plus gravity is dual to something that's gravity? Like, why would you want that? Aren't isn't the whole point to recover gravity? Yeah, for sure. Well, gravity and other things, space. You know, I'm not saying we should add gravity into it. I'm just saying maybe there's too much in it to begin with. Uh-huh. It has too much rigidity to it, it seems to me,

to be like absolutely fundamental. It also has complete arbitrariness, like which quantum field theory do we plunk on this conformal geometry? Well, in the case of one of the cases, it's four-dimensional super Yang-Mills theory with a group S, U, N, and certain field representations, right? I mean, it's a particular quantum field theory. So I think I'll just say again that it's just a stepping stone, but it can't be anything like a fundamental description.

anything like a fundamental description. Brian Green suggested that space-time is fundamentally woven with wormholes that connect and tangle quantum degrees of freedom. Have you heard of this? It's an extension of ER equals EPR. Right. Yeah, I have heard of it. What do you make of it? ER equals EPR, that's Einstein-Rosen equals Einstein-Podolsky-Rosen. Einstein-Rosen

refers to the maximal extension of the Schwarzschild solution, black hole solution of general relativity. It's a kind of weird space time that has, as you go in towards the black hole, you go through a throat and come out the other side and there's a whole other side of the universe. And the throat that connects the two sides is called the Einstein-Rosen Bridge. And in the context of ADS-CFT, what is the dual conformal field theory to this kind of a configuration? The answer was it's actually two CFTs. So we actually have a CFT that's kind of associated with the asymptotic region on one side of space-time and one on the

other side. But then in what sense are they connected to each other? You could imagine they're completely independent quantum field theories that have nothing to do with each other, then they couldn't be dual to a single spacetime which is connected one side to the other. And the answer is that in the context of ADS-CFT, if the quantum state of the two conformal field theories is correlated in an entangled way, So it has, it's basically some giant Einstein-Podolsky Rosen pair of CFTs that are extremely entangled with each other.

Then the space-time that's dual to that has this Einstein Rosen bridge connecting the two sides. That's where the idea of ER equals EPR came from initially, I think. Now you could say, okay, but is it only a property of that very special situation or can we generalize it? And Susskind and Maldacena, I think, coined the ER equals EPR term to suggest that this connection is not just a property of that one very special situation, but it's actually a very general thing. And in fact, this kind of entanglement applies even in a single ADS space. So if you, let's see, can I explain this?

Yeah, this gets pretty technical to explain this, but let me try to boil down to the essential thing. Remember we talked earlier about the entanglement of the vacuum of quantum fields when we chop space in half by an imaginary division, right? But every place you chop space has this huge amount of entanglement between the two halves in the vacuum state. And you might say, well, what's special about the vacuum? Well, nothing is special. If I add a bunch of particles, let's say I add everything in this room, the state is still very close to the vacuum state.

And at very short scales, I still have the same entanglement that I would have had in the actual vacuum state. Wait, why is it if you added everything in the room that the state is close to the vacuum? Because everything in the room is operating on a scale of order of centimeters and meters and millimeters,

or even of atoms on a scale of angstroms. But the lion's share of the entanglement is happening at much smaller scale. Understood. Like way down to the Planck scale, which is where it's cut off somehow. Essentially, all this enormous amount of entanglement exists no matter what state we're in when we divide space in half. So the idea is that that's what it even means to have two sides of a boundary of space.

Suppose I did the following thought experiment. I take the vacuum of space, I put my imaginary boundary, which has a huge amount of entanglement on the two sides. And then I remove all of that entanglement by modifying the state on this side and modifying the state on this side and disentangling it until I've got it completely separated so that the state here is totally uncorrelated to the state here.

What would happen then? Would I still have a space that's connected between there? Actually, I would have an infinite negative energy density. I would have a state whose gravitational back reaction is so big that it probably sort of cleaves space into two halves. The idea is to take this maximally extended black hole space time that I started talking about with the two CFTs being entangled and that being dual to the Einstein-Rosen bridge, and realize that that relationship between entanglement and connectivity of space is actually a general one. The fact that space in this room is connected from this side of my imaginary boundary to this side has something to do with the fact that empty space is full of entangled vacuum fluctuations.

Another side of this story has to do with the metric. So far I've been only talking about the quantum field fluctuations, right? But I think I mentioned earlier that there are two things that fill empty space, always, the metric and the vacuum of the quantum fields. I suspect that this is a passing stage in the history of physics, that we treat those two things separately. That there isn't really a separate metric degree of freedom. In fact, if you just show me the vacuum fluctuations,

I can measure the metric in the behavior of the vacuum fluctuations. The metric is encoded in the nature of the correlations of the vacuum fluctuations. So the metric is kind of superfluous and redundant in the description if I just knew the vacuum fluctuations now or the vacuum state. That gives rise to the idea that maybe we should try to rewrite quantum field theory and get rid of the metric and just express anywhere when you write your quantum field theory down where rid of the metric and just express anywhere that when you write

your quantum field theory down where you need a metric, just put in the metric that you extract from the quantum field state itself and that way get a self-consistent scheme where the metric is strictly emergent from the quantum fields. That's also something I've thought about and even worked on a little bit. But I suspect in the future we'll find that the metric needs to go as a fundamental ingredient in the recipe. How have others taken your entropic idea of gravity in ways that you either agree with or disagree with? So one small technical extension of it has to do with, can we go beyond general relativity, adding higher curvature terms to the field equations? I've worked on that and so have other people. I sort of agree with it, but I actually think it might be all wrong because to resolve the contribution of the higher curvature, but I actually think it might be all wrong because to resolve the contribution of the higher curvature terms, I think might require working on such a small

scale that the idealizations that I made in my original derivation don't apply anymore. I don't have a good enough control of the definition of the heat in the Clausius relation. I don't have a good enough definition of the local Rindler horizon because I have to take curvature into account. So I'm not convinced yet that there's a meaningful way to include higher curvature terms. But I don't think that's really what you have in mind, because that's just a sort of a slight technical extension of what I did, if it worked at all. There's a bunch of other ideas out there that are related to the relation between thermodynamics and gravity. And to be honest,

what I've seen looks not very closely related to what I've done, and also not as conceptually clear from what I can tell. On the other hand, I took it in a different direction in a paper in 2015, 10 years ago, which I think was a significant improvement of what I did back in 1995, which was to focus not on local Rindler horizons, but to focus on regions of space that are ball-shaped. And I formulated this maximal vacuum entanglement hypothesis, which seems to be a different

way of inferring the Einstein equations, and probably a better way to understand the relation between the entropy, the horizon entropy and boost energy. I don't know how much you want to go into it, but it's a more statistical approach to this relation as opposed to thermodynamic one. Well, before I get into that, I'm confused about something you said earlier. So let's say you have this boundary

and then you have some entanglement across it. You were saying something like if you want to disentangle this, like cut the threads, it's as if you're putting in what information or energy? You would have to put in a huge energy to cut the threads, and that energy would have a huge gravitational effect. And then you said that it would cleave them apart as if they were separate, but isn't it the case that when you have gravity it would push, it would pull together? So I wasn't sure

about the metaphor here. It's like, I know maybe it's not a metaphor, but you're putting in information or energy and then why are they going to move apart? Yeah, I don't, I didn't mean that they will move apart. I meant that any physical connection, I won't be able to pass through them from one side to the other like I could normally. I see. What exactly would happen, I'm not sure. It's related to this idea you might've heard come up

a few years ago of the firewall. There was an idea that to explain the black hole information paradox, we had to invoke the concept that actually a black hole horizon is not a smooth place in space-time, but it's actually got quote unquote firewall due to an infinite energy density there that kind of separates the inside from the outside. And there again, it wasn't talking about separating like literally peeling them apart and moving them away from each other, but it was like putting a boundary in which regular space-time doesn't even exist, so you couldn't hope to go from one side to the other as you normally do.

Now it's an interesting question, what would happen? Like, could I calculate using general relativity if I put in a planar boundary with an infinite energy density and the correct pressure to correspond to the state I would get by like clip, snipping all those entanglements and removing them? That would be some extremely excited state of the quantum field.

It would have a huge fluctuating energy momentum tensor. And can I describe the space time that gravity would bring about in the presence of that stress energy tensor? I'd like to know the answer to that. I once started trying to figure that out. I never finished. I never got anywhere with it. But I think it's perhaps possible to get somewhere in the nature of the curvature singularity that would appear there.

You know, is it that space would just close off on each side? And in that sense, it would be cleaved? I don't know. But what I do know is it would be a situation where you simply couldn't pass through unscathed from one side to the other of the wall. Something we haven't talked about was how observables on the boundary must stay on the boundary, referencing Marov's work and how that's connected to diffeomorphism invariance.

And then there was something else I wanted to talk about, about the gluing. I forgot what it's called, Koronov or Karnava or Korovo gluing. Oh yeah. Let's see, what was the name of that guy again? It's a mathematical relativist who showed that you could create solutions to Einstein's equation that, is that what you're talking about? Yeah. Yes, yeah.

That outside of some region, they're indistinguishable, but they're actually very different on the inside. Yes. Yes, exactly. Why don't you explain at two levels, one for a layman and then one for a graduate student or a physics researcher or what have you about diffeomorphism invariance, what that has to do with that observables on a boundary, what the heck that has to do with the black hole information paradox and Merrill Alves' work.

Hi everyone. Hope you're enjoying today's episode. If you're hungry for deeper dives into physics, AI, consciousness, philosophy, along with my personal reflections, you'll find it all on my sub stack. Subscribers get first access to new episodes, new posts as well, behind the scenes insights, and the chance to be a part of a thriving community of like-minded pilgrimers. By joining, you'll directly be supporting my work and helping keep these conversations at the cutting edge. So click the link on screen here.

Hit subscribe and let's keep pushing the boundaries of knowledge together. Thank you and enjoy the show. Just so you know, if you're listening, it's C-U-R-T-J-A-I-M-U-N-G-A-L.org, KurtJaimungal.org. Yeah, well, this is all Marelf's idea that I embraced. I mean, I thought it was a great idea and kind of compelling, although the conclusion I drew from it

is not endorsed by Marelf himself. So you should interview him too. is not endorsed by Meroff himself, so you should interview him too. But yeah, so the key thing is that as a consequence of what is diffeomorphism invariance? Okay. In general relativity, the symmetry is so huge that the way we The symmetry is so huge that the way we coordinate time and space, the numbers we assign to label points in space and time, are completely meaningless. That led to a lot of confusion, even on Einstein's part,

even when he's the one that figured out the theory. But it's a key property of the theory. One consequence it has is that the dynamics of everything inside a bulk of space-time is generated, in this mathematical sense, by the Hamiltonian operator that actually is a surface integral at the boundary. Marov calls it the gravitational flux integral. It's sort of analogous to the way, and it measures the total energy inside the system. So you might be familiar with the fact that you can measure the total electric charge in a region of space

by surrounding that region with a big surface and measuring the flux of the electric field through the surface, and that'll tell you how much charge is inside there. Similarly, in gravity, if you measure the flux of this quantity very far away that includes everything in space, you'll know how much energy is in this space. But energy is the quantity that is conserved because of time translation symmetry and in quantum mechanics, and the operator that describes energy is the generator of time evolution. And so, Merloth's point is, since we know that in a generally covariant theory, or diffeomorphism invariant theory, the Hamiltonian is a boundary term, then we know that any observables that

we measure at the boundary, when we try to evolve them forward in time, we would take quantum commutators of those observables with this boundary Hamiltonian. Everything we would be calculating would be taking place within the algebra of boundary observables. If that algebra is closed, meaning when you take a commutator of two things in it, the result is another thing in the same algebra, then the observables at the boundary would

evolve into themselves over time, over any amount of time. And that means that any information you had about those observables at a given moment of time, some initial time, you would also have access to that same information at any other time. Because the relation between the observables at one time and another is completely governed by the algebra at the boundary. That was Merle's point. And he called that boundary unitarity.

That's has implications for the black hole information paradox, which is, um, suppose I throw some stuff into the space time from the boundary and I aim it so it collapses and forms a black hole. Let's say the black hole emits Hawking radiation and evaporates. Quantum field theory makes it look like, well, what's coming out of the evaporating black hole is completely random and information is being lost. Whatever information about this, whatever I sent in to form the black hole,

that information is wiped out and lost because all I get coming out of the black hole is random Hawking radiation and that's kind of the nature of that leads to the black hole information paradox. It seems like the information I had initially about what formed the black hole got lost. Actually there's even more information that got lost because the entanglement we were talking about earlier between a quantum fluctuation of a field and its partner behind the horizon, that correlation also gets lost when Hawking radiation happens. So it looks like when you just think about quantum field theory locally, you are losing a lot of information.

But Marolff says, oh, but it can't be that way. Any information you had initially, you'll never lose at the boundary. So that's good, but then what about the argument that says we lost all that information? Right. But think about that argument. It used the concepts of local quantum field theory.

Like it said, oh, but if I go down near the horizon of a black hole, I have these entangled pairs. I'm now losing that entanglement. But that information is not described by a local observable in general relativity. This is where your earlier question about how do you get rid of paradoxes by realizing that the question you're asking is not meaningful. So you're asking what happened to the entanglement between the part of the fluctuation and its partner behind the horizon? Didn't I lose it?

How come I haven't I lost unitarity? But the thing is in a gender in a diffeomorphism invariant theory, that entanglement between a quantum fluctuation and its partner is not a meaningful observable. Of course, it's meaningful approximately. If I just jump into the black hole and I set up a little laboratory as I'm falling across the horizon, I could measure that. But that's a different question than the kind of fine-grained question that's being asked in the Black Hole Information Paradox, which is what about all of the entanglement of everything, of every degree of freedom?

So my resolution of the paradox would be to say you didn't have any right to say that you lost that Then you better not use these approximate notions of observables, which don't really apply in a diffeomorphism invariant theory. You have to take into account what's called the gravitational dressing of all of your observables. You have to localize where you were in space-time when you measured that correlation. What was it you measured? How do I know what point on the horizon at what time that particular correlation existed? You could say, well, I jumped in at 10 o'clock,

my clock passed a certain amount of time. You have to refer everything to a reference system and take into account the gravitational effects of your reference system. And what Merle's argument says in a nutshell is, okay, if we just stay at the boundary or we have a well-defined reference system, and we only talk about well-defined observables at the boundary, then we're never gonna lose any information about those observables. And therefore, there's no paradox because we're not

asking the wrong questions. Now the viewer may be wondering what paradox question was I talking about? Just so you know, we cut out the question because it wasn't the right time it took us off course, but I'll just restate that question now for the audience. The question was about paradoxes and at some point, well, not at some point, you want to resolve paradoxes, how do you resolve them? What are the different methods? In one of your lectures, which I'll put on screen, you suggested that the way that we've historically resolved some paradoxes in physics, like the twin problem paradox from relativity,

was to change what is a meaningful question. Right. So that's what you were referring to. Yes. And well, so do you want me to articulate that in the case of the black hole information paradox? Well, I would like you to talk about some of the previous paradoxes in physics and then how they were changed or resolved by saying, well, such-as-such is not meaningful, but this is meaningful, and then talk about the black hole paradox. meaningful, but this is meaningful, and then talk about the black hole paradox. Right. So we'll, for example, let's say the twin paradox in special relativity. If you have two twins that are the same age, but then they separate from each

other and they go through different life paths, one might accelerate far away and then come back and they come back together, a different amount of time has elapsed for the two of them. So that seems paradoxical if we have the idea that actually there's a common time that that everything experiences in the universe and we could just look at the cosmic clock that's ticking for both of us and it's ticked the same amount for me as it has for my twin. So when we come back together, we must have aged the same amount, right? And the answer is wrong because what is the nature of time is not a cosmic clock. It's actually a property of a particular path through space and time.

Time is like the length along a curve in space-time. It's the time along a curve in space-time. It doesn't have any global meaning. So we deny the meaningfulness of the premise that made it seem paradoxical in the first place. Another example I gave, I think, in that talk was the Gibbs paradox I gave, I think in that talk was the Gibbs paradox of entropy of mixing. And well, that's a technical situation to describe, but the resolution of it was that things that you thought were, it was meaningful to distinguish from each other, to count as separate,

actually are completely indistinguishable. So it was meaningless to count them as separate in the first place, to count them as separate in the first place, to count them as distinct in the first place. Okay, so now use that to talk about the black hole paradox. We seem to have a paradox because on the one hand, when you just look at quantum field theory as a description of something happening in a space time, it looks like the formation and evaporation of a black hole is destroying information.

That is, accessible information once the process is complete of formation and evaporation, we have random stuff that came out and we can't reconstruct from it what went in. And that's paradoxical because there are other reasons to think that we can't possibly lose information because quantum mechanics says everything evolves unitarily. That means it's a mathematical term that has the implication that all information is perfectly preserved at all times.

It's transformed from one form to another, but it's never lost. No new randomness is introduced according to quantum mechanics that could destroy this information. So that's why it's considered a paradox, because there are two things that people think both seem correct, local quantum field theory, unitarity of quantum mechanics, and yet they seem incompatible when a black hole forms and evaporates. of quantum mechanics, and yet they seem incompatible when a black hole forms and evaporates. And my take on the paradox, which I get from Marolff's boundary unitarity argument, is that actually one half of that argument is just wrong. The local quantum field theory analysis is concerned with quantities that aren't even well defined, sharply enough

to formulate the paradox. That is, the idea of the information in entanglement across the horizon, it's not consistent, it's not an observable in general relativity because we haven't pinned down the location and space and time and the quantities that we're talking about measuring sharply enough for it to be a well-defined observable. Make that more concrete. So how do you decide whether or not the information has been

destroyed when a black hole forms and evaporates? Let's say you could gather up all of the Hawking radiation that came up afterwards. You're supposed to put that in your laboratory and make the most refined precise quantum measurement of the state of that radiation and all of its correlations with its different parts with essentially infinite precision. To check whether or not you've lost the information, you have to measure it extremely precisely. But the thing is you have to measure it more precisely than we've even accounted for the

information loss in the first place. Because when we tried to make the argument that there was a paradox involving loss of information and entanglement and so forth, we weren't really talking about precisely defined observables. Diffie-morphism invariance introduces a challenge when you try to define an observable that doesn't exist in non-gravitational theories. In quantum field theory without gravity, you could say, I want to know the value of, let's say, the electric field squared at this point in space at exactly this time.

Yes. And that should have some value. Well, it's a quantum operator, but it has some matrix elements and some expectation value. It's a well-defined thing in the theory. Maybe I should actually smear it over a little region to make it really well-defined. Sure.

But I don't have to worry about saying, well, where was the point in time that I did it? I just say, well, it's like 10 centimeters from the edge of my desk at three o'clock in the afternoon, etc. and everybody just accepts that's defined what I'm talking about, where and when and what I'm measuring. But with general relativity, that doesn't work because I can't just refer to coordinates. The coordinates become meaningless in general relativity. To say where it is, I have to actually talk about the desk

that it's near. And then the desk has a gravitational field and that affects the geometry itself. And actually, of course, I can't just talk about the desk because where's the desk relative to the room, relative to the space outside? And where's the earth relative to the sun? And where's the Milky Way relative the Sun? And where's the Milky Way

relative to everything else in the universe? To pin down what you mean, in general relativity, you have to introduce the whole system and then make a kind of self-consistent description of what it is you've measured. Now, obviously, for practical purposes, you can often completely ignore that. But that's because there's a pretty stable building that I'm working in every day. So if I tell somebody come to room 3151 at 2 o'clock, the quantum gravitational corrections to the meaning of that statement or the fuzziness is not practically relevant because we live in a pretty stable world on the timescale of my lifetime or something, right? Or at least of my week.

Yeah, speak for yourself. Right. But the point is that when you're asking a question like the Collecal Information Paradox, you're requiring almost infinite precision on measurable quantities and therefore those practical purposes definitions of observables become inadequate to the task. Meralf's viewpoint said, okay, let's just take the big view out at the boundary where we kind of turn off gravity because we're at the asymptotic region where gravitational fluctuations are not relevant.

And we only allow ourselves to talk about observables there. Then can we formulate the paradox just in terms of those? And it seems to me what Marov told us is, no, we can't. There's no paradox then. Everything evolves unitarily. When you were giving the analogy of the sphere for the electric charge and you're looking at the flux on the sphere, that's a spatial boundary that we're putting. And it's not even the full boundary, it's just a spatial circle or sphere.

Now for this boundary, is it the boundary of space-time, not just a spatial boundary? Yes, of space-time in the sense that it's a spatial boundary that's extending through time as well. So it's persisting in time at some large radius. And does Merle's argument rely on it being a compact space, like the space-time must be compact, or does it matter? No, it doesn't. The sharpest version of his argument works with an asymptotically anti-de Sitter geometry

of space-time, but he did argue that it could also apply in an asymptotically flat space-time. Where it would not apply is in a compact space. Like our universe might actually be compact without any boundary. And in that case, we couldn't formulate his argument the way he has done. I find it, even though I don't think the universe we live in

does not have an asymptotically anti-de Sitter region, presumably, I still think it's highly useful as a kind of theoretical laboratory to just restrict attention to those space times that do have that kind of an asymptotic boundary, just to make a sharp formulation of some theoretical statement we have control over. We're not anti- sorry, we're not asymptotically desider or we're not- Anti-desider.

Yeah, we're not asymptotically anti-desider, but we are asymptotically de sitter. Well, we don't know. We might, you mean in the future, we might be, but we don't know yet. Actually there's new evidence, remember, from some new observations that the dark energy might actually be decaying. It's not constant in time. There's a great economist article on that on the DESI results. I'll place that on screen and in the description. Great. Yeah, so it might be that we don't, but in any case that would have been a time boundary, not a space boundary. Okay, so but there's an interesting problem with

our issue that Merall's explanation raises, which I should mention because I make it sound a little bit easier than it is to understand how he gives, what the nature of his answer would be. Well, the answer that I extract from his statement, namely, it's one thing to say that you never lose any information in this boundary algebra. It's another thing to say, okay, what am I supposed to measure to recover the information? Where is it stored? In what sort of measurements?

And I think we don of it is that it's in the multiple moments of the gravitational field and there are quantum correlations with each other. There's very interesting work by Suvrat Raju and his collaborators have a lot of interesting work trying to characterize what you would have to measure at the boundary to pick up on this information, like to recover the information. And they're very complicated observables involving very high, you know, products of operators at very small scales. you know, products of operators at very small scales. But I don't think that invalidates the idea. I think it actually helps the idea to identify

something about the kind of observables you'd have to measure to extract the information. What is it exactly about black hole physics that the black hole solutions to general relativity provide some insight into GR more so than other metric solutions? So first of all they have singularities inside them which means that space and time break down somewhere inside the black hole and there are zillions of black holes in the universe and new ones are formed all the time. And every time that happens, space and time as we know it end somewhere inside. Tell me more about that. You know, space is normally,

you can think of it as a series of nested spheres. If we pick an origin, expanding of larger and larger radius that fill up space. But inside a black hole, instead of them spheres getting bigger and bigger area, they have like the same area but there's still a distance between them, their area is not increasing. Space gets stretched out like that, the spheres get smaller and smaller. The length gets longer and longer until space is literally like stretched and squeezed into a filament. And then it just maybe ends.

So it's a fundamental breakdown of their basic concept of space and time inside black holes. So that's one thing. Also, of course, black holes led us to black hole entropy and Hawking radiation and the whole idea of the, the vacuum being thermal when you restrict to one side of a boundary. Also the attempt to understand black hole entropy is what actually led Maldicena to his ADS-CFT conjecture, which now people think is a pretty solid thing.

So the ADS-CFT, it's string inspired, but not string contingent. Now this whole entropy from black holes, you have found that this entropy is not just something that characterizes black hole, but is a property of space-time itself. So that implies to me it's black hole inspired, but not black hole contingent. Right. Yeah, absolutely. But I think you were asking me, like, what did we learn from black holes or why do black

holes play an important role? Right, right. In other words, what is it about black holes in the same way string theory has plenty that's string inspired but not string contingent. It seems to me like there's plenty that's black hole inspired, but then turns out to not be black hole contingent. What is it about black holes that allows for that? I also have the same question for string theory. What is it about string theory? Let's imagine it's not the actual theory of everything. Well, then what would it be about string theory that's giving such insight? Like, why would it be? But that's a question for a string theorist. Note, I have a three hour presentation on an overview of the current state of string theory at the graduate level. Link on screen and in the description.

I think this has more to do with just how does physics evolve in general. I mean, why did heat engines lead to thermodynamics and statistical mechanics and ultimately quantum mechanics? Well, it was just some place to focus our attention where fundamental principles were at play and they led physicists down a path of discovery. So black holes are exotic objects that lead us into strange situations to think about and try to understand. And that means that we're going to put our theories to the test and run into things we don't know how to explain and thereby hopefully extend our knowledge. So tell us about how your work compares to Eric Verlindes. I don't know. I haven't been able to really understand in detail what Eric's ideas are.

How about Ramsdonk? If I'm pronouncing that correctly, Ramsdonk, Von Ramsdonk. How does your work compare to his? The place, the thing we've discussed so far that relates to what he emphasized was this ER equals EPR idea and the role of entanglement in the vacuum in the structure of space and the connectedness of space. So I think we see eye to eye on that. In the context of ADS-CFT, Mark and others also managed to derive Einstein's equation

in a kind of statistical way using the concept of entropy and equilibrium. And that actually is what inspired me in my 2015 paper to try to localize what they did without using ADS-CFT. But there's a quite close link between those two things. This gets us into the Ryutake-anagi entropy. And so there's a connection in ADS-CFT between entropy in the conformal field theory across a boundary of a region and geometry in the bulk space-time that's dual to that region. And the specific geometry that it's linked to is the area of the surface, the minimal surface area that ends on the boundary at the boundary of the boundary region. Let me give the simplest example I can think of of this.

Let's say we have a boundary that's like a sphere and we decompose it into two hemispheres. Okay? Then in the boundary theory, between the two hemispheres there's a circle and there's entanglement entropy across that circular boundary between the two halves. But in the bulk space-time, that circle is the boundary of a big disk. And the area of that disk is supposed to be divided by 4G, G being Newton's constant, the area of that disk divided by 4G. In other words, the Bekenstein-Hawking entropy associated with the area that divides the space is supposed to be dual to or equivalent

to the entanglement entropy in the conformal field theory between the two hemispheres. That sets up a direct link between entanglement entropy in the conformal field theory and geometry in the bulk. And the work of Mark van Remsnock and other people on the, that's sort of related to what I did is they said, well, okay, suppose instead of just considering one state, we look at all different states of the boundary theory. They have different amounts of energy in them. The geometry in the bulk is varied. The area varies in a certain way. in the bulk is varied. The area varies in a certain way. We know something about the relationship in the boundary theory between entropy variation and energy variation, not

to do with gravity, just the relation between entropy and energy variation. What does that imply about the gravity in the bulk? Could we derive the Einstein equation? And they did manage to derive first just the linearized Einstein equation for very small changes of the state. And Mark and Brian Swingle had an argument that they could extend that even to nonlinear changes of the state. And when I saw that work is when I thought of trying to basically emulate that line of reasoning, but without using the CFT boundary, but just choosing my own local region in space with its own local boundary.

And I found that I also was able to infer the Einstein equation from an assumption of maximal entanglement in the vacuum. Is there anything about your approach that rules out classes of string theory or loop quantum gravity or any of the other approaches to quantum gravity? I don't think so because I'm just looking at things. Remember I mentioned earlier how thermodynamics is fault tolerant and doesn't require you to know about the microscopics. Yes. In that sense, I think we're working like, level I'm thinking about with this thermodynamic reasoning or even

the statistical one using quantum field theory is immune or blind to the fundamental substructure. So what are you thinking about these days? I've started, well, one thing is I'm thinking again about the principles that went into my prior work that we've been talking about, trying to rethink some things. One thing about my 2015 paper that I found extremely striking was that

when I said that I assumed the entropy is maximized, I had to say maximum with something held fixed. So what did I hold fixed? If I'm talking about a ball-shaped region, I could have held the radius of the ball fixed, or its area or its volume. And it turned out I had to hold the spatial volume of the ball fixed in order for the Einstein equation

I inferred to have the correct relationship between the gravitational constant and the Bekenstein-Hawking entropy of the boundary. I find that really striking and the Bekenstein-Hawking entropy of the boundary. I find that really striking because it means that there's something special about holding the volume fixed. I have no idea why I should hold it fixed compared to the say the radius or some other quantity. It's a natural quantity to hold fixed.

It's a very specific conclusion. I would have gotten an inconsistent Einstein equation in the sense that the gravitational constant in my derived Einstein equation wouldn't be, wouldn't have the right value for the area entropy to be area divided by four times that constant. It would have been some other numerical factor. And from the physics we know already from Bekenstein and Hawking, that would have been wrong.

So the fact that there was some choice that worked correctly impresses me, and the fact that that choice was the volume requires explanation, and I don't have the explanation. Would graviton loop corrections shift the entropy's density relation to G, the alpha? I think they would renormalize G. And when we talk about like the Beckensien-Hawking entropy we're always talking about the gravitational coupling measured at large distance scales. So all those loop corrections are already subsumed into the value of the gravitational constant that we're referring to.

If we could probe at smaller and smaller scales so we could start to see the running of the gravitational coupling strength, then we would see some change. Right. Do you imagine gravitons exist or is there something about either your theory or your hunches that suggest it doesn't? I suspect they have to exist at some effective level, but I definitely don't think, I don't even think space-time and the metric is fundamental, so I certainly don't think, I don't even think space-time and the metric is fundamental,

so I certainly don't think they're absolutely fundamental. But I used to think when I first did my 95 work that maybe this thermodynamic perspective suggests that gravity isn't governed by quantum mechanics at all. And I think that can't be right, because we know that quantum fields interact in a perfectly respectable and respectful way with gravity, and quantum mechanics is a kind of universal theory. It wouldn't make sense for two interacting things to have to be such that one of them is subject to the laws of quantum mechanics and the other thing is not. I mean, just completely not.

So I think at some approximate level, it must be that gravity is subject to, at the effective level, to quantum mechanics and therefore gravitons at some level exist. The analogy I like to bring up is a Bose-Einstein condensate. You know what that is? It's a quantum fluid made of a bunch of atoms. Microscopically, it's just a bunch of atoms cooled together to an extremely low temperature. They interact with each other and they form a kind of fluid. And that fluid, or you could call it a quantum gas also, it supports sound waves.

You could say, okay, are those sound waves quantum quantized? Are there phonons in a Bose-Einstein condensate? And the answer is yes. At some level of description, yes, there certainly are. But if you try to look at a sound wave with too high a frequency or too short a wavelength, it just disappears and you just see atoms. There is no such thing fundamentally as a sound wave. The ingredients of the condensate

are just individual atoms altogether. So- That's a good analogy. I think of it the same in space time. If you don't probe it too closely, yeah, some effective gravitons must exist. Professor, it's been a blast. Thank you for spending so much of your time with me.

All right, you're welcome. Of course you hit everything. You're a professional. Ah, thank you. I've received several messages, emails, and comments from professors saying that they recommend theories of everything to their students, and that's fantastic. If you're a professor or a lecturer and there's a particular standout episode that your students can benefit from, please do share. And as always, feel free to contact me.

New update! Started a sub stack. Writings on there are currently about language and ill-defined concepts as well as some other mathematical details. Much more being written there. This is content that isn't anywhere else. It's not on Theories of Everything. It's not on Patreon. Also, full transcripts will be placed there at some point in the future. Several people ask me, hey Kurt, you've spoken to so many people in the fields of theoretical

physics, philosophy, and consciousness. What are your thoughts? While I remain impartial in interviews, this substack is a way to peer into my present deliberations on these topics. Also, thank you to our partner, The Economist. Firstly, thank you for watching, thank you for listening. If you haven't subscribed or clicked that like button, now is the time to do so. Why?

Because each subscribe, each like helps YouTube push this content to more people like yourself, plus it helps out Kurt directly, aka me. I also found out last year that external links count plenty toward the algorithm, which means that whenever you share on Twitter, say on Facebook or even on Reddit, etc, it shows YouTube, hey, people are talking about this content outside of YouTube, which in turn greatly aids the distribution on YouTube. Thirdly, you should know this podcast is on iTunes, it's on Spotify, it's on all of the audio platforms. All you have to do is type in theories of everything and you'll find it. Personally, I gained from

re-watching lectures and podcasts. I also read in the comments that hey, toll listeners also gain from replaying. So how about instead you re-listen on those platforms like iTunes, Spotify, Google Podcasts, whichever podcast catcher you use. And finally, if you'd like to support more conversations like this, more content like this, then do consider visiting patreon.com slash Kurt Jaimungal and donating with whatever you like. There's also PayPal, there's also crypto, there's also just joining on YouTube. Again, keep in mind, it's support from the sponsors and you that allow me to work on

toe full time. You also get early access to ad free episodes whether it's audio or video, it's audio in the case of Patreon, video in the case of YouTube. For instance, this episode that you're listening to right now was released a few days earlier. Every dollar helps far more than you think. Either way, your viewership is generosity enough. Thank you so much.