## Sunday, January 24, 2010 ... /////

### Why gravity can't be entropic

In the past weeks, there have been two neutral if not positive TRF articles about Erik Verlinde's alternative interpretation of gravity as an entropic force:

Gravity as a holographic entropic force
Erik Verlinde clarifies some issues

Future text (August 2011):

Once more: gravity is not an entropic force
At the beginning, I thought that Erik meant something sophisticated that could work - a new dual (yet universal) way of looking at the gravitational phenomena.

But right now, after the helpful explanations by Erik, I am afraid that I am certain that he shares certain basic misconceptions about physics with the advocates of spin foams, loop quantum gravities, causal dynamical triangulations, octopi swimming in the spin foam, condensed matter gravities, and many other stupid things of the same kind. So in this sense, he shouldn't be quite surprised that these people are trying to build on his paper as a new context to repeat their old incoherent flapdoodle.

I will try to summarize the reasons why nothing like that can ever work because Nature disagrees with the very basic pillars of this system of ideas - and all systems that share certain general assumptions.

But let me begin with a specific new criticism directed against Erik's picture. Let's look at an ordinary double-slit experiment with a massive particle such as an electron or a neutron. The neutrons will turn out to be the best ones. (Update: Many months after this article was written, a preprint also argued that gravity can't be an entropic force because of neutron interferometry experiments.)

Everyone knows the double-slit experiment, so I have immediately added the unusual ingredient due to Erik Verlinde. I have rotated the picture by 90 degrees and placed it in a gravitational field. The upper and lower slits are placed at different altitudes. In his preprint, he argues that the entropy of two gravitationally bound objects depends on the distance between them i.e. on the altitude.

In particular, he argues in equation (3.6) and above it that if a probe (small point mass) is shifted by Δx away from the holographic screen (and therefore closer to the center of a gravitational field which means "down" in our case), the entropy changes by Δx/L where L is the Compton wavelength of the small massive particle. To avoid infinities, let's consider neutrons whose Compton wavelength is 10^{-15} meters or so. In Erik's opinion, the entropy of the Earth-neutron system depends on their distance. So the numbers of states corresponding to the neutron near the two slits differ.

So if you move such a neutron 1 meter closer to (or further from? Who cares...) the holographic screen, there will be a higher number of microstates available to you. For each microstate at one position, there will be exp(10^{15})) states where the neutron is at the other position. These entropy differences may be so huge because Erik assumes that they're being taken from the maximum entropy carried by the holographic screen - which resembles the entropy of an equally sized black hole. The latter is the maximum entropy you can squeeze in a given volume and it is proportional to the area in the Planck units.

Now, the distance (height difference) between the two slits doesn't have to be quite one meter. But it may be substantially longer than the neutron Compton wavelength which means that the ratio between the number of states will be more than astronomical.

Clearly, a neutron going through the two slits can only interfere with itself if the microstates are sharply defined, don't decohere from one another, don't mix up with many other states, are not measured, and so on. There's no doubt that a discrepancy between the number of states corresponding to the upper slit and the lower slit would destroy the interference pattern.

But the interference is known to exist, even in the gravitational field. That much is known even for the electrons. This proves that for each position "x" of the interfering particle, regardless of the position of "x" in the gravitational fields, there must exist exactly one state that describes the situation. That's necessary for the "one-particle" Schrödinger's equation to work even in the gravitational fields. So even electrons instantly falsify Erik's philosophy because in the reality, the interference pattern is not destroyed. However, the picture is even more manifest and constraining in the case of neutrons.

In 1975, Colella, Overhauser, and Werner did the first experiment that tested the effect of a gravitational field (of Earth) on interference; their paper had many follow-ups and boasts 339 citations at this moment.

Using a neutron interferometer (which is dozens of centimeters in size), they exactly found the result that the equivalence principle predicts: the interference pattern is just "freely" falling in the gravitational field, just like the classical neutrons would. The equivalence principle works even when it comes to the quantum phenomena such as interference. Gravity and its equivalence principle work not only when many chaotic things and phenomena cancel: it works even when a single elementary particle is falling down.

The pattern is not destroyed in any way and the phases are shifted exactly as you would think if you thought properly. It's been experimentally verified that Schrödinger's equation including the gravitational potential energy works. Later, it became possible to verify not only the uniform gravitational field but even the tidal forces - the non-uniformities of the gravitational field. Everything works properly. You can see such tidal forces in the interference pattern.

Erik's idea is in trouble regardless of the "time scale of relaxation". If his thermalization process occurs before the neutron hits the screen, the interference pattern will be destroyed. If the thermalization is slower, the interference pattern will be predicted at an unshifted place - because gravity only arises from the thermalization in his picture - which will contradict the observations that the phases and interference patterns are exactly as shifted as the equivalence principle predicts. There's no way to escape the contradiction simply because Erik's mechanism for gravity (which is a force that we observe) - a mechanism linked to entropy - causes some inevitable side-effects such as the loss of coherence (which are certainly not observed).

The idea that the number of microstates - the exponential of the entropy - depends on the position of the elementary particles has thus been safely ruled out.

The different branches of the wave function couldn't interfere with each other if there had been no one-to-one map between the states at different altitudes of the neutron or if there were some thermalization going on before the neutron reaches the photographic plate. In our discussions, Erik (and Wilke) defended a very fast (Planck-time?) thermalization (in order to keep the system at equilibrium at all times) which only makes the things related to interference worse because the interference pattern dies even faster.

Recall that I have argued that Erik's dynamical picture is fundamentally irreversible, unlike gravity.

At the end, Erik (and Wilke) agreed that there is some inherent irreversibility that can't be eliminated but they blamed it on the gravitational waves which I think is indefensible. While I am certain that the gravitational waves emitted by a binary states are essentially pure, calculable, coherent states (exponentials of a graviton creation operator) with a negligible entropy, the definition of irreversibility and the constraints coming from it may look confusing to others which is why I chose the simple interference pattern in this article which should not be confusing.

In fact, I didn't have to talk about decoherence. If the number of microstates depended on the position of the objects, such as the neutron, there could exist no linear complementary momentum operators for the separate objects - because the momentum operators must differentiate with respect to positions, but one can't differentiate with respect to "x" if the number of components of the wave function itself (i.e. the number of microstates) depends on "x". One can't subtract a 1-dimensional vector from an exp(10^{15})-dimensional vector which would be needed to define the derivative.

The idea that there is any "chaos" hiding behind the fundamental forces such as gravity is fundamentally wrong for many other reasons. These reasons are morally equivalent to the arguments above but they address different traditions and flawed alternative theories from the history of physics.

The most important one among them was the...

Luminiferous aether.

In the 19th century, physicists wanted to "model" the electromagnetic field as a mechanical system with many wheels and gears: at the end, they even produced a working prototype. ;-)

It was a completely irrational movement with no scientific justification. But many physicists, including a few giants, have simply found mechanics (which was already old) more natural than field theory (which was new, and it was originally meant to approximate many-body mechanics), so they badly wanted such a picture. It's often hard for the people to understand that a newer conceptual picture may be fundamental. (But it always can - there's nothing wrong with being newer. What matters is whether the principle is right.) That's why some people wanted to reduce field theory to mechanics 150 years ago and why some of our contemporaries want to reduce quantum mechanics to a deterministic theory, among other examples of ill-motivated, misguided physics.

Einstein's 1905 relativity revolution can be summarized as a successful assassination attempt against the aether. Einstein appreciated that the Galilean principle of relativity must morally hold not only for the mechanical phenomena but also for the electromagnetic ones. One shouldn't be able to determine whether her train is moving, not even by using optics. After all, Maxwell's equations do seem to imply that the speed of light is always "c" - and they don't even expect us to specify a frame.

Years before relativity, Lorentz actually managed to prove that Maxwell's equations were Lorentz-invariant but he couldn't possibly understand that the transformations ("changes of variables") formed a group (which we call the Lorentz group today - because there's no way to avoid this irony) or that it had anything to do with the Galilean choices of the inertial frames. Einstein was necessary for these advances that may look trivial today.

Maxwell's equations therefore have to hold in all inertial frames, too. That, bizarrely, implied that the speed of light was constant in all frames: it isn't changed to "v+c" or "v-c". Once Einstein convinced himself that this additional postulate had to be valid and something basic about the space and time would have to be altered, nothing could already have stopped him from finding the correct new theory of space, time, and their relationship, the special theory of relativity. It simply followed from the postulates.

Einstein often acknowledged another important role played by Lorentz who wrote down the right explanation of the electromagnetic phenomena in various materials. Lorentz realized that there is only one fundamental electric (E) and one fundamental magnetic (B) vector at each point of space and time. The vectors D,H were derived by mixing E,B with the information about the charge and spin carriers in the material. This made the vacuum much "emptier" and Einstein could ultimately "empty it" completely: he removed the rest of the aether and showed that it couldn't exist because it would be inconsistent with relativity.

The aether is inconsistent with relativity because of many related reasons. Pretty much all of them also belong among the diseases of all the "emergent" theories of space, time, and gravity that have been proposed in literature.

If your spacetime history resembles anything like a spinfoam, it's easy to see that it can only look isotropic in at most one reference frame. If one frame makes it look isotropic, it is easy to apply the Lorentz transformations to see that the "spin network" - a slice of the spin foam - will be Lorentz-contracted in other frames.

There are many other, equally obvious ways to see that there can't be any aether in the vacuum. If the material filling the vacuum were resembling water, it would carry a nonzero entropy. But relativity instructs us to study not only the entropy density - a scalar field - but also the entropy current, a vectorial field that combines with the scalar entropy density into a 4-vector field in spacetime. These things transform into each other in the same way as different components of the j^{\mu}, the electric current written in a relativistic fashion. In this case, the integrals over codimension-one slices are not interpreted as the total charge (which is quantized and conserved) but as the total entropy on the slice (which is not quantized, it's approximate, and increases). But the Lorentz properties are identical.

It's very clear that if the vacuum had a nonzero entropy density, there would only exist one privileged reference frame in which the spatial components of the entropy current would be equal to zero. Relativity says that the Lorentz invariance can't be broken by the vacuum. It follows that the vacuum can't have any entropy density.

A similar argument applied to the stress-energy tensor implies that only stress-energy tensors proportional to the metric tensor are allowed in the vacuum. Indeed, string theory agrees with these consistency conditions: the vacuum is unique and the energy density is always combined with the pressure of the same magnitude and the opposite sign. Every semi-realistic, stabilized stringy vacuum has either flat, or de Sitter, or anti de Sitter solutions.

While the precise value of the cosmological constant is not calculable at this moment - or, at least, we don't know how to choose the right one among many discrete options - string theory does imply that the vacuum fluctuations behave like the cosmological constant, i.e. satisfy "p = -rho". The latter condition - the equation of state of the dark energy - is not only a moral consequence of relativity but has also been directly tested by WMAP. It works.

Theories that don't respect the exact Lorentz invariance induce a nonzero entropy density which confirms the Lorentz breaking. They also lead to independent components of the stress-energy tensor, "p" and "rho", in the vacuum. It follows that they inevitably suffer from one new cosmological constant problem because they not only lack the explanation for why "rho" is so small, but also an explanation why "p" is equal to "-rho" and is therefore equally tiny. ;-) (Of course, they also generate infinitely many additional wrong coefficients for all interactions etc., but that's another issue.)

Holography leads us to imagine that the microstates of any system can be embedded into the quantum bits of a holographic screen that resembles a black hole horizon. However, any viable interpretation must be able to explain that the vacuum is a unique state and there are unique states for any position of the neutron in the gravitational field, and so on. String theory in general and the AdS/CFT correspondence in particular satisfy these constraints while Erik's framework does not.

It seems a pretty general temptation of some physicists to be struggling for an explanation of Nature that is crowded with chaotic phenomena that introduce a lot of mess into physics. For reasons that are completely misguided, they think that these are good things if not cool.

But the fundamental laws of Nature have exactly the opposite property. They're as ordered and organized as you can get. The equivalence principle, the postulates of quantum mechanics (the interpretation of the probability amplitudes and linearity of the operators), unitarity (the preservation of the information), the Lorentz symmetry (locally), and other similarly key principles uniformly work, and all of their combinations demonstrably work, too (even though it took some time to get convinced that there's really no contradiction).

The interference experiments yield immensely sharp results that agree with the theories amazingly well. Frequencies (and even the magnetic moment of the electron) can be measured stunningly accurately and everything works. There's just no room for any chaos here. Whoever is looking for chaotic explanations is looking for theories that are dead at birth.

So the difficult goal is not to explain why there's so much chaos or increasing entropy or violations of the principles above or previously unknown collapses of the wave function or [add almost any other kind of fashionable crap you like] behind the fundamental forces but, on the contrary, why there is none of it in Nature. People who are trying to deny the principles from the previous paragraph and invent classically chaotic "visualizations" of the fundamental forces may call themselves independent thinkers or whatever, but that won't change the fact that they misunderstand some very basic insights about all of physics.

In this case, I won't be blaming the postmodern developments of the 21st century for this deformation and recurring attempts to explain the spacetime or gravity in similarly flawed ways. There is a simple reason why I won't: the aether goes back to the 19th century if not much longer than that. Together with the attempts to "unexplain" quantum mechanics by a silly deterministic picture, these flawed "alternative attempts" are likely to stay with us for quite some time.

See also Many faces of emergence where I explain how rich the set of tricks used by Nature to obtain new phenomena from simpler ones actually is, and how narrow-minded ideas about "emergence" are assumed by most of the emergentists including Erik Verlinde.

#### snail feedback (39) :

Dear Lubos,

You have devised a clever test case for entropic gravity, but I don't think it really works. First of all because entropic gravity is constructed to reproduce 'ordinary' gravity and hence 'predicts' every known phenomena automatically. Of course standard model interactions are not incorporated, but that would just be the remark that the theory is incomplete, not that it is wrong.

This is especially the case in the double-slit experiment. For normal gravitational fields the temperature will be extremely low, so that even though the entropy gradient is huge, the force will be normal and for a fast moving neutron will be negligible. I don't think Erik Verlinde has properly defined how to do quantum mechanics and do path integrals, but from your example it is apparent that one cannot just sum over all states, at least some Boltzmann factors have to be included (indeed we're doing thermodynamics), but perhaps much more theory is needed.

As an important side remark I note that 1 m distance with a double slit for wavelengths of 10^-15 is really ridiculous: the distance should be of the order of the wavelength, so that no real astronomical numbers are encountered in the entropy differences (of course the number of states does differ by exponentially larger numbers, but this is common in thermodynamics). Actually I suspect that with the correct Boltzmann factor entropic gravity may predict the same shift in the interference pattern as Einsteins equivalence principle, I hope to calculate this soon.

Kind regards, Wilke

Dear Wilke,

my text above demonstrates that quite universally, it is never possible to design an entropic mechanism that would reproduce "every known gravitational phenomenon" automatically. What you write is nothing else than a logical contradiction.

300 years ago, LeSage gravity was also designed with the wishful thinking to reproduce all known gravitational phenomena. Except that it can't: one can easily rule out LeSage gravity. And LeSage gravity is actually a special example of Erik's picture which can be - and has been - easily falsified, too.

You have completely misunderstood the neutron gravitational interference experiment. They showed that the force acting on the neutron is simply not negligible. Quite on the contrary, these interference experiments could measure and did measure the gravitational acceleration - and even the tidal forces - on the phase shift of the neutron's wave function. It's the very point of these experiments.

So whatever theory predicts that such forces are "negligible" is instantly falsified.

Also, it is simply not true that the distances between the slits are - or even must be - close to the wavelength. Quite on the contrary, they are (and surely can be!) parametrically larger in the actual experiments that have been done.

I am starting to lose my patience and feeling of fun in these debates because your comments are getting increasingly irrational while the actual statements of Erik, as well as the right answers to the questions he raised, have become completely clear.

Best wishes
Lubos

Lubos, I was interested in your reference to Le Sage gravity, and there's a recent book devoted to this "Pushing Gravity - New Perspectives on Le Sage's Theory of Gravitation"; M Edwards (2002)

It does seem superficially quite a plausible idea although, as the book makes clear, quite a bit of dross has accumulated round it over the years.

But I wondered if you have ever posted a critique of this. If not, I and I'm sure others would be very interested in your thoughts.

Dear John,

I independently "invented" the LeSage gravity when I was 11 or so, and I was kind of excited. ;-)

But it is instantly dead if you think about it - and I actually understood it before talking to others about it.

There is a resistance of the environment. Moving objects will hit a higher number of the particles on the front side than the rear side: the excessive front collisions will therefore slow the object down.

It's a normal friction - just like if you're swimming or driving a car in the air. The name of the environment doesn't matter - the physical predictions don't depend on the name. This friction was also mentioned in a Messenger Lecture by Feynman - search for Project Tuva and watch the first ones. He declared it instantly dead - a great example of falsification, a key method of science.

The friction would slow the planets very quickly. There are probably many other wrong predictions, but one wrong prediction is enough.

Incidentally, I think it is easy to prove that LeSage theory is a special example of Erik's framework because the shadows in the "medium" of the projectiles - corresponding to the attractive gravitational field - are nothing else than non-uniformities of the medium, and such non-uniformities decrease the entropy. The bigger shadows you create, the more you reduce the entropy.

The force from the collisions with the projectiles in the medium can therefore be understood as a microscopic realization of Erik's entropic force. The special example doesn't work for the main reason as Erik's general framework. It's irreversible.

Needless to say, the general criticisms can be exported in both directions. So for example, I explained why Erik's picture would destroy the interference pictures in the gravitational field. The interference patterns would obviously disappear in LeSage gravity, too, because the bombing projectiles would instantly "measure" the interfering particle/object which would decohere.

It is really the same story. While the LeSage theory is considered a defunct 17th century pseudoscience, its generalization by Erik is a nwe hot kid on the block for Nude Socialists and others. ;-)

Best wishes
Lubos

Dear Lubos,

Took me a little courage to expose the following to the burning bright beams of your sharp brain, but hey, I decided to live by the adage of "one risk per day"!

An entropic force is caused by the difference between a lower and a higher state of entropy in a system. So, the creation of the first elementary particle ever, already should have created a microscopic entropic force. Certainly when one of these early particles lost its "anti" buddy whilst it still kept 'dreaming' of a good annihilation that would bring it to a higher entropy state.

There are many phenomena we know of that reduce entropy and thereby induce an entropic force (i.e. stretch the elastic band). For instance the entanglement of particles reduces entropy, quarks glued into protons/neutron do, but also photons in a mass that constantly pull atoms out of their preferred higher entropy states.

The process of releasing the force is of course irreversable and the dQ taken from the heat bath to "feed the force" comes with additional entropy. However the process does repeat over time. Hence, photons jumping in and out of atoms could create 'entropy' waves. And by definition their maximum speed is limited by the speed of light. One could call this a kind of "photo-entropic effect" (it would f.i. predict that a mass would become cooler when you bombard it with photons as more atoms would be pushed into a lower entropy state).

Could the sum of all these micro-entropic forces in a mass explain its inertia?

P.S.
For a black hole this would imply that the entropy is reduced to the maximum possible in our universe, hence inducing a maximum entropic force, that however can only be released via tiny entropy production (Hawking radiation), since the compressed mass is saturated with photons that can't escape.

Dear Agno,

sorry, no, but I don't agree with a single well formulated statement of yours.

It's not true that one particle in the Universe inevitably creates some entropy. The entropy is the logarithm of the macroscopically indistinguishable microstates, and if there's only one such state, the entropy is just zero.

It's equally untrue that there exist processes that "reduce" the entropy. The total entropy never decreases, at least not by more than ΔS with probability exceeding exp(-ΔS/k) which is de facto zero (probability) if ΔS is macroscopic - note that k is Boltzmann's constant which is 1.38 x 10^{-23} J/K.

The entropic force only occurs if there are many particles (or degrees of freedom, to be general) with many possible states and a difference in entropy, and the term "entropic force" is just an alternative, approximate, vague, overall way to describe the situation. The microscopic origin of an entropic force always has to depend on some fundamental forces - e.g. gravity, electromagnetism, or elastic collisions.

I can't make sense of the rest of your text but because you're talking about the reduction of black hole entropy and similar gems, I am afraid that I am no losing anything by not understanding what you're saying.

Best wishes
Lubos

Hello Lubos,

I have to admit I haven't thought this through in detail but one thing that occurs to me is that Verlinde's idea is fundamentally classical, so it seems a bit unfair to say that it doesn't work quantum mechanically. I.e., while it turns out that in the interference experiment you cite you get the proper "falling of the interference pattern" and no decoherence, it's not clear to me that a quantum version of Verlinde's idea would necessarily not produce this result. Perhaps, for example, in a quantum version of this the reason you get some sort of "falling of the interference pattern" is because you have to sum up over all possible chaotic configurations, or something of that sort, i.e., that what is happening isn't that chaos is "actually" occurring (which would destroy coherence) but rather some sort of "virtual chaos" happens in many parallel worlds, so to speak. Again, I'm speaking vaguely because no one, not Verlinde or anyone else, has worked out how one would actually use his idea in a truly quantum version of the theory.

Dear Synthetic zero,

there is nothing such as your "virtual chaos" (things are either chaotic, or not) and consequently, there doesn't exist any loophole of the kind you suggested. You have confused the notions of "statistical physics" and "classical physics". Both of them make interference of quantum particles impossible, but in this particular setup (of Erik Verlinde), the "physics" that destroyed the interference pattern was "statistical physics" i.e. chaos, not "classical physics".

When an effect depends on the identification of macroscopically indistinguishable microstates, i.e. on the concept of entropy, its qualitative behavior is identical in the classical version and quantum version, and it always breaks the coherence.

It's just your illusion - a manifestly incorrect assumption - that I have discussed a "classical version" of Erik Verlinde's picture. Of course that in order to discuss interference from individual particles, I had to discuss - and I did discuss - the "quantum version".

And the quantum version of it does destroy the interference pattern. This is a result of "entropy" - and summation of probabilities over similar states - that occurs in this picture, not a consequence of considering a "classical theory" only.

I have only considered quantum theories in my picture.

The survival of the interference picture is only possible if one first sums the complex probability amplitudes, and then squares the sum's absolute value to obtain probabilities. This procedure is equivalent to the requirement that the force that modifies/shifts the interference pattern has to be fundamental i.e. non-entropic.

You are also wrong concerning your idea that Erik proposed a classical picture. Erik's ideas only make sense in quantum mechanics - look that from his equation (3.5), most equations contain Planck's constant and therefore inherently depend on quantum mechanics. Your idea that this is just some "classical version" that can be "improved" to get a quantum version is a misunderstanding of Erik's picture. Holography itself - his starting point - is a property of quantum gravity only: it doesn't exist in classical gravity.

I clearly have a different thinking than the rest of the world. From my optics, it may take 5 minutes - or at most 1 hour - to see that the precise thing that Erik Verlinde is proposing is wrong. I am flabbergasted by the idea that some people will study it for weeks, months, years, or centuries. People who need more than 1 hour after seeing and thinking about these arguments to see that the idea can't work should quit physics because they have no talent for it.

Cheers
Lubos

Sorry, I should have been more clear. What I meant is that Verlinde's idea is not fully quantum mechanical in that it depends on what currently passes for quantum gravity theories; i.e., theories that aren't fully quantum mechanical because they only work at certain scales and have other limitations: they aren't complete theories. For example, the holographic principle itself seems to imply some sort of dimensionality to spacetime (even though it "emerges" spacetime, it's assuming things like the boundary of a virtual volume, and so on). To my mind, a fully quantum theory of gravity would ideally not assume boundaries, where spacetime itself would emerge out of a much less structured substrate of some kind. Right now we have a situation where even the problem of quantum observation hasn't been worked out --- what actually happens when anything is observed? What is an interference pattern falling in a gravitational field, in a fundamental sense?

That is to say, existing "quantum" theories of gravity are kludges. In particular I think the notion of coherent superposition may be seen in a more fundamental sense to be an artifact of the mechanism of observation or detection, something that at least in my view hasn't been fully explained (i.e., the preferred basis problem in the Everett interpretation). If there's anything to Verlinde's idea then it might not work to think about superposition using one of the current quantum gravity kludges, rather in a more fundamental theory (whatever that might be) you might be able to preserve the observed effect but via a radically different mechanism. That is to say, I think Verlinde's idea cannot be a complete explanation but perhaps it could be a start to an explanation that could work within a radically different context.

Dear Synthetic Zero,

Verlinde's *results* are not fully (or partially) quantum mechanical because they're inconsistent with basic facts about quantum mechanics such as the existence of interference patterns in an external field.

But its assumptions surely are fully quantum mechanical. Holography, which he builds upon, only exists in "fully quantum mechanical" theories of gravity.

Whether a particular theory is consistent at all scales is an entirely different question from the question whether the theory is quantum mechanical.

You say a lot of vague things about what we don't know about the most profound questions about spacetime. But Verlinde's idea was exactly meant to remove this fog from gravity, and replace it with something specific. So your fog has nothing whatsoever to do with this discussion.

Also, it's nonsensical to say that "coherence is an artifact" of anything. It is an "artifact" of the most important fact about Nature, namely that it follows the postulates of quantum mechanics. If they are "artifact", then everything is an artifact.

At any rate, once coherence is lost, you can't ever recover it.

To summarize, what you write makes no sense whatsoever, and it would be good if you reduced these contributions somewhat. Thanks a lot.

Lubos

Hi Lubos, I'll defend the deterministic way of thinking from Einstein's point of view. Einstein himself spent his last years looking for "deterministic rules" that were the underbelly of quantum mechanics, a pill he troubled with swallowing. The idea was that the universe is deterministic on plack scales, but that somehow quantum mechanics would emerge at small scales, and GR would emerge at the largest scales. If Einstein himself thought it was worth devoting his last years to, then any physicist should be open minded to consider such theories less they think Einstein was a misguided fool with poor intuition.

Now to Verlinde. In Verlindes view he does not discuss how the bits operates, it's a complete hand waving maneuver that he does not attempt to solve. Any attack on him for this is probably well deserved. However, he does suggest that these bits though are the smallest possible units that can describe the universe, sorry using atoms and large scale particles doesn't seem to be fundamental enough to me either. They're way too large. Every dollar bill can be divided into 100 pennies, get my drift?

Working with the context of bits and not knowing they're underlying rules, I myself would make a few general assumptions assuming their existence:

1. Bits would have to make up particles. Particles must emerge from this information like a hologram. I tend to think of Magic Eyes at this point where it requires an observer to see the picture encoded in the information.

2. These bits of energy can fluctuate up and down perhaps in some dynamic pattern that follows rules, but hey maybe even following QM rules. Therefore, one might assume they have one degree of freedom.

2. Energy is conserved, so if one bit is fluctuating up, then another must fluctuate down.

Based on this one can apply the equipartition theory to a group of N bits and assign an average energy each bit holds. Assuming that the bits are entropically trying to average their energies out, then his model shows how gravity emerges as these bits average their energies out and approach an average energy.

Although his theory is radical and I myself have considered your points. I would agree with you that he could easily be wrong and you could easily be right. I'm not a good enough physicist to know (hah that's why I own a carpentry business now). However, it is quite remarkable that he gets the correct answers using his model. Some "coincidences" are not so easy to explain away.

So then is "virtual energy" or "holographic energy" real? Perhaps it is something real that exists at plank scales, but perhaps not.

I also tend to take a comprehensive view of the world and consider the philosophical view of the world as well. I often ask myself questions like, "If a tree falls in the forest and nobody is around to hear it does it make a sound? If no living beings exist can the world have an appearance?" These philisophical questions lead me to believe that the universe is nothing but information and it takes an observer to "see it" much like a Magic Eye, so holographic approaches to the universe are very enticing to me in that respect.

Verlinde shouldn't be let off the hook though and I hope that you and others challenge his ideas or prove them right or wrong. We all are seeking the truth and unfortunately to get to that destination means taking every possible path so that we can find the dead ends and turn the other way.

Physics needs bad physicists, just remember that. Bad physicist often get jobs at patent offices b/c they're not good enough. But...they just might be crazy enough...and that's what we need to solve this answer, some crazy thinking.

Dear Bookie,

apologies but science is not another religion where just different prophets are being worshiped in the same uncritical irrational way as e.g. in Islam. Science is about impersonal methods to find the objective truth about Nature.

Einstein's opinions about QM were demonstrably wrong - it has actually been demonstrated - and no scientist can be or should be "open-minded" about this question just because Einstein was confused. This has been scientifically settled and whatever Einstein thought or felt about it is only relevant for the historians of science, not for scientists themselves.

If it is necessary for you, I will also write that when it came to quantum mechanics, Einstein was a misguided fool with poor intuition. OK?

On the other hand, I also disagree with your comment that Einstein was crazy. During his miraculous year in particular, he was a smooth bureaucrat in perfect suits and organized haircuts. The idea of Einstein as a crazy chap doesn't refer to the Einstein at the times when he made the most important things. See Clifford's recent posting about this issue. Of course, Einstein was very unusual, even as a young officer, from some other viewpoints, but he didn't fit the category of "average" crazy people in any way. What you write is a historical myth.

I also disagree with your comments about Erik's paper. Erik doesn't suggest that the information has to be stored in binary digits - that would be stupid because the very point of information-based arguments like his argument (and even the correct ones that do exist in physics and that are valid) is that they're independent of the way how the information is stored or interpreted.

That's the whole point of entropy and information as concepts that the "formats" can be converted to each other and none of them is privileged. The idea of information encoded as "bits" all the time is just the idea of people with a very limited imagination who can understand some basics of computer science but who are completely incapable to understand physics because in physics, the information is never stored in these simple, well-defined, isolated bits of information. The Hilbert space for no interesting system in physics is exactly isomorphic to a tensor power of a two-dimensional Hilbert space. Look at Hilbert spaces of a Hydrogen atom, of a molecule, or a vibrating string to get a better idea how the information is stored in the state of physical systems in actual physics, rather than computers - which is an entirely different thing.

Best wishes
Lubos

"Moving objects will hit a higher number of the particles on the front side than the rear side: the excessive front collisions will therefore slow the object down."

Well, isn't this true even without Le Sages particles? Space is not that empty, is it?

Isn't it a fact that every little part of universe is actually filled with all kinds of waves/particles going in every possible direction? I mean, where ever you position yourself and whatever direction you look at, even with just naked eye, you will 'see' something. Always. Not even mentioning CMB or neutrinos or such, just photons. Is it hard to imagine that earth is shielding "something"? I know it is unusual to consider the Sun as a absorber, but I can imagine that it is a damn good one.

I am not a physicist. By any definition. But I always find it funny to see the lengths of imagination you will go through and how easily you look the other way when it suits you.

I know it's a childish concept, but ratio of shielding effect of object "shadow" being exact 1/r2 is just too appealing to me.

Dear Looka,

you ask: "Well, isn't this true even without Le Sages particles? Space is not that empty, is it?"

It's definitely not true without Le Sage's particles. The vacuum in quantum field theory (or string theory) is "not empty" but you must understand what the "non-emptiness" actually is. It is filled with virtual particles, not real particles.

Virtual particles only last for a finite time, so if they're able to change the momentum of an object, the change is abruptly "undone" as soon as the virtual particle ceases to exist. One of the consequences is that there is no "slowing down" of objects in the vacuum. A stable object with a velocity "v" will have the same velocity forever: the momentum is conserved. This is exactly true in quantum field theory, even when all of its subtle phenomena are introduced, and we also know experimentally that it has to be true. Any hypothesis that violates this principle of inertia is instantly falsified.

Your question: "Isn't it a fact that every little part of universe is actually filled with all kinds of waves/particles going in every possible direction?"

Again, yes, but they're virtual particles and they have none of the effects you incorrectly attribute them because they're not real particles.

You continue: "I mean, where ever you position yourself and whatever direction you look at, even with just naked eye, you will 'see' something. Always. Not even mentioning CMB or neutrinos or such, just photons."

This has nothing to do with the question. CMB is not a part of the vacuum CMB is obviously composed out of real photons, not just virtual photons. But the CMB is completely negligible relatively to gravity. If you used the CMB photons as the Le Sage particles, and you considered the shadows etc., the force that you would get by this would be vastly lower than gravity. Easy to know why - if it were different, we would have to include this extra CMB-LeSage force in every calculation. Moreover, gravity could be turned off just by shielding microwaves - which would be very easy. :-)

You: "I am not a physicist. By any definition. But I always find it funny to see the lengths of imagination you will go through and how easily you look the other way when it suits you."

If you think that there exists just an infinitesimal piece of an asymmetry of my imagination and my looking, it's just because your intelligence is far too low to know what is the right attitude. In other words, your accusations are just about your being an idiot.

You: "I know it's a childish concept, but ratio of shielding effect of object "shadow" being exact 1/r2 is just too appealing to me."

Great but it is a theory that has been excluded for a few hundred years and you can't really revive dead theories in physics unless you modify them. Falsification in physics is eternal, and the LeSage theory is damn dead.

Best wishes
Lubos

Second, I am very sorry, but I certainly wasn't referring to you as individual, but to physicists attitude in general perceived to a layman, myself included. It is my general notion that majority of great minds throughout the history of physics were always too quick to dismiss other people's theories, and almost infinitely stubborn in their own. Surely, I didn't mean any disrespect to you personally in any way and, again, I am sorry if it was interpreted as such.

Now, back to LeSage. Thanks for clearing CMB radiation, but how can we really exclude the possibility of ever finding out any such particle? I find it easier to believe in non-friction inducing mass absorbed currently undetectable particle than many other generally accepted but only theorized phenomena.

Didn't we see frictionless fluid motions at extremely low temperatures?

Also, what about impact of all macroscopic objects (comets, space dirt, rocks) or even free floating microscopic ones (molecules of gas)? Shouldn't that slow down Earth then?

Furthermore, shouldn't friction actually increase orbiting speed, but only reduce orbital potential energy?

Yes, theory was killed 300 years ago, but I consider that to be in favor of re-mentioning it.

Please feel free to disregard this reply if you think it is inappropriate for you common audience or you just don't have time to explain physic basics to random visitor. I'm pretty sure I am way over my head here. :)

Thanks again and kind regards,

Looka

Lubos,

Some clarification for Neutron experiment you were referring.

Best,

Lubo: I am sory to say this, but you really don't understand what you talking about:

"It is really the same story [LeSage's and Verlinde's theories]. While the LeSage theory is considered a defunct 17th century pseudoscience, its generalization by Erik is a nwe hot kid on the block for Nude Socialists and others. ;-)"

LeSage founded his theory (wich was no pseudoscience, only a hypothese that failed) on the corpuscular wiew on matter and particles; ie, it consisted on hard material particles. Verlinde talks about particles in a modern sense. Predictions from the two theories can't be the same, and it can't be "the same story".

It is also a bit ironic that you behave like you are a much better and smarter scientist then Verlinde; wich you certainly not are. It is a good idea to cool down and try to reduce the air in your ego a little.

PS. I am not even sure LeSage's and Verlinde's theories are similar in some ways. This seem to be something you have made up yourself, only to associate Verlinde with an idea that is still popular in pseudoscience. Your behavior is not serious.

Dear nymodernism,

you're not "sure" whether Verlinde's and LeSage's theories are "similar" because you don't have the slightest clue about physics. You're just an obnoxious troll.

I have explained that these two theories are not just "similar": LeSage's theory is a special case of Verlinde's theory. And it is very easy to see why. Here is the reason, once again.

In LeSage's theory, objects A and B are attracted because in between them, there is a "shadow" of LeSage's particles. The relative excess of LeSage's particles on the external side pushes objects A,B towards one another.

This whole thing therefore relies on the non-uniformity of
the distribution of the LeSage's particles that is larger when the gravitational potential energy is larger (objects are further from each other). When this non-uniformity goes away, the force of gravity disappears, too.

This non-uniformity means that the entropy is not yet maximized. The entropy tries to maximize itself by pushing the objects towards each other. When all objects coincide, the distribution of the LeSage particles in space becomes uniform and their entropy is maximized.

So these are the very same kind of theories and one can formulate them in such a way that it's not just a similarity: they're in the same universality class.

These theories are excluded because they predict many unobserved effects such as irreversibility - which has been known to be a deadly problem of LeSage's theory for more than 200 years but some people have forgotten about this basic physics.

Another problem is that the real gravity, as we observe it e.g. in neutron interfereometry, acts in agreement with the equivalence principle and with the laws of Newton or Einstein even on individual particles. However, LeSage/Verlinde's force could only converge to a particular macroscopic formula after the force is averaged over an ensemble of particles. That's much weaker an agreement with gravity than what has been supported experimentally.

Yes, I was the first one who wrote this criticism in the context of Verlinde's theory. But that's no reason to be ashamed. ;-) I am right and every person with the basic knowledge of physics must know and does know that I am right and Verlinde is wrong.

Best wishes
Lubos

Dennis Overbye just published an article in the New York Times about this theory. Unfortunately they have already closed the comment section, so I couldn't post a link to this page. There are over 200 comments, but apparently none of them from people who read the paper and understood it.

Dear Mitchell, thanks.

Yes, of course, I noticed the article. It's pretty bad. Dennis Overbye who was at the top of my U.S. MSM science journalists list dropped by 1 place immediately.

Raphael Bousso politely tells him that after a journal club, everyone at Berkeley - including the early enthusiasts - would know that Erik's picture made no sense.

Dennis didn't know what this comment meant. Instead, he was building on hyperpolite clichés by Andy Strominger and others who say that they love similar crackpot papers because they support discussions etc.

Well, if discussions are the main or only real value of that job, why doesn't Andy discuss papers by Lee Smolin, Jack Sarfatti, or any other crackpot, for that matter, all the time?

It's bad that the selection of good ideas and filtering of nonsense is defunct - and maybe even reverted - when it comes to modern sources of influence such as the newspapers. Arbitrarily bad rubbish gets promoted if its author together with some journalists have the interest to do so and are given the freedom to cherry-pick and distort the testimonies of others - which they almost always do.

Erik Verlinde can't possibly believe the dumb things he is saying today - that gravity doesn't exist for him, and so on. I guess that if you bring him to the window and tell him "jump", his acts will still show that he does believe in the existence of gravity, after all.

Best wishes
Lubos

in this post

http://www.science20.com/hammock_physicist/it_bit_entropic_gravity_pedestrians

"One such aspect has to do with the question of the reversibility of entropic gravity forces. Some have claimed that entropic forces are necessarily irreversible. In other words, in a system with entropic gravity it would in general not be possible to cause the system to trace back its history.

Reversible Entropic Forces

The claim that entropic forces are necessarily irreversible is a misconception. Verlinde has tried to argue against this wrong concept, but he failed to note a key point. Key is that if the underlying microscopic (Planck scale) dynamics is reversibility, so will be the emerging entropic force."

Dear nemo,

a completely reversible entropic force is impossible in the real world by the very definition of the entropic force: it is the force driving the system to the loci of the configuration space where the entropy is higher.

One can only consider an idealized concept of an isoentropic process - or reversible adiabatic process. But only processes that occur "infinitely slowly" can be approximated in this way. A general interaction between objects moving and changing by finite speeds - or even speeds comparable to the speed of light - cannot be described as an adiabatic process by any stretch of imagination.

These are absolutely elementary facts about thermodynamics that undergraduate students learn in their thermodynamic courses. Also, you find these facts written in all fair introductions to thermodynamics. A random page on Wikipedia, Joule expansion, for example correctly states that a route that keeps entropy constant (i.e. keeps thermal equilibrium at all times) "can only be realized in the limit where the changes happen infinitely slowly."

The fact that Erik Verlinde or Mr Hammock are ignorant about these elementary things don't make them any less elementary.

Isoentropic (or constant entropy) processes require all the bodies that are in contact to have the same temperature. That's explicitly violated in Verlinde's picture where the temperature is determined on pairwise relationships between the objects. There would surely be lots of heat transfer and entropy increase which is an irreversible process.

The entropy changes that Erik Verlinde would need to make the gravity work would not only be nonzero: they would be astronomical, comparable to the black hole entropy which is the largest entropy that a fixed-mass localized physical system can have. LeSage's defunct theory of gravity died for the same reason: it predicted friction that would slow objects down: that's a manifestation of irreversibility. The advantage of LeSage relatively to Verlinde was that the coefficient in front of the entropy was adjustable in LeSage's picture so one could hope that the produced entropy could be made small (which didn't really work, either, but there was a hope): however, the entropy in Erik's picture is of the order of the black hole entropy for the same masses, so it is surely not small in any case. The induced irreversibility would be gigantic and it would abruptly stop all motion.

Best wishes
Lubos

Dear Lumo,
I think that you are taking too many things that we think are correct as facts. Your arrogance is overwhelming. Einstein would have trouble with your thoughts.
I think that Eric's theory needs scrutiny and more work. I do not agree that it is completely wrong.

Cheers,
Joel

Dear Joel, do you actually think that you have found any imperfection or possible loophole in my multiple proofs that Verlinde's staements can't be right, or did you just come here to spread bitterness and fog without having a clue?

Do you actually think that your content-free emotional scream may be viewed as an answer to my thoughtful analysis?

The statements have already undergone scrutiny and no other serious physicists think they're correct which is why papers are only being written by authors who are not exactly 1st or 2nd class physicists.

More work is the last thing that this hyped nonsense needs. The first it needs is less hype i.e. less work because there is nothing to work on here. It's just a collection of a few statements that may be easily shown to be incorrect if one looks what is actually being said.

Cheers
LM

Lubos, now that entropic gravity is no longer entropic, it makes sense! :-)

The claim now is that gravity away from horizons is an adiabatic reaction force, which degenerates into a true entropic force at horizons, where the adiabatic approximation breaks down. When Erik said that the entropic force doesn't increase entropy, he meant that entropy is an adiabatic invariant for the reaction force.

arxiv:0709.2136 derives gravitational precession within an adiabatic approximation and made the whole thing much more plausible to me.

As for Erik's new cosmology, he admitted in discussions at Perimeter Institute that he was uncertain about a lot of details. I think there's still a great possibility that some version of these ideas will provide a unified holographic explanation for dark matter and dark energy.

Another important detail is that it's only a formal "entropy" and "temperature" appearing in Erik's equations. There's something non-standard about the meaning of adiabaticity in the context of reaction forces, which I'm trying to pin down. But here's a quote:

"In thermodynamics 'adiabatic' is used in a macroscopic sense to refer to a process occurring
in a thermally insulated system, so that there is no flow of heat to or from the surroundings.

"In reaction dynamics, the word has been used in a microscopic sense, with a range of meanings which have only a tenuous relationship to the thermodynamic meaning or the etymology. Whereas the thermodynamic meaning relates to conditions imposed on a process by an observer, the microscopic meaning relates to conditions under which the process occurs
naturally."

Dear Mitchell, sorry to say but what you write (and what Verlinde is saying these days) still makes no sense whatsoever. It's just masking the crackpottery he has been previously spreading under a thick layer of fog.

The 2007 paper you referred to is about Berry's phase which is a quantum phase induced by an adiabatic change of parameters. But the adiabatic change of parameters must be pushed by another, external force: the adiabatic change is not the first driver. The external parameters are being slowly changed by an external agent so that the entropy doesn't increase - that's what we mean by "adiabatically" - and we may study the reactions of a particular system to these slow external changes. But the slow external changes are driven by an independent force, e.g. by muscles of a human controlled by the human's "free will": there is no "formula" for "what the adiabatic changes should be". The "spontaneous" force acting on the parameters - without an independent driving force - is zero.

The same is true for any other paper about the "adiabatic reaction force" in this context, e.g. one by Berry himself (with Shukla).

The term "adiabatic reaction force" was just used by Verlinde to replace "entropic force" because everyone has understood by now that gravity isn't an entropic force, also because entropic forces are *irreversible*. But when the entropy actually isn't increasing, the entropic force goes to zero.

So saying that the "adiabatic reaction force" is nonzero is the same childish mistake as talking about "forces induced by a constant gravitational or electric potential". By a simple calculation, d0/dx = 0, we get zero. You can't have it both ways. Forces related to entropy are either irreversible, or zero. Each of these conditions is incompatible with basic properties of gravity.

Cheers
LM

Hi Lubos - I understood Erik to be saying that different degrees of freedom could spontaneously develop different characteristic timescales of evolution, and that when you construct an effective theory for the slow degrees of freedom, it will contain these reaction forces. The phase-space volume beneath a given energy level is very nearly conserved, and the log of this volume is his "entropy".

Dear Mitchell, you're fooling yourself all the time.

In a unitary quantum theory - and even in a classical theory with a time-dependent "overall" Hamiltonian for all degrees of freedom - the volume of the phase space below some energy (or, quantum mechanically, the number of microstates in it) is *exactly* conserved.

This volume actually doesn't depend on dynamics at all: it is a universal function of the overall energy and the overall energy is exactly conserved. Because this phase space has a constant volume, the "entropy" calculated from this volume in Verlinde's sloppy way (as a logarithm) is also constant which means that the force is zero.

There's really no way - except for introducing errors into physics by hand - how you could get an entropy-based force that would still lead to reversible phenonomena. It's a contradiction. Any dynamics based on entropy differences is irreversible by the first key property of the entropy, the second law of thermodynamics.

Regardless of tiny mutations of the wording, you still haven't gotten rid of the basic error that was present in this Verlinde stuff from the beginning. You still seem to think that the number of microstates - or volume of phase space - corresponding to the Sun and the Earth at different distances depends on the distance (maybe even exponentially with a huge extra coefficient in the exponent).

But this is impossible: it would violate unitarity in a dramatic way. The Sun and the Earth are getting closer and further every year, so whatever microstate for the fast degrees of freedom you have in January when the Sun-Earth distance is minimal must also have their counterparts, in a one-to-one fashion, in July when the distance is maximal. So the phase space volume beneath "E" is obviously independent on how you realize "E" - pretty much by definition. In particular, it must be independent of the Sun-Earth distance, otherwise this distance couldn't change in both ways in a unitary fashion.

Much more strongly, we know from physics - obviously from string theory but we don't really need string theory - that the Sun-Earth system carries no gravitational entropy, surely no entropy that would scale like A/4G with a macroscopic value of A - i.e. an entropy comparable to the black holes of macroscopic dimensions. The Sun and the Earth only carry a very tiny entropy, essentially equal to the number of atoms in them, and this entropy has clearly nothing to do with gravity. In principle, you could consider frozen planets orbiting each other. The gravity wouldn't change but the entropy would be (nearly) zero.

Only event horizons may produce a large entropy of order A/4G. No horizons means no entropy. I can't believe that this elementary point known from the early 1970s is still being misunderstood in 2011.

Cheers
LM

Hopefully we can agree that the growth of a horizon is an entropy-maximizing process. So what about horizon formation?

Consider a black hole of a given size. It has a large gravitational entropy. Now consider various ways that it could have formed (gravitational collapse of a gas cloud, infall of gas onto a neutron star, collision of two neutron stars, etc). In each of these situations, before a horizon forms, there is negligible gravitational entropy. The region of phase space containing the black hole is a region of convergence for many dynamical trajectories, which is how a system moving along any such trajectory can experience a big jump in total entropy when the horizon forms. It's entered a bigger region of phase space.

Somehow there is a transition from a situation (no black hole) in which maximization of gravitational entropy plays no dynamical role, to a situation in which it does, because the black hole now exists and its horizon can grow. Erik isn't saying any more that gravity outside of a horizon is maximizing an entropy, but he's saying that its form is determined by conservation of the phase space volume for the fast degrees of freedom, and when slow and fast timescales converge, you get horizons and a transition from a kinetic to a thermodynamic regime.

I still think there must be an insight there which is both not trivial and not wrong. :-)

As a result of this discussion, I think I have at least identified the crucial proposition of "entropic gravity 2.0", which is that the phase space volume for the fast variables, associated with a uniform gravitational potential surface on which the escape velocity is "v", should be (A/4G)v. When v=c, a horizon forms, and the thermodynamic regime takes over.

Dear Mitchell,

you write: "I still think there must be an insight there which is both not trivial and not wrong. :-)"

Is that your primary assumption? That would explain why nothing you wrote makes any sense to me because this assumption of yours is probably completely wrong.

Some configurations of matter - such as the Sun - don't collapse into a black hole. Others do. When they do, the huge black hole entropy is produced during the time when the horizon gets formed. What's the problem?

Why would you describe the simple process of a formation of a black hole by - seemingly deliberately - cryptic sentences such as "phase space containing the black hole is a region of convergence for many dynamical trajectories"?

The phase space of a black hole corresponds to microstates of a black hole which are the generic microstates of a localized matter with the same value of the mass and charges. So once you get to the path when the black hole is formed, you're inevitably visiting the whole phase space. However, for (low-density) objects such as the Sun, there is a barrier that prevents you from the formation of a black hole. Instead, you are kept in a tiny subspace of the phase space, macroscopically known as the "state of the Sun", so there's no gravitational entropy, so there's no justification to talk about it.

You: "Erik isn't saying any more that gravity outside of a horizon is maximizing an entropy, but he's saying that its form is determined by conservation of the phase space volume for the fast degrees of freedom, and when slow and fast timescales converge, you get horizons and a transition from a kinetic to a thermodynamic regime."

I have no idea what to do with these sentences. This is just a sequence of pure rubbish. A black hole maximizes the entropy among the bound states of the same mass and charges and angular momenta, so when you create it, you maximize the entropy. When you don't create it, you don't quite maximize it. What else do you think you can say about these obvious things that hold for every system - and its highest-entropy macrostate - and that have been known for 100+ years?

Moreover, there are no "fast degrees of freedom" describing two frozen planets orbiting each other. There are no fast degrees of freedom at all because the system's entropy vanishes. So these non-existent fast degrees of freedom can't be responsible for anything. But as I explained, even if there were fast degrees of freedom, the total amount of phase space corresponding to these fast degrees of freedom would have to be totally independent of the values of the slow degrees of freedom, by unitarity and reversibility.

I can't get rid of the feeling that you have decided to become a mindless parrot of some complete and self-evident crackpottery. Have you been paid for that? Or do you really fail to see that what you keep no writing is just pure rubbish?

Your last short comment makes no sense, either. First, you seem to have restored the speed of light as a quantity not equal to one. But why didn't you do the same thing with hbar and k_Boltzmann? Moreover, your power of c is incorrect. The actual entropy in normal units is

S = A.c^3.k_{Boltzmann}/(4.hbar.G)

So your powers of k, hbar, as well as c are just wrong. But even if all those exponents were not wrong, what the hell are you saying? Another detail is that the phase space corresponding to a black hole has volume not A/4G but rather exp(A/4G), in the c=G=hbar=k=1 units.

Sorry, you must be completely drunk or on crack right now because I know that your texts are usually more coherent than this one.

It's surely nonsense that the entropy gradually grows as your "proportionality to escape velocity v" suggests. There is nothing continuous about the evolution of the entropy. The current entropy of the Sun is 2 x 10^{63}. If it were to collapse to a black hole, its radius would be a few kilometers - 10^{39} Planck lengths or so - so the entropy after the collapse would abruptly jump to 10^{78} or so, by 15 orders of magnitude. The entropy of a star is parameterically negligible relatively to a black hole entropy: after all, it typically scales like A^{3/4} only instead of A. You should first learn these basics of physics before you decide to promote your opinion about a would-be ambitious (crackpot) statements about quantum gravity.

Cheers
LM

Yes Lubos, I am imprisoned in a Dutch crack house and I don't get my fix unless I promote Erik's theory. But I'm not doing a good enough job, so they're going to give me a few days to get my act together.

You see, Mitchell, that my guess was right on the money. Every detail of your behavior betrayed you. ;-)

Here is the picture I got from Erik's recent talks.

We can describe the universe by a matrix with D-branes on the main diagonal and open-strings off the diagonal. We can put the state of the universe into approximately block-diagonal form. Black holes are blocks in which diagonal and off-diagonal entries are in equilibrium. When matter outside a black hole falls in, the matrix elements connecting the matter block to the black hole also enter equilibrium, and the black hole grows. Finally, for the gravitational interaction between two objects outside a black hole, we integrate out the matrix elements connecting their blocks (the open strings).

I may be fuzzy on the details, but isn't all of that perfectly orthodox?

I then understand Erik to be saying two things. First, the growth of a black hole is an entropic process, occurring in a phase space of volume exp(A/4G). Second, the ordinary gravitational interaction is not an entropic force, but the matter degrees of freedom on the diagonal do still "feel" the volume of the off-diagonal phase space, through something like a Berry phase, and this determines the effective form of the interaction. (A/4G)v is Erik's guess as to the log of this volume. (v must be dimensionless, i.e. it's v/c.) A horizon forms when v=c, and the diagonal degrees of freedom go into equilibrium with the off-diagonal degrees of freedom.

Dear Mitchell,

the first paragraph is a standard knowledge of Matrix theory. Yes, forces may be derived from integrating out off-diagonal elements. And yes, maximal participation of the off-diagonal elements - when they're as important as the diagonal ones - occurs with black holes.

But this picture of Matrix theory has nothing to do with entropic gravity. There is nothing "entropic" or "adiabatic reactionic" about either of the steps in the previous paragraph.

You say: "...matter degrees of freedom on the diagonal do still "feel" the volume of the off-diagonal phase space..."

Nope, we know that this "feeling" can't exist. You can't "feel" the entropy of states that have nothing to do with states in which you are in, and even if you interpreted this bizarre statement in some way - like counting intermediate states that may be exchanged - the force wouldn't be linear in entropy or its derivatives in any sense. It could be proportional to the number of microstates, but there would also be couplings etc.

What you write is just obviously and demonstrably false. You're clearly trying to be vague - and so does Verlinde - but try to formulate any actual formula that would link the force in a matrix model to the entropy of anything or its derivative, and it will take a few seconds to show that this formula is wrong.

There's just nothing entropic or adiabatic about these forces in quantum gravity - and matrix models are just a description of quantum gravity, completely valid one, so what holds for quantum gravity obviously holds for matrix models as well.

Cheers
LM