Wednesday, November 30, 2016

Dear Dr. B: What is emergent gravity?

    “Hello Sabine, I've seen a couple of articles lately on emergent gravity. I'm not a scientist so I would love to read one of your easy-to-understand blog entries on the subject.


    Michael Tucker
    Wichita, KS”

Dear Michael,

Emergent gravity has been in the news lately because of a new paper by Erik Verlinde. I’ll tell you some more about that paper in an upcoming post, but answering your question makes for a good preparation.

The “gravity” in emergent gravity refers to the theory of general relativity in the regimes where we have tested it. That means Einstein’s field equations and curved space-time and all that.

The “emergent” means that gravity isn’t fundamental, but instead can be derived from some underlying structure. That’s what we mean by “emergent” in theoretical physics: If theory B can be derived from theory A but not the other way round, then B emerges from A.

You might be more familiar with seeing the word “emergent” applied to objects or properties of objects, which is another way physicists use the expression. Sound waves in the theory of gases, for example, emerge from molecular interactions. Van-der Waals forces emerge from quantum electrodynamics. Protons emerge from quantum chromodynamics. And so on.

Everything that isn’t in the standard model or general relativity is known to be emergent already. And since I know that it annoys so many of you, let me point out again that, yes, to our current best knowledge this includes cells and brains and free will. Fundamentally, you’re all just a lot of interacting particles. Get over it.

General relativity and the standard model are the currently the most fundamental descriptions of nature which we have. For the theoretical physicist, the interesting question is then whether these two theories are also emergent from something else. Most physicists in the field think the answer is yes. And any theory in which general relativity – in the tested regimes – is derived from a more fundamental theory, is a case of “emergent gravity.”

That might not sound like such a new idea and indeed it isn’t. In string theory, for example, gravity – like everything else – “emerges” from, well, strings. There are a lot of other attempts to explain gravitons – the quanta of the gravitational interaction – as not-fundamental “quasi-particles” which emerge, much like sound-waves, because space-time is made of something else. An example for this is the model pursued by Xiao-Gang Wen and collaborators in which space-time, and matter, and really everything is made of qbits. Including cells and brains and so on.

Xiao-Gang’s model stands out because it can also include the gauge-groups of the standard model, though last time I looked chirality was an issue. But there are many other models of emergent gravity which focus on just getting general relativity. Lorenzo Sindoni has written a very useful, though quite technical, review of such models.

Almost all such attempts to have gravity emerge from some underlying “stuff” run into trouble because the “stuff” defines a preferred frame which shouldn’t exist in general relativity. They violate Lorentz-invariance, which we know observationally is fulfilled to very high precision.

An exception to this is entropic gravity, an idea pioneered by Ted Jacobson 20 years ago. Jacobson pointed out that there are very close relations between gravity and thermodynamics, and this research direction has since gained a lot of momentum.

The relation between general relativity and thermodynamics in itself doesn’t make gravity emergent, it’s merely a reformulation of gravity. But thermodynamics itself is an emergent theory – it describes the behavior of very large numbers of some kind of small things. Hence, that gravity looks a lot like thermodynamics makes one think that maybe it’s emergent from the interaction of a lot of small things.

What are the small things? Well, the currently best guess is that they’re strings. That’s because string theory is (at least to my knowledge) the only way to avoid the problems with Lorentz-invariance violation in emergent gravity scenarios. (Gravity is not emergent in Loop Quantum Gravity – its quantized version is directly encoded in the variables.)

But as long as you’re not looking at very short distances, it might not matter much exactly what gravity emerges from. Like thermodynamics was developed before it could be derived from statistical mechanics, we might be able to develop emergent gravity before we know what to derive it from.

This is only interesting, however, if the gravity that “emerges” is only approximately identical to general relativity, and differs from it in specific ways. For example, if gravity is emergent, then the cosmological constant and/or dark matter might emerge with it, whereas in our current formulation, these have to be added as sources for general relativity.

So, in summary “emergent gravity” is a rather vague umbrella term that encompasses a large number of models in which gravity isn’t a fundamental interaction. The specific theory of emergent gravity which has recently made headlines is better known as “entropic gravity” and is, I would say, the currently most promising candidate for emergent gravity. It’s believed to be related to, or maybe even be part of string theory, but if there are such links they aren’t presently well understood.

Thanks for an interesting question!

Aside: Sorry about the issue with the comments. I turned on G+ comments, thinking they'd be displayed in addition, but that instead removed all the other comments. So I've reset this to the previous version, though I find it very cumbersome to have to follow four different comment threads for the same post.


  1. Ok, using the Google comments was a total disaster and in addition now that I've turned it off the comments have entirely vanished and aren't even to be found on G+. At least I seem to have managed to turn off the captcha which recently has been incredibly annoying.

    Having said that, someone complained that I didn't mention AdS/CFT as an example for emergent gravity. This comment seems to have vanished too, so sorry if I can't recall the details. But the reason I didn't mention AdS/CFT as a case of emergent gravity is that it's a bad example. In AdS/CFT gravity is emergent from a gauge theory, but the gauge theory is also emergent from gravity. The whole point of the duality is that both sides are equally fundamental. I wrote about this here. Best,


  2. While on that note I wonder if you've written a blog on why confirmation of the existence of gravitons the quanta of gravity waves in and of itself would still not yield to a theory of quantum gravity

  3. Synchlavier,

    The blog is the full website. As in "I am writing a blog." The "log" in "blog" stands for "log". The individual entries are blogposts, or articles or threads or essays or call them what you wish, but don't call them "blog."

    Gravitons are the weak-field limit. Finding a graviton might or might not tell you something about the UV completion. Most likely not much.

    1. Uh oh.. yeah..apologies I'd written the question at an airport while waiting on someone

  4. I am eagerly awaiting your opinion on Erik Verlinde's new paper. It made quite a splash over here in the Netherlands. Even outside theoretical physics, or physics as such. But his 2010 paper too made the newspapers, be it in 2009 even before he had written it down.

  5. sabine:

    "The “emergent” means that gravity isn’t fundamental, but instead can be derived from some underlying structure. That’s what we mean by “emergent” in theoretical physics: If theory B can be derived from theory A but not the other way round, then B emerges from A.". i know you don't want to engage on a discussion about emergence but you should at least define it correctly. emergent behavior need not be derivable from any underlying structure. that's a reductionist view. to most workers in the field (e.g. Nobellst P.W. Anderson), emergent phenomena is usually not describable in terms of an underlying structure. and when it is derivable, it is not necessarily better then when it is not. e.g. Einstein said "A law is more impressive the greater the simplicity of its premises, the more different are the kinds of things it relates, and the more extended its range of applicability. Thermodynamics is] the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown.” personally, i prefer theories of physics that will never be overthown to those that will be overthrown.

  6. naivetheorist,

    You misread my statement. I explicitly explained in the first sentence what the "emergent" means in "emergent gravity" and in the second sentence what we mean by that in theoretical physics. Yes, there are a few physicists who indeed manage to believe in strong emergence. As they say, exceptions prove the rule. I elaborated on the distinction between strong and weak emergence here. However, there aren't any cases of strong emergence, so I don't see the point in talking about that. For all we presently know, the only emergence which exists is weak emergence and the idea of strong emergence is plainly inconsistent with established physics.

    You seem to believe that reductionism is a philosophy, but it's not. It's a hypothesis that's supported by centuries of research.

    I don't really care what type of theories you prefer and I don't know how that's relevant for anything.



  7. B:

    "I don't really care what type of theories you prefer and I don't know how that's relevant for anything.". why do you feel it is necessary or useful to make snarky responses (or do you not realize that your comments can be viewed this way)? such attacks (like Trump's tweets) only make you come across as being both petty and nasty. you might want to try to control your emotional reaction to comments unless they are personal attacks on you, which my comment wasn't.


  8. naivetheorist,

    You have made a statement I regard irrelevant and I have very unemotionally told you that I think it's irrelevant. As response you complain I'm the one being emotional. Speak of projection.

  9. Dear Bee, you mention the possible promise of the research approach largely stimulated by Jacobson's seminal paper that suggests the GR Field Equations are essentially a thermodynamic equation of state - which, ala Verlinde, leads to gravity being possibly considered as an 'entropic force'. What do you think about the claim that experimental results on cold neutrons in a gravitational field contradict this possible 'emergent' thermodynamic/entropic nature of the force of gravity?

  10. David,

    Not very much. See, nobody knows how to apply this (so-far very immature) model to quantum systems. Any such conclusions hence relies on additional assumptions. What you then show is that either the original model or the additional assumptions are incorrect, which isn't much of a statement. Honestly, I have forgotten the details, but I read the papers on that when they came out and that's what I recall. Best,


  11. " to our current best knowledge this includes cells and brains and free will. Fundamentally, you’re all just a lot of interacting particles. Get over it. "

    If we made even one iota of progress on the hard problem of consciousness, to the "best of our knowledge" might actually mean something. But, we haven't, and it doesn't. This statement is as much "religious", as it is scientific. I'm also surprised how quick folks are to dismiss free will. Without it, one isn't really even doing science! To quote Anton Zeilinger:

    "We always implicitly assume the freedom of the experimentalist… This fundamental assumption is essential to doing science. If this were not true, then, I suggest, it would make no sense at all to ask Nature questions in an experiment, since then Nature could determine what our questions are, and that could guide our questions such that we arrive at a false picture of Nature"

  12. Evan,

    Another one who is being annoyed? Well, it seems then I have to repeat it once again. The laws of nature that we have found imply that the equations that determine the behavior of large things follow from the underlying laws. There is no known way to AVOID this. There isn't any known exception to this. If you claim that strong emergence exists, then you are the one making an extraordinary claim. It's your claim that's religion - mine is solidly on the side of scientific evidence. Unfortunately, most of the people who - like you - go about and make big claims don't even know what they are talking about. That we don't know what consciousness is is entirely irrelevant for the discussion.

    Yes, I know that Zeiliger holds this opinion. I think it's a big mistake to make this assumption and it's indeed the reason why there's so much mush on the foundations of quantum mechanics. There isn't any evidence which actually supports this. Best,


  13. Sabine, I have had a basic question for a long time. What is AdS space? where does it exist in our world?
    I understand we live in a de-sitter space. Does Anti-de-sitter space exist inside a black hole?


  14. Emergent gravity makes sense to me; emergent spacetime does not. Can you explain WHERE and WHEN the qubits from which spacetime emerges exist? Are their interactions “happening” in a Platonic heaven?

  15. Gabe,

    That space-time is emergent means you use the qbits to define what "where" and "when" means. Ie, your question makes no sense.

  16. Mars,

    That's a good question. I'll bookmark this for a future "Dear Dr B."

  17. Sabine,

    If you re-read my comment, I made no claims. I was just pointing out your claim that free will is "emergent" is a non-evidence based claim. Not only that, it is good to realize the claim is based on a materialistic/reductionist world view, or paradigm. As we all know, all worldviews/philosophies/paradigms ultimately prove themselves limited, so it can be dangerous to apply them to phenomenon that are poorly understood, like consciousness and free will. And, consciousness may be irrelevant to the discussion, but you're the one that mentioned an aspect of consciousnesses (i.e. free will) in this blog article.

    In all fairness, you did say "to the best of our knowledge". I just think the best of our knowledge is pretty darn weak when it comes to free will (or consciousness, in general) at this point in time. I'm of the personal opinion that it would be hubris to think otherwise, but I know that's not a very common opinion here.

    You're probably also aware that Roger Penrose feels consciousness is non-computational, or non-algorithmic, and ultimately cannot be modeled by our known laws of physics.

    Clearly, the jury is still out on all this and I think it's safe to say none of us have much of a clue here. So, in the meantime, I suggest that we don't "get over it" and keep an open mind.

    Anyhow, don't take me the wrong way, you've got a great blog here, with well-written, thought-provoking articles, including this one. Carry on! and Cheers!

  18. Thank you Sabine for your clear explanation. I just took a course and learned a little about the work of Erik Verlinde. Promising!

  19. Evan,

    You are plainly wrong to think that it's based on no evidence and I find it remarkable how you simply ignore what I am telling you. I am telling you that to our best current knowledge of the laws of nature the behavior of large objects follows from that of its constituents. There isn't any known way to avoid that. There isn't any known exception. You are clinging onto the belief that maybe somehow a miracle can happen, just that you can't tell me how (and neither can Penrose). You are calling reductionism a world view or a paradigm. It's not - it's science. It's the probably most solid part of all of science that we have.

    If you're having a hard time understanding what I'm saying, I suggest you read Sean Carroll's recent book "The Big Picture". He explains it very well. Best,


  20. I tend to be skeptical of emergent gravity ideas. There have been several developments in quantum gravity research in the last few decades that indicate that general relativity and quantum mechanics are not as incompatible as once was believed.
    Loop quantum gravity, asymptotic safety, causal dynamical triangulations: they all hint that a quantized version of GR is well-behaved in the high-energy, nonperturbative regime.

  21. Sabine, great blog post as always. As a condensed matter person who just finished teaching undergrad stat mech for the semester, emergence is a favorite topic, and I was thinking about writing a post of my own about emergent gravity, but now that might be superfluous.

    One question. Isn't your take on strong emergence approaching the "no true Scotsman" argument? I mean, yes, somehow the sixfold symmetry of snowflakes must be effectively encoded in the underlying quantum mechanical properties of the individual water molecule, but emergent rigidity of solid ice and the sixfold symmetry of crystals nucleated from the vapor under certain conditions is rather non-obvious. It seems like strong emergence is defined in such a way that it's impossible to ever have.

  22. Douglas,

    It is possible to have strong emergence but that requires (to make a long story short) a breakdown of effective field theory. And a breakdown not just in a way of "is no longer practical" or "can't be calculated" but in a way of "doesn't follow" and "stops here at this point". There isn't any example of that.

    I actually think it can happen and I have an example for that but it's still unpublished. So for what the rest of the world is concerned, the sensible scientific approach is to say it can't happen. (There are a few examples in the literature for such cases, but they all rely on some "infinity" in one or the other way, which imo isn't a realistic system.)

    And yes, of course, it's defined so that it can't happen. But please don't blame me for that. I had a hard time trying to figure out what philosophers mean by strong emergence exactly because, from a physics perspective, it seems rather obviously impossible.

    Problem is - as you can see here and in many other of my comment sections - the vast majority of people doesn't even understand the point. They just have some vague idea that maybe large systems can ignore the microscopic laws somehow, not realizing the problem is that via the microscopic laws we already have a macroscopic law for the system, and any other law is either identical. Or one needs a good argument why the law we already have doesn't apply. Best,


  23. The discussions about strong emergence do remind me of the discussions on determinism of time. Is the future completely predetermined by the state of the universe now? Yes, if we ascribe to causality.

    After the fact, we can always find the causes of any event. However, we are stubbornly unable to predict the future. And there are arguments that, in a worst case scenario, we cannot produce a prediction of a future event faster than normal time flowing.

    In the same way, all "emergent behaviors" might directly follow from the laws of nature and reductionism. But we might not be able to "predict" the behavior of water until we rebuild nature in all its complexity and size to a precision that implies we just created water and looked what happened.

  24. Sabine,
    You keep saying I don't understand you. Did it ever occur to you that I do understand what you're saying, but I just have a different point of view? For example, I do not agree that reductionism IS science. Reductionism is philosophy. Science is a method. Particularly, a method that should be kept as free as possible from philosophy and any other predisposed way of viewing reality. Part of the problem, as I see it, is we too often confuse the scientific method with the popular "philosophy" of the day. Dangerous, because philosophy can effect the way we interpret the data collected via the scientific method, locking us into a box. I claim that is what is happening here. The only reason you think a miracle would have to happen is because you're viewing a reductionist explanation of consciousness as being the only possible explanation. Since that explanation has been forthcoming for quite some time, I would say it's possible it is more you, than I, that is waiting for a miracle. I'm just keeping an open mind to the potentiality that consciousness may not be amicable to a reductionistic, or at least a fully reductionistic, explanation. I argue this is the wise thing to do with any phenomenon that stubbornly defies explanation under current thought. How often does history have to teach us that? So, I'm hedging my bets, if anything, which is the opposite of waiting for a miracle. Of course, I'm fully aware this kind of thinking is anathema to mainstream scientific thought. But, that's alright, I've never been afraid to think for myself.
    I will leave this my last post and let you have the last word, if you choose to respond. This is turning into a distraction from the main thrust of your blog post, so apologies for that. Have a good one, cheers!

  25. Even,

    Well, I'll have to tell you once again that you don't seem to understand what I'm saying. I did not, not here and not anywhere else, say that 'a reductionist explanation of consciousness [is] the only explanation'. And no, reductionism is not philosophy. It's a hypothesis that is confirmed by countless experiments.


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