Theories of Everything with Curt Jaimungal - Ginestra Bianconi: The Physicist Who (Unexpectedly) Derived Gravity From Entropy

Episode Date: July 13, 2026

I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE Ginestra Bianconi thinks gravity can be derived from entropy — and that gravity itself is fundamentally anti-reductionistic, since it's about geometry rather than isolated particle interactions. In this episode, the network-topologist-turned-gravity-theorist explains her "Gravity from Entropy" action, which treats matter and geometry symmetrically through a geometric quantum relative entropy (not the horizon entropy of Verlinde or Jacobson). She details why it reduces to Einstein's equations at low energy while predicting a dynamical, always-positive dark energy term (the "G field"), how it may avoid black hole singularities and reproduce the area law without invoking holography, and why she believes understanding the brain may be harder than understanding quantum gravity. We close with her advice for young researchers. I hope you enjoy. TIMESTAMPS: - 00:00 - Information Content of Geometry - 07:38 - Geometric Quantum Relative Entropy - 15:58 - Geometrizing the Matter Field - 23:45 - Emergent Dark Energy - 30:12 - Statistical Mechanics vs Thermodynamics - 37:59 - Structure and Dynamics Interplay - 45:20 - Holography and Area Law - 51:23 - Interdisciplinary Research Vision LINKS MENTIONED: Ginestra's Webpage: https://webspace.maths.qmul.ac.uk/g.bianconi/ Ginestra's Papers: https://scholar.google.com/citations?user=ycQXwWgAAAAJ Gravity from Entropy [Paper]: https://arxiv.org/abs/2408.14391 Geons, Black Holes, and Quantum Foam [Book]: https://amazon.com/dp/0393319911?tag=toe08-20 The Thermodynamics of the Gravity from Entropy Theory [Paper]: https://arxiv.org/abs/2510.22545 Notes on Some Entanglement Properties of Quantum Field Theory [Paper]: https://arxiv.org/abs/1803.04993 Inflation from Entropy [Paper]: https://arxiv.org/abs/2509.23987 Thermodynamics of Spacetime: The Einstein Equation of State [Paper]: https://arxiv.org/abs/gr-qc/9504004 More Is Different [Paper]: https://www.science.org/doi/10.1126/science.177.4047.393 Information, Physics, Quantum [Paper]: https://philpapers.org/archive/WHEIPQ.pdf Network Geometry with Flavor [Paper]: https://arxiv.org/abs/1511.04539 Black Holes and Entropy [Paper]: https://physicsgg.me/wp-content/uploads/2014/03/black-holes-and-entropy_bekenstein.pdf Ginestra's Lecture on Higher-Order Networks: https://youtu.be/o4TWDTgqQKY Elan Barenholtz [TOE]: https://youtu.be/A36OumnSrWY Frederic Schuller [TOE]: https://youtu.be/Bnh-UNrxYZg Erik Verlinde [TOE]: https://youtu.be/ilVImMHcr_g Ted Jacobson [TOE]: https://youtu.be/3mhctWlXyV8 Karl Friston [TOE]: https://youtu.be/2v7LBABwZKA Subir Sarkar [TOE]: https://youtu.be/epkuoytFJWA Stephen Wolfram [TOE]: https://youtu.be/FkYer0xP37E Roman Yampolskiy [TOE]: https://youtu.be/TgFmA-Qwsek Eva Miranda [TOE]: https://youtu.be/6XyMepn-AZo Cumrun Vafa [TOE]: https://youtu.be/kUHOoMX4Bqw Neil Turok [TOE]: https://youtu.be/zNZCa1pVE20 David Kaiser [TOE]: https://youtu.be/_yebLXsIdwo Ivette Fuentes [TOE]: https://youtu.be/YWbjI-QsH2E Philip Mannheim [TOE]: https://youtu.be/rNXNHYvS7zU FOLLOW: - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Substack: https://curtjaimungal.substack.com/subscribe - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - Crypto: https://nowpayments.io/donation/TOE - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices

Gravity from entropy is a new theory that quantify the information content of the universe. It somehow challenged the reductionist approach. This is Genestra Bianconi, Professor of Applied Mathematics at Queen Mary University of London, an architect of modern network science. Over the past few years, she went into the continuum despite coming from the discrete sector and published the radical paper, Gravity from Entropy. On this channel, I. Kurchaimungle, interview researchers regarding their theories of reality with rigor and technical depth. Today, Beyond Connie's case, that gravity can be derived from entropy,

how dark energy emerges from her equations on its own, always positive, not anti-decider, and we close with the advice she gives her PhD students. The work keeps me awake at night is the second quantization of this theory. Maybe there is no single static solution of the black holding gravity from entropy, and maybe this singularity is avoided. What is gravity? Well, I think we know that gravity is a fundamental force, and we know this since Newton,

but it's a particular fundamental force, because it's somehow, from my perspective, challenge the reductionist approach, because it is about geometry, and this is what we learn from Einstein, and geometry is what allow all the other fundamental force to occur in nature. So somehow, I think, that gravity is about geometry and how geometry interacts with matter fields. And this is a general question. I mean, for my perspective, this question goes all.

also behind gravity itself, because it is a problem of the interplane between, generally speaking, structure and dynamics that is at the fundamental mathematical level common to many different other fields. How did a network topologist like yourself get interested in gravity? Yeah, yeah. So this is a nice question. In my career, I started doing research in this discrete structure that are networks from northern links. And then I move from networks to Simplicial Complex, which allows to capture a discrete geometry and topology of a lot of system

and also real data that can be described with this system. I cannot maybe overstate that maybe in most of my research since now, I have always focused on the interframe between structure and dynamics. And this is very central, for instance, in network theory as well. But, you know, there are important results in network science, so for instance, how, you know, the presence, the topology of the network, so the presence of big hub can affect epidemic spreading, or things like that. But recently it is becoming clear that topology and geometry also play a fundamental role

in shaping the interplane between structure and dynamics. And I've been working a lot on how topology shapes dynamics in network and this is an important mathematical problem that has implications for machine learning up to brain research. but if you want to build this theory

that is a theory that includes topology, geometry and dynamics, there are two aspects. One aspect is that you want to write a theory that capture this interplane using information theory because ultimately you want to study, to describe the system in terms of their information content, and maybe we can go back to that. But on the other side, you don't have enough mathematics in the discrete,

so also the notion of curvature is not well-defined in the discrete setting, a very important proposal. I was giving a seminar at ICTP in Trieste in Italy, and somebody told me, But if you are doing this, why don't you do that in the continuum? Right. And I answered, no, I will never go in the continuum. And then I reflected on this.

And, you know, yes, so the continuum of this theory has to do a lot with gravity. And then why don't pacing the real challenging problem that is quantum gravity? gravity and gravity. Because, you know, somehow I think may be a bit controversial to understand the brain is more difficult to understand quantum gravity. I'd like to bring people up to your results to have them understand it. And one of the ways to do so is psychologically you had a resistance to going into the continuum. Why? Why did you say, no, I'm not going to go into the continuum? Yeah, because all my life I was doing in the, I was working in the discrete.

And somehow I was raised with a belief that maybe also quantum gravity should be discreet or that, you know, nature should be discrete ultimately, which can be the case. But yes, so then we have gauss, we have women, they're all watering in the continuum. So it's not that I will not think about turning gravity from entropy into a continuum in the discrete theory. But for the moment, I like the continuum because the mathematical quantity are well defined. And conceptually, I can focus on the innovation of the idea. Okay. Can you tell me what you were thinking about? What led you to think about gravity? So your friend or colleague said, you need to go into the continuum.

but into the continuum for what? Like, what were you trying to do such that the advice was to go to the continuum? Yes, so I was setting up a challenge that I think is urgent and emerging in the context of complexity and network theory. That is a comprehensive theory, which includes that address the interplane

between structure and dynamics using topology and geometry and viewing this under the lens of information theory. So I strongly believe that the advance in this context will be very important for the theory of complexity,

but I think that also mathematically speaking, the problem are common with the interplane between geometry and matter field in gravity. Okay, so now under your theory, under your new result, what is gravity?

So gravity from entropy is a new theory that stems from an action, and this action quantify the information content of what are the microscopic degree of freedom of the universe, essentially. And the idea is to describe this information context of this matter and geometrical degree of freedom using the metric. So you have two metric, the true metric of space time, and the metric induced by the matter field and curvature. And the action, that is the gravity from entropy action, describe this interplane between matter and geometry by using as Lagrangian what I call a geometric quantum relative entropy

between these two metrics. So you have a tension between these two metrics? that trying to be close to each other. So it's like the matter field telling the metric how they would like to see the true metric and the true metric telling the matter field how to move. And this is essentially, you know, it's building on our inside of Einstein equation.

But actually Einstein equation have this interplaying us beautifully summarized by John Wheeler. but this interplane is not expressed at the level of the action. So instead, the gravity from entropy leveraged this principle of the interplane between matter and geometry already at the level of the action with this information theory, Lagrangian. Let me see if I can summarize for myself and for the audience. So there's entropy which has various incarnations like Shannon entropy and Von Neumann entropy, and Boltzman entropy and so on and so forth. Roughly speaking, they all earn the right to be named

entropy by quantifying some distribution of what you don't know. Now, one of the various forms of entropy is called Horizon slash Boundary Entropy, which is defining some screen where you're saying, I don't know what the heck is going on beyond this screen, and I'm going to attach a number to how much I don't know what's going on, to how many microstates are consistent with whatever's the macroscopic view. That is what Eric Verlinde and Ted Jacobson use. But there's another kind of entropy called relative entropy, which for the people who have watched Carl Fristin and heard about his free energy principle, it's roughly speaking that you have a model of the world and then something happens and then you want to know how surprised should I be, how much information should I glean,

how much should I learn? And if something is drastically surprising, then you should learn plenty. if your model of the world is pretty much correct because you're just a perfect person, well, then you don't have much entropy at all. You take this other approach, this relative entropy approach. You take this relative entropy, put it in action, and then extremize it. Yes. So it's the concept of relative entropy is quite nice. The gravity from entropy action is quite innovative also from the point of view of statistical mechanics. So just to make things clear, right, the entropy is usually, you know, Boltzmann definition

is the logarithm of the number of micro-state compatible with the macro state of a system. And this is huge, right, because the entropy described the second law of thermodynamics, which is, of course, one of the building block of physics. And because the entropy, the defining this way, never decreases, so as the tendencies of increasing.

And people are usually quite impressed by this second law of thermodynamics and things like that. But for my perspective, it's just a measure of quantify what you know about the system in terms of information theory. So the relative entropy is a different concept, right, is when you want to compare two different state, for instance, two different quantum state, and express how much information in a quantum state is codified in the other quantum state. So if one quantum state describe the real geometry and the other quantum state describe the geometry that kind of the matter and the curvature would like to see, right, this graph. from entropy action described this tension

between these two. And actually, another property of this action is that it treats in some sense very symmetrically the geometry

and the matter field because they are just, you know, describe in terms of two metrics and is comparing these two metrics with this

geometric quantum relative entropy. So you have this tendency of these two metrics to try to be close to each other.

to approximate each other. But actually, the gravity from entropy action doesn't have only the Lagrangian, but as also the measure. And the measure actually plays also an important term, right? So conceptually, the gravity from entropy action wants to describe this tension between these two metrics, wanted to be close to each other.

But at the same time, there is a nice mathematical aspect of it because these entropy is defined, like the trace of a logarithm, and one of the property, mathematical properties, is that the trace of the logart means the logarithm of the determinant.

So when you express this relative entropy, you know, conceptually the idea is that you have these two different entropy, but the idea is that this entropy also quantify the numbers

of microscopic degree of freedom of this interplane between matter and geometry. So you have at the same time, you know, an understanding in depth of a relative entropy and an understanding as a Boltzmann-like entropy. And I have a paper that is now in press in PRD, which show that actually if you consider this action and you calculate this action over Friedman universe,

which are an approximation of the solution of the modified gravity equation, You find that actually this Lagrangian decreasing time so that, you know, you have these two metrics kind of trying to be close to each other. But actually they are integral, so the action which integrates over the measure and can be interpreted as a entropy increase in time. So the universe is consistent with an action that describes the total entropy that increase in time, while the relative entropy locally decrease in time. So that's an interesting aspect in terms of statistical physics. I'll be placing links as well as visuals to your work on screen so that people can dive even deeper and then even earlier

to some of what you're saying like Simplicial complexes and so forth. So if you're listening to this and you're driving and you're wondering what the heck does this correspond to in terms of what does it look like, you can feel free to watch the podcast safely as you drive. Don't do it while you drive and pull over. Okay, what are these two metrics then? Like, what is one?

Is one just flat, the flat case, and then the other is whatever the Einstein curvature would be? Like, it seems like it sounds, which is why I'm putting your work on screen, but it sounds like you're putting Einstein's equations in already to get out Einstein's equations. Like if we're already motivated by, let's see how matter would tell spacetime how to curve,

well then we have some idea of Einstein's equations going into it. That's what it sounds like. So Dispel, tell me what is going on with these two metrics. What are they? So now there is no assumption of any Minkowski background. Absolutely not. So the true metric is the true metric, the one that defines the richest color, the Riemann curvature. So it is the true metric as it is.

And the metric induced by the matter field and curvature, it's a geometry. it's a geometrization of the matter field. And this builds on a different insight. The first inside is gauss, the first fundamental form of gauss, which express practically, you know, in the simplest setting, you can say, you know, you have your manifold, which might be curve or whatever, your general Laurentian manifold.

And then you have, let's say, say a scalar field which define a dimension, an additional dimension, and then this color field you can imagine as a surface defined on your original manifold because it's, you know, your scholar field defined on the manifold. Now, for this surface, there is a notion of metric-induced by this function, and this is described by the first fundamental form of chaos, and this is the metric induced by this field. So the idea is in gravity from entropy is that there is not only a scholar, but there is a higher order description of the matter field.

So at each point you have a scholar, a one form and a two form, and here the old setting of differential geometry comes about that is very fundamental for this theory. And then you define the metric induced by the matter field encirpature. similarly as, you know, extending somehow Gauss, that's fundamental form of Gaup. And this is, and the expression of this metric used by the matter field and curvature, is inspired by the literature in Bonneumann algebra, and, you know, there is a beautiful paper by Witten in a review model physics that discuss a closely related definition of entropy, which is again a relative entropy,

which is called the Arachyentropy for one-nomah algebra as a very important measure for entanglement that can overcome the problems of, you know, entanglement entropy for quantum field theory

that is ultraviolet divergent. So the connection is not established fully, but it's been very important for the formulation of this theory for me and there are things to explore whether again what is the connection

between the gravity from entropy action and entanglement and the Iraqi entropy but the idea is that yes this action treats matter field and geometry on the same footing by geometrising

the matter field and the curvature and from this aspect is much more symmetric than the Einstein-ilbert action plus the matter field, right? Because the matter field has the matter action has only minimal coupling. And there is no symmetric way

of treating the two. While in gravity from entropy, it's fully symmetric and you treat them on the same footing and interpret them in the light of their mutual information content relation. And the beauty is that this action leads to modify gravity equation.

So my lead to testable prediction that goes behind Einstein equation, but it reduced to Einstein equation in the low energy limit. So everything we know in the low energy limit remains valid. But of course, the gravity from entropy equation of motion can be used to probe the high energy limit. I subscribe to the economist. Their science and their AI coverage is among the best I've found anywhere. And I say that as someone who reads plenty of it. I'll give you some examples.

They just ran an analysis on how attitudes towards science are changing in American politics and what this means for research and funding in scientific institutions moving forward. This sort of high-quality reporting is fantastic. They even covered how dark energy may be weakening over time. Now, if that holds up, it completely changes our. understanding of the universe's fate. If you watch this channel, those are exactly the kinds of questions that we explore every week. I subscribe to the economist because their science and their AI reporting regularly surprises me with how deep it goes. And they're also, of course,

known for global affairs, both political and economic reporting. They are top tier, and interestingly and flatteringly, Toe is one of the only podcasts that the economist partners with. So as a listener, you get an exclusive 35% off. That's not a deal that they have just anywhere. Head to Economist.com slash T-O-E to subscribe. That's economist.com slash T-O-E for 35% off. Okay, one of the questions occurring in the audience's mind may be, okay, there are many different re-derivations of Einstein's field equations or GR.

And so then the question is, okay, so what? So what if we found some new formulation? You're saying the so what is at least that, well, matter and geometry are now on the same footing, whereas before they were seen as separate. You treat them both with mutual information. Then another is that you get modified gravity, which will lead to testable interpretations, and furthermore that this has implications for quantum gravity. Yes.

So, I mean, this aspect is very crucial because gravity from entropy actually, action stems from this idea that you can treat the metric as quantum operator and practically write quantum relative entropy among them. But it's still not in second quantization. So the program is there and I'm still working on, you know, even problem, even more high energy limit, right? Because it could be that this is a theory. Being classical, maybe it could be that, you know,

If you really address the full second quantization aspect, you get still more effect. Yes, this is extremely new, less than two years old. Your paper, I think, is from 2025, if I'm not mistaken. Yes. Someone also, in December, just took your work even further. Inflation without the inflaton, something like that. There is a paper that also acknowledged you. Yes, yes.

this is a group based in China. They have started the challenging task to integrate this equation, and they looked at this model, and they showed that it might lead to inflationary behavior or in absence of a scholar field. Yeah, but I mean, it's also interesting. I mean, one of the prediction of the model, and this comes from my original paper,

is actually that, you know, this modified gravity equation are consistent with a dark energy term, which is a dynamical cosmological constant, which is always positive and vanishing in the low energy limit, but is dynamical and is expressed in terms of a new quantity which I introduce, which is called the G-field, which is an emergent field of the theory, which encode this interplane between structure and dynamics,

and is responsible for this dark energy term, is a bit like, you know, is emerging mathematically as a Lagrangea multiplier of the theory, but we know that Lagrangea multiplier in statistical mechanics can have a physical meaning, like for instance, the temperature is a Lagrangian multiplier of the energy and has a physical meaning. In the same time, in the same way, you know, this G field that is emerging as a Lagrangea multiplier, we want to give a physical meaning

to that. And when we do that, you know, this action that it looks like the relative entropy, when you express in terms of this G field becomes much closer to the Einstein action. And the differences are mainly two. One is that the metric is dressed by this G field. So it's like the true metric is not exactly what interacts with matter, but what interacts with matter is a dress metric with this G field. And you have a cosmologic, a dark energy term, which is a dynamical cosmological constant that depends on this G field.

So an important test about prediction is to see if this can shed some light into, know, the abel tension or other property. What do you mean when you say that the metric is dressed? Yeah, so practically, you know, this geometric relative entropy can be written in terms of this G-field, and then there will be, in term of the G-field, it appears to have three term. One that you can identify with something closer to Einstein-ilbert-Ackron is a sort of dress richie's color because it's formed by the richy tensor contracts with this dress

metrics and the remand tensor contracts with this dress metric. And another term that is the matter action that, you know, is these things that comes from the geometric induced by the matter field and curvature, it is contracted with this dress metric. So is it just stress metric? Instead of the metric, you have the metric constructed with this G-field. So it's like the matter fills this stress metric. Earlier when talking about that there are disadvantages of discrete approaches, for instance, one was that curvature isn't well-defined.

However, there are some discrete approaches to quantum gravity, like causal set theory and causal dynamical triangulations. Even Wolfram has an approach that's discrete. So what are the errors in those approaches, in your opinion? There must be something that's not convincing about them. Well, I think one advantage of the gravity from entropy approach is that it leads to Einstein equation in the low energy limit. These, to my understanding, is not always the case for many quantum gravity approach, or at least might be quite difficult to obtain. And respect to other modified gravity,

that there is a huge literature on modified gravity, but the gravity from entropy has the advantage that there is a motivation, there is a physical motivation for choosing this action, right? It's not just, you know, the next term in the Fourier series or things like that. There is this information theory and, statistical mechanics, understanding of the interplane between matter and geometry. Respect to other, you know, approach using entropy, of course, the approach is fully statistical mechanics. So it embraced the microscopic degree of freedom. While, you know, approaches

that are based on horizon entropy, they are typically thermodynamics in spirit. So they start with the area law, which is of course fundamental, but the area law to my understanding is mostly coming from a thermodynamics description of gravity, while I think it is important to have a microscopic description. And also in this respect, you know, people that try to do kind of entropic approach to gravity, sometimes they are coming from the perspective of theoretical physics,

and they try to be sympathetic with, you know, people that do research in statistical mechanics or, you know, condensed matter, which is of course seen as, you know, very applied. But actually, I'm coming from, you know, complexity theory, natural theory, but I have a very solid statistical mechanics understanding. And for my perspective, actually, statistical mechanics and field theory are the same thing, right? It's just changing an eye with, you know, in the big rotation, right? So statistical mechanics is a fundamental theory, actually, and it is possible to write an action that is a field theory action and at the same time as statistical physics action is not that. that if you want to go towards statistical physics, you need to go toward, you know, soft matter or things like that. Yes, right.

Jacobson's paper is literally titled Einstein as an equation of state or something like that, which is a thermodynamic term. So why don't you spell out for the audience the difference between thermodynamics and statistical mechanics? Why you see the latter is having an advantage here? So, thermodynamics has been

fundamental and it arise from the study of eton genes so practically the efficiency of eton genes it arise from

very practical consideration during the industrial revolution and of course there is this second law of thermodynamics

which is quite fundamental, but at the level of claususus result, we don't have any understanding of where it comes from. And this was the genius of Borsman, which described the H theorem. And the H theorem showed that H, which is definition of entropy, really is an increasing function. And so this is shown in a particular setting of what is

call the ideal gas. So practically you have a particle bouncing around with given velocity, and they have an interaction that is hardcore interaction. So when they bounce to each other, they scatter around. But then there is no interaction at all. And this ideal gas is our most profound understanding of the second principle of thermodynamics. And this entropy is the number of microscopic configuration compatible with the macroscopic configuration of this gas, right? That's the beauty and the universality

of statistical mechanics. So practically, you want to describe macroscopic law from a microscopic understanding of the degree of freedom. You don't need to know all the detail of your system. You need to capture the important

information theory content of the microscopic degree of freedom. And this has been fundamental and pervasive in all physics, I would say, and also behind. So practically, our understanding of face transition or face of matter comes from statistical mechanics, our understanding of, you know, classical and quantum phase transition, our understanding of also, you know, the building block of quantum information and quantum computation comes from this rich interplane between statistical mechanics and information theory, and without mentioning AI, of course. And so this idea is that the idea is that information theory is such a pervasive concept

that is already a common language across many different. disciplines. And with gravity from entropy, this idea, this information idea are reflected in an alternative action for gravity, which is the gravity from entropy action. And it's interesting and I think it's quite stimulating because, you know, in statistical mechanics there are possibly two point of view, right, or even three point of view. So one point of view is the one of emergence. So it's the one that, of course, has been possibly the most fundamental approach to statistical mechanics,

is that from the microscopic degree of freedom, you explain what happens macroscopically. And this has been fundamental coming from, you know, a pivotal paper by Phil Anderson. More is different. But then there is another thought, another line of. idea is that nature, the fundamental aspect of nature is information theory. And actually this has been put forward by John Wheeler, It from Beat. And so, you know, gravity from entropy comes from this kind of point of view that actually maybe we can have a statistical mechanics theory for the fundamental degree of freedom

of geometry and matter field. Of course, it might be that, you know, there is a next theory that builds on gravity from entropy and finds that is an emergent theory, but for the moment, it is conceived as a fundamental theory of geometry. So instead, in here I come back to what we were saying before, so gravity, instead of being a fundamental interaction in this reductionist approach, in which you look at the, you know,

at what happens at the interaction, when two particles interact, gravity is a reductionist theory in which the object is the geometry itself. So in this sense, is similar also to, you know, network approach in which you want to study the interplane between geometry and dynamics. What's the difference between entropy and information? So entropy can be used to pontify information. So in your theory, should it actually be gravity from information

because information is the more fundamental quantity or a substance or what? No, it's gravity from entropy because the action is an entropy. But the entropy capture the information content of the microscopic degree of freedom. Ah, okay. So what do you suppose is actually existing then? because entropy usually counts something. So what in your mind is going on? Yes.

So in my mind is the metric, this true metric, are kind of encoding the degree of freedom of geometry and matter field. Does that mean that an information here means the degrees of freedom of the matter field? or what? Information is both. The idea of gravity from entropy is that it captured the information content present

in the true metric that can be codified by the metric induced by the matter field and curvature. So it is the interplane between the two kind of degree of freedom. The geometrical

and the matter field degree of freedom are described at the same time. So what would you say is the primary difference between your approach and Eric Verlinde's approach? Well, my approach stem from an action,

and I don't use concept related to holographic screen. So I want to capture the microscopic degree of freedom of geometry and matter field and their interplay. So I think in Verlinde approach, there is no focus at all in the interplaying between geometry and matter field. It's very limited. You mentioned early on that this interplay between structure

and then dynamics is important to you. Can you please outline what is structure, what is dynamics, and what does it mean for them to interact? So in gravity, in gravity, my assumption is that what we know about structure is geometry. So is the metric. So, of course, there can be theory or research meant to represent, you know, where this metric come from. But, you know, I assume there is a metric and that, you know, the structure is in some sense,

the structure, like in quotation mark, is in some sense captured by the geometry. And the dynamics is just the matter field, you know. I use bosonic matter field. I use more recently some fluids for cosmology. The idea is that you can put there all matter fields. So the idea is that what I'm working on is that to formulate a gravity from entropy approach in which you can put the standard model there. Are you planning on going back to the discrete case or are you now happily living in the continuum?

You know, I have my research agenda in networks, but for the moment in gravity from entropy, I would stay in the continuum. Well, what about complexity theory? You mentioned that briefly, but how does complexity theory enter into this? Yeah, yeah. So, as I say, you know, information theory is so fundamental and so pervasive, and we got such impressive. result using information theory and, you know, with quantum computation, we might see even more. But actually, it is in many aspects perceived that information theory alone is not enough. And one needs to enrich that with geometry and topology. And so you really need for many different fields, starting from the brain to AI, you need an information theory that capture the degree of freedom of geometry.

So from this point of view, geometric quantum relative entropy could be used potentially to address question also beyond gravity and addressing this need, a need of an information theory of geometry. Kurt here, note that if you'd rather listen to Toe, we're on Spotify, iTunes, everywhere with a podcast catcher. You can just search my name or theories of everything. And also, remember to hit subscribe. If I recall correctly, in 2021,

you were speaking to the Network Science Institute, and you said, I think you were working on this. And at that time, you said it wasn't physics yet. Let me know if I'm mistaken. And anyhow, the point, my question was, Well, I was wondering when in your mind did it then cross over into physics? When did it become physics? Yes.

So it becomes physics practically immediately when I decided to go in the continuum. Ah. Because it's really strange, but in complex system, most of the problem are in the discrete. So if you want to go to the continuum, you know, gravity is the most likely way to go. And this came, you know, after a trip that, I made in the stage and, you know, and also this seminar at the CTP. I felt the need, right, to establish the relation between this theory that I was trying to formulate in complexity and something perceived as more fundamental.

And this is the outcome and I'm very happy because, you know, for me, I'm kind of new in gravity and, you know, traditional theoretical physics. And it is a fantastic playground. It's fantastic progress that has been made, you know, in gravity. Somehow there are so many different directions that you need to be guided by your physical understanding of the problem. But for me, it's a nice new direction at this point of my career. And I am embracing it and enjoying it. So what's the reception been like?

Yeah, the reception has been open. Yeah. So there are people, I think, mostly in cosmology, are quite interesting and they feel the need to work on modified gravity approach. You know, there is this abode tension. There are different problems. There, of course, dark energy, somehow dark matter. So cosmologies are now becoming very welcoming for this theory.

And yes, I had a very nice conversation. Of course, you know, I'm not in the stream of thoughts that start with the holographic screen. So there is also some clash there of our understanding. Of course, I think that, you know, the area law is fundamental. but I think is a macroscopic field. And what I want to say is that actually gravity from entropy to some extent reproduce the area law from the microscopic degree of freedom. So this is so practically the Lagrangian is defined over volume.

So if you integrate over a black hole, you know, until the sparship radius, you find a dimensionality reduction. And this is essential. Because practically, olography has been, you know, a kind of explanation of the area law coming after Beckenstein. Beckenstein didn't use the holography. And it's a very simple conceptual idea is that just if you have the entropy, which is the logarithm of the number of degree of freedom, typically the entropy is scales like the volume. So in order to have it in such a way that it scales with the area, the degree of freedom must be only.

on the surface, on the horizon. But actually this assumption builds on the idea that, you know, the degree of freedom are the same in every point, you know, inside the black hole. And in gravity from entropy, because gravity from entropy doesn't depend only on the richly tensor or richly color, but depends also on the remand tension and so on the whale curvature. So what happens is that the degree of freedom in a black hole, right, the degree of freedom inside are not always the same.

Depends on the distance from the origin. And so when you integrate something that is not homogeneous, you can get a dimensionality reduction. So that's the beauty of gravity from entropy. And so for the moment, I don't feel the need to use a, holographic screen. And I think that, you know, there are many important inside coming from the area law, but if we are looking for a fundamental theory, we need to go behind the area law. So is this an immersion theory of gravity then?

So gravity from entropy assume that the geometry exists. And so it builds on Einstein inside that gravity is a theory of geometry. but it provides new understanding of the interplane between matter field and geometry, but it doesn't want to explain where geometry comes from. This is not the goal of gravity from entropy. So as long as Einstein theory might not be considered emergent gravity, but in some sense it is because, you know, Newtonian forces come from geometry. Also gravity from entropy is.

is at the same level, right? So it assumes that the metric exists and capture the information content of this metric and of course, you know, Newtonian gravity comes from the geometry, exactly as in Einstein gravity. Of course, a problem could be, you know, where geometry comes from from the beginning, but this is not tackle in gravity from entropy.

What is emergent is instead this dark energy term that is dynamical and is new because it emerged from the theory and is driven by this G field. Right, and it's positive. And it's positive. And that's a positive thing. Yes. So what are some of the open problems that you're working on right now or some of your colleagues are working on or maybe your students? What's bothering you right now about this theory and you're tackling it? Yeah, so of course there are the cosmological implication

and the relation with prediction and, you know, possible experimental validation of the theory. Then there are aspects related to the second quantization, and then there are aspects related to entangement. So how this gravity from endanglement, action is related to entanglement and archa entropy. And then, of course, maybe if one wants to go, also going in the discrete.

But what keeps me awake at night is the second quantization of this theory. What is the second quantization? And why is it so difficult or tricky in this case? Yeah, so, I mean, this is the real problem in quantum gravity, right? So to combine gravity with our field theory, second quantization approach of the other fundamental force, it is notoriously difficult. This is where the community has explored different direction. And of course, there might be the need for define the gravitation, right, which mediate the gravitation,

interaction, but the quest is open, right? There are many different approach. The graviton would be emergent in your view? Probably not. It would be fundamental. Yeah, you know, it's also to be questioned if the graviton really exists, right? Maybe there is something else, right? Because the metric is described by Birbein, is described by, you know,

pin connection. There are different options. It's not that you need to start from the metric itself. I just spoke with Philip Mannheim, who doesn't believe the Graviton exists, actually. Did I hear you correctly that you use vile curvature as well? I used the entire Riemann tensor. So this includes all the component, also the one that vanish, that do not contribute to the richest color, yes.

So this is an important aspect and this is what makes, you know, the entropy of the black hole non-trivial because practically in empty space, the gravity from entropy action is non-zero. And so if the richest color is zero, right, the gravity from entropy action depends on all the component of the remand tensor. So it's non-zero. And so you can integrate over the volume. it is not homogeneous all over, and this is an important aspect. And another important aspect is actually that this theory provides also some correction at the Planck scale

also in flat geometry. Interesting. So the theory treating geometry together with Matterfield find some correction at the Planck scale already in flat geometry. And what about what's going on at the singularity? Now, I know that's a question that's notoriously difficult. I'm asking you at the beginning of developing a theory, but I'm curious.

Yeah, so the idea is that, you know, possibly the singularity would be avoided by the gravity from entropy theory, because you have this G-field that enters into the action, and this G-field is dynamical. So for instance, for the Svarsil solution, the Svarsit solution is a good approximate solution to the black hole because it's a solution of the Einstein equation that are approximate equation of the gravity from entropy theory. But actually, you know, close to the singularity, this G field becomes dynamical. So maybe there is no single static solution of the black hole in gravity from entropy. and maybe, you know, this singularity is avoided. Professor, what advice do you give your PhD students consistently?

One advice, which is, I think, easy to follow is to read articles and to study. Another advice is to try to follow what you like, you know, try to express your, what you like. you know, you try to express your vision of reality in what you do, and I enjoy, enjoy what you do, you know, try to have fun. It's not always the case, but, you know, I think that that's part of why we do science we do because we want to enjoy it, you know. What's a piece of advice that you keep coming back to that someone gave to you? So, for instance, one advice is why don't you go in the continuum? right? This is an advice coming from a random person that was at my seminar. We didn't talk, we didn't discuss, but it was very important for me. And another thing that I learned

that possibly was not an advice, but try to explore and to go in other community and see what they do. So if you are in a big conference, you know, very interdisciplinary, try to pop up some time in a session from another community and you will find answer to your question possibly. If you think about your problem quite abstractly, so this has been very important for me to formulate gravity from entropy. I had this idea and I was at the DPG meeting, you know, speaking about my topology in networks,

and then I went to listen at session about gravity and information, and it was inspiring and useful. So try to look at nature with surprise, and maybe things will turn nice. Professor, thank you for spending so much time with me. Thank you. Hi there. Kurt here, if you'd like more content from theories of everything and the very best listening experience,

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