This Physicist (Just) Found A New Origin For Gravity

Gravity from entropy is a new theory that quantify the information content of the universe. [music] It's somehow challenge the reductionist approach. >> This [music] is Genestra Bianconi, professor of applied mathematics at Queen Mary University of London and architect of modern network science. Over the past few years, [music] she went into the continuum despite coming from the discrete sector and published the radical [music] paper gravity from entropy. On this channel, I Kirtchev Mongol interview researchers regarding their theories of reality with rigor and technical depth. Today, Bianconi's case that [music] gravity can be derived from entropy, how

dark energy emerges from her equations on its own, always positive, [music] not anti-de Sitter, 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 [music] solution of the black hole in 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 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 from Einstein and 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, from my perspective, this question goes also behind gravity itself because it is a problem of the interplay between generally speaking structure and dynamics that is at the fundamental mathematical level common to many different other fields. >> How did a network topologies like yourself

get interested in gravity? >> Yeah, yeah, so this is this is a nice question. I mean in my career I was I started doing research in in this discrete structure that are networks for from node and links and then I move from networks to simplicial complex which allows to capture discrete geometry and topology of a lot of system and 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 interplay between structure and dynamics and this is

very central for instance say in network theory as well. But you know, there are important results in network science 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 interplay between structure and dynamics and and I've been working a lot on how topology shapes dynamics in network and this is an important mathematical problem that you know, has implication for machine learning up to

brain research. But you know, if you want to build this theory that is a theory that include topology, geometry, and dynamics. Um there are two aspects. On One aspect is that you want to uh write a theory that capture this interplay um using information theory because ultimately you want to study to describe the system in term of their information content. And maybe we can go back to that. Um but on the other side of you don't have enough mathematics in the discrete. So, also the notion of uh curvature is um not well defined in the

discrete setting. Yet, there are very important proposal. I was giving a seminar at ICTP in Trieste, in Italy, and somebody told me that 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 and then why don't facing the the real challenging problem that is quantum gravity and gravity um because you know, some somehow I think maybe

a bit controversial to to understand the brain is more difficult to understand quantum gravity. >> [laughter] >> I'd like to bring people up to your results and 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 I was raised with a belief that maybe also quantum gravity should be discrete or

that, you know, nature should be discrete ultimately. Um which can be the case. But um yes, so that then we have Gauss, we have Riemann, they're all working in the continuum. So it's not that I will not think about turning gravity from entropy into a continuum discrete theory, but for the moment I like the continuum because the mathematical quantity are well defined and and conceptually I can focus on the innovation of the 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 I was setting up a challenge that that I think is is urgent and emerging [clears throat] in in the context of complex complexity and network theory. That is a comprehensive theory which include that the address the interplay between structure and dynamics using topology and geometry and viewing this under the lens of information theory. So I I I strongly believe that the

advance in this context will be very important for the theory of complexity, but I think that also, you know, mathematically speaking the problem are common with the interplay between geometry and matter field in gravity. >> Okay, so now under your theory, under your new result, what is gravity? >> So, um um 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 contact of this matter and geometrical degree

of freedom using the metric. So, you have two metric, the the true metric of uh space-time, and the metric induced by the matter field and curvature, and the action that is the gravity from entropy action describe this interplay 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 metric that trying to 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 and this is essentially, you know, it is building on our insight of Einstein equation, but actually, Einstein equation have this interplay as beautifully summarized by John Wheeler, but this interplay is not expressed at the level of the action. So, instead, the gravity from entropy leverage this principle of the interplay between matter and geometry already at the level of the action with this information theory um 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 Boltzmann entropy and 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." >> Yes. >> 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 Karl Friston 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. But if your model of the world is pretty much correct because you're you're just a 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 the action and then extremize it. >> Yes. So, it's the concept of relative entropy is is quite nice. The gravity from entropy action is 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 microstates compatible with a macrostate of a system. And and this is is huge, right?

Because the entropy described the the second law of thermodynamics, which is, of course, one of the building block of of And so, because the entropy this defining this way never decreases, so as the tendency of increasing. And people are usually quite impressed by this second law of thermodynamics and things like that. Um but for for my perspective, it's just a a measure of quantify what you know about the system in term of information theory. So, the relative entropy is a different concept, right? It is 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 gravity from entropy action describe 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 uh in term 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 has also the measure. And the measure actually uh plays also an important term, right? So, conceptually, the gravity from entropy action wants to describe this tension between these two metrics, wanted to to be close to each other. But at the same time, there is a nice mathematical aspect of it because um this entropy is defined

like the of the logarithm and one of the property, mathematical properties that the trace of the logarithm means the logarithm of the determinant. So, when you express this uh relative entropy, you know, conceptually the idea is that you have these two different uh entropy, but the idea is that these entropy also quantify the numbers of mean microscopic degree of freedom of of of this interplay between matter and geometry. So, you have at the same time, you know, an understanding in type of a relative entropy and an understanding as a Boltzmann-like entropy. And I have a

paper that is now in in press in PRD, which show that actually if you consider this action and you calculate this action over over Friedman universe, which are an approximation of of the solution of the modified gravity equation, you find that actually, um, this uh Lagrangian decrease in 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 describe the total entropy that increase in time, while the relative entropy locally decrease in time. So, that's uh interesting aspect in term of statistical uh 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 you're wondering what the heck does does 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're driving, you pull over. Okay, what are these two metrics then? Like what is one What 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 space-time 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, no, there is no assumption of any Minkowski background, absolutely not. So, the true metric is the true metric, the one that defines the Ricci scalar, 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 metricization of the matter field, and this builds on a different insight. The first insight is uh Gauss, the first fundamental form of Gauss, which express

practically, you know, in in in the simplest setting, you can say, you know, you have your manifold which might be curved or whatever. Your general Lorentzian manifold. And then you have, let's say, a scalar field which define a dimension an additional dimension. And then the scalar field you can imagine as a surface defined on your original manifold because it's, you know, a scalar field defined on the manifold. Now, for this surface, there is a notion of metric induced by by this function. And and this is described by the first fundamental form of Gauss. And this

is the metric induced by by this field. So, the idea is in in gravity from entropy is that there is not only a scalar, but there is a higher order description of the matter field. So, you have a at each point you have a scalar, 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 and curvature similarly as, you know, a standing somehow goes from the first fundamental form of gout. And

this is a And And the expression of this metric induced by the matter field and curvature is inspired by the literature in in von Neumann algebra. And, you know, there is a beautiful paper by 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 Araki entropy for von Neumann algebra as a a very important measure for entanglement that can overcome the problems of you know, entanglement entropy for for quantum field theory that is ultraviolet divergent. So, the connection is not established

fully, but it's been it's been very important for the formulation of of this theory for me. And there are things to explore whether again what is the connection with the between the gravity from entropy action and entanglement and the Araki entropy. But the idea is that yes, this action treats matter field and geometry on the same footing by geometrizing the matter field and the curvature. And from this aspect is much more symmetric than the Einstein-Hilbert 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 modified gravity equation, so my lead to to test about 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, um but of course uh the gravity from entropy equation of motion can be used to to probe

the 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, TO 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/toe to subscribe. That's economist.com/toe for 35% off. Okay, one of

the questions occurring in in the audience as mine may be, "Okay, there are many different re-derivations of Einstein's field equations or 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, the these aspects is is is is very crucial because you know, gravity from entropy action stems from this idea that you can treat them the metric as quantum operator and practically write a 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 probably 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 more

more more effect. >> Yes, this is extremely new, less than 2 years old. The your your paper, I think is from 2025, if I'm not mistaken. >> Yes. >> Someone also in December just took your your work even further. Inflation without the inflaton, something like that. There was a paper that also acknowledged you. >> Yes, yes, this is a group in in in based in China. They have started the challenging task to integrate this equation and they looked at at this model and they showed that it might lead to inflationary behavior also in absence of

a scalar field. Yeah, but I mean it's it's also interesting I mean, one of the prediction of 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 and vanishing in the low energy limit. But it's is is dynamical and is expressed in term of a new quantity which I introduce which is called the G field which is an emergent field of the theory which encoded this interplay between structure and

dynamics and is responsible for this dark energy term. Is a bit like you know, is is emerging mathematically as a Lagrangian multiplier of the theory. But we know that Lagrangian 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 has a Lagrangian multiplier, we want to give it a physical meaning to that. And and when we do that, you know, this action that it looks

like the the relative entropy when you express in term of this G field becomes much closer to the Einstein action. And And the differences are are 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 dressed metric with this G field. And you have a cosmological a dark energy term, which is a dynamical cosmological constant that depends on this G field. So, an important testable prediction is to see if this can can

shed some light into, you know, the Hubble 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 term of this G field. And then there will be in term of the G field, it it appears to have three term. One that you can identify which with something closer to Einstein-Hilbert action. It's a sort of dressed Ricci scalar because it's formed by the Ricci tensor contracts with this dressed metric and the Riemann tensor contracts with this

dressed metric. And And another term that is the matter action that you know, is distinct that comes from from the geometric and used by the matter fields and and curvature it is contracted with this dressed metric. So, it's a just dressed metric. Instead of the metric, you have the metric contracted with this G field. So, it's like the matter feels this dressed 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 I I think one advantage of the gravity from entropy approach is that it it leads to Einstein equation in the low energy limit. This 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 you know, there is a huge literature on modified gravity.

But the gravity from entropy it 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 interplay between matter and geometry. Respect to other, you know, approach using entropy, of course, the approach is fully statistical mechanics. So, it embrace the microscopic degree of freedom. While you know, you know, approaches that are based on horizon entropy they are typically thermodynamics in spirit. So, they

start with the area law >> Right. >> which is of course fundamental, but is 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 uh, approach to gravity. Sometimes they are coming from the perspective of theoretical physics. And they kind try to be sympathetic with, you know, people that do research in statistical mechanics or you do condensed matter, which is of course seen as, you know, very

applied. But actually, I'm coming from, you know, complexity theory, network theory. But I have a very solid statistical mechanics understanding. And from my perspective, actually, statistical mechanics and field theory are the same thing, right? It's just uh, changing an I with with a, you know, in the weak 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 past time as statistical physics action. And it's not that if you want to go towards statistical physics, you need to go

toward, you know, soft matter or [laughter] 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 do you see the latter as having an advantage here? >> So, um, it's very This is thermodynamics is is is been fundamental and, uh, you know, it arise from the study of heat engines. So, practically, the efficiency of heat engines, it it arise from very practical consideration uh,

during the industrial revolution. And of course, you know, there is this second law of thermodynamics, which is quite fundamental, but at the level of Clausius result, we don't have a any understanding of where it comes from. And this was the genius of Boltzmann, which described the H theorem, and the H theorem showed that H, which is is definition of entropy, really is an increasing function. And so, this is is shown in a particular setting of what is called the ideal gas. So, practically, you have a particle bouncing around with given velocity, and they have an

interaction that is hardcore interaction. So, the when they bounce to each other, they scatter around. But then they there is no interaction at all. And and this ideal gas is is our most profound understanding of the second principle of of thermodynamics, and and and this entropy is the number of microscopic uh compatible with a macroscopic configuration of this gas, right? That's the beauty and the universality of statistical mechanics. So, practically, you want to describe macroscopic uh law from a microscopic understanding of the degree of freedom. You don't need to know all the detail of of

your system. You need to capture the important information theoretic content of the microscopic degree of freedom. And this has been fundamental and and pervasive in all physics, I would say, and also behind. So, practically, our understanding of phase transition or phase of matter comes from statistical mechanics. Our understanding of, you know, classical and quantum phase transition, our in this of also, you know, the building block of quantum information and quantum computation comes from this rich interplay between statistical mechanics and information theory and without mentioning AI, of course. And so this this idea is that the

the idea is that information theory is such a pervasive concept that as is already a common language across many different uh disciplines. And with gravity from entropy, this this idea, this information idea, are reflected in an alternative action for for gravity and and which is the gravity from entropy action. And it it's it's interesting and and I think it's is is quite stimulating because, you know, in statistical mechanics, there are possibly two points of view, right? Or even three points of view. So one point of view is the one of emergence. So it's it's it's

the one that, of course, has been uh possibly the most fundamental uh approach to statistical mechanics is that from the microscopic degree of freedom, you explain what happens macroscopically. And this uh has been fundamental coming from, you know, pivotal paper by Phil Anderson, More Is Different. But then there is uh 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 by John Wheeler, It from Bit. 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 of geometry and matter field. Of course, uh it might be that, you know, there is a next theory that builds on gravity from entropy and find that it is an emergent theory, but for the moment, it is conceived as a fundamental theory of geometry. So, instead and here I come back to what we 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 particle interact, gravity is a reductionist theory in which the object is the geometry itself. So, in this sense, is is is is similar also to, you know, network approach, in which you want to study the interplay between geometry and and dynamics. >> What's the difference between entropy and information? >> Um so, entropy can be used to quantify information. >> So, in your theory, should it actually be gravity from information because information is the more fundamental quantity or 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 >> [laughter] >> So, that in my mind is that the metric, this this true metric, are kind of uh 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 or what? >> Information is is both. The 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 interplay between the the two kind of degree of freedom. The 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 I I want to

capture the microscopic degree of freedom of geometry and matter field and their interplay. So, I think in in Verlinde approach, there is no focus at all in the interplay between structure 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 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 is just a matter field, you know, I I use bosonic matter field. I use a more recently some some fluids for cosmology. The idea is that you can put there all matter field. 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 you now heavily living in the continuum? >> You know, I have my research agenda in in 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 basic and we got such impressive

results using information theory and you know, you know, with quantum computation, we might see even 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 you really need for many different fields starting from the brain to AI. You need need an information theory that capture the degree of freedom of geometry. So, um from this point of view, geometric quantum relative entropy could 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 Tao, 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 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 become physics practically immediately when I decided to go in the continuum. >> Ah. >> Because it's really strange but in in complex system, most of the problem are in the discrete. So, if you want to go to the continuum, you know, gravity is is is is the most likely way to go. And And this came, you know, after a trip that I made in in in the state. And, you know, and also this seminar at the ICTP. 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 This is the outcome. And I'm very happy because, you know, for me, I'm kind of new in in gravity and, you know, traditional theoretical physics. And it it it it is a a fantastic playground. It is fantastic progress that been made, you know, in gravity. Somehow, there are so many different direction that you need to be guided by your physical understanding of of of the problem. But for me, is a nice new

direction at this point of my career. And I am bracing it and enjoying it. >> So, what's the reception been like? >> Yeah, the the reception has been open. Yeah, so there are people, I think mostly in in cosmology, are quite interesting and they feel the need to work on modified gravity approach. You know, there is this Hubble tension, there are different problem, there of dark energy, somehow dark matter, so cosmologies are now becoming very welcoming for 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 holographic screen, so there is also some some clash there of our understanding. Of course, I think that, you know, the area law is fundamental, but I think it's a macroscopic field. So, and 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 the Lagrangian is is is defined over volume. So, if you integrate over a black hole, you know, until the Schwarzschild radius, you find a dimension reduction. And this

is essential because practically holography has been, you know, kind of explanation of the area law coming after Bekenstein. Bekenstein didn't use the holography. And is 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 in such a way that it scales with the area, the the of freedom must be only on the surface on 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 Ricci tensor or Ricci scalar, but depends also on the Riemann tensor, and so on on on the Weyl 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 and and so when you integrate something that is not homogeneous, you can get a a dimensionality reduction.

So, that that's the beauty of gravity from entropy. And so, for the moment, I I don't feel the need to use a holographic screen. And I think that, you know, there are many important insight coming from the area law, but if we are looking for a fundamental theory, we need to to go beyond the area law. >> So, is this an emergent theory of gravity then? >> So, gravity from entropy assume that the geometry exists. And so, it builds on Einstein insight that gravity is a theory of geometry, but it provides new understanding of the

interplay 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 is at the same level, right? So, you assume that the metric exists and capture the information content of this metric and of course, you know, Newtonian gravity comes from 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 tackled in gravity from entropy. What is emergent is instead this dark energy term that is dynamical and is is is new because it emerged from the theory and is is 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 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 entanglement. So, how this gravity from entropy uh action is related to entanglement and Araki entropy. And then of course, maybe if if one wants to go also going in the discrete. But what, you know, keeps me awake at night is the second quantization of this theory. >> What is second

quantization? And why is it so difficult or tricky in this case? >> Yeah, so I mean, this is the 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. There, you know, this is a word the community uh has explored different direction. And of course, there might be the need for define the graviton, right? Uh which mediate the gravitational interaction, but the quest is open, right? There uh many different approach. >> The graviton would be emergent in your view? >> Uh

probably not. >> It'd be fundamental? >> Yeah, you know, it it's also to be questioned if if the graviton really exists, right? But maybe there is something else, right? As this, you know, because the metric is is described by vierbein, is described by, you know, spin connections. So, there are different option. It's not that you need to start from the metric itself. You >> I just spoke with Philip Mannheim, who doesn't believe the graviton exists, actually. Did I hear you correctly that you use Weyl curvature as well? >> I I use the entire Riemann tensor.

So, this includes the all the component, also the one that vanish that the that do not contribute to the Ricci scalar, 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 state in in the empty space, the gravity from entropy action is non-zero. And so, also if the Ricci scalar is zero, right, the gravity from entropy action depends on all the component of the Riemann tensor, so is is non-zero and so you can integrate over over the volume. It is not

homogeneous all over and this is an important aspect. Another important aspect is actually that this theory provides also some correction at the Planck scale also in in flat geometry. >> Interesting. >> So, the theory treating geometry together with matter field uh finds some correction at the Planck scale already in flat in flat geometry. >> And what about what's going on at the singularity? Now, I know that's a question that's notoriously difficult and 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 Schwarzschild solution, the Schwarzschild solution is is a good approximate solution to the black hole because you know, is solution of the Einstein equation that are approximate equation of 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? >> Um one advice which is I think easy to follow is to read articles and to study. Uh another advice is to try to follow your what you like, you know, you're try to express your vision of of reality in what you do and 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. Uh, you

know. >> What's a piece of advice that you keep coming back to that someone gave to you? >> Um, so for instance, one advice is why don't you go in there? Continue, right? This is an advice coming from a random person that was at my seminar. We We didn't spoke. We didn't discuss, but it was very important for me. And another thing that I learned that possibly was not an advice, but you know, try to explore and to go in other community and and see what what they do. So if you are in a big

conference, you know, very interdisciplinary, I do pop up sometime in a session from another community and you will find answers to your question possibly. If you think about your problem quite abstractly. So this is is is 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 network physics and then I went to to listen at session about uh, gravity and information and it was inspiring and useful. So, try to to look at the nature with surprise and

maybe it thinks 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, then be sure to check out my Substack at kurtjaimungal.org. Some of the top perks are that every week you get brand new episodes ahead of time. You also get bonus written content exclusively for our members. That's c u r t j a i m u n g a l dot org. You can also just search my name

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