# The heating and cooling of space and time

Updated: Mar 4

In today’s blog we talk to Dr. Thanu Padmanabhan, Distinguished Professor at the Inter-University for Astronomy and Astrophysics at Pune, India, about his thermodynamic framework for gravity and its predictions for the cosmological constant.

**David**: What triggered your work in the spacetime-thermodynamic parallel?

**Thanu**: Many of us were concerned by the fact that about 50 years of serious effort towards putting together the principles of quantum theory and gravity hasn’t led us anywhere, to put it bluntly. We thought that this is because we have completely misunderstood the nature of gravity. This led us to realise, as we made progress, that the description of gravity in the standard approach should be thought of as being similar to the description of a fluid like water, in fluid mechanics. If you take the equations for fluid mechanics, and apply the principles of quantum mechanics to them, you will get something like a quantization of a sound wave, and phonons. You are never going to get the atomic structure of water. This is exactly what has been happening in the case of gravity.

So there is this fluid that we call spacetime and it has its own thermodynamics. How do we know that? Let us take one step back. How do I know if I take a glass of water it is made of molecules? You don’t have to perform experiments at Angstrom scales to understand that. You only have to keep it in a microwave oven and heat it up. This is exactly what Boltzmann told us and he completely cut through all the nonsense which was going on about the nature of heat at that time. He said that if you can heat something, it must have microstructure, which can store the energy. So if something shows heat content, it must have microstructure; the superficial layer of fluid dynamics is a continuum limit of the statistical mechanics of the underlying layer. Now it turns out that there was already evidence available to show that spacetime has heat content. Spacetime has temperature and it also has entropy; the product of these two gives you the heat content. Once one realizes this, you understand you have to describe the dynamics of the spacetime in thermodynamic language. This was the main difference between our approach and many other approaches available in the market.

**David**: Can I ask you about the heat and entropy aspects of this? They come into this curved spacetime through Hawking’s result?

**Thanu**: No. It is much more general than that? Historically, entropy was first assigned to black hole horizons by Bekenstein. And in the initial stages, e.g., in a famous Les Houches meeting, Hawking didn’t believe black holes have temperature. He did the computation and he found, lo and behold, that it has temperature. So it is “Bekenstein entropy” and “Hawking temperature”. They were, of course, first discovered in the context of black holes. Very soon, two gentlemen, Bill Unruh and Paul Davies, showed that it is a much more general result. What happens is that when you have a light front, technically called a null surface, it blocks information. Once you have blocked information, a loss of information, there is an entropy associated with it. And almost everything has energy so you now have both entropy and energy, and thus you get a temperature as well. I can just point to one location in space at a given instant in time and say that this point has non-zero heat content with respect to a particular observer. There will be observers who will associate heat content with this point --- which means there are microscopic degrees of freedom which these observers can associate with that point. This result is very general and applies to any event in spacetime. In fact, Hawking’s result is just a special case of a general result that spacetime has temperature and entropy.

**David**: But not all observers would agree.

**Thanu**: No. But even black hole temperature and entropy is not the same for all observers. This is another fact which is not often emphasised. That is, if you take a black hole, and you have an observer freely-falling into it, he’s going to describe its thermodynamics very differently from you and I who will stay at a safe distance from a black hole. So black hole entropy and black hole temperature are observer-dependent as much as any other thermodynamic parameter. This is often not emphasized and one sort of believes that black hole entropy is some observer independent, invariant entity, while the temperature of an accelerated observer is somewhat mythological. That is not the case. Both of them depend on the observer.

**David**: In thermodynamics, the parallel then suggests that these quantities are observer-dependent as well.

**Thanu**: Right. That is absolutely true. If I take a glass of water, and I ask you what its temperature is, you should tell me ‘I cannot tell you because you have to tell me how the glass of water is moving’. If the glass of water is accelerating, it’s temperature is different from if it’s not accelerating. So the entire framework of thermodynamics is observer-dependent. But for a glass of water it is a very weak observer-dependence and more of a curiosity. In the case of spacetime it becomes a lot more important.

Other people have tried to link gravity with thermodynamics, some even before us. The key point where we have made a departure, thereby leading to fresh insights, is the following: Many people try to derive Einstein’s equation using thermodynamic arguments. But once you get that, what do you write down? You write a geometrical quantity on the left hand side and you equate it to a matter quantity on the right hand side. That uses standard, completely geometrical, language and that is not thermodynamics. So what we said is ‘Look. This is not the way to look at it at all’. The Einstein’s equation itself has to be rewritten and interpreted in a purely thermodynamic language. In this approach the evolution of spacetime is essentially due to the heating and cooling of the spacetime. You can take a three dimensional region of the space and ask how the heat content of that region is changing with respect to time. It turns out that this change will be driven by the difference between the number of degrees of freedom in the boundary of the region and the number of degrees of freedom in the bulk. When these are equal, the heat content will not change with time. When these are different, that difference will drive the spacetime to a thermodynamic equilibrium. In this approach the language used for description is totally thermodynamic.

**David**: Time evolution is associated with differences between the bulk and the boundary.

**Thanu**: That is right. It is some kind of holography but not in the way string theorists use that term. This is a more primitive use of the term holography closer to the way ‘t Hooft originally used. There are surface degrees of freedom. And there are bulk degrees of freedom. And in equilibrium, when spacetime is static, these two are equal. One can show that for Einstein’s theory.

**David**: So this means that AdS/CFT, all these results are equilibrium…

**Thanu**: None of that is needed here. Here we are talking about a normal, down to earth, three dimensional space and its heat content. You take a region of space in your room, enclosed by a two dimensional surface. There is a way of defining the number of degrees of freedom on the surface. It is not the degrees of freedom of some CFT sitting somewhere in a fictitious AdS space. You don’t need a negative cosmological constant, AdS. None of them. You just take the degrees of freedom on the two dimensional boundary, say on the surface of a football, and the bulk degrees of freedom inside the football and the heat content inside. Of course it is not a football but it is a spacetime that we are talking about. Then one can write down an equation describing the heating and cooling of the inside and show that this equation is implied and implies Einstein’s equation.

So the Einstein’s equation has a complete parallel in thermodynamics. This is enormously surprising. But that is the proper way to look at it. When we did that, we also found that this solves a very age old mystery. Most of the time in physics, only when you solve something that you actually realize that it needed a solution in the first place! Let me describe that.

If you take normal matter and you change the zero level of the energy of matter, the matter sector doesn’t care. If you add or subtract some constant energy the normal matter of the standard model doesn’t care. The dynamical equations are invariant. Technically, you will say that if I add a constant to the Lagrangian, the Lagrange’s equation doesn’t change. But if you add a constant to a Lagrangian, gravity recognizes it. Gravity cares about the zero level of the energy. So this so-called ‘beautiful’ theory of gravity actually breaks a symmetry! Matter sector has more symmetry than gravitational sector has.

We realized that we actually need to restore this symmetry to gravity. This is extremely important because it has immediate bearing on the cosmological constant problem which is considered ‘the’ question in theoretical physics. In the thermodynamical approach to gravity, when you do everything the proper way, you find that the equations are actually invariant under the change of the zero level of the energy. The technical term is that the stress tensor is changed by a constant times a unit tensor. More simply stated, you change the zero level of the energy. When you change the zero level of the energy, the gravitational thermodynamic equation, i.e. the gravitational equation written in thermodynamic language, remains invariant. It has a greater symmetry than in the standard geometric language description. At the same time, when you solve the equation, the cosmological constant comes out as a constant of integration. It gets you the “cosmological constant without cosmological constant”, so to speak.

**David**: I would like to go a little deeper on the structure of GR in this parallel. You talk about the heating of spacetime. It seems like you’re using something from thermodynamics and you’re sneaking it into the spacetime paradigm. But the paradigms are parallel and should meet at some point if the parallel is exact. So GR is curvature of spacetime and space is…

**Thanu**: The paradigms are exactly equivalent mathematically. Let me try to explain that. This is related to a historical accident. You see, first we had the development of GR. We had solutions like black holes, which were all beautifully geometric. Everybody loved it. And then came the Hawking’s result. And you found that certain spacetimes, very special spacetimes like black holes, have a temperature. Everyone who has read *A Brief History of Time *is familiar with this. Then came the result of Davies and Unruh who said that: ``Look, you don’t need a black hole. Any horizon will have a temperature.” What happened is that people then started asking the question: ‘ How come certain geometric aspects of spacetime have a thermodynamic interpretation?’. That’s a completely wrong question. Because spacetime can be hot, Boltzmann’s paradigm tells us that it has microstructure. So you can write down a thermodynamic equation, which we are writing, to describe spacetime. So the right question you should ask is: ‘How does a thermodynamic description also have a geometric interpretation?’ That is the mystery. Not the other way around.

**David**: So is this a practical implementation of Mach’s principle?

**Thanu**: No. Unfortunately, no; because I love Mach’s principle. We spent some time to understand whether the Mach’s principle can be incorporated in it. The only thing which we can say is that in the absence of all matter, there is no gravitational field in our approach. This is one version of Mach’s principle. If you take it in that sense, this is an implementation of Mach’s principle. But that is a very vacuous way of looking at Mach’s principle. If you let me be a little technical again, I can give the following analogy: In Newtonian gravity you write the Poisson equation relating matter density to gravitational potential. So that the matter density produces a potential φ. If I put matter density to zero you get Laplace’s equation. This has non-zero solutions; φ = 0 is not the only solution. But if I just write the same equation in an integral form using a Green’s function, then I can choose the boundary conditions such that when ρ goes to zero, φ goes to zero. So the integral representation of some equations can have the appropriate boundary conditions and as a result of it can incorporate Mach’s principle. It is actually possible to rewrite Einstein’s equation in an integral form which incorporates it. What we are doing is somewhat similar. So to that extent it incorporates Mach’s principle but I wouldn’t make a claim that we are saying something new about Mach’s principle. That is sad but that is the state of affairs.

**David**: Is Lorentz symmetry emergent?

**Thanu**: OK. Yes and no. If you look at the discrete degrees of freedom of spacetime, these discrete degrees of freedom are not like atoms in a solid lattice. I have to be careful here because it is a subtle point. Suppose you take a solid-like lattice, and ask whether rotational symmetry is emergent. Then the answer would be that the length scale is much bigger than the lattice spacing you have the continuum limit with rotational symmetry. If I rotate the solid by 37 degrees you will always find another atom because you are coarse graining over a very large scale. So in that sense the rotational symmetry is emergent in the continuum limit of the solid. But if you take a gas, the rotational symmetry is already built in to a greater extent. Because, in the case of a gas, molecules are randomly located and not in the form of a lattice; So if you take a particle and rotate the system by 37 degrees, you are very likely to find another particle. I mean the probability is very high that you would find it in a dense gas. So the rotational symmetry is more inherent in a gaseous system compared to a lattice solid system.

The equations which we have describe a system which is more like a fluid or a gas than a solid. Therefore, in that sense, Lorentz symmetry is already built in. But at the same time the system has discrete degrees of freedom. So only in the continuum limit you actually write down the Lorentz group etc. to describe the system. In that sense it is emergent. It is emergent in that very specific sense. But not in the sense of the rotational symmetry emerging from a solid when you coarse grain.

**David**: So this is a very different paradigm. So many questions…

**Thanu**: We can go back and forth. I mean you don’t have to streamline the questions.

**David**: One question I’ve wondered about is that GR seems to imply that objects tend to move toward regions where time runs more slowly. Can we shed some light on that?

**Thanu**: That is an interesting way of putting it. It’s a nice point of view. I’m not completely certain it is technically correct. For example, a planet which is orbiting the Sun on a circular orbit, is not moving toward a region where the time is running slower because time is running at the same rate everywhere on a circular orbit. But a particle which is falling radially into the Sun will move like that. But even there I’m not sure. If you take, for example, a cosmological solution, it seems to have something like a repulsion. I mean even without a cosmological constant. Ordinary radiation or matter dominated universe which is expanding. Matter seems to be going away from a point. So it is not true that all solutions of gravity have this feature.

**David**: In GR there is tremendous difficulty understanding black holes in finite regions. We always have this asymptotically flat condition.

**Thanu**: That’s correct.

**David**: Otherwise we can’t make sense physically of what’s going on. Does the thermodynamic parallel have some insights?

**Thanu**: There is something interesting in the following sense. Usually when things are not asymptotically flat you ask what makes it so. And invariably cosmology kicks in. Of course, you can cook up solutions but, by and large, the most natural situation is if you write down a black hole solution in a universe which has, say, a cosmological constant. The universe will have a deSitter-like behavior at very large distances and it will have a black hole like behavior at small scales. So you need to understand that.

What our paradigm tells us is that there are two places where thermodynamic equilibrium can break down. I need to explain this in slight detail. We have already said that what we normally understood to be gravity is just the thermodynamics of a spacetime fluid. Now, it is a thermodynamic description but underlying it there is a statistical mechanics. So you have to ask when the Einstein equations arise as thermodynamic equations and when Einstein’s equations break down. When does the thermodynamic limit break down in a fluid? Normally you would say that when you go to smaller and smaller scales, when the mean free path of the molecules is compatible with the scale you are probing, you do not have thermodynamics. That is known. But there is another place where thermodynamics breaks down in a fluid.

**David**: When you don’t have equilibrium.

**Thanu**: Yes! You have an explosion inside the fluid, for example. Then it might not have thermalized at a large distance and achieved the thermodynamic limit. So in the same sort of way, the Einstein equations break down at Planck scales, which is like the mean free path of the atoms of spacetime. But it can also break down on very large scales. The symmetries of the Einstein equations can then go haywire. I claim that this is the root cause of us having a cosmic background which breaks Lorentz symmetry. After all, we know that the CMB selects a frame in which there is a special class of observers; In, say, 20 years down the line, somebody is going to give you a small gadget which will hook to the dipole anisotropy of the CMB and tell you in which direction your car is moving! It is just a question of technological sensitivity. In principle, you can tell which way you are moving, by comparing yourself with the CMB. It also tells you a universal time by the temperature of the radiation. This reference frame could come about because at very large scales the Einsteinian symmetries break down. And there is a preferred situation. This is qualitatively argued in my work but not demonstrated quantitatively.

So now to come back to your question about non-asymptotically flat spacetime. Non-asymptotically flat spacetimes are special cases where the thermodynamic limit has broken down at very large scales. And it selects out certain degrees of freedom and certain backgrounds and things like that so it has to be understood in that context. I’m trying to simplify it but this is roughly the idea.

**David**: The implication is that GR doesn’t apply to the Universe on the largest scales.

**Thanu**: Yes, GR doesn’t apply at very large scales in the Universe. Exactly. In fact, we can write down an equation for that. Take the volume within the Hubble sphere, that is a sphere of Hubble radius *c*/*H*, and ask what drives the expansion of this volume. Just take dV/dt. It turns out, lo and behold, that it is just given by the surface degrees of freedom minus the bulk degrees of freedom. And as the Universe evolves, the de Sitter solution kicks in as an equilibrium solution when the bulk degrees of freedom and the surface degrees of freedom are equal. Then the volume of the Hubble sphere doesn’t change because the Hubble radius doesn’t change for a de Sitter Universe.

The next question is whether this equation is exact or whether there are correction terms to it. We believe there are correction terms to it. So at very large scales, there could be corrections to GR and the whole thing is how we translate all these back to observable signatures. In that we have not succeeded yet.

**David**: So is this something that you’re working on?

**Thanu**: This is something that we are very much working on but technically it is very complicated. It is like non-equilibrium thermodynamics versus equilibrium thermodynamics. Same level of complexity.

**David**: You mentioned this before. That quantizing gravity doesn’t make sense. What are people getting in the different approaches in which they are quantizing gravity? They are getting sort of the equivalent of the phonons or something like that depending on what they’re using. What is string theory doing when they quantize…?

**Thanu**: Well, you are asking the wrong guy! You should ask a string theorist and he will tell you the success story of the string theory! Just like I told you the success story of my theory! Let me first make the charitable comment that there is probably some truth in string theory. Ok? I mean you can’t get this kind of miraculous mathematical results without there being a germ of truth. But the point is, it also has a huge amount of extra baggage and the signal is lost in huge amount of noise.

But my most important complaint or objection against all these conventional approaches is that they miss the two most important clues Nature has given to us about gravity. First is that null surfaces block information. Therefore, they have entropy and temperature. String theory says nothing about it. Loop quantum gravity says nothing about it. These are added structures in these approaches and not fundamental ingredients. They don’t come in intrinsically. The equations of gravitational field in string theory or loop quantum gravity are not thermodynamic equations. That is my first objection.

Second one is that these approaches say nothing about the cosmological constant problem. This is an elephant in the room. The fact that there is a cosmological constant and the fact that if I add a constant to the matter Lagrangian, that changes the zero point level, gravity doesn’t care about it; it has weathered through all these phase transitions in the early universe so nicely. This feature is not incorporated. They have absolutely no idea about the cosmological constant.

On the other hand, our approach actually predicts the numerical value of the cosmological constant. It requires some assumptions about the information content of the early pre-geometric phase, but once there is a phase transition from a pre-geometric phase to the geometric phase, early on in the universe, what does not change is the total number of degrees of freedom. This is like taking, for example, solid ice and melting it. Lots of things change. But the total number of atoms remains invariant. So total number of the degrees of freedom does not change in this pre-geometric phase to geometric phase transition. We could relate it to the information content of the universe and determine the numerical value of the cosmological constant. Our approach was not designed to solve this problem. That is why we are very kicked about it. When you do this the numbers come out right. And you can actually predict the value of the cosmological constant.

Just to sum up the conventional approaches like string theory etc., ignore the cosmological constant problem as well as the thermodynamic description of spacetime. These, I believe, are the two vital clues about the nature of gravity. So you have thrown out two vital clues and you are trying to build a theory with the conventional QFT approach. Because that approach has been so prominently successful – i.e quantum field theory is a great success story in quantising other interactions – and we are just pushing it into this. Well, that doesn’t work.

**David**: So let’s talk about the cosmological constant. The numbers that you are getting. Are they making sense?

**Thanu**: Yes. They make a lot of sense. What happens is that you take an observer in the universe, and you ask how much information about the universe he can gather. He lives to eternity. He never dies. So if he lives all the way to infinity, what is the total amount of information he can get? If the cosmological constant is zero, he can get an infinite amount of information. But if the cosmological constant is non zero, he can only get a finite amount of information. You can quantify what I mean by information. So you can write down a formula that relates the numerical value of the cosmological constant to the information content that can be acquired by an eternal observer. I have a formula relating these two quantities and everything else in it is known. Now, I need to know what is the information content. When I plug it in, I get a numerical value for the cosmological constant. I can give arguments saying that this information content has to come from the principle I told you: viz., that the number of degrees of freedom should not change when you go from a pre-geometric phase to a geometric phase. That information content happens to be 4π. It is the surface area of a sphere of unit radius. You plug that in and there are no free parameters in the equation. The equation has cosmological constant on the left hand side, the amplitude of the primordial perturbations – which are measured by COBE and all that – on the right hand side, and a couple of cosmological parameters that are very well measured. You plug these in and you can calculate the value of the cosmological constant. It agrees with the observed value to one part in a thousand. With no free parameters. So we believe it makes a lot of sense.

We have to understand this concept of information at a much deeper level, which we are trying to do. Information is an elusive concept. It is not like energy or angular momentum or something. You give me any system and I can write down an expression for its angular momentum. But if I ask you about the information content of a rock, it is very difficult. It is very contextual. So we have come up with a definition of information appropriate to the cosmological context. And we need to understand it at a deeper level.

It is also important that until you have the new symmetry of the theory, i.e. if you add a constant to the matter sector, the gravitational equations remain invariant, this approach to cosmological constant does not make sense. Suppose gravitational equations are not invariant under the zero level of energy. And I tell you the cosmological constant has a specific value. You will go and add a constant to the matter sector and the cosmological constant value has gone astray. So these two things go hand in hand. Only when the theory has thermodynamic interpretation, so that addition of a constant to the matter Lagrangian is a symmetry of the theory, I can even start asking if you have a model to predict the numerical value of the cosmological constant. Otherwise, the numerical value of the cosmological constant doesn’t make sense. So they all cling together very well. That we think is very encouraging.

**David**: We’ve been taught that gravity is the curvature of spacetime. Let’s replace that with the statement that gravity is about the heat…

**Thanu**: The thermodynamics of a fluid we call spacetime.

**David**: Ok. The thermodynamics of a fluid we call spacetime. So there’s a more general picture that incorporates GR. In the same sense that we can see Newton inside GR, we can now start talking about seeing GR…

**Thanu**: Yes. That is definitely true. But the way you see this is… How do I put it?... I want to be completely clear as to what has been achieved and what is conjectural. When you go from Newton to general relativity, general relativity not only embeds Newtonian theory inside it, but it also has other things. It has Mercury’s perihelion precession. It has the bending of light etc. In the same way, when I embed GR in this thermodynamic paradigm, I get more. More like the value of the cosmological constant. And some ideas about how at very large scales the cosmology is behaving etc. But most of GR is retained, just as Newtonian gravity is retained in general relativity, in this thermodynamic approach. If you ask me whether the planetary orbits are going to change in the thermodynamic paradigm, the answer is no. On those scales GR is indistinguishable from the thermodynamic theory. So we have not been able to come up with an experimental test which will just nail this thing down. That would have been lovely. Only things which we have are evidences like the cosmological constant and things like that, but with that disclaimer, it is true that GR is embedded in a much larger paradigm of thermodynamic atoms of spacetime. Yes.

**David**: Ok. So we can look for new predictions at the largest scales but also on very small scales. So what about the Big Bang? Do you have a way of thinking about that?

**Thanu**: Big Bang is not small scale because the way we think about it is not like a cracker explosion, right? The entire universe was contained so I’m not sure I would call it small scale. Near Big Bang the major unsolved problem is the singularity. Whether inside the collapse of a black hole or at the Big Bang. This is again a point where I have a complaint against usual theories of quantum gravity because you claim you understand black holes, but you only understand some peripheral structure of a black hole near the horizon. What happens at the singularity? So if a quantum theory of gravity cannot tell me what happens to my colleague who jumps in to the black hole and what happens to him as his clock keeps running, then we have failed. I mean that is one of the things that you need in a good theory of quantum gravity.

What happens near a singularity is that the discrete structure of the spacetime manifests itself as what we call the zero point length of spacetime. That is just like you have a zero point energy due to quantum fluctuations. There is a zero point length to the spacetime. If you take two events in spacetime and you measure its distance, and square the distance, the squared distance has fluctuations. When the two points come closer and hit each other, the squared distance goes to zero in the classical theory, but in virtually any quantum gravity model, including this thermodynamic approach, you’ll find that a small residue is left, which is of the order of the Planck length squared. Because of this, the singularities are naturally avoided in this theory. What you find is that there is a mechanism built in, just because of discrete structure, there is a minimum length in the theory, and nothing can go below that. So there is a natural mechanism available for solving the Big Bang problem, so to speak, that you cannot have a singularity.

What replaces the singularity is a transition to a pre-geometric phase, which is like ice and water. So the picture which emerges is something like this: you take a huge block of ice and you put a heating source inside it. What the heating source does is to first melt the water around it and this waterfront, so to speak, becomes bigger and bigger, expanding outward. So there is a region inside where the water has greater symmetry than solid ice. This is standard solid state physics because water has rotational symmetry while in the solid lattice you don’t have rotational symmetry, as I mentioned before. So you get a more symmetric phase inside around the heating source. And the outside is in a less symmetric phase. This is exactly what Big Bang is. So the Big Bang in some sense is a big melt, speaking figuratively. These pre-geometric degrees of freedom, which are the degrees of freedom of ice, are getting converted into the geometric degrees of freedom, which the degrees of freedom of the water. At the edge where they are separated, there are these two phases coexisting and this is where equilibrium thermodynamics breaks down. In the water, I can use equilibrium thermodynamics. In the ice, I can use equilibrium thermodynamics. When ice is changing into water, that borderline is the very large scales of the universe. So it ties up the very large scales and the very small scales in this picture. And at very small scales, the zero point length, makes sure that the singularities will be avoided. Just to be very clear we have worked out all these in some simple toy models and the zero point length idea works out fine but we don’t have a comprehensive model of the universe where we can show how this happens and what is this phase transition etc. These are all work in progress.

**David**: Are your ideas compatible with the current picture in which the universe started in a low entropy state?

**Thanu**: You have to be careful here. There is the second law for matter and there is the second law for the gravitational thermodynamics. Or rather the thermodynamics underlying what we call gravitational physics. Now, the gravitational aspect of the second law, is proved for black holes etc., but when you take the entire spacetime as a thermodynamic entity and write down the equations and ask what happens, what happens is that it is driven towards an equilibrium. As the equilibrium is reached nothing further happens. Asymptotically the universe reaches de Sitter state. Once the geometry asymptotically becomes de Sitter state, then whatever happens to matter in de Sitter space kicks in. And that would be the natural heat death. We are not contributing anything new for that part. This is known physics.

**David**: What do you make of these recent observations that challenge the cosmological constant?

**Thanu**: Are you referring to the Hubble constant?

**David**: I’m referring to the dark energy questions starting in 2016. There were some papers claiming that the observational evidence based on the supernovae was called into question.

**Thanu**: I am with the mainstream physics. There are lots of technical issues with these observations so these guys are doing a great job of pointing it out. But I think there is dark energy and accelerating motion. One reason is that we can ignore the entire supernovae data. Just from Planck data, from CMB, I can sort out the cosmological parameters. Not so accurately once I have thrown out a huge amount of data. But still it indicates that the total Ω is like 1. And the observed Ω of matter is much less. The cosmological constant is still a best fit. So it is not just supernovae anymore. I think dark energy is here to stay.

**David**: What is the reaction to your ideas?

**Thanu**: That GR is like the thermodynamic limit of degrees of freedom underlying it, virtually anyone would agree. So if you talk to a string theorist he would say ‘Oh, yes of course! The atoms of spacetime are our strings”. Or, if you talk to loop quantum gravity guy, they’ll say ‘Yeah, these are the structures which we have”. At some stage when we started talking very seriously about this emergent gravity paradigm, and popularised it, everybody jumped in and has sort of internalized it. This idea that the classical gravity is some kind of coarse grained description of microscopic degrees of freedom, everyone will agree.

Now the results related to Einstein’s equation being written in a thermodynamic language etc. is 100% algebra so there can be no disagreement about it. There is nothing that you can question about that. So the community has no issues with that.

The problem where I face huge resistance within the community is in my approach to the solution for the cosmological constant. I make this big claim of solving the cosmological constant problem. That I am actually giving you the numerical value of. So I had gone around giving talks all over the place etc., and I have talked to friends and colleagues. Everybody is intrigued by this result. Again, there are no technical objections in the sense of the algebra or inconsistencies. So the whole thing hinges on whether it is a numerical coincidence. I write down something and I have numbers like e to the minus 36π squared which you usually see only in the papers of crackpots. You know, guys who come up with the value of the fine structure constant etc. Of course, they know that I’m a pretty serious guy but they find it very intriguing that it is almost numerological.

Is it just a numerical coincidence? That is a matter of opinion right now. We don’t think it is a numerical coincidence for the simple reason that this was never our intention. When the emergent gravity paradigm was developed we didn’t think that it would have anything to say about the cosmological constant. It just came as an offshoot. And then we calculated it. I wrote first a preprint, which I didn’t even publish, in which I goofed up in the sense that I ignored the matter dominated phase of the universe. I approximated it because instead of solving a cubic equation it was easier to solve a linear equation! So I worked it out and then I found that I couldn’t quite get the numbers right. But I just put it up as an idea. It is there in the arXiv (See arXiv:1210.4174) . A few years later, with a co-author, who happens to be my daughter, Hamsa Padmanabhan, we did a far better job. She said ‘Look. The matter dominated phase will make a difference’. Then she calculated it and found that it made a difference. So we wrote a joint paper saying that if you do that, it comes out right (See arXiv:1703.06144). So, in our own minds we know that we didn’t tune anything. First, when I got the wrong result, there is an arXiv paper which gives the wrong result, just saying ‘this is the idea’. The 4π is the key. I was getting it, almost there but not quite. Then we have a far more improved version which gets everything right.

So we believe in it, but the community is skeptical. They don’t know why this is working. Some of them feel that there is something very deep here. And there are others who feel ‘No, no, no. This is just a numerical coincidence. We shouldn’t make much of it’. But if you take that out, rest of the results are accepted by the community because they are not very controversial.

**David**: One thinks of the typical path that new ideas experience. First they get ignored. Then people have strong objections…

**Thanu**: This is true. I started this programme in 2002 and until something like 2012 nobody really took great notice. Then it slowly started picking up and now it is doing quite well. Many people have started “borrowing” these ideas! Yeah. So that always happens. It is so fascinating. In my personal philosophy I don’t care too much about it. And I am at a stage in my career where I can afford to spend time doing these sort of things.

**David**: But it’s nice to have interesting conversations and not just getting objections that don’t make any sense.