Thursday, January 14, 2010 ... Deutsch/Español/Related posts from blogosphere

Erik Verlinde: comments about the entropic force of gravity

Written by Dr Erik Verlinde (see Twitter)

Table of contents:
► Logic of the paper (right below)
The essential new points of the paper (click)
Comments about irreversibility (click)
Logic of the paper

The paper (abs, PDF) is not technical, but some background is needed, more than just being able to read the text and the equations. The text explains the logic, but apparently some important points are misunderstood. Clearly, I should do a better job in making them more clear. But it is my impression that the misunderstanding is partly due to a lack of background or a difference in reference frame. Because the logic of the paper is being misrepresented in some reports, I add here some clarifications.

So here is an attempt to address some of the points that I think are not appreciated or generally understood.
Previous article on the same topic: Gravity as a holographic entropic force and Why gravity can't be an entropic force
The starting point is a microscopic theory that knows about time, energy and number of states. That is all, nothing more. This is sufficient to introduce thermodynamics. From the number of states one can construct a canonical partition function, and the 1st law of thermodynamics can be derived. No other input is needed, certainly not Newtonian mechanics. Time translation symmetry gives by Noether's theorem a conserved quantity. This defines energy. Hence, the notion of energy is already there when there is just time, no space is needed.

Temperature is defined as the conjugate variable to energy. Geometrically it can be identified with the periodicity of euclidean time that is obtained after analytic continuation. Again there is nothing needed about space. Temperature exists if there is only time.

It is possible to introduce other macroscopic variables that are associated with a finite but still large subset of the microstates. Let us denote such a variable by x, at this point this is just some arbitrary choice. It can be any macroscopic variable that singles out a collection of the microscopic states. So specifying x in addition the to energy gives more detailed description of the microscopic states, but nothing more. So it is not even necessary to think about x as a space coordinate. Nevertheless one can define a number of microstates denoted by Omega(E,x) for given energy E and for a given value x for this macroscopic variable x.

Next one can introduce a formal variable called F and introduce in the partition function as the thermodynamical dual to x. Following just standard statistical physics (I avoid the word mechanics, since Newton's law is not necessary) one can obtain the 1st law of thermodynamics.
dE = T dS - F dx.
This makes clear that F is a generalized "force", but it has nothing to do with Newton's law yet. It is defined in terms of entropy differences. The macroscopic force that is obtained in this way has no microscopic origin in terms of microscopic field. The force is entirely a consequence of the amount of configuration space and not mediated by anything. There is no space yet.

The meaning of the statement that space is emergent is that the space coordinates x can be viewed as examples of such macroscopic variables. They are not microscopically defined, but just introduced as a way of singling out part of the available micro states. It is my impression that not all readers have understood or appreciated this essential point. Hence, if the number of states depend on x there can be an entropic force, when there is a finite temperature. This is all, nothing more. Again, for this point I don't need to assume Newtonian mechanics. It does not exist yet in this framework.

The other central point paper is that if one chooses a macroscopic coordinate x that corresponds to a fixed position in a non-inertial frame, that Newton's law of inertia
F = ma
will be the consequence of such an entropic force. This has to be. There is no other way it can arise, simply because x is not a microscopic variable. It is obvious. Nevertheless, it is a fundamental new insight that has not been noted before. This is not an empty or circular statement. It says something about the way that the function Omega(E,x) should behave as a function of x. All this can be derived and defined without the input of Newtonian mechanics.

The other formulas presented in the paper are just there to illustrate that indeed it is possible to get gravity from this kind of reasoning, and that it is consistent with the ideas of holography. But the main point concerns the law of inertia. The derivation of the Einstein equations (and of Newton's law in the earlier sections) follows very similar reasonings that exist in the literature, in particular Jacobson's. The connection with entropy and thermodynamics is made also there. But in those previous works it is not clear WHY gravity has anything to do with entropy. No explanation for this apparent connection between gravity and entropy has been given anywhere in the literature. I mean not the precise details, even the reason why there should be such a connection in the first place was not understood.

My paper is the first that gives a reason why. Inertia, and hence motion, is due to an entropic force when space is emergent. This is new, and the essential point. This means one HAS TO keep track of the amount of information. Differences in this amount of information is precisely what makes one frame an inertial frame, and another a non-inertial frame. Information causes motion.
This can be derived without assuming Newtonian mechanics.

So the logic of the part of the paper dealing with inertia is:
microscopic theory without space or laws of Newton → thermodynamics → entropic force → inertia.
The part that deals with gravity assumes holography as additional input. But this is just like what has been done before. It is also not the main point of the paper. Gravity in a way does not exist in Einstein's theory either. But one would like to recover the gravity equations. The logic here is
thermodynamics + holographic principle → gravity.
The obvious question is of course, where does the holographic principle come from? Of course, it was extracted from the physics of black holes. But the holographic principle can be formulated without reference to black holes or gravity. Hence, it can be taken as a starting point, from which one then subsequently derive gravity. Again, this part is in essence not new. Jacobson followed exactly the same logic.

This way of turning the logic of an existing argument around is done more often in physics, and it is known to lead to much more clear formulations of a theory. The example that comes to mind is the way that Dirac used the result of Heisenberg that p and q do not commute, which was obtained in some roundabout way, and made it in to the starting point for quantum mechanics. This is how it is being taught today.

Anyhow, I hope this clarifies some points, and removes some of the misunderstandings.

The essential new points of the paper

I have noticed another point of the paper that is not appreciated in blog discussions. For many years, there have been previous works in the literature that discuss the similarity between gravity and thermodynamics. In particular in Jacobson's work there is a clear statement that if one assumes the first law of thermodynamics, the holographic principle, and identifies the temperature with the Unruh temperature, that one can derive the Einstein equations. This is a remarkable result. Yet it is already 12 years old, and still up to this day, gravity is seen as a fundamental force. Clearly, we have to take these analogies seriously, but somehow no one does.

I studied the previous papers very well, and know about them for years. Many people have. We have seen a recent increase in papers following Jacobson, and extending his work to higher derivative gravity, and so. But from all of these papers, I did not pick up the insights I presented in this paper. What was missing from those papers is the answer to questions like: why does gravity have anything to do with entropy? Why do particles follow geodesics? What has entropy to do with geometry?

The derivation of Jacobson does not take in to account the fact that the mass of an object and therefore its energy can change due to the displacement of matter far away from it. There is action at a distance hidden in gravity, even relativistically. The ADM and Komar definitions of mass make this non-local aspect of gravity very clear. This non-local aspect of gravity is precisely what the holographic principle is about.

Jacobson's argument is ultra local, and assumes the presence of stress energy crossing the horizon. But there is no statement about an entropic force that is influencing particles far away from the horizon. My point of view is an attempt to take a much more global view, and map out the information over a bigger part of space, even though initially I can only do that for static space times.

The statement that gravity is an entropic force is more then just saying that "it has something to do with thermodynamics". It says that motion and forces are the consequence of entropy differences. My idea is that in a theory in which space is emergent forces are based on differences in the information content, and that very general random microscopic processes cause inertia and motion. The starting point from which this all can be derived can be very, very general. In fact we don't need to know what the microscopic degrees of freedom really are. We only need a few basic properties.

For me this was an "eye opener", it made it from obscure to obvious. It is clear to me know that it has to be this way. There is no way to avoid it: if one does not keep track of the amount of information, one ignores the origin of motion and forces. It clarifies why gravity has something to do with entropy. It has to, it can not do otherwise.

When I got the idea that gravity and inertia emerge in this way, which is close to half a year ago, I was really excited. I felt I had an insight that makes clear what gravity is. But I decided not to publish too quickly, also to allow time to make it more precise. But also to see if the idea that gravity is entropic would still appear to me as new as exciting as my first feeling about it. And it does. Now, almost half a year later, I still feel that way.

For instance, the similarity between the entropic force for a polymer and gravity is a real clue to something important. The fact that it fits in well with an adapted version of the work of Jacobson gives additional support. The derivation of the Einstein equations is not really new, in my mind, since it technically is very similar to the previous works. And I agree that the other line of the paper that discusses inertia is heuristic, and leaves some important gaps. But nevertheless I decided to publish it anyway, because I think this approach to gravity is the right one, it is different, very different from everything that is done today.

Everyone who does not appreciate that this view is different from previous papers are missing an essential point. If space is emergent, a lot more has to be explained than just the Einstein equations. Geodesic motion, or if you wish, the laws of Newton have to be re-derived. They are not fundamental. This has not been discussed anywhere, not even noted that it is the case.

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

Some people may think that when we develop string theory further that eventually we will learn about this. I am not sure that string theory is the way to go. In any case, not if we keep regarding the definition in terms of closed strings as being microscopically defined, may be equivalent to some other formulation. And not if we keep our eyes closed for emergent phenomena. Graviton's can not be fundamental particles in a theory of emergent space time and gravity.

So what is the role of string theory, if gravity is emergent? I discussed this at some level in the paper. It should also be emergent, and it is nothing but a framework like quantum field theory.

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

Of course, I would have liked to make things even more clear or convincing. In this paper, I use heuristic and you might say handwaving arguments. The issue of motion: why is the acceleration a that I introduced equal to the second time derivative of the position? If one assumes the equivalence principle, it is clear. Also coordinate invariance would be enough. But I do not have a very precise way of seeing how that emerges. How to go from just information to a Lorentzian geometry in which general coordinate invariance is manifest. Some assumptions have to be made.

But again, this are questions that others have not been even started to think about. These are questions that have not been even addressed by previous works. But they are essential. When one really understands this well, there should be no doubt that gravity is emergent and forces are driven by entropy.

This is the essential idea, which is really new and important, and which in my view justifies this level of reasoning, certainly in a first paper. It is clear that this is not the final paper on this subject. This is also my own view. I clearly did not answer all of the questions. In fact, my approach probably raises more questions than it answers. But it should be obvious that these questions are important, very fundamental and their answers should lead us in a completely new direction. Our theories will have to based on new paradigms.

I find all this still very exciting and will continue to work in this direction.

And remember, quantum mechanics was also not developed in one paper. Do you think de Broglie knew exactly what he was talking about? Leaps based in intuition are sometimes necessary. They are an important part of progress in science, even if they do not immediately give complete finished theories of Nature.

Comments about irreversibility

Entropic forces and the 2nd law of thermodynamics
15/01/10 02:21

Let me address some other confusions in the blog discussion. The fact that a force is entropic does not mean it should lead to irreversible processes. This is a complete misunderstanding of what it means to have an entropic force. This is why I added section 2 on the entropic force. For a polymer the force obeys Hooke's law, which is perfectly conservative. No doubt about that.

Just last week we had a seminar in Amsterdam on DNA. Precisely the situation described in section two was performed in lab experiments, using optical tweezers. The speaker, Gijs Wuite from the Free University in Amsterdam, showed movies of DNA being stretched and again released. These biophysicists know very well that these forces are purely entropic, and conservative. The processes that involve these forces are for all practical purposes reversible. Indeed, the movies that were shown clearly exhibited this reversibility, to a very high degree. In fact, I asked the speaker specifically about this, and he confirmed it. They test this in the lab, so it is an experimental fact that entropic forces can be conservative.

I explained this in section 2. So please read it again, study it and think about it for a little longer. When the heat bath is infinite, the force is perfectly conservative. For the case of gravity the speed of light determines the size of the heat bath, since its energy content is given by E=Mc^2. So in the non relativistic limit the heat bath is infinite. Indeed, Newton's laws are perfectly conservative. When one includes relativistic effects, the heat bath is no longer infinite. Here one could expect some irreversibility. In fact, I suspect that the production of gravity waves is causing this. Indeed, a binary system will eventually coalesce. This is irreversible, indeed. This all fits very well, extremely well, actually with the fact that gravity is an entropic force. Of course, when I first got these ideas, I worried also about irreversiblity. I knew about the polymer example, but had to study it again to convince myself that entropic forces can indeed be conservative. But it is a well known fact for biophysicists.

Another useful point to know is that when a system is slightly out of equilibrium, it will indeed generate some entropy. But a theorem by Prigogine states that the dynamics of the system will adapt itself so that entropy production is minimized. Yes, really minimized. This may appear counterintuitive, but I like to look at it as that it seeks the path of least resistance. So this means that there ill in general not be a lot of entropy generated. At least, the system will do whatever it can to minimize it.

By the way, it is true that the total energy of a system of two masses m_1 and m_2 is given by the total mass M=m_1+m_2. But the natural expression for the entropy gradient due to change in relative position is that instead of being proportional to the smalles mass, that it is proportional to the reduced mass m_1m_2/(m_1+m_2). This is the only natural expression that is symmetric in m_1 and m_2. And indeed, by the same argument as in the paper one recovers the right force. I thought of putting that in the paper, but I thought it was kind of trivial. This point of confusion is not difficult to solve, it seems to me.

Another point that may not be appreciated is that the system is actually taken out of equilibrium. If everything would be in equilibrium, the universe would be a big black hole, or be described by pure de Sitter space. Only horizons, no visible matter. If a system is out of equilibrium, there is not a very precise definition of temperature. In fact, different parts of the system may have different temperatures. This means that there is no problem also with neutron stars. In fact, I got these ideas precisely by thinking about what causes neutron stars to collapse if one considers them from a holographic perspective. I concluded that the cause was purely entropic. By the way, physical neutron stars do not have exact zero temperature. But the temperature I use in the paper is one that is associated with the microscopic degrees of freedom, which because there is no equilibrium, is not necessarily equal to the macroscopic temperature.

The microscopic degrees of freedom on the holographic screens should not be seen as being associated with local degrees of freedom in actual space. They are very non local states. This is what holography tells us. In fact, they can also not be only related to the part of space contained in the screen, because this would mean we can count micro states independently for every part of space, and in this way we would violate the holographic principle. There is non locality in the microstates.

Another point: gravitons do not exist when gravity is emergent. Gravitons are like phonons. In fact, to make that analogy clear consider two pistons that close of a gas container at opposite ends. Not that the force on the pistons due to the pressure is also an example of an entropic force. We keep the pistons in place by an external force. When we gradually move one of the pistons inwards by increasing the force, the pressure will become larger. Therefore the other piston will also experience a larger force. We can also do this in an abrupt way. We then cause a sound wave to go from one piston to the other. The quantization of this sound wave leads to phonons. We know that phonons are quite useful concepts, which even themselves are often used to understand other emergent phenomena.

Similarly, gravitons can be useful, and in that sense exist as effective "quasi" particles. But they do not exist as fundamental particles.


Comment by L.M.: to see why the description of gravity above cannot work, see Why gravity cannot be driven by entropy.

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reader Erik Verlinde said...

For the polymer case it is easiest to see that an entropic force can be conservative. Suppose one attaches a bead to the polymer, and considers motions that are slow compared to the microscopic dynamics that is responsible for the thermalization of the polymer degrees of freedom. In those case the system will stay in thermal equilibrium and no entropy is generated. It is true that heat is transferred from the heat bath to the polymer. But both are in thermal equilibrium at the same temperature. There is no entropy production in that case. Energy and entropy conservation for this case have been discussed in the paper.

For the gravity case the formula d/dx S(M(x),x)=0, which is in section 5 actually would guarantee that there is no entropy production, and that energy is conserved as well.

reader Luboš Motl said...

Dear Erik,

I don't think that what you write is possible.

The heat may only be transferred from the heat bath to the polymer if the polymer is at a lower temperature than the heat bath. In the case of the polymer, it means that it is longer, more stretched. In that case, such a polymer has a lower entropy and, I think, also a smaller temperature.

But if that is the case, then it is equivalent to heat flowing from a hotter object to a colder object. Such a heat transfer is accompanied by the increase of the entropy by delta Q / T where delta Q is the heat and T is the temperature.

That's how Rudolf Clausius started to understand the second law of thermodynamics in 1865.

If entropy differences create work, then this work is irreversible, by the very basic laws of thermodynamics understood in the 19th century.

The only way how the molecule may be in equilibrium is that it is already maximally shrunk and its own entropy is maximized at the beginning. But if that is the case, you won't get any force.

I think that what I say is completely obvious, and your story is logically inconsistent even according to a simple linguistic analysis. If a system is in "equilibrium" it really means that its macroscopic parameters won't be changing. If they're changing - if the force is nonzero - it means that the system couldn't have been at equilibrium. And if it wasn't at equilibrium, the entropy has to increase, so it is an irreversible process.

What you effectively need to assume to reject all the logic above is that all objects have always the same temperature that is, moreover, constant in time. In that case, the entropy may perhaps be preserved because it becomes E/T, proportional to the energy. But that's not possible if you describe generic physical systems. Temperature can't be constant.

Best wishes

reader Unknown said...

Dear Lubos,

Actually Erik's comment about conservative entropic forces makes perfect sense, I will try in a slightly different way to make this clear.

The entropic force is by definition the force needed to pull the polymer so that the polymer just does not move. Of course this force can do work, F dx, and hence change the entropy and the energy of the polymer. We must have F dx = T dS because of the way the entropic force is derived (i.e. biggest force that can do work). Although of minor importance I prefer to imagine a spring instead of a bead, since it introduces a clear energy scale for the polymer and hence a temperature. It doesn't matter very much if one just tunes parameters such that all work done goes either in kinetic energy or spring energy. Either way the energy taken from the heat bath also takes entropy and this entropy equals the extra entropy of the polymer (assuming F dx = T dS) and hence temperatures are equal.

Two remarks: first note that the polymer itself has no energy scale, but attains one due to the definition of F. Secondly the process becomes irreversible iff the entropic force is not entirely used to do work, also think of the opposite process: pulling the polymer out of the bath and so doing work in a reversible manner.

As a different example we can start with the polymer and spring in equilibrium (hence F_spring = T dS/dx) and push the spring a little bit. With some thinking you will soon find out that if the spring is perfect this will oscillate forever. Of course this can be compared with the earth orbiting the sun when viewing gravity as an entropic force.

Kind regards, Wilke van der Schee

reader Luboš Motl said...

Dear Wilke,

thanks for your comment. I think that you are not carefully defining the meaning of the letters like "S", use them in different meanings, and the rest of your derivation is based on circular reasoning.

I think that sometimes, you mean the total entropy by "S", sometimes it is just the polymer. And you say "the claim about a non-increasing entropy must be right because of a derivation of the force that assumes that the entropy doesn't increase".

In reality, "T dS" is the infinitesimal heat "delta Q" that flows from one subsystem to another. If it flows at a finite rate (rather than an infinitesimal one), and Erik surely needs a finite rate because it means a finite force, it must mean that it is flowing from a strictly warmer object to a strictly colder object: the temperature difference must be finite, not infinitesimal.

Such a finite heat answer always increases the total entropy. In other words, finite-speed reversible processes simply can't exist.

See first four sentences of any basic text about reversible processes in thermodynamics (click). They can only be reversible if the parameters of the system are being changed infinitely slowly. In other words:

Reversible processes are always quasistatic, but the converse is not always true.

This Wikipedia quote is from the Sears-Salinger textbook of thermodynamics.

In any real-world scenario, fully reversible processes are simply impossible. It's just an idealization that can be used for extremely slow processes (i.e. for processes with no inertia or momentum), and only for some of them.

Any finite-rate flow of entropy is inevitably irreversible and the total entropy increases.

Best wishes

reader Agno said...

Just another thought about how to obtain an entropic force that is conservative.

Consider a closed system that is in a thermodynamical equilibrium. As soon as this closed system gets accelerated, the particles in the system will be pushed out of their preferred equilibrium state due to inertia (yes I know, that is the force we aim to derive). However, to build up the point from micro to macro: we might also see this force as a (subset) of accelerated microstates that are constantly ‘playing catch up’ towards reaching the thermodynamic equilibrium again. Or stated differently, there is never sufficient time to fully decribe a (subset) of microstate(s) in bits on a holographic screen once they get accelerated. That is the tension that causes the force. It's almost like the uncertainty principle + the first law of thermodynamics that together induce gravity.

Assuming gravity is an entropic force (yes, circular reasoning again), we could try to see what happens when we inject F=ma into the TdS = Fdx equation and also assume equipartition of energy:

E=(kT)/2 (Equipartition)

dS= a (k/(2c^2)) dx

With dx being a subset of microstates (and reflecting emerging space) and dS just being the tension in bits (or a bit of a tension...) between the aspired full description of the thermodynamic equilibrium state and acceleration (a) constantly causing troubles to reach it. If the variable x is equivalent to 'space' and if Verlinde's claim is true, then this macrovariable should predict the curvature of space-time in line the GR-equations.

reader Luboš Motl said...

Dear Agno,

thanks and apologies: of course one can recognize the equations you write - but everything you say about them is incomprehensible or incorrect to me.

One can invent a circular reasoning of this sort, but it is also possible to "cut" the circle and show that any point on the circle, and therefore any other circle, is an invalid proposition.

If some subsystems are equilibrium, the rate of entropy transfer in between them is inevitably zero (or infinitesimal), so all the derived entropy-induced accelerations have to be zero, too. After all, "equilibrium" does mean that the forces are balanced so that the system doesn't move or change.

To make these things move (for thermodynamic reasons), they must clearly be out of (thermodynamic) equilibrium, and if they are, the entropy will increase and irreversibility follows.


reader Agno said...

Dobre den, Lumo,

Thanks for a swift response. Your logic seems sound to me and it's very hard to reason against that.

However, the thought of gravity as an entropic force as presented by Erik Verlinde, is still appealing and therefore allow me one last creative tweak.

The laws of thermodynamics are all derived under the caveat of a system that is not accelerated as a whole. However, we do empirically know, that an accelerated mass (let's see that as a closed thermodynamical system), does possess inertia.

What if we use the Unruh effect as an additional temperature (Tu), that should be added to a system in a thermodynamic equilibrium (Te) once it gets accelerated? The logic is that the Unruh effect predicts that also a vacuum that is only filled with virtual particles will have a temperature. So, why shouldn't we add that temperature also to a system comprising of for instance molecules?

In that case the formulae would become:

Te dS=F dx (Te = T of equilibrium state)
Tu = a h/(kc2Pi) (Unruh effect)

Accelerated system:

(Te + a h/(kc2Pi) dS = F dx

Since there is no heat dQ transferred from outside the system (Tu originates from the quantum level), but still the temperature has increased, the entropy must have decreased. And this is what creates the fully reversible entropic force and directly relates F to a.

I realise I have to prepare myself for some Lumo candidness now... :-)



reader Luboš Motl said...

Dear Agno,

these are courageous attempts of yours ;-) but temperatures can't be "added" in this way. Temperature is not an extensive quantity: it's an intensive property. In fact, it is the first example of an intensive property.

Your addition reminds me of Feynman's story, Judging Books By Their Covers. Search for "red stars" to get to the part where the textbook was adding temperatures of different stars. Feynman exploded in anger - and for a good reason. It makes no physical sense to add them.

A temperature describes an equilibrium, and its inverse is proportional to the periodicity of the imaginary time. The inverse periodicities can never be added. The only way how you can get close to adding them is when the temperature is linear in energy, and you actually add energy. Energy is extensive.

But for that to happen physically, you need energy flows, and when this energy comes as heat, you need heat transfer. And heat transfer only occurs at a finite rate if it goes from a strictly warmer to a strictly cooler body.

More generally, I don't know how this strange addition could help you even if it were possible. You still haven't proven that there is an acceleration, so the "Unruh term in temperature" of yours is zero to start with.

Best wishes

reader Agno said...

Dear Lumo,

Not giving up yet and please allow me one more creative tweak.

Suppose that as Erik states) most objects in the universe are not in an thermodynamic equibrium state. In this universe we have two masses m1 and m2 that approach eachother. Both masses are thriving for an equilibrium state and to accomplish that they both need some finite heat (dQ) from their environment (a heat bath). But then they will start to fight for the same heat. Both masses try to collect heat the heat from the space between them. This competition is what we perceive as gravity. The total effect of each mass accomplishing their (temporary) equilibrium state is still a net increase in entropy (and therefore irreversable). But that should no longer be a problem since due to the constant interaction of m1 and m2 with their environment, they will be pushed out of their equilibrium again and become once more "entropy hungry".

So, gravity as the "battle force for entropy" between two systems at a certain proximity, that are both out of their thermodynamical equilibrium?

reader Agno said...

Or to put it into a more graphical format. Isn't this what Verlinde alludes to when he speaks of "differences in entropy between masses compared to the environment around them"? In such a model you don't really need to worry about the higher degree of entropy per individual system and the associated concern around irreversibility.

reader Luboš Motl said...

Dear Agno, I think that you also misunderstood the notion of a "heat bath". A heat bath is a system whose heat capacity is so large that it can give you whatever heat you need to eventually achieve the thermal equilibrium.

So you never need to "compete with someone else" for the heat from the heat bath because there's infinitely much of it for anyone on the market. By definition, there's no "problem of the commons" inside the heat baths. Clear?

Moreover, your competition could never give you an interaction between pairs of objects. It would still be just a force acting on individual objects only, independent of th properties of other objects.

reader Agno said...

Dear Lumo,

Your heat bath explanation is clear, however my thought was that even in a situation of an unlimited heat supply, there could be local heat differences created in space, that are induced by the way an object that is not in a thermodynamical equilibrium 'sucks' heat in to thrive for it's highest entropy state.

I know this is wild thinking but the path this object internally choses to migrate from a lower entropy towards its highest entropy state, is a path of least resistance aimed to minimise the incremental entropy produced (Prigogine). This preferred path between states could be tranformed into a curve that shows how external heat is being 'sucked' in and could explain how the heatbath locally gets curved in space-time.

Or is this utter non-sense? It actually might be since if we extrapolate this logic to black holes (maximum curved heat bath), it would imply that black holes are objects that are furthest away possible from a thermodynamical equilibrium (i.e. have highest possible entropic force potential).

reader Unknown said...

Dear Lubos,

All quasi-static processes, where the intermediate states are in thermal equilibrium, are reversible.

The force a polymer exerts is precisely the one you get by calculating it in the quasi-static way. Your argument that one needs a finite rate to get a finite force is utter BS. One can measure the force without the polymer contracting one bit.

Erik's idea is probably that the relaxation times of the microscopic degrees of freedom are much smaller then the typical time-scales associated with our observations of gravity, that one can consider it to be in quasi-equilibrium at any point in time. With the non-conservation due to the finite rate orders of magnitude smaller then what we can measure.


reader Luboš Motl said...

Dear Gerben, you seem to misunderstand what a quasi-static process means.

It is a process that happens infinitely slowly. This adjective is a necessary, but not a sufficient, condition for a process to be reversible.

The statement that it happens infinitely slowly prevents one from having any inertia.

Your comment that the relaxation times should be much shorter than the observation times for gravity would be a complete physical catastrophe for the model because that would mean that the entropy increases by something comparable to the black hole entropy of the same size within a much shorter time than the time normally taken by the gravitational phenomena. Such a fast relaxation would make the things more irreversible, not less so.

The main problem to start with is that there must be a finite temperature difference, otherwise thermodynamic forces can't push the system to change, except infinitesimally quickly. If it is so, entropy will inevitably grow as the heat flows from the warmer object (e.g. heat bath) to the cooler one (e.g. the polymer). If this happens very quickly, it means that the entropy increases very quickly, so it's immediately irreversible.

At any rate, they're irreversible. Only fine-tuning can prepare reversible processes, but only in the case when all changes to the system are done infinitely slowly.


reader Unknown said...

Dear Lubos,

The reversible nature is still unclear. Of course you are right that the process should be infinitely slowly, that is exactly what Erik means with 'motions that are slow compared to the microscopic dynamics'. If this difference is many orders of magnitude the force will be conservative to a very high precision. Of course there is/can be a very small irreversible difference, which in normal gravitation is caused by gravitational waves (see Erik's blogs). In the limit c->inf these should become infinitely small. This is one of the most beautiful features of the theory! It naturally explains gravitational waves when c is finite.

There may be another clear example of when a process is sufficiently slow: an expanding gas moving a piston. If the gas atoms move much faster than the piston (typically the case) the pressure on the piston will at any time be equal to its equilibrium value (~1/V). It is only in this case that the force is conservative. Imagine putting a perfect spring opposed to the piston, to reverse its motion: if one assumes P ~ 1/V and calculate the end state, the piston will have returned to its original position! If the gas atoms however would move at speeds comparable to the speed of the piston, the pressure during the expansion will be much lower (and higher during compression). In this case the motion is not reversible. This clearly illustrates what quasi-static and infinitely slowly means: if the speed of the motion << speed of relaxation to equilibrium then the process is reversible and hence the entropic force is conservative.

reader Luboš Motl said...

Dear Wilke,
thanks for your comments.

I agree that if the irreversibility could go away in the "c=infinity" limit, one could avoid the "obvious" discrepancy concerning irreversibility.

Still, I think you won't avoid the non-immediate contradictions. The gravitational waves, as we know them, really don't carry any macroscopic entropy because they're coherent. The microstate corresponding to the emitted wave is pretty much unique and calculable (it's the exponential of a combination of creation operators for the graviton with the right direction and frequency etc.).

When they're emitted in the real world, the total entropy doesn't increase much, surely not by amounts comparable to the black hole entropy of black holes with the same masses. The entropy only increases when internal processes occur in the star - they're irrelevant for its center-of-mass gravity with others - or when a black hole horizon is being formed (then the entropy grows hugely).

I feel that Erik doesn't care that the entropy changes are not what they should be, and the temperatures of different objects are not the real temperatures. So he uses real temperatures and fake temperatures (needed for his picture), and the same thing for the entropy.

And I am convinced that all such "dual" definitions of the thermodynamic quantities are simply contradictions. We know what the temperature of difference objects are, and what the temperature increases are, and so on. If one gets or needs a completely different number and a different entropy, it's simply a contradiction, and the new theory is ruled out.

Note that the energy carried by waves goes like a^2 (squared acceleration) which could be OK. I am helping you to write some "convincing" scaling laws that are completely absent in Erik's discussion so far.

It could be an OK scaling because the forces are proportional to "a", and the rate of entropy increase from a temperature difference proportional to "a" would be proportional to another "a", giving a total of "a^2" scaling.

However, it's a right minimal result for a wrong quantity: this is the energy carried by the gravitational waves. The entropy in the gravitational waves is not proportional to a^2 - it is not macroscopic at all.

This is related to all other paradoxes one gets from a different number of microstates, as a function of the distances, for example the loss of coherence of the neutrons' interference patterns in gravitational fields that have been experimentally verified.

They confirm the exact equivalence principle at the quantum level, and falsify all "chaotic" explanations of the gravitational force. If there were some entropy increase connected with the motion of neutrons in the gravitational field - even a tiny increase of entropy (by a few bits) - that would also mean that one is "measuring" the neutron by imprinting the information about its state to the additional "heat bath" of entropy, and such an imprinting or entropy increase would simply spoil the interference pattern which is not occurring (it's called decoherence, after all, and it's universally linked to the entropy-increasing irreversible processes).

So I am convinced that the very qualitative picture is dead.

Best wishes

reader Will Nelson said...

Was there some discussion of the neutron decoherence that I missed? Because that seems like a real fatal flaw to me.

In the case of the stretched polymer, and I guess all other "entropic" forces, the real source of the force is collisions or interactions with other system components. The stretched polymer wants to fold up because particles are bouncing off of it, putting bends in the straight segments.

But each particle bounce is going to decohere the wavefunction. I would think it might be possible to calculate the magnitude of this decoherence and compare it to the experiments cited by Lubos.

I don't claim to have any insights to offer here, but would be interested to see the comment thread touch on this.

reader Ralph Frost said...


I agree that there are many advantages in setting structure (order, entropy) as fundamental, particularly when one faces the uncanny mapping between specific protein-foldings that form abstract math sumbols and expressions, and other physical features. It's a reasonable first approximation of a working common denominator.

Ralph Frost

reader Brian Oxley said...

Will you post a followup based on th new work from Jae-Weon Lee, et al?


reader Luboš Motl said...

Dear Binkley, nope, I don't think that the paper deserves a separate article - and not even one big comment - on TRF.

It's crackpottery, and unlike Erik's paper, it's not even original in any way and it's not written by people who have actually done something valuable in their careers. Cheers, LM

reader Ralph Frost said...

Conceptually, readers and thinkers MAY find it helpful to immediately formulate the new fundamental as structured~duality rather than information.

The variety of trial theories and models discussed reveal different sorts of structural codings. Folks can start out speaking about "information", but a short ways down the path that term cracks under the strain. Our reality: the physical features, the models and our own conscious and unconscious features all turn out to be nested structured duality, rather than "nested information".

Think about it.

Ralph Frost

reader Unknown said...

As per Mr. Verlinde, gravity does not exist because gravitation is a result of more basic thing... thermo dynamics. Correct me if I am wrong...

What would he say next, we all don't exist. Because we are result of our parent's marriage

So why are we listening to a guy who doesn't exist????

Dear Mr. Verlinde, it takes a lot easier to coin a word jugglery in science than discovering a scientific fact.... Newton gave us a scientific fact

reader Unknown said...

As per Mr. Verlinde, gravity does not exist because gravitation is a result of more basic thing... thermo dynamics. Correct me if I am wrong...

What would he say next, we all don't exist, because we is result of more basic thing... Our parents' marriage!!!

Dear Mr. Verlinde, it is a lot easier to coin a word jugglery in science than discovering a scientific fact.... Newton gave us a scientific fact.

reader Señor Karra said...

Hi Lubos,

I Would like to hear your comments on the seminal paper from Jacobson on this idea ( ). I fail to see what is Verlinde analysis adding up over this. Specially i would like to hear if you think the double-slit interference pattern in a gravitational well also disproves this result

reader Luboš Motl said...

Dear Senor Karra, first of all, Erik's statement about gravity being the enthropic force is wrong, see e.g. this text for a detailed proof.

I discussed Jacobson's 1995 derivation here. I agree that Erik just took some statements that were present de facto in Jacobson's heuristic derivation and made a separate paper out of them. Unfortunately (for science), he only took the wrong remarks of Jacobson's paper that didn't follow from the main calculation in that 1995 paper.

But in the EU, politicians pay lots of money for garbage, so Erik Verlinde got 3 million dollars for his complete bullshit for which he lost credibility among scientists who remain up to their job.


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