Origin and Cause of Gravity and Entropy

[Perpetual Student]

I just read an article about this in the Sept 25 edition of Science News:
On the Origin of Gravity and the Laws of Newton: Erik Verlinde
LINK

LINK

LINK

Are any of the physicists here familiar with Verlinde's ideas? Any thoughts?

 

[AlBell]

bump.

Hopefully Sol, or another guru, will respond.

 

[Perpetual Student]

More:
He says,

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.

LINK

and:

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.

Is he possibly on to something? I have no clue!

 

[The Man]

Well, certainly not trying to pawn myself of as a physicist or a guru, but I have printed the paper and it may take my some time to get through it. I must say that initially I find the idea rather baffling and the assertion in the abstract…

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

…sounds a bit like putting the cart before the horse (and I didn’t know there was an “entropic force”). As gravity and the curvature of space time is the cause of those positions and changes in that positional information. Though I’m certainly speaking out of turn as I haven’t read the paper yet, basically I’m just posting so I will be subscribed to the thread for when I do read the paper or one of those gurus chimes in

 

[MattusMaximus]

I read that Verlinde paper this summer. It seems interesting, but I saw nothing which made it any different from a number of other "interesting" ideas being bantered around the theoretical physics journals. Once Verlinde and his colleagues start to propose some tests which could distinguish these ideas from others and put them on more solid footing, then perhaps I'll give them more validity. Until then, it makes for good reading on a boring night

 

[The Man]

One of the problems that first occurred to me MattusMaximus, as the information is directly related to energy and mass, including the distribution (over the degrees of freedom in some spatial volume) it may be difficult to come up with a test that can distinguish the one concept from the other (the cart or the horse in front). Though certainly, again only preliminarily, I can see some possible advantages to taking such an informational approach in trying to quantify gravity, basically due to the quantification inherent in data bits. The other question that comes to my mind, again only initially as I’ve only been able to scan the paper, is if or can such an “entropic force” and informational approach be applied to quantum field theories like QED and QCD?

 

[The Man]

Well, having looked over the paper in some detail now, I’m still left with my original surmise about putting the cart before the horse. Now certainly one can get a different perspective on the horse (a driving force) and the cart (that which contains the information of energy, position and momentum driven by the horse) by having them the other way around. Particularly a more preferable view of the horse from the cart. Unfortunately, the conclusions tend more towards the disavowing of gravity as fundamental force rather than the unification with the other fundamental forces I’d hoped to find indicated. Perhaps that is the case, and much as MattusMaximus noted before I don’t see "anything different from a number of other "interesting" ideas being bantered around". In fact it is based on some assumptions of such (particularly in the holographic description). Also in the vector (a force being a vector, having magnitude and direction) vs. scalar (temperature being a scalar, just having magnitude) consideration (addressed more specifically in section 3.4). Unfortunately, as I had hoped at the beginning of the paper, I didn’t see any subsequent reference to the arrow of time (a direction in time specifically related to entropy) or even a tensor formulization of gravity based on these assumptions (unless I missed something). However, that didn’t seem to be the authors intent, apparently instead being the possible discounting of gravity as a fundamental force. I’m still left with the problem of if this proposition is actually testable in a way that will unequivocally distinguish it from our current concept of gravity.

The author gives a possibility, with his own caveat (in section 6.4).

Does this view of gravity lead to predictions? The statistical average should give the usual laws, hence one has to study the fluctuations in the gravitational force. Their size depends on the effective temperature, which may not be universal and depends on the effective value of ~. An interesting thought is that fluctuations may turn out to be more pronounced for weak gravitational fields between small bodies of matter. But clearly, we need a better understanding of the theory to turn this in to a prediction

Sorry “~“ was supposed to be the reduced Plank constant (h bar) but it didn’t come out in the copy and pasted quote.

One of my first problems with this paper is the “entropic force” described in the first sections and exemplified by essentially spring actions. Where an applied force results in a lower entropic state and the removal of that constricting force results in a return to the more entropic state. The inference being that gravity is an emergent property resulting from this tendency to return to a more entropic state (hence the “entropic force”) . The question then comes as to the origin of this initial force resulting in the currently less entropic state, as it can not itself be such an “entropic force”.

 

[my_wan]

I like it, but it does fall short in many ways. Note that the source of entropy is undefined. Verlinde even gave a general opinion that it wasn't inconsistant with string theory for this reason. Here is another paper with a thermodynamic interpretation.

The Einstein equations for generalized theories of gravity and the thermodynamic relation δQ = T δS are equivalent

We show that the equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation δQ = T δS. Our proof relies on extending previous arguments by using a more general definition of the Noether charge entropy. We have thus completed the implementation of Jacobson's proposal to express Einstein's equations as a thermodynamic equation of state. Additionally, we find that the Noether charge entropy obeys the second law of thermodynamics if the matter energy momentum tensor obeys the null energy condition. Our results support the idea that gravitation on a macroscopic scale is a manifestation of the thermodynamics of the vacuum.

 

[MattusMaximus]

One of the problems that first occurred to me MattusMaximus, as the information is directly related to energy and mass, including the distribution (over the degrees of freedom in some spatial volume) it may be difficult to come up with a test that can distinguish the one concept from the other (the cart or the horse in front). Though certainly, again only preliminarily, I can see some possible advantages to taking such an informational approach in trying to quantify gravity, basically due to the quantification inherent in data bits. The other question that comes to my mind, again only initially as I’ve only been able to scan the paper, is if or can such an “entropic force” and informational approach be applied to quantum field theories like QED and QCD?

This is an excellent point. One would expect that if the "entropic force" concept is more fundamental than, say, gravity that it could also be applied more generally to the other fundamental forces as well.

 

[my_wan]

This is an excellent point. One would expect that if the "entropic force" concept is more fundamental than, say, gravity that it could also be applied more generally to the other fundamental forces as well.

QM, in a very general way, is well described by thermodynamics, with some differences. Again, very generally, classical thermodynamics can be viewed as an ensemble of a quantity of parts, while QM can be viewed as an ensemble of a quantity of properties. In QM it is the properties that are quantized.

 

[MattusMaximus]

QM, in a very general way, is well described by thermodynamics, with some differences. Again, very generally, classical thermodynamics can be viewed as an ensemble of a quantity of parts, while QM can be viewed as an ensemble of a quantity of properties. In QM it is the properties that are quantized.

I would have to disagree. You do realize that many quantum systems can actually violate classical thermodynamics, don't you? For example, if you really do understand the Second Law in terms of statistical mechanics, then you can easily see how a quantum system of less than a hundred atoms can seemingly violate the Second "Law".

 

[my_wan]

I would have to disagree. You do realize that many quantum systems can actually violate classical thermodynamics, don't you?

Though the second law was a particularly bad example as I'll explain, of course QM violates the principles of classical thermodynamics. The foundational distinction between parts verses properties is a violation of the principles of classical thermodynamics.

For example, if you really do understand the Second Law in terms of statistical mechanics, then you can easily see how a quantum system of less than a hundred atoms can seemingly violate the Second "Law".

And can you understand that over small enough regions the temperature of a classical gas in thermodynamic equilibrium will fluctuate, in opposition to Second Law in the short term?

In fact, classically the Second Law is not fundamental. It is a derived law, derived from mechanics and the statistics of mechanistic ensembles.

Consider pool table with randomly distributed balls. On average you can expect the balls to be equally distributed on the two sides of the table. With a small number of balls there's a reasonable chance that they all end up on one side of the table or the other. With a sufficient number of balls you can forget it, it's not going to happen in a trillion years. It is this unlikelihood that dictates the Second Law. Thus the Second Law is a law of expectations, a derived law and not an law against an event. It can't be viewed as strictly valid without the limits imposed by the 1st and 3rd law. The entropy can never go to infinity, or enthalpy to zero.

When you limit the defined system to a small enough set of space, then you get these fluctuations not inherent in a larger average. This is in some sense how virtual particles were predicted, via the Uncertainty Principle. Ever heard of the Vacuum Catastrophe? It was the result of expecting these fluctuations to add up to a large positive, contrary to a classical thermodynamic perspective where equilibrium dictates that small scale fluctuations average out to zero on a larger scale.

Ever heard of Exact Uncertainty?
Schrodinger equation from an exact uncertainty principle
J. Phys. A 35 (2002) 3289-3303

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrodinger equation. Thus there is an exact formulation of the uncertainty principle which precisely captures the essence of what is "quantum" about quantum mechanics.

This was accomplished by treating the Uncertain Principle as something more akin to Brownian motion than a fundamental law or principle. It was historically Brownian motion that demonstrated the equivalence of statistical mechanics and classical thermodynamics, and empirically established the atom was more than a mathematical fiction.

I can't make authoritative claim of what QM is, but its connections to thermodynamics is vast and extensive.

 

[MattusMaximus]

And can you understand that over small enough regions the temperature of a classical gas in thermodynamic equilibrium will fluctuate, in opposition to Second Law in the short term?

In fact, classically the Second Law is not fundamental. It is a derived law, derived from mechanics and the statistics of mechanistic ensembles. ...

Yup, I know all of that and have already explained it to many here on numerous occasions. In fact, I beat you to it in this lengthy & detailed post from January 2009.

That post got me nominated

 

[my_wan]

Yup, I know all of that and have already explained it to many here on numerous occasions. In fact, I beat you to it in this lengthy & detailed post from January 2009.

That post got me nominated

That was indeed an excellent post.

I actually spend a lot of time thinking about these foundational issues and their relations to QM and spacetime. Classical physics definitely has foundational errors with its absolutes. Some residuals of which could still be lurking. EPR type issues appears to point to residual errors in the way we associate distinct parts with properties at a fundamental level. Are our fundamental constants and properties even fundamental, and what role might background independence and transfinites or RQM type concepts play in it.

The issues are too complex to make presumptuous claims here, but Verlinde's paper leans in a direction I like to think about. Even if for no other reason than to rule out certain types of modeling solutions.

 

[Perpetual Student]

Thanks for all the interesting comments.

 

[sol invictus]

I think we can be nearly certain that gravity is not an "entropic force" in the naive sense. That is, it is almost certainly not the case that gravity on large distance scales arises as a collective excitation of some microscopic granular degrees of freedom that interact without gravity, analogous to how water waves do in fact arise from H2O molecules that interact via forces that have nothing to do with hydrodynamics.

The reason boils down to Lorentz invariance. One can prove mathematically that gravity cannot be a composite field (the way a water wave is composed of molecules). Of course this proof requires some assumptions, the most important being Lorentz invariance. But Lorentz invariance is among the most precisely tested facts about the world we have, and so to break it in a way that is consistent with experiment is extremely difficult - and hence probably a bad idea unless the motivation is very good indeed.

Having said that, there is very good evidence that gravity does have a so-called "dual" description in terms of a non-gravitational theory. But this duality works in a way that is very different from the naive idea that gravity is composite. Instead, the dual theory is defined on a completely different spacetime, one that doesn't even have the same number of spatial dimensions, and the relationship between entropic forces in that theory and Newton's law of gravity is not particularly simple.

 

[sol invictus]

QM, in a very general way, is well described by thermodynamics, with some differences. Again, very generally, classical thermodynamics can be viewed as an ensemble of a quantity of parts, while QM can be viewed as an ensemble of a quantity of properties. In QM it is the properties that are quantized.

I know quite a bit about both QM and thermodynamics, and I have no idea what you're talking about. What's "an ensemble of a quantity of properties"? Can you elaborate?

 

[my_wan]

I know quite a bit about both QM and thermodynamics, and I have no idea what you're talking about. What's "an ensemble of a quantity of properties"? Can you elaborate?

Very loosely stated as I warned in each sentence, for the purpose of avoiding claims of what it is, as any such specificity would almost certainly be wrong. I could link a number of articles that attempt to model QM with various similar models. Gerard ′t Hooft being an active contributor. Yet none of these "statistically complete variables", or various types of beables are really not very convincing at this time. So don't expect me to debate the validity of any of these models, especially particular models. Even if I had particular models I was somewhat impressed with I wouldn't debate it here as if it had some authoritative value.

If your willing to entertain the a priori notion, without justification, that QM and Relativity are emergent from a common component system I'll go there, but people must realize there is no authority, claims of legitimacy, or any similar model that is as yet convincing.

Consider a standard Hilbert space where states are given by non-zero vectors. These vectors define the magnitudes of properties. Yet any given vector can be described by any number, even an arbitrarily large number, of other vectors. If you presume there's some kind of component framework to this, the inability to decompose them into a unique set of vectorial contributions is a fatal analytical roadblock to what these supposed components represent in anything approaching a classical sense. The stipulation, per Hilbert, of enough limits in the space to justify calculus doesn't even restrict such presumed components to a finite set.

Trying to draw a one to one correspondence between classical and quantum observables is a fools game. Yet the vectors can be represented as ensembles similar to classical ensembles, except without the background dependence of Euclidean vectors. Nor can they represent the same kind of absolute components plus properties in a preexisting vacuum that classical physics is predicated on. Classical physics is flawed at a foundational level, and presuming that any model postulating components structures must also contain these flaws circular logic. This thermodynamic connection is what allowed the Schrodinger's wave mechanics formulation of QM.

I think we can be nearly certain that gravity is not an "entropic force" in the naive sense. That is, it is almost certainly not the case that gravity on large distance scales arises as a collective excitation of some microscopic granular degrees of freedom that interact without gravity, analogous to how water waves do in fact arise from H2O molecules that interact via forces that have nothing to do with hydrodynamics.

[...]

Most certainly not in any nieve sense. The Lorentz invariance, I cut from the quote, is not a particularly good basis for rejecting such models for gravity. Here's why. First off you presuming that Lorentz invariance is a fundamental property, rather than derived. If we and our instruments are a product of events in this supposed component system, then it's reasonable that certain parameters of this system remains locally invariant. Globally this wouldn't hold, but if an observer is translated to another region in which a different base metric defines them, the new metric becomes the new meterstick. Thus the constants remain locally valid. This is qualitatively exactly the case as you change depth in a gravitational field. Thus it's not the legitimacy of the Lorentz transformation in question, it's the assumption of how fundamental it is.

Mathematically there is a classical incongruence due to a misfit between classical kinetic energy and the mass/energy relation. The Born rule is no small matter either. Yet, with a vacuum state presumed to be derived, classical presumptions about space are even more suspect, though the inner product structure of Hilbert space allows for some fundamental linearity.

The long distance gravitational force objection is not fatal either. We know that gravitational forces are also limited by the speed of light. Thus any local change of mass configuration will not have any gravitational effect, or even be observable, on a distant mass until the speed of light limit allows those effects to propagate to that distant mass. I've also provided grounds for presuming certain metrics of a granular field could remain locally constant, like the speed of light.
Note on Varying Speed of Light Cosmologies
Gen.Rel.Grav.39:511-520,2007
If, as we are presuming, a granular structure exist, then there is no reason to presume the speed of light is anything more than a mean of these presumed components. Akin to the way sound is classically. Thus rather than Lorentz invariance invalidating such granularities, such granularities could actually go to defining this limiting speed Lorentz transformations are derived from.

I can lay this out somewhat more concisely, but the point is more general, and aimed at a larger audience. The point is that imposing empirically valid constraints from the top down, a priori defined as fundamental, leads to incongruencies that aren't meaningful when built from the bottom up. Insisting that they are fundamental, thus imposed on the system like raisins, is not a valid strategy for invalidating bottom up theories. Though it's quiet true that to date such modeling attempts leave a lot of room for criticism, claiming invalidation from a raisin pudding application of fundamental symmetries doesn't in itself work.

 

[JoeTheJuggler]

bit of a derail. . .

On the Origin of Gravity and the Laws of Newton

Didn't the Laws of Newton originate with Newton? (Or maybe Hooke and the other giants upon whose shoulders he stood?

 

[sol invictus]

Consider a standard Hilbert space where states are given by non-zero vectors. These vectors define the magnitudes of properties. Yet any given vector can be described by any number, even an arbitrarily large number, of other vectors. If you presume there's some kind of component framework to this, the inability to decompose them into a unique set of vectorial contributions is a fatal analytical roadblock to what these supposed components represent in anything approaching a classical sense.

You've lost me entirely. Vectors appear all over the place in classical physics, for example describing the electric field, and the inability to find a unique basis isn't a roadblock to anything.

Trying to draw a one to one correspondence between classical and quantum observables is a fools game. Yet the vectors can be represented as ensembles similar to classical ensembles, except without the background dependence of Euclidean vectors. Nor can they represent the same kind of absolute components plus properties in a preexisting vacuum that classical physics is predicated on. Classical physics is flawed at a foundational level, and presuming that any model postulating components structures must also contain these flaws circular logic. This thermodynamic connection is what allowed the Schrodinger's wave mechanics formulation of QM.

I have no idea what that paragraph means, if anything.

Most certainly not in any nieve sense. The Lorentz invariance, I cut from the quote, is not a particularly good basis for rejecting such models for gravity. Here's why. First off you presuming that Lorentz invariance is a fundamental property, rather than derived. If we and our instruments are a product of events in this supposed component system, then it's reasonable that certain parameters of this system remains locally invariant. Globally this wouldn't hold, but if an observer is translated to another region in which a different base metric defines them, the new metric becomes the new meterstick. Thus the constants remain locally valid. This is qualitatively exactly the case as you change depth in a gravitational field. Thus it's not the legitimacy of the Lorentz transformation in question, it's the assumption of how fundamental it is.

It's microscopic Lorentz invariance that is needed for the proof and relevant to whether or not gravity can be an entropic force, so your objection is invalid. In other words whether or not the world is Lorentz invariant at long distances (which it obviously is not - just look around you) has nothing to do with this. What's at issue is whether the laws of physics that describe fundamental interactions between elementary particles are Lorentz invariant. We know experimentally that they are extraordinarily close to being so, and those experimental results provide an extremely strong constraint on any theory where gravity is emergent.

I can lay this out somewhat more concisely, but the point is more general, and aimed at a larger audience. The point is that imposing empirically valid constraints from the top down, a priori defined as fundamental, leads to incongruencies that aren't meaningful when built from the bottom up. Insisting that they are fundamental, thus imposed on the system like raisins, is not a valid strategy for invalidating bottom up theories. Though it's quiet true that to date such modeling attempts leave a lot of room for criticism, claiming invalidation from a raisin pudding application of fundamental symmetries doesn't in itself work.

Like raisins? What?

Anyway I didn't "impose" anything, nor did I assume anything about Lorentz invariance being fundamental. I simply pointed out that experimental data shows that the laws of physics are extremely close to being Lorentz invariant, and that (plus the Weinberg-Witten theorem) makes it very difficult to construct theories in which gravity is emergent.