The Entropy Decade

We’re only a week and a half into the new decade, but already I’m seeing a trend…

A few days ago Sean Carroll’s book From Eternity to Here came out, promoting the idea that understanding time and cosmology is all about understanding entropy. The same day saw Erik Verlinde’s arXiv preprint On the Origin of Gravity and the Laws of Newton, which argues that

Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies.

Verlinde is a well known string theorist, and the paper is somewhat of a repudiation of the motivating idea for string theory unification, that string theory predicts gravity since it has a spin two massless state. But even with the main motivation gone, all is not lost for string theory, since

The presented ideas are consistent with our knowledge of string theory, but if correct they should have important implications for this theory as well. In particular, the description of gravity as being due to the exchange of closed strings can no longer be valid. In fact, it appears that strings have to be emergent too.

This is discussed in blog postings here, here and here, and yesterday even made it to Slashdot.

Today, it’s yet more entropy, with The Entropic Landscape by Bousso and Harnik, which propounds the Entropic Principle, that:

the number of observers is proportional, on average, to the amount of entropy produced.

and claims that this principle quantitatively predicts six important aspects of cosmology.

While much of physics in the last century was dominated by a highly successful program to identify fundamental degrees of freedom of nature and understand their dynamics using increasingly deep and sophisticated mathematical formalisms, now the trend appears to be very different. Many of the most well-known theorists are pursuing research programs with the remarkable features that:

  • You don’t need to have any idea what the fundamental degrees of freedom are.
  • You don’t need any fundamental dynamical laws either.
  • You can do everything with high school mathematics.
  • The last century was a hugely successful one for physics, whether this new order will be equally successful remains to be seen.

    Update: More analysis of the Verlinde paper here, and Verlinde now has a blog and a twitter feed about it.

    Update: Verlinde is adding explanations of points in his paper and conducting a discussion of it on Lubos Motl’s blog here. He now says that, to explain quantum gravity

    I am not sure that string theory is the way to go.

    Even though under his new framework string theory explains nothing about any fundamental physics, Verlinde refuses to give up on it, arguing that:

    It should also be emergent, and it is nothing but a framework like quantum field theory.

    In fact, I think of string theory as the way to make QFT in to a UV complete but still effective framework. It is based on universality. Many microscopic systems can lead to the same string theory. The string theory landscape is just the space of all universality classes of this framework. I have more to say about it, but will keep that for a publication, or I will post that some other time.

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    30 Responses to The Entropy Decade

    1. zanzibar says:

      “I have one word for you son… biology!”

      The future of physics lies where experiments will be done, or where data is already awaiting analysis. Interpolation, not extrapolation.

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    3. Chris W. says:

      Erik Verlinde’s paper should arguably be regarded as a review article providing an accessible overview of some fairly well-known work done by others over the past 15 years. In particular, his references include the following:

      [7] T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state,” Phys. Rev. Lett. 75, 1260 (1995)

      [14] T. Padmanabhan, “Thermodynamical Aspects of Gravity: New insights,” arXiv:0911.5004 [gr-qc], and references therein.

      Padmanabhan has developed these ideas in several papers.

      In addition, see the papers of Ariel Caticha, including the following:

      “The Information Geometry of Space and Time”
      arXiv:gr-qc/0508108 [26 Aug 2005 (v1)]

      “From Entropic Dynamics to Quantum Theory”
      arXiv:0907.4335 [24 Jul 2009 (v1)]

      I would also offer the general comment that arguments from thermodynamics and statistical mechanics played an extremely important role in arriving at an understanding of the microscopic dynamics of matter in the early 20th century. I think it is eminently reasonable at this stage to suppose that explorations of the deep interconnections of thermodynamics, entropy, and gravitation will play an equally important role in arriving at the unified understanding of the dynamical underpinnings of gravity and quantum fields that we don’t yet possess.

    4. Peter Morgan says:

      The definition of entropy is hyperplane dependent, as is its thermodynamic dual, temperature. That’s a problem. [As a matter of definition, something that is not hyperplane dependent would not be entropy, although clearly it is conceptually possible to introduce “measures of randomness” that are not associated with phase space. The vacuum state of QFT on Minkowski space is Lorentz and translation invariant, and introduces Gaussian fluctuations that are hyperplane independent, but quantum fluctuations are distinct from thermal fluctuations (which, again, are not Lorentz invariant).]

      As far as empirical success is concerned, SR, GR, and QM were all inspired by empiricist approaches, of different kinds, but at least partly inspired by the 19th Century epitome, thermodynamics (in contrast to statistical mechanics). The descent back into model-building realism, particularly since 1950, say, is questionable (Chad Orzel has an IHE article in which he characterizes Physics as being about models — I imagine Pierre Duhem is turning in his grave). The descent into Platonic realism about mathematical models is even more questionable. So, the great successes of the 20th Century could be said to be more rooted in the 19th Century, and a return to an updated empiricism might be a good thing.

    5. Chris W. says:

      Peter, your link to Chad Orzel’s IHE article seems to be null. Could you post a follow-up with a correction?

    6. Chris K. says:

      In the context of mentioning Padmanabhan, he also had an attempt to refute the massless spin-2 in “From Gravitons to Gravity: Myths and Reality” to which Deser cared to reply recently

    7. Hans-Peter says:

      Peter, your irony is honest, but some of it may be a little bit misplaced.

      # You don’t need to have any idea what the fundamental degrees of freedom are.

      Of course, this attitude is wrong. We need to know the fundamental degrees of freedom. Not looking for them is a way to avoid solutions; you are right on this.

      # You don’t need any fundamental dynamical laws either.

      This point is more delicate. If macroscopic dynamics, such as space-time curvature, is a statistical effect, there is a certain independence from the fundamental dynamics. So this point may be an acceptable one, at least partly or temporarily.

      # You can do everything with high school mathematics.

      This point is also delicate. “everything” is surely too much. But Verlinde’s paper is, in large part, the non-relativistic version of Jacobson’s. And nonrelativistic gravity is done, as we all know, with high-school maths. What is wrong here? There is only one thing that is wrong: that since 1995, when Jacobson wrote his paper, almost nobody was interested in his result. Both Jacobson and Verlinde show that, independently of the specific microscopic degrees of freedom, gravity results from their statistical properties. This is an old idea, going back to Smolin and others.

      You are right to say that this cannot be the end of the story: we need to find the underlying degrees of freedom. But there are many people who do not even think that such degrees of freedom exist. For them, Jacobson and Verlinde are good: they make them start thinking.

      Besides, there should be something about Jacobson and Verlinde that you should really like: these arguments are very much 3+1-dimensional. Verlinde talks about string theory as well, but in fact everything is 3+1-dimensional. (Jacobson, for example, does not mention string theory at all.) In fact, their work is discretely pulling the rug under the idea of higher dimensions. I at least, was very much astonished to see a string theorist like Verlinde writing this, because this means that he is slowly, but definitely leaving string theory – even though he does not yet admit it.

    8. If we are considering the fundamental level of reality, and asking the most fundamental questions about dynamics, we come up against the question “What decides how things change?” At this fundamental level, the physical laws can seem somewhat arbitrary (for example, the amount of charge on an electron). In fact, at this most fundamental level, the only principle which seems likely to describe dynamics seems to come from mathematics not physics: a system will have many more possible disordered states than ordered states, so a system which changes state randomly will most likely move to a more disordered state.

      While the second “law” of thermodynamics is “just” a statistical principle, it is a mightily powerful statistical principle! This is because the basis of the second law – that “disorder will increase” – seems so obvious, and seems to appeal to a fundamental, platonic principle of mathematics. For this reason, the second law manages to appear even more fundamental and unbreakable than the other physical laws, which seem rather arbitrary in comparison. Hence Arthur Eddington’s famous quote: “If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations – then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation – well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can offer you no hope; there is nothing for it but to collapse in deepest humiliation.”

      At the most fundamental level, I would just imagine physical dynamics are described by change of entropy – I can’t imagine any more fundamental principle which could possibly describe change.

    9. Pingback: “On the Origin of Gravity and the Laws of Newton” by Erik Verlinde « The Language of Bad Physics

    10. Jack Sarfatti says:

      The award winning 2004 Ph.D. dissertation of Tamara Davis from University of New South Wales (P.C. Davies on her committee) Figs 1.1 & 5.1 are very relevant to this discussion. The dark energy density we detect in our past light cone is the inverse area of our future event horizon in our future light cone. Therefore, it’s our future event horizon that must be the hologram screen acting retro-causally in the sense of Wheeler-Feynman’s total absorber. Indeed the increase in area of our future horizon from inflation to its asymptotic constant de Sitter value in the causal diamond of our observable universe (defined by T. Davis) explains why the thermodynamic arrow of time is in same sense as the cosmological arrow and why the entropy of the early universe is so relatively small at the moment of inflation.

    11. Chris W. says:

      (I found Chad Orzel’s most recent IHE article; I’m not sure it’s the one Peter Morgan had in mind.)

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    13. Peter Morgan says:

      Hans-Peter, you react fairly strongly against Peter’s “You don’t need to have any idea what the fundamental degrees of freedom are”, but I think this is a significant aspect of a statistical approach.

      We can achieve an empirically adequate model with effective degrees of freedom, whereas at some point in the future we will need to introduce a model that has different DOFs to achieve empirical adequacy to updated experimental data. Although it is possible that there is an endpoint to this process of refinement, there is no guarantee that there is.

      Chris W., sorry about the link problem. I had in mind the IHE article referred to in Chad’s “Uncertain Principles” blog post,

    14. Kevin Knuth says:

      I would be more inclined to suggest that this is the entropy century!

      Entropy is critical because of its relationship to inference. We are finding that the “laws” of physics are rules that tell us how to make the best inferences given our current states of knowledge. Probability and entropy are central to this point of view since probability is a measure on the space of logical statements that one can make about a system, and dually, entropy quantifies (not technically a measure) the relevance of questions one can ask about a system.

      There is nothing physical about entropy. This has led to great confusion in the past. Entropy quantifies the amount of information one would need to know the particular details about a given model.

      Similarly, the idea that information drives a system is faulty. Deriving laws based on probability and entropy does involve information that the one performing inference possesses, but ultimately the system is merely “driven” in the most probable direction. The fact that we get the right answer doesn’t mean that the information is driving the system. It means that we took into account all of the relevant information in making our predictions, and that this relevant information was sufficient to make an accurate prediction.

      The result is that we don’t get a theory of *why* something evolves the way it does. Instead we get a theory telling us which is the most probable scenario.

      I have been pursuing these ideas for the last decade now along with Ariel Caticha and others, and am astounded at what the community involved in this research has uncovered. This new perspective of physical law as inferential reasoning brings a unity and utility that previous interpretations lack. My belief is that these ideas will break through the stagnation that theoretical physics saw in the last century and propel us to new heights.

    15. The only substantial clue we have as to the link between quantum mechanics and gravity is black hole thermodynamics, so entropy looks like a sensible place to start. Many of the deepest ideas in physics (Faraday’s field concept, Einstein’s relativity) came not out of sophisticated math but careful analysis of the foundations of physics.

    16. Chris W. says:

      See Erik Verlinde’s latest post (13 January), scroll down to the following paragraph, and read from there:

      If the previous papers [Jacobson, et al] had made the emergence of gravity so clear, why are people still regarding string theory as the final theory of quantum gravity? Somehow, not everyone was convinced that these similarities mean something, or at least, people had no clear idea of what they mean.

      …… … … …

    17. Tim vB says:

      Verlinde states that he does not believe that string theory is a fundamental theory any more, because gravity is not a fundamental force, but he also states that string theory has a right to exist as a UV completion of QFT, and as a tool that gives valuable hints.
      So his statement is a repudiation of string theory as the most fundamental theory, but not of string theory as a unification of the four forces (note that we have to drop the ubiquitous “fundamental” here).

      I’ll pick just two examples of the many points that confuse me, maybe someone likes to fill me in on Verlindes intentions:

      First point:
      “Many physicists believe that gravity, and space-time geometry are emergent. Also string theory and its related developments have given several indications in this direction.”

      This comes as a surprise, because in my naive understanding of string theory I always thought that the existence of spacetime is one of the axioms/starting points of the theory, so that an emergent spacetime is excluded from the very start. Was that a misconception?

      Second point:
      Verlindes talks about space to be emergent, but supposes microscopic dynamics including the existence of “time”. If you start from GR, then this is impossible: Either you have space and time or you have none. Spacetime itself describes causal relationships, i.e. relationships of events, and this requires both notions. How does one reconcile GR with having time at a microscopic level and space as an emergent macroscopic phenomenon?

      On a side note I don’t quite understand the amount of attention this paper receives. What’s so fascinating about it?

    18. Chris W. says:

      Tim vB,

      I’m not the best person to respond to your queries, but I’ll take a stab at it.

      Point 1: In string theory’s original formulation, a background spacetime was indeed assumed, but as work has pointed towards a deeper, non-perturbative formulation (M-theory) it has become doubtful that this can be maintained. Edward Witten has been fairly explicit recently that spacetime must ultimately be emergent. Exactly what this means, and what such a theory should look like, has remained obscure.

      Point 2: “If you start from GR…” Well, you don’t necessarily start from GR. Your starting point may be something that incorporates some primitive notion of time or causal ordering, which is applied in describing the evolution of some sort of pre-geometric system, out of which spacetime arises as a sort of coarse-grained or “mean-field” approximation to the underlying structure. Again, no one is sure whether, or exactly how, this can work, although a number of provocative ideas have been under investigation for quite a few years. Causal set theory is one example.

      Why all the attention? Interest in the deep interconnections of entropy, thermodynamics, and gravity goes all the way back to the 1960s, when the so-called 4 laws of black hole mechanics were formulated, essentially as theorems in general relativity. Ostensibly they simply described the geometry of balck holes, but it was quickly noticed they bore a striking resemblance to the laws of thermodynamics. As a graduate student of John Wheeler, Jacob Bekenstein decided to take this analogy seriously and conjecture that they were in fact the laws of thermodynamics in a geometrical guise. He drew out some of the implications of this, and his conjecture was soon vindicated by Stephen Hawking’s discovery that a semiclassical analysis of quantum fields near the horizon of a black hole implied that the black hole had a finite temperature measured at a distance (asymptotically), confirming Bekenstein’s suspicions. This intimate 3-way relationship between general relativity, quantum field theory in curved spacetime, and thermodynamics has been widely regarded ever since as a key guidepost towards a theory of quantum gravity. This has been reinforced in the last years by the work of Ted Jacobson and others (see earlier comments). Erik Verlinde’s prominence as a string theorist, and his remarks in the paper and on his blog about string theory in this context, suggest a significant shift in outlook on his part with respect to string theory and quantum gravity in general. (He goes out of his way to make this clear.) Of course this shift is not definitive, but we’re in a revolutionary phase in fundamental physics; little if anything can be taken for granted.

    19. Mark says:

      “This comes as a surprise, because in my naive understanding of string theory I always thought that the existence of spacetime is one of the axioms/starting points of the theory, so that an emergent spacetime is excluded from the very start. Was that a misconception?”

      To TimVB,
      You should watch the talk by Moshe Rozali on “Backgound Independence in String Theory” at Loops 07:

      Or read the corresponding paper:

    20. D R Lunsford says:

      quote “Entropy, thermodynamics and gravity go back to the 60s…”

      The first widely accessible book on GR was R.C. Tolman’s “Relativity, Thermodynamics, and Cosmology” from the mid 30s.


    21. Chris W. says:


      That quote was taken out of context. I wasn’t talking about understanding and applying thermodynamics in astrophysics and cosmology, where gravity and special relativity (relativistic energies) are important. I was talking specifically about the discovery—in the 1960s—of the unexpectedly thermodynamic character of a particular class of solutions in classical general relativity.

    22. John Baez says:

      Hans-Peter wrote:

      “…since 1995, when Jacobson wrote his paper, almost nobody was interested in his result.”

      I guess I’m almost nobody. But seriously: everyone in loop quantum gravity was very interested in Jacobson’s result; the problem was figuring out something to do with it!

    23. Tim vB says:

      Chris W., Mark,
      thanks for the answers, that was very helpful.
      At this moment I have not digested all of the offered material, so I will refrain from asking more questions with one exception:

      Chris W. wrote:
      “Well, you don’t necessarily start from GR. Your starting point may be something that incorporates some primitive notion of time or causal ordering, which is applied in describing the evolution of some sort of pre-geometric system, out of which spacetime arises as a sort of coarse-grained or “mean-field” approximation to the underlying structure.”

      It makes much more sense to me to understand Verlinde in the way you suggest: If he talks about the microscopic dynamics and it’s concept of “time”, then it is not the macroscopic notion of time connected with the emergent spacetime, but a different concept like the “causal set structure” that you pointed out.
      But I’m not sure if that’s what Verlinde means, because he mentions “space”, and space only, as an emergent concept.
      And he uses “time” to denote the causal structure of the microscopic dynamics, which made me think that he rolls back the unification of space and time of relativity theory.
      Maybe this is a simple misunderstanding caused by my overly pedantic interpretation of his use of language.

    24. Chris W. says:

      From Tim vB: And he uses “time” to denote the causal structure of the microscopic dynamics, which made me think that he rolls back the unification of space and time of relativity theory.

      The unification of space and time in relativity has come to be viewed in a somewhat different light as a result of the study of the dynamical structure of general relativity (“geometrodynamics”). You should find out more about the ADM formalism.

      The meaning and status of time in general relativity is a vexed subject, that has received much attention from physicists and philosophers of physics. How it will all shake out is not at all clear, of course (notwithstanding my own biases 🙂 ).

    25. drme says:

      Wow! Verlinde posting in Lubos’ blog?? Is Lubos still considered an important voice in the field? Amazing!!

    26. Chris W. says:

      Verlinde’s Jan. 15 post is now on his blog. It appeared first on Lubos’ blog.

      Also, although the linked titles on his main page don’t work, the three posts can be accessed as separate files:

      15 Jan: Entropic forces and the 2nd law of thermodynamics
      13 Jan: Essential points of the paper
      12 Jan: Logic of the paper

    27. Mark Wallace says:

      I enjoyed Verlinde’s paper. I was not familiar with the earlier work he references by Jacobson, so of course it really got me thinking. It immediately raised the following questions for me:
      (1) If you accept that gravity is emergent, then what is wrong with the Standard Model? Why do strings need to be added to all the QFT that makes good experimental predictions?
      (2) Having spent most of my life working with computer codes, I am intuitively comfortable with ideas like the holographic principle. Similar types of information constraints come up all the time in algorithms I work with, so it does not seem surprising to see something similar in nature. However, starting with the holographic principle doesn’t seem quite right when the author claims 3 dimensional space as an emergent phenomena. I am willing to go along and follow the logic of deriving spatial dimensions as emergent phenomena, but there wasn’t enough in Verlinde’s paper to suggest a good route. I was kind of expecting a derivation of spatial dimensions based on information-theoretic type arguments, but I could not find it.
      (3) On the other hand, time was taken as a given. I was surprised, since I would have expected for entropy based arguments that time would be one of the (many) emergent phenomena, and that 3d space and the holographic principle would be the givens.
      One way or another, I liked the paper and think I may have learned something. One we start down the route of saying Newton’s equations are like the ideal gas law, we need to be very careful, in any given context, to say what is a “given” and what emerges. The logic can get very confused if, in the process of a single argument, the author is not perfectly consistent about the givens.

    28. Chris W. says:

      The New Scientist article that Verlinde said was in the works is now on the website. (See Verlinde’s Twitter feed.)

      The author, Martijn van Calmthout, avoids dealing with some muddled aspects of the story, but overall the article isn’t bad.

      The muddle is inherent in the opening paragraphs:

      WHAT exactly is gravity? Everybody experiences it, but pinning down why the universe has gravity in the first place has proved difficult.

      Although gravity has been successfully described with laws devised by Isaac Newton and later Albert Einstein, we still don’t know how the fundamental properties of the universe combine to create the phenomenon.

      This skates right by the fact that the only forces—in a Newtonian sense—in general relativity are the non-gravitational forces that take particle trajectories away from geodesics in spacetime. So strictly speaking, talk of an entropy force must be replaced by another locution if one is to properly understand the connection of “the flow of entropy” to geodesic deviation, ie, to spacetime curvature.

      This is just one aspect of this very provocative line of thinking that could use some clarification in accounts aimed at a general readership. Ted Jacobson’s original paper avoids this problem, at the cost of using some relatively dense technical argumentation, and no explicit use of the holographic principle.

    29. Chris W. says:

      PS: Actually, footnote 5 in Jacobson’s paper makes the following reference to the holographic principle:

      Another argument that might be advanced in support of the proportionality of entropy and area comes from the holographic hypothesis[6, 7], ie, the idea that the state of the part of the universe inside a spatial region can be fully specified on the boundary of that region. However, currently the primary support for this hypothesis comes from black hole thermodynamics itself. Since we are trying to account for the occurrence of thermodynamic-like laws for classical black holes it would therefore be circular to invoke this argument.

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