Holographic Hot Horizons
    By Johannes Koelman | December 14th 2009 08:58 PM | 33 comments | Print | E-mail | Track Comments
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    Holographic Hot Horizons

    We are all familiar with gravity. Gravity is what makes us earthbound. It causes ourselves and any object in our vicinity to accelerate downward at 9.8 m/s2. Newton has shown that this holds true in a much more general sense: gravity is the acceleration field associated with any massive body. This gravitational acceleration is attractive, proportional to the mass of the body, and inversely proportional to the square of the distance to the body. Via this universal acceleration, gravity determines the celestial dynamics, it shapes galaxies and determines the ultimate fate of the universe.

    But what causes gravity? Could there be an underlying layer of reality from which gravity emerges?

    More than three centuries after Newton formulated his laws, we still don't know.

    Enter Dutch theoretical physicist and string theorist Erik Verlinde. Last Wednesday Verlinde is reported to have presented his latest work at the Spinoza Institute in Utrecht. In front of an audience that included Nobel Laureate Gerard 't Hooft, Verlinde apparently claimed no less than being able to derive gravity from the ground-up. Do I hear you mutter the words 'cargo cult science'? Maybe. However, you might want to Google “Verlinde formula” and search for author “Erik Verlinde” on arXiv. Does this convince you that we are dealing here with a well-respected scientist?

    Good, read on.

    Following his presentation in Utrecht, Verlinde gave an interview to the Dutch newspaper “Volkskrant”. This interview appeared in the science section of the Weekend Edition A summary (in Dutch) is available here. Today, a friend e-mailed me the full article. Unfortunately, the text is in Dutch and, apart from some comments related to the holographic principle, contains little or no details on Verlinde's derivation of Newtonian gravity. To make things worse, in the article Verlinde is quoted to be finalizing a publication on his theory. A quick inspection of arXiv confirms that Verlinde has indeed not yet published a paper on this subject.

    So to learn more about Verlinde's work, it seems we have to exercise some patience.

    Well, this might be too pessimistic. There is a glimmer of hope. A picture accompanies the newspaper article. Shown is Verlinde in his office, standing in front of a blackboard. A blackboard on which some scribbles and equations are vaguely visible. I have copied the photo below.

    Erik Verlinde (Photo Volkskrant)
    Are these scribbles enough to get a basic understanding of Verlinde's work? I think so.   
    (Photo Credit: Guus Dubbelman / de Volkskrant)

    Now, I am going to give you my interpretation of the blackboard scribbles, but I am certainly not going to claim that my interpretation is complete and accurate. It might, in fact, be completely beside the point. Anyone who feels to have a better interpretation is invited to put these in a comment to this blog. This is your chance to discuss a potentially important piece of work even before it is published!

    Ok, here we go.

    As already mentioned, Verlinde starts from the holographic principle. Imagine a spherical screen with radius R surrounding a physical system of mass M. According to the holographic principle, all the physics that takes place within the screen can be described by bits of information that can be thought to be located on the screen. If each bit occupies an area Abit, a total of N = 4πR2/Abit bits is available to describe the system surrounded by the spherical screen.

    Each bit is associated with a degree of freedom of the system being described. According to the equipartition theorem, each degree of freedom caries on average an energy ½kT, with k representing Boltzmann's constant and T the absolute temperature. As the screen is assumed to be at rest with respect to the system with mass M, from the perspective of the screen the total energy of the system is given by Einstein's formula E = M c2. It follows that ½kTN = Mc2.

    Substituting the expression for the number of bits (N) into this energy equation, it follows that a temperature T can be associated with the screen according to: ½kT = Abit Mc2 / 4πR2.

    The holographic screen is not a physical screen but rather a thought construct created to represent the information contained in a physical system. How can such a non-entity have a temperature? The Unruh effect lends us a hand here. According to this principle, an observer being accelerated in empty space will record a non-zero temperature of that empty space. This temperature is proportional to the acceleration: ½kT = ћ a / 4πc (here ћ denotes the reduced Planck constant [] and c represents the speed of light). Reversing this argument, a non-physical entity that has a temperature can be thought of as being accelerated.

    Equating the expression for the temperature of the holographic screen with the expression for the Unruh temperature yields: Abit Mc2 / 4πR2 = ћ a / 4πc, or: a = GM/R2 with G = Abit c3/ ћ. Et voila: Newton's law of universal gravitation...
    You get the correct value for the gravitational constant G if you set Abit equal to a Planck area (2.6 10-70 m2).

    Again: I am just interpreting some scribbles here. See this as some first impressions without giving the whole idea too much thought. There is absolutely no guarantee that my interpretations come anywhere close to Verlinde's thoughts. We will soon know more. Watch this space.

    --- Postscript ---

    Three critical notes to the above interpretation need to be mentioned here:

    1. It seems that somewhere a factor of 4 might have gone astray: according to the holographic principle each bit of information requires an area equal to four Planck units.

      At this stage I am not so worried about this. Provided the concept is right, numerical factors can be dealt with later. More worrying is the following:

    1. The value for G comes out correctly if you enter for Abit the value corresponding to a Planck area. However, the Planck area (ћG/c3) is defined in terms of Newton's gravitational constant G. Have we not introduced a circular reasoning here? I am actually not sure. Maybe the whole derivation just demonstrates that the holographic principle and the Unruh effect hang together consistently. A key step in the derivation is indeed the interpretation of the screen temperature as acceleration temperature. As explained, this step seems to invoke a reversal of Unruh's argument. This vaguely resembles Louis de Broglie's matter wave hypothesis: if waves are quantized and can behave as material particles, then it seems logical to assume that material particles can 'wave'. A brilliant intuitive move that earned De Broglie the 1929 Nobel Prize for Physics.

    2. Deriving Newton's law of gravity is one thing. More impressive would be the derivation of Einstein's field equations from holographic considerations. If Verlinde's concepts are sound, this should be feasible.


    I think Verlinde's ideas come very, very close to the models in
    "Thermodynamical Aspects of Gravity: New insights" T.Padmanabhan. Here, the free thermodynamic energy of gravity is already derived (dS = TdE + P dV) and shown to hold for almost every viable theory of Gravity. He even makes a thermodynamic interpretation of Einsteins equation of gravity.

    I have not yet finished this paper, but I think the author Padmanabhan does not make the last step of deriving gravitational attraction from the entropy and free energy, as Verlinde claims.


    Johannes Koelman
    Rob -- you are absolutely right.
    Interestingly, today Padmanabhan submitted an article to arXiv that literally describes what is summarized in my blog above. See here.
    An article on HO HO HO.

    Who says science can't make culture a little stronger??
    Hey Johannes,

    As a dutch non-physicist I've followed Verlinde's presentation. To read the full argument just visit his homepage: , click on 'Talks', and 'Gravitatie uit Informatie' (you'll need the Apple Quicktime plug-in). It is in Dutch, but I guess you'll be able to follow along.

    Basically it is gravity as a purely emergent phenomenon, stemming from an information-theoretic temperature difference (difference in entropy), causing the force on the particle. Both the proportionality of force with mass (Newton's 2nd law), and Newton's 3rd law neatly emerge from the holographic principle and thermodynamics on the Planck scale.

    I'm sure someone (not me!) is now busily deriving GR from a relativistic treatment of this argument. ;-)

    If you drop Dr. Verlinde an e-mail, maybe he might be willing to put up an English translation of the presentation... Btw the 'Origin of Gravity' presentation on his homepage is in English, and contains some of what he said in Utrecht past wednesday.


    Johannes Koelman
    Bob -- thank you, this is useful.

    I can't get the presentations on Verlinde's homepage properly displayed (something wrong with a plugin, it seems).
    Have fired off an e-mail. Let's see if he finds the time to react (I guess he better spends his time writing a publication, but who knows...)
    Seems that Verlinde's homepage is out of order now. I don't suppose anybody has made a local copy of the *.mov files?

    Thx Albert

    "I'm sure someone (not me!) is now busily deriving GR fom a relativistic treatment of this argument. ;-)"

    Allready done?


    Hi Albert,

    Thank you for the slides. They must have had lots of fun at FQXi 09, on the Caribbean Isles...

    I'm not sure if this counts as a derivation - it seems to be based on the *analogy* between the equations of thermodynamics and GR. The author is certainly not the first to notice that analogy... The oldest reference I came across is an article by Andrei Sacharov ('Vacuum quantum fluctuations in curved space and the Theory of Gravitation', 1967). The analogy seems to be part and parcel of many present-day Statistical Mechanics courses.

    The idea of Gravity as an emergent phenomenon has been around for a lot longer then I realized, as a layperson. Still, the derivation of Newtonian gravity by Verlinde from QM principles (and especially the physical picture / 'gedankenexperiment' used to do this), seems to be a new and very convincing argument indeed.

    Just finished a delicious Christmas dinner. At last some time to read thru this presentation & other references, while sipping a glass of port... or rum, maybe? I'll post a few other items later.

    Merry Christmas to you and yours! :)

    Hello Bob,

    Well, yes, I was a bit quick with that. Thank you for pointing that out. The original article in De Volkskrant does not make any distinction between ideas that have been around and Verlinde's own contribution. For instance, it quotes Verlinde in saying: "I don't consider gravity as something fundamental. It is an emergent fenomenom, that arises from a deeper microscopic reality." In the newspaper article this is presented as part of Verlinde's recent discovery. There's is no mention whatsoever that some of these ideas have been around for quite a while. I suppose this is all due to the writer of the article (who has a PhD in physics himself by the way), but for me as a layman it is quite confusing.

    It would be ever so nice to read something by Verlinde himself. Last week, late at night, I had a quick glance at Verlinde's presentations and thought: "I'll look them over some other time, there's a job and a family to consider too, you know." The next day Verlinde's website was out of order and the presentations were gone.

    Best wishes for you and your friends and family. Looking forward to your posts.


    Hi Johannes,
    I'm not a theoretical physicist (studied chemistry) but it struck me almost as too coincidental that information theory is being explored in quantum physics also (see eg a recent nature paper by Pawlowski ea "Information causality as a physical principle", here in arxiv: .
    This might hold some promise as foundation for a grand unified theory?
    Thanks for you explanation!

    Johannes Koelman
    Piet -- interesting reference.

    I am planning a blog on Wheeler's "It from Bit" paradigm. It has some consequences that few people realize, I think.

    In the meantime you might want to have a look here for a weird example of signaling and information in the quantum world we live in.
    The real father of thermodynamic derivation of the field equations is Jacobson:
    Padmanhaban is only repeating what Jacobson did, and has even stopped citing him, a real scandal, in my view.
    The Azores talk is straight on the origin. The paper by Jacobson is also quite simple to read.


    As far as I know, prof. Verlinde will be publishing tomorrow (january 7th).

    I guess we can all understand why he took the earlier presentations (and his whole homepage!) off-line during the afternoon of the 17th... Maybe these can be made available again, once the article is out?

    The 1995 Jacobson paper is fascinating to read (and it seems to be very succinct and well written) - thank you. It certainly has been cited a LOT since then! It already states that the horizon need not be a black hole event horizon, but can be any 'causal horizon'.

    Many questions, but one stands out: is there *any* hope of different phenomenology once one adopts this thermodynamic view of gravity? Any situations in which its' predictions will differ from the GR or Newtonian case?

    For instance, Jacobson mentions at the bottom of page 2: '[...] the entanglement entropy is finite and proportional to the horizon area in units of l c^2, as long as the radius of curvature of spacetime is much longer than l c.' Would this mean that on cosmological scales it would work out markedly different from the GR description?

    Back to reading...


    My own opinion is that no difference with usual general relativity can be measured. This is disappointing. With three friends, starting from Jacobson's paper, we have looked for such differences for many years. We might have overlooked some, of course. But we always dreamt of finding such a difference. We came to the conclusion that none can be measured. No differences can occur at cosmological scales for sure; differences can occur only close to Planck scale. But those are hard/impossible to measure.

    Thank you, Hans-Peter, for your comment.

    I've been reading Verlinde's paper since yesterday (interrupted by work, family, removing tons of snow, work, and removing more snow). It is truly fascinating! I hope to finish reading Jacobson's later today.

    I do share your disappointment about missing phenomenological differences. However, I can't help wonder about the statistical fluctuations in gravitational acceleration one would expect, somewhat akin to Brownian motion - of course a minute effect... In what way would that deviation depend on the test mass?

    I'll post a few more of my questions/misunderstandings under Johannes' It-From-Bit blog which he mercifully opened up. Cheers!

    Pardon my ignorance, but isn't this just another form of heat radiosity/global illumination?

    Why not do it with a Klein bottle instead of a sphere?

    There may be a few rough edges to smooth out here, but I think Verlinde is on to something here, and I mean something big!

    I was thinking about your concern about possible circular reasoning with respect to a Planck area and the gravitational constant, G. To be perfectly honest, I'm not certain. But, my gut tells me no, there is no circularity. I just think it's an internal consistency. But, I understand why this would concern you, Johannes. I've had to think about this for some time, and I'm still thinking about it.

    Wonderful stuff!

    Physics is based on mathematics is based on logic is based on anthropology is based on neuroscience is based on biology is based on chemistry is based on physics. That's pretty big circular reasoning.

    "However, the Planck area (ћG/c3) is defined in terms of Newton's gravitational constant G. Have we not introduced a circular reasoning here?"

    One has to assume something. For me Planck area seems simpler than Newton's gravitational constant G, so why not to assume Planck area instead of G? Maybe the problem is, that we have mixed the reason and the consequence?

    I like the theory, but I'm definitely confused; what predictions does the theory make for massless particles? Photons for example? Surely they have associated entropy as well, yet the entropy "gradient" doesn't seem to have the same effect as for particles with mass.


    'Massless' particles only lack rest mass. Photons have energy, so a mass is associated with them (E=Mc^2). More importantly they carry information, so they fit perfectly into this theory...

    If you are willing to consider an alternative theory of the source of gravitation, you might be interested in the work I presented last September at the First Mediterranean Conference on Classical and Quantum Gravitation, recently submitted for publication in the Journal of Physics Confrence series. I also think gravity is in some sense a side-effect of other phenomena, and I do not think (until I know more about it) that Verlinde's model is incompatible with mine. There can be more than one model of any given phenomenon; each may be useful in different ways.

    Title: "The effect of particle creation on space".

    Abstract: "General Relativity and Quantum Mechanics have been successful at describing their respective realms, but the two theories remain disjoint. We finesse this diffculty with a classical model of the Universe that unites gravitational, nuclear and electromagnetic forces. This model is derived by examining the nucleus and its atomic quanta. Newton's Law of Gravitation evolves into a formula for the gravitational field within an atom's quantum layers which has the form of Hooke's Law for the potential energy of a spring. The inward force--a reaction to the strain caused by introducing two particles into the space--drives particles towards each other. Gravity is not a mysterious attractive force acting at a distance with no mechanism, but a force acting locally with a well-defined mechanism. The force on the nucleons from the spring stress in the nucleus provides a physical basis for the strong and weak forces of quantum mechanics. The Fundamental Law of Nature gives the relationship between the strong force stress on space, gravity and the wavelength of a photon. The new paradigm offers an alternative to the Standard Model that is easy to integrate with gravitation."

    Anyone wishing to see a rough draft of the paper can email me at perfwise@gmail.comNoSpamPlease. I have been working on this for a long time and would love any possible feedback.

    does the Unruh derivation use F=ma,
    and hence using the Unruh result circularly proves F=ma?
    not familiar with it.

    New article in this weeks New Scientist - Gravity from entropy:


    What if the constants employed by Verlinde are incorrect in their numerical values? Take a look at a critique of the CODATA numerical values.

    Johannes Koelman
    Charles -- the author of that web page is utterly confused, and has a very contorted view on Planck units. You can fully trust the CODATA values. These are accepted by ten thousands of the most critical people around here...
    Johannes --Nine pairs of fundamental physical constants produce the same numerical value, which means that the constants are not unique. In fact, they represent fractal multiples of one another, only each one is called by a different name. The ten tables presented on the Earth/matriX website illustrate this point. Also, the fact that two different numerical values are employed for Planck mass means that there is an essential contradiction in the Planck constant. Verlinde employs the Boltzmann constant, the Compton wavelength and the Planck constant. The Compton wavelength is a reciprocal of the Planck implied length. Citing the number of people who believe in the CODATA does not respond to the discrepancies in the numerical values, nor does it substantiate the correctness or incorrectness of the numerical values of the constants. The question remains: what if the CODATA constant numerical values are incorrect as employed by Verlinde? Personally, I think the answer is obvious. A response would have to be at the level of the correctness/incorrectness of the numerical values of the constants and not how many people believe in those values. I submit this query with all due respect from a non-expert point of view.

    Johannes Koelman
    "Nine pairs of fundamental physical constants produce the same numerical value"
    That's right. If you take some combination of the five fundamental physical constants, and some other combination of the same constants such that the product of both combination has the physical dimension of energy, then you will get the Planck energy. Always. So there are not just nine pairs. there are infinitely many.
    "which means that the constants are not unique"
    That is not correct. It just means that there is only one combination of the five fundamental constants that yields an energy.
    Johannes, I appreciate your input and time in responding to my query. My best, Charles

    I'm just discovering the Verlinde's theory and it make sense for me... Waoooh !
    I'm not physician, but something made me trouble with all the other theory : Why there was 2 systems of physical laws in our world ? And why the physics was so complicated (with the cord theory) since 30 years.
    Everytime when we observe the nature, it take the easy way, the shorter, the more coherent.
    It's not easy to change a paradygm and needs courage!
    Thank you Mr Verlinde for your audacity and maybe we're all (innovators and conservators) in the beginning of a new era...

    Hi Johannes,

    I'm a curious non-physicist, and I've read your blog entry a few years ago. I've found it really interesting at the time, and managed to find my way back here.

    Particularly, I was fascinated by your derivation of G from other physics variables, although I did take notice of the notes at the end of your post.

    I've checked around and saw you've kept interest in the gravity-entropy matter and would like to know if your worries on the circularity of the constant derivation and the 4-factor have been addressed by you or elsewhere. If so, is there a good reference for getting to the G constant from a similar framework to that on this post?

    Thank you very much!