A mathematician named Janestra Bianone, who spent her career studying networks and topology, developed a theory proposing that gravity is not a force or the bending of spacetime, but rather a measure of the disagreement between two descriptions of the universe: the true geometry of spacetime and the geometry that matter implies. This 'gravity from entropy' framework, built on quantum relative entropy, produces Einstein's equations in the low-energy limit while generating a positive dark energy term and suggesting that black hole singularities may not exist. The theory represents a new approach to quantum gravity that treats geometry and matter as symmetrically related through their information content.
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No One Was Ready For What This Physicist Found About the Origin of Gravity
Added:In 2024, a mathematician stood at the front of a seminar room in Trieste giving a talk about networks, nodes, links, the mathematics of things connected to other things. She had never worked on gravity in her life. Someone in the audience she did not know raised a hand and asked her one short question and she answered it immediately and her answer was no. Absolutely not. Never.
Then she walked home, changed her mind, and wrote down a new starting point for gravity. One that hands Einstein's equations back to you when you ask for them. And then produces a term for dark energy that nobody put in and quietly suggests that the singularity at the center of a black hole may not be there at all. For 300 years, we have called gravity a force. For 100, we have called it the bending [music] of space and time. What if both of those are descriptions of something else underneath? Tonight, by the end, you will know exactly what she found. Get cozy and settle in. Subscribe if you have not, and stick around because before any of this can make sense, you have to unlearn what you were told entropy means. Let's begin.
[music] Part one, the force that does not fit.
There is something holding you down right now, and nobody knows what it is.
That sounds like an exaggeration, so let me be precise about it. We know exactly what gravity does. We can predict it to a level of accuracy that borders on the absurd. We can tell you where Jupiter will be in 400 years, and we will be right to within a few km. We can send a spacecraft on a 9-year journey to the outer solar system and have it arrive at a moving target the size of a small country on schedule after slingshoting off two planets on the way. We built a network of satellites whose clocks tick at a measurably different rate than clocks on the ground. Because gravity changes the flow of time, and we corrected for that difference so precisely that your phone can find you on a map to within a few meters. Nothing in the history of human thought has been tested more thoroughly than gravity. And nothing has passed more tests. And yet, if you ask a physicist what gravity actually is, at the bottom underneath the mathematics that works so beautifully, you will get a long pause.
You will probably get a description of what it does. You may get a metaphor about a bowling ball on a rubber sheet, which is a metaphor most physicists dislike because it explains gravity by quietly assuming gravity.
What you will not get is an answer. That gap between how well we can predict something and how little we understand it is the strangest situation in modern physics. It has lasted a 100red years.
And in the last 2 years, a mathematician who had never worked on gravity in her life, who came from a completely different field and had publicly said she would never go anywhere near this kind of problem, published a paper that proposes a different answer to that question. Not a small refinement, a different starting point for the entire thing. Before we get to what she found, you need to understand why the question was so stuck in the first place. And to do that, I want to walk you through the shape of the problem because the shape is the whole story. Modern physics recognizes four fundamental interactions. There is electromagnetism, which is responsible for light, for chemistry, for the fact that your hand does not pass through the table. There is the strong nuclear force which binds the particles inside an atomic nucleus together against their own furious electrical repulsion. There is the weak nuclear force which sounds like an afterthought but which is the reason stars can burn at all because it governs the reactions that turn one kind of particle into another. And there is gravity. Three of those four live comfortably inside a single mathematical framework called quantum field theory.
In that framework, a force is not really a pull or a push. It is an exchange. Two particles interact by trading a quantum of a field between them and the mathematics is organized as a sum over every way that trade could happen. It is a strange picture, but it is the most successful picture ever constructed.
Certain predictions from quantum field theory have been confirmed to something like 12 decimal places. That is the equivalent of measuring the distance from here to the moon and being wrong by less than the width of a human hair.
Gravity has never joined that framework.
Not for lack of trying. The attempt has been going on since the 1930s, and some of the finest minds in the history of the subject have spent their careers on it. The problem in plain terms is that when you try to treat gravity the way the other three are treated, the mathematics produces infinities. Now, infinities appear in the other theories, too. That is not by itself fatal.
Physicists developed an elaborate and well- tested set of techniques for absorbing those infinities into a handful of measured quantities so that after you have measured a small number of things once everything else becomes predictable. That procedure is called reormalization and it works for gravity.
It does not work. In 1986, two physicists named Mark Gorov and Austo Sanotei carried the calculation far enough to prove it properly. They showed that at what is called the two-loop level, the infinities in general relativity do not cancel and cannot be absorbed. Every time you push the calculation to a higher level of precision, you need new quantities that nobody has measured and nobody can measure. The theory does not stop working at ordinary energies, which is why everything from planetary orbits to gravitational wave detection works fine.
But as you push toward extreme energies, the theory quietly stops being able to predict anything. It runs out of road.
The scale where it runs out has a name.
It is called the plank scale and it is far outside we can reach. The relevant length is around 10us 35 m which is smaller compared to a proton than a proton is compared to you. The relevant energy is around 10^ the 19th giga electron volt which is roughly a quadrillion times more energy than the most powerful particle collider ever built can deliver. So we cannot go and look. We can only reason. That is the standard way the problem is described and it is accurate as far as it goes.
But there is another way to describe it that I find much more interesting and it is going to matter enormously for everything that follows. Consider what those four interactions actually are.
And notice that one of them is not like the others. Electromagnetism happens inside space and time. The strong force happens inside space and time. The weak force happens inside space and time. You can imagine a stage and on that stage particles interact according to those three sets of rules. Gravity is the stage. That is Einstein's insight and it is worth sitting with for a moment because it is easy to hear it without absorbing it. Einstein did not say that gravity is a force that acts between massive objects. He said there is no force. He said that mass and energy change the shape of space and time and that objects moving through that change shape are simply going as straight as they can. The Earth is not being pulled around the Sun. The Earth is going straight in a space that has been bent.
You're not being pulled into your chair.
Your chair is pushing you upward out of the straight path you would otherwise be falling along. So, gravity is not a fourth member of a family of three. It is a description of the geometry that the other three take place within. And when you list it alongside the other three, as we always do, you are quietly making a category error that we have all agreed to overlook because it is convenient. This is the thought that opens the door to everything else in this video. Because if gravity is a statement about geometry rather than an interaction inside geometry, then the failure to fit it into the framework built for interactions is not a technical difficulty. It is not a matter of not being clever enough yet. It might be that we have been trying to describe the wrong kind of thing with the wrong kind of tool and we have been doing it for 90 years. There is a way of putting this that I want to plant now because we will come back to it several times tonight. Physics has been built with enormous success on a reductionist approach. You take a system and you break it into parts and you ask what happens when two parts interact. That approach explained chemistry in terms of atoms, atoms in terms of nuclei and electrons and nuclei in terms of quarks.
It is one of the most productive ideas anyone has ever had. But gravity resists it. There is no natural way to ask what happens when two pieces of geometry interact because geometry is not made of pieces in that sense. Geometry is a relationship. It is a statement about how everything sits relative to everything else. And the question of how structure relates to what happens on that structure turns out to be a question that appears in a great many fields most of which have nothing to do with physics at all. Hold on to that because it is where our physicist comes from. She did not arrive at gravity through relativity or through particle physics or through string theory. She arrived at gravity through the mathematics of connection. She spent her career studying how the shape of a network determines what flows across it.
And she followed that question until it walked her straight into Einstein's equations and she was by her own account not at all happy about where it was leading her. She said no. For a while she said no quite firmly and then she changed her mind and what came out of that has cosmologists paying attention has produced a term for dark energy that nobody put in by hand and may have quietly removed the singularity from the center of a black hole. But before any of that can make sense we have to talk about the woman who said never.
Part two I will never go into the continuum.
Janestra Bianonei is a professor of applied mathematics at Queen Mary University of London and for most of her career she has been one of the people building the modern science of networks.
If that sounds like a small field, it is not. Network science is the mathematics of things connected to other things, nodes and links, points and the lines between them. It sounds almost trivially simple. And that simplicity is exactly why it turned out to be so powerful because an enormous number of systems in the world reduced to that description.
The internet is a network. A power grid is a network. A social group is a network. A protein interaction inside a cell is a network. A brain is a network in the most literal sense with something like 86 billion nodes and 100 trillion connections between them. What network scientists discovered over a few decades is that the shape of a network determines what happens on it in ways that are often unexpected and sometimes dramatic. Take epidemic spreading, which is the standard example. If connections in a population were spread evenly so that everyone had roughly the same number of contacts, then a disease would spread in a fairly predictable way and there would be a clean threshold below which it dies out. But real networks are not even. They have hubs, a small number of nodes with an enormous number of connections. And once you have hubs, that clean threshold can vanish entirely. A disease that should have burned out instead finds a hub and reaches everywhere. That is a result about structure. And it changed how people think about dynamics. The lesson generalizes far beyond disease. What flows across a network and how fast and whether it survives depends on the architecture of the connections in ways that you cannot deduce by looking at any individual piece. Bianone spent years on that interplay and then she pushed further from networks into something called simplicial complexes. Here is the idea without the jargon. A network only knows about pairs. A link connects exactly two nodes, but a great many real relationships are not pair-wise. Three people can be in a conversation together in a way that is genuinely different from three separate two-person conversations. Three proteins can form a complex that none of the pairs would form. So mathematicians extended the network idea. Instead of only points and lines, you allow triangles and tetrahedra and their higher dimensional relatives. Once you do that, your structure stops being a diagram and starts having a shape. It has geometry.
It has topology. It has holes and cavities and curvature in a discrete sense. This is where Bianone lived mathematically for a long time. And it is a discrete world. Everything is made of countable pieces. there is a smallest unit. Nothing is smooth. That was not just a professional habit. It was close to a belief. She has said that she was raised with the idea that maybe quantum gravity should be discreet. That nature at the bottom might be made of countable pieces rather than being smooth all the way down. That is not a fringe position.
Incidentally, several serious approaches to quantum gravity are built on exactly that assumption, and it may well turn out to be right. But for her, it was more than an intellectual option. It was the water she swam in. All her life, as she puts it, she worked in the discreet.
There was a problem, though, and it was a mathematical one. She was trying to build something ambitious. Her stated goal was a comprehensive theory of the interplay between structure and dynamics, one that used topology and geometry, and that viewed the whole thing through the lens of information theory. In other words, a general framework for how the shape of a system and the behavior on that system determine each other, written in the language of information. To do that you need well- definfined mathematical quantities and in the discrete setting some of the ones you need most are not well defined at all. Curvature is the clearest example in smooth geometry curvature is a precise thing with a precise definition worked out in the 1800s and refined ever since. In the discrete setting on a network or a simplicial complex there is no single agreed definition of curvature. There are several proposals. They are interesting proposals. They do not agree with each other. So if your theory requires curvature and you're working in the discrete, you're building on ground that has not settled. She was giving a seminar at the International Center for Theoretical Physics in Trieste in Italy presenting exactly this challenge.
Picture the room. This is not a keynote address in a packed auditorium. This is a working seminar at a research institute. The kind of talk where the audience is a few dozen specialists and half of them are there to argue. She's standing at the front laying out the problem. she has set for herself. She wants a theory of structure and dynamics built on topology and geometry and information. She explains where the mathematics is missing. She explains that in the discrete curvature does not have a settled definition and that this is holding her back. Someone in the audience raises a hand. She does not know who they are. They are not a collaborator, not a friend, not someone she has any prior connection with. And they ask her a very short question. If you are trying to do that, why do you not do it in the continuum? She answers immediately. She does not consider it, does not pause, does not qualify it. She says no. She says, and this is close to her own words, that she will never go into the continuum. And that is the end of the exchange. They do not discuss it.
They do not talk afterward. The seminar carries on. The day ends, and by any reasonable reading, nothing has happened at all except that she thought about it.
She went away and she reflected on it and something began to give because the more she considered it the more she recognized that the person was right about the mathematics. The continuum has what she needed. Gaus and Reman had built the machinery of smooth geometry in the 1800s and it is complete and it is exact and every quantity she needed had a definition that everyone agreed on. In the continuum she could stop fighting with the tools and start thinking about the actual idea. and there was something else. She realized that the continuum version of the theory she was trying to build had a great deal to do with gravity. That should not be surprising once you see it. And it is worth spelling out because it is the hinge of this whole story. What is general relativity? It is a theory about the relationship between the shape of a thing and what happens on that thing.
Matter arranges itself in space. Space responds by curving. The curving determines how matter moves. that is structure and dynamics in the continuum written down more precisely than in any other field of science. So she was not switching subjects. She was following one question into a room she had never intended to enter and discovering that the people already in that room had been working on her problem for a century without either side realizing it. She has described the moment of decision with a certain rhyess. Why not face the really challenging problem? She asked herself. Why not gravity? Why not quantum gravity? And then she added something that I think tells you a great deal about how she sees the world. She said a little controversially that in her view, understanding the brain is a harder problem than understanding quantum gravity. Sit with that for a second. The most notoriously difficult unsolved problem in theoretical physics, the one that has consumed generations, and she is describing it as the more tractable of the two things on her desk.
That is the person we are dealing with.
Not an outsider who wandered in by accident and not a crank with a theory of everything. A serious mathematician with a deep background in statistical mechanics who looked at quantum gravity and thought honestly that this might be the easier one. I want to mark this moment because it is the smallest and most human part of tonight's story. And it is also the part that almost did not happen. A theory that is now being extended by research groups on the other side of the world that produces a term for dark energy out of nothing that may remove the singularity from the center of a black hole exists because a person whose name was never recorded asked a one-s sentence question at a seminar and because the person they asked it to said no and then changed her mind on the walk home. She was asked later what advice she keeps coming back to and this is the one she named. advice from a random person at her seminar. They did not talk. They did not discuss it. And it was, in her words, very important for her. So, she went into the continuum.
She took the machinery of smooth geometry and the information theory she had spent her career developing and the statistical mechanics she'd been trained in, and she wrote down an action for gravity that nobody had written down before. To understand what she wrote, you need to understand entropy, not the version you have heard, the one about disorder and decay and the universe running down. That version is a bad translation. You need the real one, and it is both simpler and stranger than the popular story. And once you have it, everything else in tonight's journey will click into place.
Part three, what entropy actually is.
Entropy has the worst public relations of any concept in physics. You've almost certainly encountered it as disorder.
Entropy always increases, so things fall apart. So your room gets messy and your coffee gets cold. And eventually the universe winds down into a cold uniform nothing. It gets used as a metaphor for decay, for the inevitability of decline, for the sad arithmetic of things not lasting. There are novels built on it.
There are song lyrics. Almost none of that is what the word means. And the gap between the popular version and the actual version is where tonight's theory lives. So let us build it properly from the beginning because if you understand this one idea correctly then the rest of the evening becomes clear. Entropy did not begin as a philosophical concept. It began with steam engines. In the early 1800s Europe was in the middle of the industrial revolution and the central technology of that revolution was the heat engine. You burn something, you get heat, you turn the heat into motion.
Every factory and every locomotive ran on that trick. And a very practical question hung over the whole enterprise.
How good can a heat engine get? If you put in a certain amount of heat, how much motion can you extract at best?
In 1824, a young French engineer named Sadi Caro worked out the answer. And it was not the answer anyone wanted. There is a hard ceiling. No engine, no matter how cleverly built, no matter how perfect the materials, can convert all the heat into work. Some fraction is always lost and the fraction is set by the temperatures involved and by nothing else. It is not an engineering problem.
It is a law. Out of that work came the second law of thermodynamics formalized by Rudolphius who gave the quantity its name. Entropy in that original formulation is a bookkeeping device. It tracks the heat that becomes unavailable. And the second law says that in any closed system this quantity never decreases. it goes up or at best it stays flat and it never runs backward. Now, this is a genuinely enormous result. The second law is one of the sturdiest statements in all of science. It is the reason a broken cup never reassembles. It is the reason you cannot unscramble an egg. It is arguably the reason there is a difference between the past and the future at all, since nearly every other fundamental law of physics works equally well in either direction of time. But notice what Clausius did not provide. He gave a law.
He did not give a reason. He could tell you that the quantity always increases.
He could not tell you why. It was a rule the universe seemed to obey, discovered by people trying to build better engines with no explanation underneath it. The explanation came from Ludvig Boltzman.
And this is the part worth slowing down for. Boltzman's move was to stop looking at heat and start counting. Imagine a box of gas. just a box with a great many particles bouncing around inside it. In the simplest version, the one physicists call an ideal gas, the particles do not attract or repel each other at all. They have no interaction except that when two of them meet, they bounce. That is the entire model. Particles, velocities, collisions. Now, from the outside, you can measure a few things about that box.
You can measure its temperature. You can measure its pressure. You can measure its volume. That is your description of the box. the macroscopic description and it consists of about three numbers but inside the box there are an enormous number of particles and each one has a position and a velocity that is the microscopic description and it consists of something like 10 to the 23rd numbers for a box of ordinary air that is a one followed by 23 zeros there are more particles in a lungful of air than there are grains of sand on every beach on Earth by a very wide margin here is Boltzman's question given the three numbers numbers you measured from outside, how many different arrangements of the inside would produce exactly those three numbers? Not one, not a few, an almost unwritable quantity of them.
You could swap any two particles and nothing measurable changes. You could nudge one particle's velocity slightly and compensate with another and nothing measurable changes. The number of microscopic arrangements consistent with a single macroscopic description is so large that writing it in ordinary notation is not possible. Boltzman's definition of entropy is the logarithm of that number. That is it. That is the whole thing. Entropy is a count of how many ways the small scale details could be arranged while the large scale description stays the same. It is not a substance. It is not a force. It is not a tendency toward decay. It is an inventory of possibilities. And once you have that definition, the second law stops being mysterious and becomes almost obvious. Ask yourself why gas spreads out to fill a room instead of gathering into one corner. In the popular telling, there is some force of disorder pushing it apart. There is not.
Nothing pushes it. The reason is simply that there are overwhelmingly more arrangements in which the gas is spread out than arrangements in which it is bunched in a corner. The particles are moving randomly. They are not trying to spread out. But if you shuffle a system that is moving randomly, it will end up in a common configuration rather than a rare one. Because common configurations are common. That is all. The second law is not a law of decay. It is arithmetic.
It is the statement that if you keep shuffling, you will find yourself in one of the many rather than one of the few.
Boltzman proved a version of this with what is called the H theorem, showing that his quantity really does increase for the ideal gas. It was the first time anyone had derived a macroscopic law from microscopic behavior, and it was so unpopular in his lifetime that it contributed to a long and bitter fight over whether atoms even existed.
Boltzman died believing he had lost that argument. He had not. Now, I want to draw out the point that matters most for tonight, because it is easy to slide past. Entropy counts what you do not know. Notice how the definition was constructed. You measured three things from outside. Everything you did not measure all 10 to the 23rd numbers of it is uncertainty. And entropy is the size of that uncertainty. If you knew every position and velocity exactly, the count would collapse to one and the logarithm of one is zero. Perfect knowledge means zero entropy. So entropy is not a property of the gas alone. It is a property of the relationship between the gas and a description of the gas. It measures the gap between what is there and what you have specified. It is in the most direct sense a measure of information. This is why Benone says something that sounds almost dismissive about the second law. People are usually quite impressed by the second law of thermodynamics. She notes and things like that. But from her perspective, it is simply a measure that quantifies what you know about a system in terms of information theory. That is not deflation. That is precision. Entropy is not about decay. It is about description. And once you see it that way, a door opens. Because if entropy measures a relationship between a system and a description of it, then you can start asking what happens when you have two descriptions.
There is one more distinction to draw before we move on. And it is the one that Bianone uses to separate her approach from everything that came before it in this area. It is the difference between thermodynamics and statistical mechanics. Thermodynamics is Carno and Claussius. It is the macroscopic view. It works with temperature, pressure, heat, and entropy as bulk quantities. And it produces laws that are correct and useful and that do not explain themselves. Thermodynamics can tell you that a systems entropy will increase. It cannot tell you what entropy is made of. Statistical mechanics is Boltzman. It is the microscopic view. It starts from the small scale degrees of freedom and derives the macroscopic behavior from counting. And this is a much deeper kind of theory because it explains rather than describes. The difference matters enormously. Nearly everything we understand about phases of matter comes from statistical mechanics. Our understanding of phase transitions, classical and quantum, comes from statistical mechanics. A great deal of the foundation of quantum information and quantum computation comes from the interplay between statistical mechanics and information theory. And as Bianone points out, so does most of modern machine learning, though that is a story for another night. She makes one further remark here that will matter later, and I want to plant it now. From her perspective, statistical mechanics and field theory are the same thing. The mathematics that describes a box of particles and the mathematics that describes a quantum field are related by a single formal move, a substitution of one symbol for another that mathematicians call a wick rotation.
Statistical mechanics is not a lesser, more applied cousin of fundamental physics. It is fundamental physics wearing different clothing. So keep the two versions of entropy in your head.
Thermodynamics, a law with no explanation. Statistical mechanics, an explanation built out of counting that tells you entropy is the size of your ignorance. That is one kind of entropy.
There is another kind and it is the one that this whole theory is actually built from. It does not measure what you do not know. It measures the distance between two different things you might believe.
Part four, the other entropy.
Boltzman's entropy asks a single question about a single system. How many ways could this be arranged given what I know about it? Relative entropy asks a different question, and it needs two things instead of one. It asks, given that I have one description of the world, how much of what I would need is already contained in the other? That is a comparison, not a count. And it turns out to be one of the most useful quantities in mathematics, though it goes by a variety of names in a variety of fields, and most people who use it in one field have no idea it is being used in the others. Let me give you the version that will make it stick. You walk around carrying a model of the world. Not consciously, mostly. You have expectations about how heavy a glass will be when you pick it up, how a stare will feel underfoot, how a familiar voice will sound. You're constantly predicting and you almost never notice because you are almost always right.
Then something happens and the question relative entropy answers is how surprised should you be. If your model was already excellent, if the thing that happened is what you expected, then the surprise is near zero and there is nothing to learn. You already had the information. But if something happens that your model assigned almost no chance to, the surprise is large and there is a great deal to learn and your model needs to change. Relative entropy is a number that quantifies exactly that. It measures how much information is gained when you replace one description with another or turned around how much of the second description is already codified in the first. Anyone who has spent time with theories of how brains work will recognize the shape of this immediately because a whole framework in neuroscience is built on the idea that living systems are constantly minimizing precisely this quantity. A brain in that account is a machine for reducing surprise. It builds a model. It checks the model against the world. It computes the mismatch and it either changes the model or changes the world until the mismatch shrinks. Hold on to that image because it is almost exactly what is about to happen to spaceime. In quantum mechanics, the same idea exists in a more refined form. States in quantum mechanics are described by objects that hold not just probabilities but phases and correlations. And the quantum version of relative entropy compares two such states. It asks how much of the information in one quantum state is codified in the other. It is a standard and heavily used tool in quantum information theory and it has a set of mathematical properties that make it extremely well behaved. Now why does Bianone build a theory of gravity out of this rather than out of ordinary entropy? Because ordinary entropy is a property of one thing and gravity in her reading is not about one thing. It is about the relationship between two things. It is about matter and geometry and specifically about the fact that neither of them make sense without the other. A comparison quantity is the natural mathematical shape for a relationship. Before we can go further, there is a piece of mathematics I need to hand you. It sounds technical. It takes about a minute and it is the reason this theory is more than an elegant metaphor. So it is worth the minute. These entropies in their quantum form are written as the trace of a logarithm. Trace is a simple operation.
You take a square array of numbers and you add up the entries down the diagonal. logarithm you already know and there is a mathematical identity one that has been known for a long time which says that the trace of a logarithm equals the logarithm of a determinant.
The determinant is another quantity you can extract from a square array of numbers and it has a geometric meaning.
It tells you how much the array stretches or shrinks a volume. That identity is a bridge and it carries a great deal of weight because on one side of it you have a relative entropy, a comparison between two descriptions, an information theoretic quantity about surprise and codification and how much one thing tells you about another. And on the other side, you have something that behaves like a Boltzman entropy, a logarithm of a quantity related to volume and counting, the original kind, the one that tallies how many microscopic arrangements are compatible with a macroscopic state. So the same expression can be read both ways. Read it as a comparison and it tells you about the tension between two descriptions of the universe. Read it as a count and it tells you the number of microscopic degrees of freedom in the interplay between matter and geometry.
That is not a coincidence and it is not a pun. It is why the theory can make contact with thermodynamics later and why the second law will eventually fall out of it rather than having to be imposed. Two languages, one object.
There is one more thing worth understanding about how an action is built because we are almost at the moment when the actual theory arrives and I want you to have the right picture in your head. In physics, an action is not a synonym for an event. It is a specific technical object and it is arguably the single most powerful idea in theoretical physics. Here is what it does. Suppose you want to know how a ball moves when you throw it. The way you probably learned is to apply forces at each instant and follow the trajectory forward step by step. But there is another way and it is the way modern physics actually works. You consider every possible path the ball could take. For each path, you compute a single number by adding up a certain quantity along the whole path. That number is the action. And then you find the path for which the action is at an extreme value, usually a minimum. That path is the one nature takes. It is a wildly different way of thinking about physical law. Instead of asking what happens next, you ask which whole history is optimal. And it is not a curiosity. Essentially, all of fundamental physics is now written this way. Electromagnetism has an action. The standard model of particle physics has an action. General relativity has an action called the Einstein Hilbert action written down in 1915. Which means that if you want to propose a new theory of gravity, you do not argue about forces. You write down a different action and you see what falls out of it.
That is the whole game. Everything in a physical theory, every equation of motion, every conserved quantity, every prediction is contained in the action.
Choose the action and you have chosen the universe. And it is worth noticing what the standard action for gravity looks like because its shape is what Bianca is objecting to. The Einstein Hilbert action has a term for geometry.
It is built from the curvature of spaceime and it is elegant and short and it produces Einstein's field equations.
But the universe contains matter as well as geometry and matter has to be included. So you add a second term, a matter action, and you attach it to the geometry using a procedure called minimal coupling, which is exactly what it sounds like. The simplest possible way of joining the two with no extra structure assumed. It works. It has worked for over a century. But look at the shape of it. Geometry appears one way. Matter appears another way. They are two different kinds of objects stapled together with the least assumptive joint available. And that a symmetry sits oddly next to the most famous sentence ever written about Einstein's equation. John Wheeler, the physicist who also gave us the term black hole, summarized general relativity like this. Matter tells how to curve and spacetime tells matter how to move. That sentence describes a conversation. It describes two parties in a reciprocal relationship, each shaping the other. It is quoted constantly in every documentary and every textbook because it captures the theory perfectly. But here is what Bianone noticed and it is the kind of observation that is obvious only after someone makes it that reciprocity is a property of the equations. It is not present in the action. The action, the thing physicists regard as the deepest expression of a theory, the place where the principles live, does not contain the conversation. It contains geometry and separately matter joined as simply as possible. The beautiful symmetry that Wheeler described emerges afterward when you turn the crank. It is not in the premise. So the question becomes, what would it look like to build the conversation into the action itself?
What if instead of geometry plus matter, you wrote down a single quantity that measures the relationship between them?
What if the fundamental object were not a description of two things, but a measurement of how much they agree? That is the theory. And to write it, you need matter and geometry to be the same kind of object so that you can compare them.
So, Benone made matter into a geometry.
Part five, two maps of the same room. To compare two things mathematically, they have to be the same kind of thing. You cannot ask how far apart a color is from a duration. So if the plan is to write an action that measures the relationship between matter and geometry, the first job is to make matter into a geometry.
The object that describes geometry and relativity is called the metric. It is worth being clear about what it is because the word sounds more forbidding than the idea. A metric is the rule for measuring. Give it two nearby points and it tells you the distance between them.
Give it a path and it tells you the length. Give it a world line and it tells you how much time passes for whatever is traveling along it. That is all a metric does and it is everything.
Because once you know how to measure distances and durations at every point, you know the entire shape of the space.
Curvature is not extra information layered on top. Curvature is what you find when you compare the measuring rules at neighboring points. And notice they do not quite line up. In general relativity, the metric is the gravitational field. There is no separate thing called gravity that acts on top of geometry. The geometry is the gravity. Bianone's theory has two metrics. The first is the true metric of spaceime. This is the honest one, the real geometry, the object that defines the curvature of the universe. And I want to be very clear about something because it is the first objection people raise. And it is a fair objection. She is not assuming a flat background and then adding curvature to it. There is no hidden assumption of an underlying flat spacetime. She is explicit about this.
The true metric is simply the true metric whatever it happens to be defining the full curvature of the world. The second metric is where the invention happens. It is called the metric induced by the matter fields and the curvature. And it is in effect the geometry that matter implies. Here is the intuition and it comes from Gaus.
Carl Friedrich Gaus in the early 1800s was working out how to describe curved surfaces and he introduced a construction that is now taught in every differential geometry course. Suppose you have a surface. Now define a function on that surface, a number attached to every point. You can picture that function as height. At each point you rise by however much the function says. What you have drawn is a new surface sitting above the original. And that new surface has its own geometry, its own rule for measuring distances.
Gaus showed how to compute it. And the result is called the first fundamental form. It is a metric induced by the function that is the seed of the idea. A field defined on a space imprints a geometry onto that space. Bianone takes this and extends it. Instead of a single scalar function, the matter content in her theory is described at each point by a richer collection of objects drawn from differential geometry. A scalar, a one form, and a two form. If those names are unfamiliar, the intuition is that they are the natural mathematical objects for describing quantities that have no direction, quantities that have a direction, and quantities that have an orientation in a plane. It is the standard vocabulary for fields in modern physics. And from that collection, following Gaus's logic, but generalized, you can build a metric. So now you have two metrics, two rules for measuring the same universe. I want you to hold them side by side for a moment. Imagine you have two maps of the same room drawn by two different people who are not allowed to speak to each other. The first map is the true one. Every wall in its actual place, every distance exact, every corner where it really is. This is the geometry as it is. The second map was drawn by the furniture. Not literally, but that is the picture. It was drawn from what is in the room and where it sits. It says, "Given this table and this chair and this bookshelf against this wall, here is the shape the room ought to be. It is the geometry the contents imply, the shape matter is voting for. Now lay one over the other.
They almost match. Almost. In most places, the lines fall on top of each other, and you would need a magnifying glass to see any difference. But not everywhere. There are places where the two maps disagree, where the true geometry is not quite what the matter implies, or the matter is not quite arranged the way the geometry expects.
And that disagreement is measurable. You can put a number on it. The number is a relative entropy. How much of one description is contained in the other, how surprised the first map should be by the second. Now let the two maps be alive. Let them pull toward each other.
The matter is telling the geometry what shape it ought to be. The geometry is telling the matter where it can go.
Neither of them wins. They strain toward agreement continuously everywhere and they never quite arrive. That straining is gravity. That is the theory. That is gravity from entropy. The action the fundamental object from which everything else follows is a geometric quantum relative entropy between the true metric of spaceime and the metric induced by matter and curvature. The lrangeian is a measure of how much two descriptions of the universe disagree with each other and the universe evolves so as to extremise that disagreement. Let me draw out why this is a genuinely different move rather than a rewarding. Go back to Wheeler's sentence. Matter tells spaceime how to curve and spacetime tells matter how to move. In standard general relativity, as we said that reciprocity is a result. It emerges from the equations after the fact. The action itself contains geometry and matter as two separate kinds of thing joined minimally. In gravity from entropy, the reciprocity is the premise. The action is nothing but the reciprocity. It is a statement about the relationship and geometry and matter enter it symmetrically because both of them have been made into metrics and the action compares metric to metric. Bianone puts it directly the theory leverages the principle of the interplay between matter and geometry already at the level of the action using an information theoretic lrangian.
Wheeler's sentence stops being a summary of the output and becomes the input.
There is a second ingredient that matters and that is easy to skip past.
So let us not skip it. An action is not only a lrangian. It is a lrangian integrated over spaceime with a certain waiting. And that waiting is called the measure. In many theories the measure is uninteresting bookkeeping. Bianone is explicit that in this theory it is not.
The measure plays an important role in its own right. That will matter enormously when we get to black holes and it will matter in a way I do not think you will see coming. Keep it in your pocket. Now, a fair question at this point and one that gets asked immediately by anyone hearing this for the first time is this circular. If you set out with the intention of writing down something that captures the idea that matter tells spaceime how to curve and then you write down something that captures the idea that matter tells spaceime how to curve and then Einstein's equations come out. Have you actually learned anything or have you put the answer in at the start and then found it again? This is the right question to ask and it deserves a real answer. The answer has three parts and we will spend the next part of tonight's journey on them because they are what separates a rewarding from a theory. The first is that the equations that come out are not Einstein's equations. They are modified equations that reduce to Einstein's under specific conditions and differ otherwise which means they can in principle be tested. The second is that the action produces things nobody put in, including a term for dark energy and arguably an explanation for the entropy of a black hole. And the third is that the whole structure is built in the language of quantum information from the ground up, which is precisely the language people have been trying to translate gravity into for 50 years. But the shortest version of the answer is this. In physics, how you say something determines what you can say next. And this is a new way of saying it. So let us see what falls out. Part six, the equation that gives Einstein back. When you have an action, the next step is mechanical. You extremise it. You ask which configuration of the universe makes that quantity stationary and out come the equations of motion. So Bianone extremis the entropic action and out came a set of modified gravity field equations. Two things about those equations matter more than anything else. And I want to take them in order because the order is what makes the second one interesting. The first is that in the low energy limit they reduce to Einstein's field equations. Let me explain why that sentence is doing more work than it appears to. General relativity is not a theory that might be right. It is a theory that has been confirmed to remarkable precision in every regime we can reach. It predicted the bending of starlight around the sun confirmed in 1919. It predicted the procession of Mercury's orbit, which had been an unexplained anomaly for decades.
It predicted that time runs slower in a stronger gravitational field, confirmed with atomic clocks carried on aircraft and later with clocks separated by a difference in height of about 30 cm. It predicted gravitational waves which were detected in 2015 after a century of waiting from two black holes merging over a billion lighty years away. Any new theory of gravity that does not reproduce all of that is dead on arrival. That is not a high bar in the sense of being difficult to want. It is a high bar in the sense of being difficult to clear. And Bianone points out something about her own field that outsiders rarely hear. Reducing correctly to Einstein's equations in the appropriate limit is not automatic for approaches to quantum gravity. For several serious programs, it is difficult to establish and in some cases it remains genuinely open. When you build a theory from radically different starting principles, getting the familiar physics back at the end is often the hardest part rather than the easiest. So the entropic action clears the bar. Everything general relativity gets right, this framework gets right in the regime where general relativity applies. Nothing you know about orbits or lensing or gravitational waves or the timing of satellite clocks is threatened. The second thing about those equations is that outside that limit they are different. They are modified gravity equations in the high energy regime where curvature is extreme or where the coupling is strong. They make different predictions than Einstein's do. And that is the entire point because a theory that makes exactly the same predictions as the old theory in every circumstance is not a theory. It is a translation. This one departs which means it can be checked. Now at this point an entirely reasonable objection arrives and it is one Bianone has been asked directly. There is an enormous literature on modified gravity.
Physicists have been proposing modifications to Einstein's equations for as long as there have been Einstein's equations. Hundreds of them exist thousands of papers. So what makes this one different from any other entry in a very crowded field? Her answer is about motivation and it is worth understanding because it goes to the heart of how theoretical physics actually works. Most modified gravity theories are built by adding terms. You take the Einstein Hilbert action and you add something to it. Maybe you add a term involving the square of the curvature. Maybe you add a term involving the curvature times some new field. There are systematic ways to organize these additions. And the standard approach is to write down every term allowed by the symmetries of the problem. order them by how important they should be at low energies and keep the first few. That is a legitimate way to proceed and it has produced useful physics. But notice what it is not. It is not an explanation. When you add the next term in an expansion, you're not saying anything about why the universe should contain that term. You're exploring a space of possibilities and checking which ones survive contact with the data. As Bianone puts it, it is just the next term in the series. Gravity from entropy is not built that way. The action was not chosen because it was the next available option. It was chosen because it means something. It is the information content of the interplay between matter and geometry. There is a reason the action takes the form it takes and the reason is prior to the mathematics. That distinction is worth more than it sounds. Physics has a long history of theories that were correct because they were principled rather than because they were fitted. Einstein did not arrive at general relativity by adding terms until the numbers worked.
He arrived at it by insisting on a principle that free fall and being at rest should be locally indistinguishable and following it until the mathematics forced his hand. The equations came from the principle, not the other way around.
There is a second thing that separates this framework from most modified gravity and it is the symmetry we talked about last part. In almost every modification, geometry gets the interesting treatment and matter remains an afterthought. Coupled minimally entering through a term that is essentially unchanged from the standard version. Here matter and geometry enter as the same kind of object. They are two metrics compared through their mutual information content. That is not a cosmetic difference. It changes what the theory is capable of expressing. And the third difference is the language. The action is written as a quantum relative entropy. Bianone treats the metric as a quantum operator and writes a relative entropy between such operators. The framework was built in the vocabulary of quantum information from the ground up, not translated into it afterward. That matters because the central difficulty of quantum gravity has always been that general relativity and quantum theory speak languages with no obvious dictionary between them. Starting in one of the two languages is a strategically different move than starting in neither.
I want to give you one historical parallel here because it makes the point better than any argument I could construct. When Einstein was working toward general relativity, he was not the only person modifying Newton.
Newtonian gravity had a known problem, the orbit of Mercury, whose closest approach to the sun drifts around by a small amount that Newton's law could not account for.
The size of the discrepancy was tiny, about 43 seconds of arc per century, which is roughly the angle a coin would make at a distance of several km. And there were plenty of proposed fixes.
Some people suggested an unseen planet closer to the sun than Mercury, and gave it a name, Vulcan, and searched for it for decades. Others suggested adjusting the exponent in Newton's law very slightly, so that gravity fell off not quite as the square of the distance, but as something a hair different. That adjustment worked. You could tune it to match Mercury exactly and it was worthless because it explained nothing.
It was a number chosen to fit a number.
Einstein's theory got Mercury's orbit right without a single adjustable parameter because the answer fell out of a principle about the equivalence of freef fall and rest. That is the difference between fitting and explaining. And it is why physicists care so much about where an action comes from rather than only about what it predicts. So when Bianone insists that her action has a reason behind it, she is making the claim that matters most for whether a modification of gravity is worth anyone's time. Now I want to be careful and honest here because this is a young theory and I am not going to oversell it. The framework is not yet in second quantization. That phrase will get its own part later tonight. But the short version is that this is currently a classical field theory written in quantum information language rather than a fully quantum theory of gravity. It is a step toward one. It is not one yet.
Bianone says so plainly, and the fact that she says so plainly is a large part of why the work is being taken seriously rather than dismissed. It has also not been confirmed by any observation. There is no experiment that currently distinguishes gravity from entropy from general relativity. What there is instead is a set of predictions that could in principle be checked and a set of theoretical results that came out unexpectedly. And it is those unexpected results that have made cosmologists start paying attention. Because here is the thing about a well- motivated action. If you write down something for a good reason and then things start falling out of it that you did not put in, that is when a theory starts to become interesting and something did fall out, something nobody asked for.
When Biancone worked through the mathematics, a quantity appeared in the equations that she had not introduced.
It entered the way a piece of bookkeeping enters as a device for enforcing a constraint. The kind of thing that usually gets divided out at the end and forgotten. It did not get forgotten. It is now arguably the most physically consequential object in the entire theory. It has been proposed as a candidate for dark matter. It is responsible for the theory's dark energy term and it may be the reason the center of a black hole is not what we have been told it is. She calls it the G field.
And to understand what it is, we need to take a step back and put together everything we have built so far.
Part seven, the ghost in the equations.
Let us step back for a moment and put the pieces on the table together because we have covered a lot of ground and the next stretch of the journey depends on having all of it in view. We started with a problem. Gravity does not fit into the framework that describes the other three forces. And the reason may be that gravity is not that kind of thing. Gravity is geometry and geometry is the stage the other forces perform on. We met a network scientist who spent her career studying how the shape of a system determines what happens on it.
Who was asked a single question by a stranger at a seminar in Trieste who said she would never go into the continuum and who then did. We rebuilt entropy from the ground up. Not decay, not disorder, but a count of how many microscopic arrangements are compatible with what you know. a measure of the gap between a system and a description of it. We met the second kind of entropy, relative entropy, which compares two descriptions and asks how much of one is contained in the other. And we found the mathematical hinge, the identity between the trace of a logarithm and the logarithm of a determinant, which lets the same expression be read either as a comparison or as a count. Then we built the theory. two metrics, the true geometry of spacetime and the geometry that matter implies, constructed by extending an idea of Gaus. Two maps of the same room, one drawn honestly and one drawn by the furniture laid over each other almost matching, straining toward agreement and never quite arriving. The action is the measure of their disagreement and gravity is what that straining does. And we found that extremisizing that action gives back Einstein's equations in the low energy limit and gives something different outside it. That is where we are. Now here is where it gets strange. When you actually carry out the mathematics, a new quantity appears. Biano calls it the G field and nobody put it there. It arrives as what mathematicians call a lrangee multiplier. If you have not met one, the idea is simple enough. Suppose you want to find the highest point on a hillside, but you are restricted to walking along a particular fence line.
You cannot just find the summit because the summit may not be on the fence. So you introduce an extra variable that enforces the constraint, solve the enlarged problem, and the extra variable does its job and drops out. It is a technique, not a thing. It is scaffolding most of the time. But there is a long and slightly uncanny tradition in statistical mechanics of lrangege multipliers turning out to be real. And the standard example is one you have used every day of your life without thinking about it. Temperature is a lrangee multiplier. That sounds like a provocation, but it is a straightforward technical fact. If you set up the statistical mechanics of a system by asking which distribution of microscopic states maximizes entropy while holding the average energy fixed, you need a multiplier to enforce that constraint.
That multiplier is what we call inverse temperature. It enters the mathematics as bookkeeping purely as a device for holding energy in place. And yet temperature is not bookkeeping.
Temperature is the thing you feel when you put your hand near a fire. It is the thing that determines whether water is ice or steam. It is one of the most physically real quantities in existence.
And it arrived in the theory as an accounting device. So when a new lrangege multiplier shows up in a statistical mechanical treatment of gravity, the responsible thing to do is not to divide it out. The responsible thing is to ask what it means and that is exactly Benone's position. Lrangege multipliers in statistical mechanics can have a physical meaning. So we want to give a physical meaning to this one.
When you do that, something clarifying happens to the mathematics. If you take the entropic action, which in its raw form looks like an unfamiliar relative entropy, and rewrite it in terms of the G field, it separates into pieces you recognize. One piece looks very much like the Einstein Hilbert action, the standard action for gravity. It is built from the curvature of spaceime in a form Bangone describes as a kind of dressed reach scalar. The reachi tensor contracted with a modified metric together with the full reman tensor contracted with that same modified metric. Another piece looks like a matter action built from the geometry induced by matter and curvature again contracted with the modified metric. So the entropic action once you let the G field into the description becomes much closer to the familiar action for gravity. It is not the same but it is recognizable and the differences are specific and few and the most important difference is that word dressed. Here is what it means and it is one of the ideas I most want you to take away tonight.
What matter interacts with is not the bare metric of spaceime. It is the metric dressed by the G field. Think about the two maps again. Everything we said before still holds, but now there is something between them. The true geometry is there. The geometry that matter implies is there. And matter does not couple directly to the true geometry. It couples to the true geometry wearing something over it. A layer, a modification, a field that sits in between. The geometry that is and the geometry that matter feels are not the same object. That is a considerable claim. In general relativity, there is one metric and everything couples to it.
That universality is one of the deepest features of the theory. The reason all objects fall the same way regardless of what they are made of. A fact tested to extraordinary precision. Biancone's framework does not break that in the regime where it has been tested because the whole structure reduces to Einstein's equations there. But at the level of principle, it introduces a distinction that did not exist before.
There is the geometry and there is what matter sees. And the G field, this thing sitting between them is not fixed. It is dynamical. It has its own behavior, its own evolution, its own response to circumstances. It is not a constant modification applied uniformly to the universe. It is something that can change from place to place and from time to time. There is a broader lesson in this that is worth naming because it recurs throughout the history of physics and it is one of the reasons theorists take their own mathematics seriously.
Over and over quantities that entered the equations as conveniences have turned out to be things. The electromagnetic potential was introduced as a calculational shortcut, a way of avoiding having to track fields directly and was regarded for a long time as having no physical reality because you can shift it around without changing anything measurable. Then in 1959, Yakira Haronoff and David Bow pointed out that in quantum mechanics, the potential produces an observable effect on electrons even in regions where the field itself is zero. And the experiment was performed and the shortcut turned out to be real. Antimatter arrived as an unwanted negative solution in an equation that Paul Drack was reluctant to throw away. And four years later, a posetron was photographed in a cloud chamber. Nutrinos were invented on paper as a desperate accounting fix to save conservation of energy in radioactive decay. And their author apologized in writing for postulating a particle that could never be detected and 25 years later it was detected. The pattern is consistent enough that it has become a working instinct. If a well-mivated theory produces an object you did not ask for and that object refuses to cancel out and it starts doing physical work in the equations, the historically correct response is to take it seriously rather than to explain it away. The G field is doing physical work. That is the case for treating it as more than a device. So what is it? Biancone's characterization is that the G field encodes the interplay between structure and dynamics, which is a way of saying that it is the same object she spent her entire career studying in networks, having found its way into gravity through the continuum. The relationship between a shape and what happens on that shape has become a field in its own right. In the discussion around the theory, it has been suggested that the G field might be a candidate for dark matter. That should be handled carefully and I am flagging it as speculative because it is at the exploratory end of the research and nobody is claiming it is established but it is not an idle suggestion either. Dark matter is at bottom extra gravitational influence that does not correspond to anything we can see. A dynamical field that dresses the metric and changes how matter couples to geometry is structurally the right kind of thing to produce extra gravitational influence without any luminous source. That is one open thread. There is another and it is much further along and it is the one that made cosmologists sit up. Because the G field does not only dress the metric, it also produces something else in the equations. A term that has been the single most stubborn number in physics for a quarter of a century that standard theory misses by more orders of magnitude than any other prediction ever made. And that determines what happens to every galaxy in the sky between now and forever. Nobody put that in either.
Part 8, dark energy for free.
In 1998, two independent teams of astronomers measuring the brightness of distant exploding stars arrived at a result neither of them wanted. They were trying to measure how much the expansion of the universe was slowing down.
Everyone assumed it was slowing down.
Gravity pulls, matter attracts, and after the initial expansion, the pull of everything on everything else should gradually apply the brakes. The only question was how hard the supernovi came back dimmer than they should have been.
Dimmer means farther. Farther means the expansion has not been slowing at all.
It has been speeding up. There is something pushing the universe apart and it is winning and it accounts for something like 7/10 of the total energy content of everything that exists. We call it dark energy. And that name is an admission rather than an explanation. It means we can measure its effect exquisitly well and we do not know what it is. The standard way of writing it into the equations is as a cosmological constant, a term Einstein originally added to his field equations for entirely different reasons and later regarded as an error. It is a constant energy density built into space itself.
Put a positive value in that slot and the universe accelerates which is what we observe. Now here is the disaster and it deserves to be stated in full because it is the largest quantitative failure in the history of physics. Quantum field theory says the vacuum is not empty.
Fields fluctuate even when nothing is there and those fluctuations carry energy. So there is a natural prediction for what the cosmological constant should be and you can compute it. When you do the answer exceeds the observed value by something in the region of 120 orders of magnitude.
120 orders of magnitude. That is a 1 followed by 120 zeros. To give that some shape, the number of atoms in the observable universe is around 10 to the 80th. The discrepancy between our prediction and reality is 40 orders of magnitude larger than the number of atoms in everything. That is what physicists mean when they say the cosmological constant problem. It is not that the number is hard to derive. It is that our best framework, the one that gets other quantities right to 12 decimal places, gets this one wrong by more than any prediction has ever been wrong. Against that background, consider what Bianone's equations do. The modified field equations are consistent with a dark energy term. It arrives as a dynamical cosmological constant expressed in terms of the emergent G field and it has three properties that each deserve their own sentence. It is always positive. It vanishes in the low energy limit and it is dynamical, meaning it can change rather than being fixed once and for all. Take the first property because it is the one a working theorist would notice first and it is a bigger deal than it sounds.
Producing a positive cosmological constant is hard. Producing a negative one is comparatively easy. This is not a small technical detail. It has shaped the entire landscape of theoretical physics for the past 25 years. The most powerful and productive idea in quantum gravity over that period. The correspondence between a theory of gravity in a space and a theory without gravity on its boundary was formulated in a universe with a negative cosmological constant. Not because anybody thought we live in one. We plainly do not. It was formulated there because that is the case where the mathematics is tractable. And the effort to construct stable solutions with a positive cosmological constant in that framework has been one of the longest running technical arguments in the field with serious researchers arguing that it may not be possible at all. Whole conferences have been held about whether our own universe, the one we can see out the window, is even allowed by the leading candidate theory. So a framework that produces a positive dark energy term without being asked to, is doing something that other frameworks find genuinely difficult. In the accounts of this theory, the value that emerges is described as small and positive and as aligning with what we observe of the accelerated expansion considerably better than pre-existing alternatives manage. I want to slow down here because this is a moment worth feeling rather than just noting. A mathematician who works on networks sat down to write an action describing the relationship between structure and dynamics. She was not trying to explain dark energy. Dark energy was not the target. It was not in the motivation, not in the setup, not in the design of the mathematics. She wrote down a quantity measuring how much two descriptions of the universe disagree with each other, extremised it, and out of the machinery came a term that pushes the universe apart with the right sign at roughly the right scale. The number that determines the fate of everything you can see. The number that decides whether every galaxy outside our local group eventually crosses over an in horizon and vanishes from the sky forever, leaving whatever comes after us with a universe that looks empty. The single most badly predicted quantity in the history of science. It arrived as a side effect. There is a particular feeling that produces in a physicist and it is not triumph. It is closer to suspicion. When something you were not looking for falls out of your equations with the right properties, you have either found something real or made a mistake and the two feel identical from the inside, which is exactly why the theory is now being worked over by other groups. That is what should happen. Now take the third property that the term is dynamical rather than constant because it connects directly to two open wounds in observational cosmology. The first is the Hubble tension. We have two independent ways of measuring how fast the universe is expanding. One works from the early universe, reading the pattern of light left over from a few hundred,000 years after the beginning and using our model to project forward.
The other works from the nearby universe, measuring distances to relatively close galaxies directly and watching how fast they recede. The early universe method gives a number near 67 km/s per mega parc. The late universe method gives a number near 73. Those should agree they do not. And for years the expectation was that as measurements improved the gap would close because that is what usually happens with discrepancies of this kind. Instead the measurements improved and the gap held and the statistical significance grew rather than shrinking. It is now one of the most discussed problems in cosmology and the possibilities have narrowed toward two unpleasant options. Either something subtle is wrong with one of the measurements or something is missing from the model of how the universe evolves between the early epoch and now.
The second wound is newer and arguably more serious. Large surveys mapping the positions of millions of galaxies across cosmic time have produced results suggesting that dark energy may not be constant, that its strength may have been different in the past. This is an active and evolving question and I want to be careful not to overstate it because the significance depends on which data sets you combine and the analysis is genuinely difficult and the community has not settled. But the possibility is now on the table in a way it was not a few years ago. And notice what a dynamical cosmological constant is. It is a dark energy term whose strength can change over cosmic time.
Bianone names this directly as the important testable prediction whether the dressed metric dark energy term can shed light on the Hubble tension or related properties. That is the point where a theoretical framework stops being a philosophical proposal and becomes something that can be checked against a survey. There is one more result from this direction and it is the most elegant thing in the entire framework. So let us end this part with it.
The follow-up work asks what happens when the entropic action is evaluated over the standard cosmological solutions. The ones describing a roughly uniform expanding universe. The answer has two levels and they run in opposite directions. The lrangian the relative entropy between the two metrics decreases with time. Locally the two maps are converging. The geometry that is and the geometry that matter implies are getting closer to each other as the universe ages. But the action which integrates that lrangian over the measure across all of spaceime can be interpreted as an entropy that increases with time. So the universe this theory describes has a total entropy that grows which is the second law of thermodynamics. While the local disagreement between structure and matter shrinks the second law is not put in. It is not assumed. It falls out of the same action that gives you Einstein's equations and dark energy as a consequence of the geometry of the expanding universe. The reason your coffee goes cold, the reason the past is fixed and the future is not, the reason you can remember yesterday and not tomorrow, the reason you will grow old turns out in this framework to be the same statement as the expansion of the universe, which raises an obvious question, and it is one that a great many physicists have asked before Bianone in a great many different ways.
If gravity and thermodynamics keep turning out to be the same subject, then how far back does that go? Is she the first person to notice that entropy and gravity are entangled with each other?
Not remotely.
There is a 50-year argument behind this.
And if you do not know it, the black hole result waiting for us in two parts from now will not land the way it should. Part n. The long argument about whether gravity is real. The idea that gravity and entropy are secretly the same subject did not begin 2 years ago.
It began with a graduate student who was told he was wrong. In the early 1970s, Jacob Beckinstein was working under John Wheeler at Princeton and Wheeler put a puzzle to him that sounds like a joke and is not. Suppose you take a cup of hot tea and drop it into a black hole.
The tea had entropy. Now it is gone. And the black hole, according to the theory as it stood, is described entirely by three numbers. Its mass, its charge, and its spin. Nothing else. No memory of what fell in. So the entropy of the universe has just decreased. And the second law of thermodynamics, one of the sturdiest results in all of science, has been violated by the simple act of throwing away your drink. Baconstein's answer, published in 1972 and 1973, was that black holes must have entropy of their own. And when he worked out what it should be, he found it was proportional to the area of the event horizon. The area, not the volume.
Almost nobody believed him at first, including Steven Hawking, who set out to show the idea was wrong and instead proved it was right. In 1974, Hawking demonstrated that black holes radiate, that they have a genuine temperature, and that when you work through the thermodynamics, the entropy is exactly what Beckenstein had claimed with the constant now pinned down. A black hole's entropy is proportional to the area of its horizon measured in units of the plank area. Now, why is that strange?
Let us go back to Boltzman. Entropy is the logarithm of the number of microscopic configurations. And for essentially every ordinary system that counts scales with volume. Double the size of the box and you double the number of gas molecules and the entropy doubles. This is so reliable that it is barely worth stating. Degrees of freedom fill space. A black hole does not do that. Its entropy scales with the surface. Take a black hole and double its radius and its volume goes up 8-fold while its horizon area goes up four-fold and it is the four-fold number that the entropy follows.
Whatever is doing the counting inside a black hole, there is dramatically less of it than there should be. And the shortfall is exactly the amount you would expect if all the counting happened on the boundary.
The response to this developed over the following two decades is the holographic principle. If the entropy scales like the area, then perhaps the degrees of freedom genuinely live on the surface and the interior is in some sense a projection of information stored on the boundary. Perhaps a region of space is like a hologram, a three-dimensional image encoded on a two-dimensional film.
That idea turned out to be extraordinarily productive. In 1997, it was made precise in a specific setting in the form of a correspondence between a theory of gravity inside a particular kind of space and a theory without gravity living on that space's boundary.
Two descriptions, one with gravity and one without, containing exactly the same information. It became the most cited idea in theoretical physics for a generation. Meanwhile, a parallel thread was developing. In 1995, Ted Jacobson published a paper with a title that tells you the whole story, the Einstein equation as an equation of state. He showed that if you assume the Beckenstein Hawking relationship between entropy and area holds locally everywhere for every observer, and you then apply the standard thermodynamic relation connecting heat, temperature, and entropy, Einstein's field equations fall out. Read that again because it is one of the most underappreciated results in modern physics. Einstein's equations derived from thermodynamics, not analogized to thermodynamics. Derived.
An equation of state in ordinary physics is a relationship like the one connecting the pressure, volume, and temperature of a gas. It is not fundamental. It is what emerges when you look at an enormous number of particles from far enough away that you stop seeing them individually. Nobody thinks the gas law is a fundamental law of nature. It is a summary. Jacobson's suggestion was that Einstein's equations might have the same character. Not fundamental law, but summary. Not the deep truth about spaceime, but the bulk behavior of something smaller that we have not identified. Then in 2011, Eric Valinda published the most publicly famous version of this line of thinking.
He argued that gravity is an entropic force. An entropic force is a real and familiar thing. And the standard example is a rubber band. When you stretch a rubber band, it pulls back. There is no fundamental force of rubber band. What is happening is that the long molecules inside can be arranged in far more ways when they are coiled than when they are extended. So a stretched band is in a low entropy state and random thermal motion drives it back toward the overwhelmingly more numerous coiled arrangements. The pull you feel is statistics. Valinda's proposal was that gravity works the same way. He set up holographic screens, surfaces carrying information, and showed that if you assume information is stored on them in the manner Beckenstein's formula suggests, then a mass approaching such a screen produces a change in entropy, and the resulting entropic force reproduces Newton's law of gravitation. That paper got enormous attention, and it is where the popular headline comes from. Gravity is an illusion. Gravity does not exist.
You will find that framing all over the internet. It overstates the claim considerably and it is worth being precise about why because the distinction is one of the more useful things you can carry away from tonight.
Emergent is not the same as unreal.
Temperature is emergent. There is no such thing as the temperature of a single atom. Temperature is a statistical property of a great many particles. Temperature is nonetheless entirely real and it will still burn your hand. Pressure is emergent. sound is emergent being nothing but a pattern of pressure in a medium and it will still deafen you. The claim that gravity might be emergent is a claim about what level of description it lives at, not a claim that it is not there. Valind extended his framework in 2016, arguing that emergent gravity naturally produces extra gravitational pull in galaxies without requiring dark matter, reproducing an empirical pattern in galactic rotation that had been noticed decades earlier. That claim is genuinely contested in the professional literature. Some early tests using gravitational lensing around isolated galaxies were read as supportive.
Analysis of galaxy clusters of the leftover light from the early universe and of how cosmic structure grew over time have been widely regarded as difficult for the framework to accommodate. The argument is unresolved and it is a real scientific argument, not a suppressed truth. There is also a serious experimental objection to strongly thermal versions of entropic gravity that gets far less attention than it deserves.
Experiments with extremely slow neutrons bouncing in Earth's gravitational field have shown that they occupy discrete quantum bound states and neutron interferometry has shown that gravitational effects on quantum phase preserve coherence rather than destroying it. Critics have argued that this sits badly with a picture in which gravity emerges from a thermal environment because a genuinely thermal origin would be expected to wash out exactly that coherence. And there is a third thread running alongside all of this which is the idea that spacetime itself is built out of quantum entanglement. In 2006 it was shown that in the holographic setting the entanglement between a region of the boundary and its complement corresponds to the area of a surface in the interior. In 2010, it was argued that if you reduce the entanglement between two parts of a boundary system, the corresponding regions of the interior geometry move apart. And if you remove the entanglement entirely, the space pinches off and separates into two disconnected pieces. In that picture, distance is a measure of correlation.
Two things are near each other because they know about each other. So that is the family. Beckenstein and the area law, Hawking and the temperature, holography, Jacobson and the equation of state, Valinda and the entropic force, entanglement building geometry, half a century of increasingly serious evidence that gravity and information are the same subject seen from different angles.
Which brings us to the question of what exactly the enone is doing differently.
Because if a great many people have already connected entropy to gravity, why does another connection matter? Her answer has two parts and both of them are sharper than they first appear. The first is that her approach stems from an action and it does not use a holographic screen at all. Valinda's argument is a force argument. Set up a screen, put information on it, move a mass toward it, compute the resulting force. Bianone is a variational principle. write down a quantity, extremise it, get equations.
Those are different kinds of theory. And she considers Valinda's framework to have very limited focus on the interplay between geometry and the matter field, which is the entire content of hers. The second difference is deeper and it is the one we set up two parts ago. Horizon entropy approaches in her characterization are thermodynamic in spirit. They start from the area law and the area law, however fundamental it may be, is a macroscopic statement. In the same way that Carninal ceiling on engine efficiency is a macroscopic statement, it tells you a relationship. It does not tell you what the relationship is made of. Hers is statistical mechanical. It works upward from the microscopic degrees of freedom rather than downward from a bulk law. And she makes a further point about who tends to be on which side of that divide, which I found revealing. Researchers coming from theoretical physics, she notes, sometimes approach entropic gravity while being merely sympathetic towards statistical mechanics, treating it as an applied subject. The domain of condensed matter and soft materials rather than of fundamental theory. Her position is that this gets it backwards. Statistical mechanics is a fundamental theory. It is possible to write an action that is simultaneously a field theory action and a statistical physics action and doing so does not require descending into applied territory which sets up the confrontation this whole part has been building toward the area law is the crown jewel of the thermodynamic approach. It is where the entire field started. Baconstein and Hawking gave us entropy proportional to horizon area and holography was invented to explain why.
And Biancone's position is that a fundamental theory has to go beyond the area law, not start from it. She does not feel the need for a holographic screen, which sounds on the face of it like she has thrown away the most important clue in the subject. Unless the area law comes out of her theory anyway, from the inside without holography, it does. And how it does that is the strangest thing in this entire story.
Part 10, the black hole that reduces its own dimensions.
I want to take the area law apart before we put it back together because there is an assumption hidden inside it that has been sitting there for 50 years in plain sight doing an enormous amount of unexamined work. The puzzle once more entropy counts microscopic degrees of freedom. For every ordinary system that counts scales with volume for a black hole it scales with area. Something is missing from the interior. The holographic inference goes like this. If the entropy scales like the area and entropy counts degrees of freedom, then the degrees of freedom must be on the surface rather than in the interior. The inside is a projection. The information lives on the boundary. Now watch the step in the middle. Why does entropy normally scale with volume? Because the degrees of freedom are distributed uniformly. That is why if you have a box of gas at uniform density, then twice the volume means twice the molecules. So twice the count, so twice the entropy.
The scaling with volume is not a law of nature. It is a consequence of homogeneity. It follows from the assumption that the inside of the box is the same everywhere. Which means the inference from area scaling to surface degrees of freedom carries that same assumption along with it silently.
The argument runs the inside would give volume scaling if the degrees of freedom were uniform. But we observe area scaling. Therefore, the degrees of freedom are not really inside.
But there is another way out of that logic and it has been sitting there the entire time. What if the inside is not uniform? If the density of degrees of freedom varies with position inside the black hole, then integrating over the volume does not have to give you something that scales like a volume.
Integrate an inhomogeneous quantity in the right way and you can get an answer that scales like an area. No projection required, no screen required. The information stays in the interior. It is simply not spread out evenly. This is Biancy's observation and her theory does not just permit an inhomogeneous interior. It requires one for a specific and rather beautiful reason. Here is why it comes down to which piece of curvature the action is built from. And this is worth going slowly on because it is the technical heart of the result.
Curvature in general relativity is described by an object called the reman tensor. It carries the complete information about how spaceime bends at a point. But you can split it into two parts and physically they mean different things. The first part is built from the Reichi tensor and the Reichi scaler.
Roughly speaking, this piece describes how curvature changes volumes. If you release a small ball of dust in free fall, the reachi part tells you how the volume of that ball changes. And crucially, Einstein's equations tie this part directly to the matter present.
Where there is no matter, this part of the curvature is zero. The second part is called the whale curvature. This piece does not change volumes. It changes shapes. Release that same ball of dust in freef fall near a massive object. And the whale part is what stretches it into an ellipsoid, pulling it long in one direction and squeezing it in the others. It is what we experience as tidal forces. It is what would eventually stretch an unfortunate astronaut falling toward a black hole.
And here is the essential fact. Whale curvature survives in empty space outside a star, outside a planet, outside a black hole where there is no matter at all. The reachy part vanishes and the whale part does not the tidal stretching is still there. Gravity still reaches into the vacuum and whale curvature is how now the standard action for gravity the Einstein Hilbert action is built from the reachi scaler that is its entire content which means that in a vacuum where the reachi scaler vanishes the Einstein Hilbert action gives you nothing empty space as far as that action is concerned contains nothing to counton's entropic action depends on the full reman tensor not only the reachi part all of it including the components that never touch the reach scaler including the whale curvature. So the entropic action does not vanish in empty space.
That single fact reshapes everything in the vacuum around and inside a black hole where the standard action has nothing to say. The entropic action is non zero. There is something to count out there. And because the whale curvature varies with distance from the center, growing enormously as you approach it, the density of what there is to count varies too, which means the interior is not uniform. The degrees of freedom in a black hole depend on the distance from the origin. And now the pieces fit together. The langian is defined over volume. So to get the total entropy, you integrate it over the volume out to the horizon. But you are integrating something that is not homogeneous with a density that changes as you move inward. And when you carry out that integral properly, you get what Benone calls a dimensionality reduction.
A volume integral that behaves like an area. The area law recovered by counting the inside. Let me put you in it because this is the part that deserves to be felt rather than only understood. You're falling inward through a black hole's horizon and you have been given an unusual instruction. Do not look at the scenery. Count. For 50 years, the picture said there would be nothing to count. That the interior was either uniform and therefore contradicted by the entropy or a projection of something written on the surface behind you. That the inside of a black hole was in a sense not the real thing. The real thing was the boundary and you are falling through an image. That is not what you find. You find something to count everywhere all the way down and the amount of it changes as you go. Near the horizon, it is thin. As you fall, it thickens. The tidal curvature climbs.
The shape distorting part of gravity that never needed matter to exist. And the density of information climbs with it. You're moving through a gradient.
Nothing here is uniform. Nothing here is empty in the way empty was supposed to mean. And when you add it all together across the whole volume from horizon to center, the total does not scale the way a volume scales. It scales the way the surface behind you scales. Not because the interior was an illusion, but because the interior was never evenly filled, and the arithmetic of an uneven filling comes out looking like a boundary. The area law was never evidence that the inside was empty. It was evidence that the inside was not the same everywhere. Bianone's position on holography follows straight from this, and she states it with a certain diplomacy. She regards the area law as fundamental and important. She simply regards it as a macroscopic field, a bulk statement, a summary of something happening underneath. Holography in her account came after Beckenstein as an explanation for the area law.
Beckinstein himself did not use holography. He got the result without it. And if we are looking for a fundamental theory, she argues we need to go beyond the area law rather than treating it as the starting point. She does not for the moment feel the need for a holographic screen. When you have the area law falling out of a volume integral over the interior, you do not need to move the information anywhere.
Now there is a second consequence of that same technical fact and it is quieter and I think it is stranger because the entropic action depends on the full reman tensor and treats geometry together with matter fields.
The theory produces corrections at the plank scale even in flat geometry. flat, not near a black hole, not in the first instance of the universe, not in any extreme environment at all. The theory says that something is happening at the smallest scales everywhere, in the space between your hands, in the space inside an atom, in the emptiest region between two galaxies, where there is less than one particle per cubic meter, and light travels for millions of years without meeting anything. Bianone's phrasing is careful and specific. The theory treating geometry together with the matter field finds corrections at the plank scale already in flat geometry.
The corrections are unmeasurably small.
Let me be honest about the scale of that unmeasurability. The plank length is about 10us 35 m. The smallest structure any human instrument has ever resolved is around 10 - 19 m. So we are talking about a scale 16 orders of magnitude below our best resolution which is roughly the ratio between the width of a human hair and the distance from here to the sun. Nobody's detecting this soon but it is not nothing because of what it means about the claim being made. This is not a theory that only speaks about the extremes. It is not a correction that switches on near a singularity and switches off in ordinary life. It says that empty flat space has an information content and a texture and that the reason it looks blank to us is only that we are enormous. You are at this moment sitting inside something that is not smooth. Not in a way that will ever affect your day, but not blank either.
And that same thought followed inward instead of outward leads to the last and boldest thing this theory has to say.
Because if the geometry is dressed everywhere and the dressing is dynamical, then there is one place in the universe where the dressing stops being a small correction and takes over completely. It is the place where physics is supposed to end.
Part 11. What keeps her awake?
Ask a physicist what they are proud of and you will get a polished answer. Ask them what keeps them awake at night and you will find out where the theory actually is. Bianone was asked and her answer was immediate. Second quantization.
Let me explain what that means because it is the wall that every attempt at quantum gravity eventually runs into.
And understanding why it is a wall tells you a great deal about the shape of the problem. The phrase comes from a historical accident and the name is misleading. So set the words aside and take the idea. First quantization is what you learn first. You take a particle and instead of a definite position, you give it a wave function, a spread out object describing where it might be found.
That is the quantum mechanics of the 1920s. Second quantization goes further.
It says that the fields themselves are the quantum objects and particles are what you get when you excite a field.
There is an electromagnetic field filling all of space and a photon is a ripple in it. A quantum of excitation.
There is an electron field and every electron in the universe is a ripple in that one field. Which is why every electron is exactly identical to every other one. Particles are not fundamental. Fields are and particles are what fields do. That framework is quantum field theory. And it describes three of the four interactions with the precision we talked about at the start of tonight's journey. It is the language modern physics is written in. Gravity has never been successfully written in it. And that is essentially the whole of the quantum gravity problem. Now, where does gravity from entropy stand? It is further along than a purely classical theory because the action treats the metric as a quantum operator and writes a quantum relative entropy between such operators. The quantum information language is genuinely in there structurally from the start. That is why the lrangian is called a geometric quantum relative entropy rather than just a relative entropy. But it is not in second quantization. Bianone is entirely direct about this. the program is there, the direction is clear, and the work is not done. And she flags something that I think is the most tantalizing sentence in this entire story because the theory is currently classical in this sense. She says it could be that if you really address the full second quantization, you get still more effects. More effects, not corrections, not refinements. Things the framework has not yet shown, waiting on the other side of a step nobody has taken. That is what an open frontier actually sounds like. Not a triumphant claim, but a person telling you honestly that there is a door in the theory she is not opened and she does not know what is behind it and it is keeping her up.
There is a related question that gets even more provocative and it concerns what would carry gravity if you did complete that step. The natural expectation is a graviton. If the electromagnetic force is carried by photons, then gravity should be carried by graviton's quant of the gravitational field. That is the standard picture and it is what most people assume any theory of quantum gravity has to deliver.
Biancone was asked whether the graviton would be emergent in her framework. Her answer was probably not, which is to say if it exists, it would be fundamental rather than something that appears at larger scales. And then she immediately questioned whether it exists at all. Her reasoning is technical but the shape of it is accessible. We keep saying the metric is the fundamental object but that is a choice rather than a requirement. The geometry of spaceime can be described in more than one mathematical language. It can be described through the metric. It can be described through what are called verbine which are local reference frames attached to each point. A set of rulers and clocks carried around the manifold.
It can be described through spin connections which specify how those frames rotate as you move. Those are genuinely different starting points, not just notations. And some of them are far more natural than the metric when you want to include the kinds of particles that make up ordinary matter. And if you start from a different object, the thing that gets quantized is different. And the quantum of the gravitational interaction need not look like a graviton at all. So, one of the most confident assumptions in the field, the one particle that a great deal of theoretical work has been organized around finding a consistent description of gets a shrug. Maybe there is something else. There is a second open thread on her list and it connects this theory to one of the largest ideas in modern physics. The construction of the metric induced by matter and curvature was inspired by literature on vonoyman algebbras and Benone points specifically to a review by Edward Whitten discussing a closely related notion of entropy called the Iraqi relative entropy. Here is why that matters in plain language.
If you take a region of space and ask how entangled it is with everything outside it, quantum field theory gives you an answer of infinity. The problem is at the boundary. There are unlimited degrees of freedom at arbitrarily short distances right at the dividing surface and they contribute without limit. This is not a minor technical annoyance. It is a genuine obstruction to using entanglement entropy as a fundamental quantity in field theory and it has been a persistent difficulty for decades. The relative entropy of the Iraqi type is well behaved exactly where entanglement entropy is not. It is a measure of quantum correlation that survives the mathematics rather than diverging.
Bianone is careful to say the connection is not fully established. It was important in the formulation of her theory rather than being a proven bridge. But the relationship between the entropic action, entanglement, and horizon entropy is explicitly on her list of open problems. And if that connection gets made properly, it would tie this framework directly into the entanglement build space-time program.
We discussed two parts ago two independent roots arriving at the same place from opposite directions would be a considerable thing. She has more on the list. Getting the full standard model of particle physics inside the framework which currently works with basic matter fields and more recently with fluids for cosmological applications. That is the test of whether this describes our universe or a simplified relative of it. and going back into the discreet eventually though for now she is staying in the continuum which I find quietly funny given how this all started but we have one more result to cover and it is the boldest thing in the theory so let us end this part there the singularity at the center of a black hole general relativity predicts a point where curvature and density become infinite where the equations produce not a large number but no number at all documentary describes it as the place where physics breaks down. And that phrase is usually delivered as though it were a fact about the universe. Almost no physicist believes it is. A singularity in a theory is nearly always a signal that the theory has been pushed past its range of validity, not a discovery about reality.
When the equations of fluid dynamics produce an infinity, we do not conclude that the ocean contains a point of infinite density. We conclude that treating water as a continuous fluid has stopped being appropriate. The expectation has been that a full theory of quantum gravity would do the same thing for black holes and remove the singularity by describing what the classical theory could not. Bianc's framework offers a possible route and she describes it with the care of someone at the frontier of her own work rather than someone making an announcement. The reasoning runs like this. The classic description of a non-rotating black hole worked out by Carl Schwarz in 1916 while serving on the Russian front and less than a year before his death is a solution of Einstein's equations. Einstein's equations in this framework are the low energy approximation to the entropic field equations. So the classic solution is a good approximate description of a black hole here and it remains good across most of the region we care about.
But close to the singularity, the G field becomes dynamical. Remember what the G field is. It is the emergent thing. The lrangee multiplier that refused to stay bookkeeping. The layer that dresses the metric so that what matter interacts with is not quite the bare geometry. Everywhere in ordinary circumstances, it is a small correction.
So small that Einstein's equations describe everything we have measured. At the center, it stops being small. It takes over. The dressing becomes the dominant feature rather than a modification. and the assumptions behind the classical solution stop holding. And Bianone's conclusion is stated as an open possibility rather than a claim which is exactly the right register.
Maybe there is no single static solution of the black hole in gravity from entropy and maybe the singularity is avoided. Read that carefully because there are two separate claims folded into it and the second one is the larger. The first is that the infinity might be removed. That is what everyone hopes for and expects from a quantum theory of gravity. The second is that a black hole might not have a single static solution at all. Not that the singularity is replaced by something small and dense. That the object may not sit still. That the thing we picture as the most permanent, most unchanging, most utterly finished object in the universe may be at its core in motion. I want you to sit with what that does to the picture you have carried. You have seen the illustrations, the funnel, the disc of glowing material, and at the center a point marked as the place where our understanding ends. That point has been used to argue about the limits of knowledge, about whether reality contains contradictions, about whether the universe has holes in it. And it may simply be an artifact of using the wrong action. Not a place, not a hole in reality, not the edge of what can be known, just the shadow that one mathematical formulation casts when you push it further than it was built to go, disappearing the moment somebody writes down a different one. If that is right, then some of the most dramatic features of our picture of the universe are not features of the universe. They are features of our own equations, and we have been reading our arithmetic and calling it the world. Which brings us finally to what she actually found.
Part 12. What she actually found?
We have been carrying a question all night and I promised you an answer. So here it is plainly. What this physicist found about the origin of gravity is that gravity may not be a force at all.
It may be a disagreement. The universe carries two descriptions of itself.
There is the geometry that is the true shape of spaceime. Every distance and every duration as they actually are. And there is the geometry that matter implies, built from what is present and where it sits, the shape the contents are voting for. Two maps of the same room drawn independently laid one over the other. They almost match. They never quite match. And the measure of their failure to match is an entropy, a number quantifying how much of one description is contained in the other. Everything gravity does is what that mismatch does.
The Earth going around the Sun. Your weight in your chair. The bending of starlight around a star. The slowing of clocks near massive objects.
Gravitational waves crossing a billion lightyear from two black holes that merged before there were animals on Earth. The expansion of the universe accelerating outward, pushed by a term that arrived in the equations without being invited. All of it is two descriptions of the world straining toward each other and never arriving.
You have spent your entire life being held down by an argument that cannot resolve itself. That is what she found.
Now, let me put the honest boundaries around it because a claim that size deserves them. This theory is not established. It is not accepted physics.
It has not replaced general relativity and nobody involved says it has. It is a young framework published in a leading journal in 2025 being extended and tested by other groups. The second quantization is unsolved and its author names that as the thing that keeps her awake. No observation currently distinguishes it from Einstein's theory.
It may turn out to be wrong. But look at what it has done in its first two years.
It reduces to Einstein's equations in the low energy limit which is not a formality and which several serious programs struggle to establish. It produces a positive dark energy term that nobody put in in the direction that is theoretically hard to get. It recovers the entropy of a black hole from account over the interior without holography by noticing an assumption that had gone unexamined for 50 years.
It suggests the singularity may not exist. A separate group has already shown that the framework can produce an inflating early universe without any inflate on field without the extra ingredient standard cosmology has to add by hand. And the second law of thermodynamics falls out of the same action unforced. That is a considerable amount of unforced consequence for a 2-year-old theory written by someone who had never worked on gravity. Now, let me place it in the largest frame available because Bianone does and the way she does it is worth carrying home. She says there are two great traditions in statistical mechanics. The first is emergence. You start with microscopic degrees of freedom and you explain the large-scale behavior that follows from them. That tradition was crystallized in a famous 1972 paper by Philip Anderson titled more is different arguing that each level of complexity has laws of its own that are not simply the previous level restated. It is one of the most influential ideas in modern science. The second tradition belongs to John Wheeler and it goes by the phrase it from bit.
The proposal is that information is not something we use to describe the universe. Information is what the universe is made of and material things are what information looks like from inside. Gravity from entropy sits in the second tradition. The claim is not that gravity is made of small things that add up. The claim is that gravity is what the information content of geometry and matter looks like when you write it down carefully. And there is a distinction inside that which I want to get exactly right because it is the kind of precision that makes an idea land properly rather than dissolving into slogans. Bianone was asked whether the theory should really be called gravity from information since information sounds like the more fundamental thing.
She said no, it is gravity from entropy because the action is an entropy. The entropy is the quantity you can actually compute. The information is what the entropy quantifies. And asked what she thinks actually exists in her picture.
Her answer was the metric. The true metric encoding the degrees of freedom of geometry and matter together. Not a computation, not a simulation, not bits in a machine, a geometry whose information content is what the theory measures. Which means this is not the claim you have seen circulating that the universe is a computer. And I do not want you leaving tonight with that. It is something more careful and I think more interesting that the fundamental object in physics might be a relationship rather than a thing. There is also a question this theory does not answer and Biancone is unusually clear about it which I appreciate. Gravity from entropy assumes that geometry exists. It builds on Einstein's insight that gravity is a theory of geometry and then asks what the information content of that geometry is. What it does not do is explain where the geometry came from in the first place. That question is not tackled. She says so directly. So the theory is not a theory of everything. It is one floor of the building, not the foundation. And she leaves open the possibility that there is a next theory beneath this one in which gravity from entropy itself turns out to be emergent from something more basic. For now, she says, it is conceived as a fundamental theory of geometry, which leaves us exactly where the deepest questions always leave us. We may be about to understand what gravity is. We will still not know what geometry is or why the universe has a shape at all. And that may be the last question rather than the next one. There is one more thread to close and it is the one I have been holding since the second part of tonight's journey. Remember where all of this came from. Not from relativity, not from particle physics, not from any of the established quantum gravity programs. It came from network science.
From the study of how the shape of a set of connections determines what flows across them, structure and dynamics. And Bianone's view is that this was never really about gravity. It was about a mathematical problem that appears everywhere. Information theory, she argues, has been extraordinarily powerful and extraordinarily general.
But it is increasingly clear that information theory alone is not enough.
What it lacks is geometry and topology.
What a great many fields need from neuroscience to artificial intelligence is an information theory that captures the degrees of freedom of geometry. That is what she built. Gravity is where she tested it. Which means if she is right, that the same mathematics describing why you fall toward the ground may also describe what happens in a network, in a brain, in a learning machine, not by analogy, by identity. The same equation applied to different structures. And she said with what I can only describe as a straight face that she considers understanding the brain to be the harder of the two problems. So, let me leave you where she leaves her students. She was asked what advice she gives them consistently, and it was not what you would expect from someone who has just proposed a new action for gravity. Read articles, she said. Study, follow what you like, try to express your vision of reality in what you do, and enjoy it because it is not always possible, but that is part of why we do science at all. and asked what advice she keeps coming back to herself. She named the stranger at the seminar in Trieste, a person she does not know, whose name is not recorded anywhere, who asked one question and then never spoke to her again. Why do you not do it in the continuum? Then she added a second thing she had learned, and it was not advice exactly, more a habit. Go into other communities. If you are at a large interdicciplinary conference, wander into a session belonging to a field that is not yours. And if you are holding your problem abstractly enough, you may find your answer sitting in somebody else's room. She mentioned that this is how the theory began to take shape. She was at a meeting to talk about topology and networks, and she went to sit in on a session about gravity and information because it sounded interesting. And then the last thing she said, which I have not been able to stop thinking about since, try to look at nature with surprise, and maybe things will turn out nice. That is the advice of someone who spent her career in the discreet said she would never go into the continuum and then went because a stranger asked and she was willing to be surprised by her own answer. So here is where we end tonight. For 300 years we have described gravity as a force. For 100 we have described it as the curving of spaceime and there is now a serious proposal published tested extended by other groups that both of those are descriptions of something else underneath. Two accounts of the same universe. One written by the geometry and one written by the matter inside it, straining toward an agreement they never reach. Every moment of your life has taken place inside that gap. It has never once let go of you. It has held the ground under you and kept the moon in its orbit and pulled every star in the sky into being out of a cloud that would otherwise have drifted apart. And it has done all of it not by pulling but by failing continuously and precisely to reconcile two descriptions of the same room. And if that is right, then the most reliable fact of your existence is not a thing at all. It is an argument and it is still going on everywhere right now underneath
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