Erik Verlinde: Why My Entropic Gravity Transcends Jacobson's

Added: 2026-05-11

[00:00:00]I want to get to entropic gravity. So  entropic gravity is a large umbrella, and sometimes it refers to Ted  Jacobson’s results, which we’re not referring to here. And I would like to know  the relationship between yours and Ted Jacobson.

[00:00:16]So my understanding is Ted Jacobson used  Clausius’s entropy along with Rindler horizons to get Einstein’s equations, whereas  you are using it to get Newton’s equations.

[00:00:28]Does yours derive Ted Jacobson’s? Does  Ted Jacobson’s derive yours? Is there not an intersection between them? How do  you view those two different approaches?

[00:00:36]Well, Ted Jacobson certainly was the  first to realize that this idea of, well, we’re skipping a step here, but this  idea that there’s some relationship between the horizon and entropy, these areas and  entropy, can be used to derive the equations.

[00:00:57]The Einstein equations. Actually, this  goes back to Hawking and Bekenstein.

[00:01:01]They wrote down laws that look like the laws  of thermodynamics that apply to black holes.

[00:01:07]And so what Jacobson showed is that if  you assume that the entanglement entropy, this quantity that we’ve been talking about, is equal to the area of some horizon surface,  then you can derive the Einstein equations.

[00:01:24]Now, one of the things that I added to his theory, because certainly in my equations I also like  to talk about deriving Einstein’s equations, which is very important, but there’s  a much more fundamental step.

[00:01:39]Because one of the things that I put in is that  I said that Jacobson basically already assumed spacetime. He assumed that there is an area.  He said there is an entanglement entropy that goes like the area. Let’s write down the first  law, and then it becomes Einstein’s equations.

[00:01:58]But I think there’s something circular about  the reasoning, because assuming spacetime also is assuming its geometry. You cannot  derive its geometry from something there.

[00:02:08]So what I realized is that, and this is  sort of what I emphasized in my paper, is that the first thing that you have to  get to is understanding spacetime. And there’s something more fundamental  than just the gravitational laws.

[00:02:22]The gravitational laws are about forces  that are changing, just already Newton’s first law. So Newton wrote down three  laws: the first law being about inertia, the second law about action is minus reaction,  and the third law being the gravitational force.

[00:02:41]In a certain way, what Jacobson does, he derives  the third law. Because if you derive Einstein’s equations, you also derive Newton’s third  law. But you don’t tell me how inertia arises.

[00:02:56]Inertia is a much more fundamental concept  that basically tells you what mass means.

[00:03:01]When we move something, why do we apply a force, need to apply a force, to accelerate it? So  F equals ma, that’s the law that I derived.

[00:03:12]And I think that’s also still  a very important thing, is that in the progress that we are making  now, we’re eventually not deriving only Einstein’s equations. We need to  derive first what space and time are.

[00:03:28]And so the fact that space and time are  emergent is something that I emphasized in my paper and that he didn’t see. So there’s  some way that my paper transcends his equations, his results. And I think it  also contains it in some form.

[00:03:48]So I think the approach is different, but  I think the emphasis that I made was much more on the emergence of space and time  itself, and also on the fundamental laws that first need to be derived, namely the  first law of Newton, the law of inertia.

[00:04:10]Okay, so gravity emerges from thermodynamics.  To me, that implies some equilibrium. But at the same time, we need gravity to drive  structure formation. And that seems to me to be non-equilibrium, manifestly  so. So how do those two cohere?

[00:04:28]Equilibrium means something in terms  of the equilibrium in the particles and everything that’s filling the universe, or  something like that. It’s kind of what we had.

[00:04:38]But if you ask what is driving the laws of  gravity, it’s not the particles that are doing this. It’s really these microscopic  building blocks of the spacetime itself.

[00:04:49]And they are in equilibrium at horizons of  black holes. They are at equilibrium at the horizon of a cosmological horizon. They’re not in  equilibrium in some arbitrary point of spacetime.

[00:05:02]And so there’s some way that equilibrium  can be distorted there. That’s one thing.

[00:05:09]But the other thing is that the expansion of the  universe and all the things that we use in our current formulation of cosmology and structure  formation are derived from Einstein’s equations.

[00:05:22]So if you first want to derive Einstein’s  equations, then these other equations follow.

[00:05:28]But I think the more microscopic description might  be quite different from what Einstein’s equation already is telling us. So the assumption  of equilibrium, I think, certainly goes into the laws of thermodynamics, but  that only needs to apply very locally, in some very small neighborhood. And this  is also what Jacobson’s argument was about.

[00:05:53]So it’s not like there’s an overall  equilibrium. So in a certain way, I should say the assumption  of equilibrium is not what is necessary for deriving the Einstein equations  or something like that. It’s only—yeah, anyway, I don’t think there’s a contradiction  between those two ways of looking at it.

[00:06:21]So structure formation, I think, is  something that eventually will fall at a much later level in deriving  those equations. So they’re not connected to the equilibrium laws that  we apply for gravitational equations.

[00:06:37]Is entanglement entropy well-defined in  collapsing or non-equilibrium configurations?

[00:06:48]Also a good question. Then people have— So we have a description of entanglement  entropy, a quite precise one, actually, in theories that have been studied for now more  than 25 years. Actually, it goes back to the ideas of Maldacena, which was building on ideas  of Bekenstein and Hawking, Susskind, ’t Hooft.

[00:07:19]But anyway, there we calculated entanglement  entropy in a very precise way. This work has been extended, where we also have dynamical situations  where we can define entanglement entropy. I mean, there’s names associated to that: Hubeny,  Rangamani, Takayanagi. I mean, there’s some people that have defined entanglement entropy also in  dynamical situations. So there’s no problem there.

[00:07:46]However, one of the insights  we are having now, actually, is one of the big discussions going on is  that there’s more than just entanglement that’s going to be important in this  microscopic description. Entanglement entropy can be defined in those situations,  but we have other things to worry about.

[00:08:08]Things like computational complexity. I’m just  dropping a word here. But there are many more concepts, going back to that word, that are  playing a role in this microscopic theory.

[00:08:21]I mean, it’s clearly going way beyond  what we can discuss in this podcast, but we are really making progress in defining  all these physical concepts in situations that are closer and closer to what we  really need to describe the real world.

[00:08:43]We’re not there yet. I mean, it’s clear  that this theory needs further development, and I think we’re making lots of  progress. But we’re still, well, years and maybe even decades away from having  this better understanding and having what I would call sort of the next theory, where  we indeed have found a more fundamental description of what we call nature,  but maybe not the most fundamental.

[00:09:10]So I don’t think that we will get to  this most fundamental description, but we will make progress towards  a more fundamental description.

[00:09:19]So when speaking about deriving space, in the  Ryu–Takayanagi, if I’m pronouncing that correctly, the formula, it relies on a spatial region  A. So does that not already encode locality, like a boundary geometry to derive the  bulk geometry? So space doesn’t emerge from entanglement per se, it’s just the bulk  emerges from boundaries plus entanglement?

[00:09:44]And you’re right, we have some understanding of microscopic descriptions in spacetime where  we have a boundary, which is called anti-de Sitter space. It doesn’t look at all  like the universe that we live in.

[00:10:00]And they have—I mean, the Ryu–Takayanagi, which  is kind of indeed the people that have done this initial work—they studied entanglement  entropy in this microscopic description.

[00:10:12]And this microscopic theory can be thought about  as living on a boundary where already is some space associated with it. And it’s true that it’s  very useful to have already some geometry there, but the emergent geometry is the one  that we have sort of in the space, which we call the bulk. It’s some  additional direction that we have to add.

[00:10:34]And you’re right that the area that we  define there is not totally emergent in the sense that it already has some definition on the  boundary. This is one of the reasons why I think AdS/CFT is not the final story of how we’re going  to understand spacetime. Because we need to get rid of this idea that there is a boundary, because  our universe doesn’t have a boundary of that sort.

[00:11:04]But it still means that we can make  progress towards it. And I think what happened in the last decade, maybe, is  using this Ryu–Takayanagi idea and see how we can formulate it in ways where  we can maybe get rid of this boundary.

[00:11:19]And so there’s this dependence on the choice  of this area that you’re talking about. And this is where I think we need new concepts, not just maybe entanglement entropy,  but also maybe this idea of complexity.

[00:11:38]But this is also where I think we are having  trouble following the ideas, for instance, of Jacobson. Jacobson did assume that we can  define entanglement entropy, did assume that we can identify it with the area, which is kind  of what Ryu and Takayanagi have done as well.

[00:11:58]And there are other people, like in particular Van  Raamsdonk—I should mention his name—because this idea that space and time are connected because  of entanglement is kind of due to Van Raamsdonk.

[00:12:11]Also, Maldacena and Susskind  have sort of advocated this, and they have this slogan, which they call  ER = EPR, which maybe you have heard about.

[00:12:22]Which I think you actually thought of a few  months before. Wasn’t there some email exchange in 2012 between you and Herman where you presaged  this idea, but you didn’t publish it, ER = EPR?

[00:12:34]That’s correct. That is correct. We already had  this idea, but I think at that time we already realized that the first idea really was due to Van  Raamsdonk. I think in that sense the credit should be going fully to him. Although the slogan was,  of course, invented by Susskind and Maldacena.

[00:12:56]But of course, I mean, there was early work by  Maldacena where he also realized that when you entangle two conformal field  theories, you get some connectivity and so on. So there’s a way that Maldacena  certainly, and Susskind also, deserve it.

[00:13:09]But we had, indeed, this idea already. But  that was in the context of black holes.

[00:13:14]And I think what we are learning nowadays  is that we maybe have to extend this idea of only using entanglement. So Susskind  is also known for the other slogan where it says entanglement is not enough. And what  he tried to add in that description is what’s called computational complexity. And I do  think that that notion is also important.

[00:13:38]So there are many steps that we still need  to go through. But maybe what I wanted to say is that Jacobson derived the laws of  Einstein, I mean the general relativity, from assuming that the entanglement  entropy goes like the area.

[00:13:58]I mean, we can derive it using  sort of these ideas that we—well, when we use Einstein’s equations, we can  derive it kind of, but we have then sort of worked the other way. So there’s  some way that the logic changes.

[00:14:11]So if we assume that entanglement goes like the  area, we can derive the Einstein equations. But this is an assumption, and you may  wonder whether that assumption is always true. And I think that there are  situations where that might not be true.

[00:14:25]And this is where I was already saying  that our universe is different from the one that we have been studying all the time, namely this anti-de Sitter space. And  maybe things work differently there.

[00:14:37]And I think I’m actually convinced that  when we start redoing our analysis of how to derive Einstein’s equations, that  in a universe where there is dark energy, which is more like our own universe,  that there can be deviations from it.

[00:14:53]And so I hope that our quest in understanding  where the gravitational laws come from will help us understand what is dark energy  and even what is dark matter. So there’s a lot of things, I think, to be discovered there.

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