Is Verlinde's Gravity Theory Based on Relativistic Assumptions?

[czes]

This criticism is absolutely invalid. MTd2 was trying to come up with something similar in the previous discussion, see the thread Gravity is not entropic force?. I repeat again: The derivation of the entropic force by Verlinde does not depend on a particular value of dx -- the force itself is proportional to the gradient of the entropy dS/dx. Similarly, derivation in 1009.5414 does not depend on any assumption on dx in the equation for the entropy change. The only relevant point in 1009.5414 is the entropy change which is associated with the change in the position of neutron, NOt with some microscopic coarse graining length. Neither verlinde's paper nor 1009.5414 depend on the microscopic details of the theory. It is surprising you are not able to understand this simple, basic point.

I rewrote some sentences from http://arxiv.org/PS_cache/arxiv/pdf/1010/1010.4729v2.pdf
Chapter IV. CONCLUSIONS AND OUTLOOK.

Do you think, the discretness of the space and holographic principle are invalid together ?
You may imagine an holographic printer. There are the plastic objects created. The real description is on a CD in computer and the printer creates a spatial image of the program which is dimensionless but each relation between information (discrete interference) creates a microstate and printer translates it into a plastic dot of which the object is built.
Isn't our space the same ?

 

[CHIKO-2010]

I rewrote some sentences from http://arxiv.org/PS_cache/arxiv/pdf/1010/1010.4729v2.pdf
Chapter IV. CONCLUSIONS AND OUTLOOK.

I do not understand, did you just copy those statements for my information, or you also agree with the criticism. If you do agree than see my previous post again.

Do you think, the discretness of the space and holographic principle are invalid together ?

No I don't think so. But what this has to do with my post to which you replied to. Do you think that space is discrete in QM? It is not.

You may imagine an holographic printer.

No, I can't imagine this :-)

 

[Fra]

(All quotes from Verlindes original paper)

"In this paper we will argue that the central notion needed to derive gravity is information. More precisely, it is the amount of information associated with matter and its location..."

Taken as a spirit of intent I fully agree with this.

The issues are in the details, not in the general idea. And the details are admittedly under development, that's why I think statements that "it's wrong" although possibly "true", aren't very constructive. This was my main message I wanted to contribute to this thread.
"...in whatever form the microscopic theory likes to have it, measured in terms of entropy."


The details which does matter (to me at least) and where Verlinde does not at this stage produce a satisfactory analysis is the nature and selection of measures of

- "entropy"
- "distance", referring to "location"

IMHO, both of these problems are related, as the entropy is defined relative to some microstructure on which there is also some distance measure. As I understand it they need to infact the constructed together, which is yet another deeper expression of the relation between entropy measures and measures on space.

This is why one can't first, define entropy in the context-free way, and then put it into the context. Verlinde somehow tries to aruge how space emerges using already existing space as a seed. I think there may be different ways to envision this, and there are problems related to this.

To clarify one thing: I do not think there exists fully objective observer invariant degrees of freedom on which this entropic reasoning takes place. That's IMHO the simplistic view of it and I don't think it will work, except approximatel or in certain limits.

I think each oberver "sees a certain complexion system" and it's relative to this the entropy is defined. So the entropy measure is, and must be observer dependent. This also means that gravity becomes a matter of perspective. An inside observer might not "see" gravity, as it's simply is doign a random walk, but from perspective another observer can see the "gravitational" interaction.

Verlinde isn't doing it like that. But his first idea I think is right. I don't see the reason to loose focus just because the details are still open.

"Changes in this entropy when matter is displaced leads to an entropic force, which as we will show takes the form of gravity"
As I think of this, is that "when matter is displaced" in my view, means "when the observers information state is updated". Because distance in my view is a construction in an abstract information space. But to resolve all these things, it gets much more involved than Verlindes construction. I figure that there are so many open questions that there wouldn't be a paper yet.

"Its origin therefore lies in the tendency of the microscopic theory to maximize its entropy."

In the light of the above, I would like to phrase this more directl in the inference terms

it's origin lies in the tendency of interacting disagreeing systems to decrease there level of disagreement. Once then spacetime is separated out of the gigantic "information space" space distance is then understood as distance in information space, and spacetime inertia is simply the information theoretic intertia of resistance against information updates.

But if you take this guide serious, like I do, Verlindes main idea is still right but his construction in that paper is far too simple as I see it, but this does not disquality the main idea at all.

Verlinde relies on

"The most important assumption will be that the information associated with a part of space obeys the holographic principle"

Partly I think this contains some of the ideas I lined out above. But not quite. Also this is a patchy kind of construction, since IMHO the holographic principl is not really understood. In the way I see this could be done, the holographic connection to the extent it makes sense follows from the construction, it's not an ad hoc assumption put in manually.

/Fredrik

 

[CHIKO-2010]

(All quotes from Verlindes original paper)

"In this paper we will argue that the central notion needed to derive gravity is information. More precisely, it is the amount of information associated with matter and its location..."

Taken as a spirit of intent I fully agree with this.

The issues are in the details, not in the general idea. And the details are admittedly under development, that's why I think statements that "it's wrong" although possibly "true", aren't very constructive. This was my main message I wanted to contribute to this thread.
"...in whatever form the microscopic theory likes to have it, measured in terms of entropy."


The details which does matter (to me at least) and where Verlinde does not at this stage produce a satisfactory analysis is the nature and selection of measures of

- "entropy"
- "distance", referring to "location"

IMHO, both of these problems are related, as the entropy is defined relative to some microstructure on which there is also some distance measure. As I understand it they need to infact the constructed together, which is yet another deeper expression of the relation between entropy measures and measures on space.

This is why one can't first, define entropy in the context-free way, and then put it into the context. Verlinde somehow tries to aruge how space emerges using already existing space as a seed. I think there may be different ways to envision this, and there are problems related to this.

To clarify one thing: I do not think there exists fully objective observer invariant degrees of freedom on which this entropic reasoning takes place. That's IMHO the simplistic view of it and I don't think it will work, except approximatel or in certain limits.

I think each oberver "sees a certain complexion system" and it's relative to this the entropy is defined. So the entropy measure is, and must be observer dependent. This also means that gravity becomes a matter of perspective. An inside observer might not "see" gravity, as it's simply is doign a random walk, but from perspective another observer can see the "gravitational" interaction.

Verlinde isn't doing it like that. But his first idea I think is right. I don't see the reason to loose focus just because the details are still open.

"Changes in this entropy when matter is displaced leads to an entropic force, which as we will show takes the form of gravity"
As I think of this, is that "when matter is displaced" in my view, means "when the observers information state is updated". Because distance in my view is a construction in an abstract information space. But to resolve all these things, it gets much more involved than Verlindes construction. I figure that there are so many open questions that there wouldn't be a paper yet.

"Its origin therefore lies in the tendency of the microscopic theory to maximize its entropy."

In the light of the above, I would like to phrase this more directl in the inference terms

it's origin lies in the tendency of interacting disagreeing systems to decrease there level of disagreement. Once then spacetime is separated out of the gigantic "information space" space distance is then understood as distance in information space, and spacetime inertia is simply the information theoretic intertia of resistance against information updates.

But if you take this guide serious, like I do, Verlindes main idea is still right but his construction in that paper is far too simple as I see it, but this does not disquality the main idea at all.

Verlinde relies on

"The most important assumption will be that the information associated with a part of space obeys the holographic principle"

Partly I think this contains some of the ideas I lined out above. But not quite. Also this is a patchy kind of construction, since IMHO the holographic principl is not really understood. In the way I see this could be done, the holographic connection to the extent it makes sense follows from the construction, it's not an ad hoc assumption put in manually.

/Fredrik

Dear Fredrik

"In this paper we will argue that the central notion needed to derive gravity is information. More precisely, it is the amount of information associated with matter and its location..."


"
More precisely, it is the amount of information associated with
matter and its location, in whatever form the microscopic theory likes to have it, mea-
sured in terms of entropy


These two quotes fully reflect Verlinde's idea. That is, according to him, gravity is caused by the change in entropy associated with gravitating bodies due to the change in their locations IRRESPECTIVE of the underlying microscopic theory. Taken as it is, the theory is WRONG!

You are repeatedly saying that the standard entropy is not the one which must be used and location/distance must be also understood differently. Yes, you well spotted the key problems of the Verlinde proposal, but have not provided yet even a slight clue how you are going to cure those problems. If such a cure exists, the resulting theory will be dramatically different from the one suggested by Verlinde. So do not hesitate to call it wrong

 

[Fra]

If such a cure exists, the resulting theory will be dramatically different from the one suggested by Verlinde. So do not hesitate to call it wrong

Well I might agree with this, but, given that this is a very underdeveloped research direction, I don't see the benefit it shooting at the few pioneers.

If we can allows ourselfs to distinguish between the spirit of intent, and the specific suggestions, then I can agree that the specific attempt is likely wrong.

My only objection is that some seem to reject everything, even the vision. I do not share that. And since many doesn't care to distinguish between details and the direction, I choose to say I agree with the direction, which does not mean I think all the details in the paper is some final answer :)

/Fredrik

 

[czes]

"In this paper we will argue that the central notion needed to derive gravity is information. More precisely, it is the amount of information associated with matter and its location..."
I also agree.

May be the entropy is not fundamental and emerges from the information backgroud.
As I wrote I am learning about the Holographic Principle and I would like to know exactly if it is right or false. Therefore I need the criticism .
I have copy the sentences from http://arxiv.org/PS_cache/arxiv/pdf/...010.4729v2.pdf just for information. May be it would be right in the information space. If the space emerges from the information relation (interferences) on a sreen, it is naturally a structure which behaves due the program written in a screen.
My idea is that each relation between information (quantum interference) encodes a Planck time dilation. It creates the space-time as we have in General Relativity.
These relations may also create many different structures like particles of matter, phonons, and microstates like in ultracold neutrons experiment.

 

[CHIKO-2010]

Well I might agree with this, but, given that this is a very underdeveloped research direction, I don't see the benefit it shooting at the few pioneers.

If we can allows ourselfs to distinguish between the spirit of intent, and the specific suggestions, then I can agree that the specific attempt is likely wrong.

My only objection is that some seem to reject everything, even the vision. I do not share that. And since many doesn't care to distinguish between details and the direction, I choose to say I agree with the direction, which does not mean I think all the details in the paper is some final answer :)

/Fredrik

Well, looking at Verlinde's theory as a spirit of intent, he is certainly not a pioneer... I would describe the spirit of the paper as follows: "macroscopic statistical" description of the world is more fundamental than "microscopic, quantum mechanical" description. Indeed, if "entropy" (whatever it is ) is a superior fundamental notion, the "microscopic description" (whatever it is) becomes irrelevant. This spirit has always failed in the history of physics, e.g. Bohmian quantum mechanics. All the progress made so far was related with the recognition that the "microscopic" structures are more fundamental. This is the vision that I fully share.

 

[CHIKO-2010]

As I wrote I am learning about the Holographic Principle and I would like to know exactly if it is right or false.

How do you suppose to know EXACTLY whether the Holographic Principle wrong or right? It is a conjecture. The most compelling THEORETICAL evidence for this conjecture is found within the string theory. We do not now whether the latter theory is correct or not...there is no even a slight experimental hint so far... On the other hand, i am not aware of any theoretical counterarguments, thought experiment that negates the holographic Principle...So it is alive only "in theory space"

 

[Fra]

Well, looking at Verlinde's theory as a spirit of intent, he is certainly not a pioneer... I would describe the spirit of the paper as follows: "macroscopic statistical" description of the world is more fundamental than "microscopic, quantum mechanical" description. Indeed, if "entropy" (whatever it is ) is a superior fundamental notion, the "microscopic description" (whatever it is) becomes irrelevant. This spirit has always failed in the history of physics, e.g. Bohmian quantum mechanics. All the progress made so far was related with the recognition that the "microscopic" structures are more fundamental. This is the vision that I fully share.

I guess it depends on what we're talking about. I don't agreee that microscopic details are irrelevant "in general" (as he is speaking of gravity specifically). But I don't think that's what Verlinde claims (at least its now how I read it)?

I think Verlindes point is that GRAVITY doesn't care about the details of the microstructure; except of course the AMOUNT of information, and the DISTANCE measure.

Again, extending the idea to all forces, like I did originally, then the details irrelevant to GRAVITY, ARE relevant, but to other forces. The separation of the full interaction into, gravity/spacetime, other interactions and internal degrees of freedom is a subtle thing. Verlinde says nothing of that, but I think the entropic gravity of his is meant of limited scope. The way I envision that fitting into the larger context is that gravity is what separates out, once the microscopic details are already assigned to other forces concerning internal degrees of freedom. The residual interaction, is then by construction independent of those already classified details. This is also why gravity IS universal. No system, can escape gravity. There is no way to shield from gravity etc.

The way this would in principle allow for other interactions is that there is an hierarchy of interactions, where you interaction by interaction separate out a residual interaction that is then by cosntruction independent of the microscopic details below it. This is how I picture unification in this scheme.

Although that gravity is totally independent of details is even an overstatement I admit since the separation of spacetime (and thus distance measure clearly depends on the details in the separation of interaction) it's not quite true. But then Verlinde has frozen this aspects. Probably to simplify.

This theory isn't on the table yet. I'm just describing general traits of it to show that at least there is no conceptual problem to envision this. But indeed my "picture" is much more involved than verlindes, but there is a key trait that is right that is the same.

I do not focus on what's wrong, but on what's right and how to move on from there ;)

/Fredrik

 

[S.Daedalus]

I haven't read the paper criticising Verlinde's idea in detail, but is it essentially the same criticism Motl expressed http://motls.blogspot.com/2010/01/erik-verlinde-why-gravity-cant-be.html" ? Basically, the gist there is that the rise in entropy causes the neutron's state space to grow, which means that it decoheres and loses any chance to interfere with itself. If things are indeed so, then experiment (neutron double slit interference within a gravitational field) has ruled out entropic gravity.

I don't think this poses much of a problem, however, because it seems to presuppose non-unitary, irreversible microscopic dynamics; however, entropic forces also exist in systems whose underlying dynamics are perfectly well reversible (Hammock Physicist Johannes Koelmann has written http://www.science20.com/hammock_physicist/it_bit_entropic_gravity_pedestrians" about this). If the dynamics underlying entropic gravity then are reversible, one should not expect decoherence.

 

[CHIKO-2010]

I guess it depends on what we're talking about. I don't agreee that microscopic details are irrelevant "in general" (as he is speaking of gravity specifically). But I don't think that's what Verlinde claims (at least its now how I read it)?

Yes, Verlinde talks about gravity specifically. My previous post reflects my understanding of the conceptual background of Verlinde's work extrapolated to other fundamental interactions (you have suggested entropic origin of ALL interaction in your previous posts)

Again, extending the idea to all forces, like I did originally, then the details irrelevant to GRAVITY, ARE relevant, but to other forces. The separation of the full interaction into, gravity/spacetime, other interactions and internal degrees of freedom is a subtle thing. Verlinde says nothing of that, but I think the entropic gravity of his is meant of limited scope. The way I envision that fitting into the larger context is that gravity is what separates out, once the microscopic details are already assigned to other forces concerning internal degrees of freedom. The residual interaction, is then by construction independent of those already classified details.

important aspect of verlinde's derivation is the emergence of space (x is treated as a macroscopic parameter characterizing ensemble of microstates on the holographic screen). Space emerges together with gravity. Even if you hierarchically separate (whatever this means) gravity from other interactions, how do you suppose to treat local degrees of freedom of those theories without space (and hence the notion of locality etc)? I don't think your thoughts are consistent even at this generic level...

This theory isn't on the table yet. I'm just describing general traits of it to show that at least there is no conceptual problem to envision this. But indeed my "picture" is much more involved than verlindes, but there is a key trait that is right that is the same.

I do not focus on what's wrong, but on what's right and how to move on from there ;)

I agree, in general, gravity can be emerging force. We know at least one theoretically consistent scenario of emergent gravity -- this is the string theory. You may come up with something new... At this point, I am just curious, what motivates you to believe in such a complicated, obscure and bizarre picture when the observed fundamental interactions (at least non-gravitational) are so beautifully described theoretically within the standard qft and, which is more important, these theories are tested experimentally with high accuracy?

 

[CHIKO-2010]

I haven't read the paper criticising Verlinde's idea in detail, but is it essentially the same criticism Motl expressed http://motls.blogspot.com/2010/01/erik-verlinde-why-gravity-cant-be.html" ? Basically, the gist there is that the rise in entropy causes the neutron's state space to grow, which means that it decoheres and loses any chance to interfere with itself. If things are indeed so, then experiment (neutron double slit interference within a gravitational field) has ruled out entropic gravity.

I don't think this poses much of a problem, however, because it seems to presuppose non-unitary, irreversible microscopic dynamics; however, entropic forces also exist in systems whose underlying dynamics are perfectly well reversible (Hammock Physicist Johannes Koelmann has written http://www.science20.com/hammock_physicist/it_bit_entropic_gravity_pedestrians" about this). If the dynamics underlying entropic gravity then are reversible, one should not expect decoherence.

The problem of reversibility of the entropic force (it can be reversible, not fully but with high accuracy) is not at the heart of the criticism in 1009.5414. Time evolution of the system is unitary, the Hamiltonian has real positive eigenvalues. I think the same must be true for the Motl's argument. In essence these two criticisms are very similar.

 

[John86]

String theory is much to static to tell us anything of Verlinde's idea

 

[Fra]

We know at least one theoretically consistent scenario of emergent gravity -- this is the string theory.

There are SOME similarities with my view and string theory. But also some big differences. I've mentioned it before (like someone cares) but if I project string theory into my view, then the objects subject to excitation (strings, branes and what it may be) are to be seens as defining the microstructure of the context that encode the interactions. Also a "string" seen as an 1D index, is the simplest possible continuum object even in the construction I envision. But they are by no means fundamental, neither sensible starting points (like they are in string theory). Also the embedding in string theory due to various consistency constrains are totally alien to my thinking. I am not surprised theere is a landscape problem.

I however do not share some typical critique against string coming from loop people. This talk about background independence etc. I see that differently, and I understand that in string theory, somehow the VISION is that the background should (if there is any sense in it) be selected dynamically by relations between collections of strings. As loong as you just have ONE string, there is no selection - thus just an big obscure landscape.

You may come up with something new... At this point, I am just curious, what motivates you to believe in such a complicated, obscure and bizarre picture when the observed fundamental interactions (at least non-gravitational) are so beautifully described theoretically within the standard qft and, which is more important, these theories are tested experimentally with high accuracy?

I can't to restate briefly if it's not already clear from past posts. But my analysis and understanding of current physics, the scientific learning process and the open problems in physics has left me in this position. I see it as the clear rational strategy, coming with a minimum of ad hoc assumptions and minimal baggage and that. It's in a sense an extreme form of inference, put in an interacting context, meaning that my view of a model is not descriptive, it's an interaction tool. The research strategy is almost a formalisation of inference where no principal distinction is made between scientific process and physical processes.

Of course, the constructing ideas are not really obscure or complicate or bizarre. It's because you see if from a different perspective.

/Fredrik

 

[CHIKO-2010]

String theory is much to static to tell us anything of Verlinde's idea

String theory (closed strings at least) is incompatible with Verlinde's idea and vice versa.

 

[CHIKO-2010]

T

Of course, the constructing ideas are not really obscure or complicate or bizarre. It's because you see if from a different perspective.

I guess I have to agree with this, i see it from a different perspective

 

[Fra]

how do you suppose to treat local degrees of freedom of those theories without space (and hence the notion of locality etc)?

The notion of locality is a key constructing principle in my view, and the notion of locality I use has nothing to do with regular spacetime specifically. It is a locality that refers to generic locations in information space (*) which is defined without prior existence of the 4D spacetime we know of.

The locality principle I use as a constructing axiom is that

The decisions(=rational actions) of a given system depends only upon the information at hand. From the decision theoretic view this is obvious, as anything else is simply irrational and nonsensial.

This is a locality in the sense that, local decision depend only on local information. Where LOCAL information refers to the set of information that defines the observer. Thus "points" in this absctract space are not really empty points, they are structures having a defined complexity and internal structure. There is a distance measure that will be constructed loosely speaking as some form of information distance, ie. a measure of how much information or how many bits of information that separates two information states.

Thus the locality we mean referring to 4D space is a special case of the more general principle.

(*) This information space is furthermore not stative, it's evolving and observer dependent. Effectively objective spaces will emerge as equilibrium points chosen by evolution, when the environment is interacting similarly constructed systems.

/Fredrik

 

[S.Daedalus]

The problem of reversibility of the entropic force (it can be reversible, not fully but with high accuracy) is not at the heart of the criticism in 1009.5414. Time evolution of the system is unitary, the Hamiltonian has real positive eigenvalues. I think the same must be true for the Motl's argument. In essence these two criticisms are very similar.

I'm not sure I understand you right -- if the evolution is unitary, then the dynamics are exactly reversible, not merely with high accuracy. And in the paper, translation along the z-axis takes pure states to mixed states, and hence, is non-unitary. As for Motl's post, if the neutron starts with zero entropy, it is in a pure state, from which, in order to 'acquire' entropy, it must evolve into a mixed one, which again requires non-unitarity. That's a general feature, since entropy is invariant under unitary transformations.

I think the mistake here is the assumption that the neutron's entropy must rise -- that's akin to saying that, in for instance an expanding gas, the entropy of every gas atom rises as the entropy of the gas as a whole does. However, the dynamics of each individual gas atom (which we can think of as some classical, hard sphere for present purposes) are perfectly reversible, even if the dynamics of the gas as a whole is not. So that the entropy in a (gravitational) system rises does not necessarily imply that the entropy of each of its constituents -- such as the neutron -- does, too, and hence, does not necessitate any non-unitary dynamics, or loss of coherence.

 

[CHIKO-2010]

I'm not sure I understand you right -- if the evolution is unitary, then the dynamics are exactly reversible, not merely with high accuracy. And in the paper, translation along the z-axis takes pure states to mixed states, and hence, is non-unitary. As for Motl's post, if the neutron starts with zero entropy, it is in a pure state, from which, in order to 'acquire' entropy, it must evolve into a mixed one, which again requires non-unitarity. That's a general feature, since entropy is invariant under unitary transformations.

Since the energy eigenvalues are all real (see (17) in 1009.5414) time evolution is unitary, that is |\psi|^2 is conserved in time. As you have pointed out this means also reversibility (recall, t-> -t is an anti-unitary symmetry). I don't think this is the problem.

The problem is the very fact that gravity, according to Verlinde, emerges due to the entropy difference related with positions of the gravitating objects.

I think the mistake here is the assumption that the neutron's entropy must rise -- that's akin to saying that, in for instance an expanding gas, the entropy of every gas atom rises as the entropy of the gas as a whole does. However, the dynamics of each individual gas atom (which we can think of as some classical, hard sphere for present purposes) are perfectly reversible, even if the dynamics of the gas as a whole is not. So that the entropy in a (gravitational) system rises does not necessarily imply that the entropy of each of its constituents -- such as the neutron -- does, too, and hence, does not necessitate any non-unitary dynamics, or loss of coherence.

I do not agree. your analogy with the gas of particles is not valid here. Here we have 2-body problem: Neutron-Earth. They gravitate because neutron changes its position (relative to Earth) and thus the entropy, according to Verlinde. More, precise analogy would be to consider two macroscopically large subsystems of the gas, where you can define entropy for each subsystem.

 

[qsa]

Since the energy eigenvalues are all real (see (17) in 1009.5414) time evolution is unitary, that is |\psi|^2 is conserved in time. As you have pointed out this means also reversibility (recall, t-> -t is an anti-unitary symmetry). I don't think this is the problem.

The problem is the very fact that gravity, according to Verlinde, emerges due to the entropy difference related with positions of the gravitating objects.



I do not agree. your analogy with the gas of particles is not valid here. Here we have 2-body problem: Neutron-Earth. They gravitate because neutron changes its position (relative to Earth) and thus the entropy, according to Verlinde. More, precise analogy would be to consider two macroscopically large subsystems of the gas, where you can define entropy for each subsystem.

if this paper and the references(11,14..) enclosed does not give you a better idea as to what verlinde is conjecturing I will try to clarify the idea later.


http://arxiv.org/PS_cache/arxiv/pdf/1003/1003.1262v3.pdf


Joakim Munkhammar
Studentstaden 23:230, 752 33, Uppsala, Sweden
E-Mail: joakim.munkhammar@gmail.com

ABSTRACT: In this paper we suggest a connection between quantum mechanics and Verlinde’s recently proposed entropic force theory for the laws of Newton. We propose an
entropy based on the quantum mechanical probability density distribution. With the assumption that the holographic principle holds we propose that our suggested quantum
entropy generalizes the Bekenstein entropy used by Verlinde in his approach. Based on
this assumption we suggest that Verlinde’s entropic theory of gravity has a quantum mechanical origin. We establish a reformulation of the Newtonian potential for gravity based
on this quantum mechanical entropy. We also discuss the notion of observation and the
correspondence to classical physics. Finally we give a discussion, a number of open problems and some concluding remarks

you can also read this

https://www.physicsforums.com/showthread.php?p=2615567#post2615567

 

[S.Daedalus]

Since the energy eigenvalues are all real (see (17) in 1009.5414) time evolution is unitary, that is |\psi|^2 is conserved in time.

I don't think that this matters -- it seems to me that the modified quantum bouncer that's solved in the paper is derived from the assumption that the neutron's state at some height is pure, and during its fall, it 'picks up' entropy -- that's what I think is invalid. (In particular, I'm not entirely sure that one can assume the state of the neutron and the state of the screen to be uncorrelated.)

I do not agree. your analogy with the gas of particles is not valid here. Here we have 2-body problem: Neutron-Earth.

I'm not too sure that to view the Earth as a single body is a very good model in a quantum context...

 

[CHIKO-2010]

I don't think that this matters -- it seems to me that the modified quantum bouncer that's solved in the paper is derived from the assumption that the neutron's state at some height is pure, and during its fall, it 'picks up' entropy -- that's what I think is invalid. (In particular, I'm not entirely sure that one can assume the state of the neutron and the state of the screen to be uncorrelated.)

Yes, neutron entropy depends on the distance to Earth, precisely according to Verlinde. Neutron, must have individual properties at distances larger than its Compton wavelength from a given screen, otherwise this problem won't have the classical limit (classical free fall). Also, neutron is represented as a macroscopic subsystem (consisting of large number of screen microstates) on the holographic screen.

I'm not too sure that to view the Earth as a single body is a very good model in a quantum context...

Of course it is OK. The problem of quantum bouncer is a quantum particle moving in the CLASSICAL gravitational potential of Earth!

 

[S.Daedalus]

Yes, neutron entropy depends on the distance to Earth, precisely according to Verlinde.

But then, I ask again -- how can this lead to unitary evolution?

Besides, IIRC, in Verlinde's original proposal, it was the entropy on the screen that that depends on the neutron's distance to it -- for each Compton wavelength of distance, the screen 'picks up' one more bit of entropy.

Also, neutron is represented as a macroscopic subsystem (consisting of large number of screen microstates) on the holographic screen.

Which is precisely why the assumption that the states of the screen and the neutron can be treated as uncorrelated seems suspect to me.

Of course it is OK. The problem of quantum bouncer is a quantum particle moving in the CLASSICAL gravitational potential of Earth!

That's not what I was talking about. Rather, consider again the gas analogy where one single gas atom is considered as one system, and all the other atoms as another. You're of course free to do that, but then, in calculating the rise in entropy, you have to be a bit careful about 'where' that rise happens, or else, you end up with one single gas atom picking up a huge amount of entropy despite the fact that it has just undergone a reversible evolution. Both systems aren't equal, in this case and in the Earth-neutron case; one has a huge number of degrees of freedom more than the other. Seems to me that just as in the gas bulk-gas atom case, there's no need, even in order for the total entropy to rise, for the entropy of the neutron to rise in the Earth-neutron case; in particular, I think one could model the situation as the neutron being a noiseless subsystem of the screen-neutron system, which would remain decoherence-free and evolve unitarily throughout.

 

[czes]

CHIKO-2010 wrote that there are problems how to falsify the Holographic Principle and idea of the discrete space.

I have an equation which connects the Quantum with Classical:

Tp / T(x) * Tp / T(y) = -a Fg / Fe
where:
Tp * Tp - Planck's time squared = hG/c^5
T(x) , T(y) -Compton time of the oscillation of the particle x,y T=1/frequence = h/mc^2
a – alfa=ke^2 /hc = fine structure constant
Fg – Gravitational Newton's interaction Fg = Gm(x) m(y) /r^2
Fe - Electrostatic Coulomb interaction Fe = ke2 /r^2

According to Matrix theory and Holographic Principle the space is made of the interfered information which are encoded on a screen (Event Horizon) but create a 3D hologram. The equation above suggests that each quantum interference encodes the Planck time dilation. We can calculate it for each Compton wave of the particle. Due to non-locality the Compton waves is distributed in the emergent space and create the Vacuum.
Such a space is discrete made of the virtual paricles-antiparticles as the relations between information encoded on a screen (Event Horizon).
The encoded Planck time dilation creates the curvature of the space as in General Relativity and discrete Events (virtual Particles-antiparticles) create difference it the entropy which causes the gravitational force as proposed Verlinde.
We can verify the equation if it is true.
You may see the simple calculation on averaged particles for gravitational time dilation, Holographic Principle bound, Dark Matter effect :
http://www.hologram.glt.pl/

 

[CHIKO-2010]

But then, I ask again -- how can this lead to unitary evolution?

I am not quite sure what exactly you do not understand in my previous post. The equation solved is the time-independent Schrödinger equation, and the energy eigenvalues are found to be REAL. Now, time evolution of a given state $$\Psi$$ is obtained as usual by applying the evolution operator U=e^iHt, $$\Psi(t)$$=U$$\Psi$$. Then it is a matter of a simple algebra to check that $$\frac{d}{dt}$$|$$\Psi(t)$$|²=0. That is probability is conserved in time, and thus time evolution of the system is unitary. Note that the amplitudes of wavefunctions are dumped in z not in t.
Don't you agree with this?

Besides, IIRC, in Verlinde's original proposal, it was the entropy on the screen that that depends on the neutron's distance to it -- for each Compton wavelength of distance, the screen 'picks up' one more bit of entropy.

Yes right. Consider two screens at x and x+\deltax with entropies S(x) and S(x+\delta x). As explained by Verlinde, S(x) is obtained by integrating out ('coarse graining') some microstates on the screen at x+\delta x. Since the entropy is an additive quantity, the entropy of "removed" microstates (they form a subsystem) is equal to the difference between the entropies of two screens. Those removed microstates describe a neutron which is merged with a holographic screen at x+\delta x, and thus neutron carries x-dependent entropy. I think this is how it is.

That's not what I was talking about. Rather, consider again the gas analogy where one single gas atom is considered as one system, and all the other atoms as another. You're of course free to do that, but then, in calculating the rise in entropy, you have to be a bit careful about 'where' that rise happens, or else, you end up with one single gas atom picking up a huge amount of entropy despite the fact that it has just undergone a reversible evolution. Both systems aren't equal, in this case and in the Earth-neutron case; one has a huge number of degrees of freedom more than the other. Seems to me that just as in the gas bulk-gas atom case, there's no need, even in order for the total entropy to rise, for the entropy of the neutron to rise in the Earth-neutron case; in particular, I think one could model the situation as the neutron being a noiseless subsystem of the screen-neutron system, which would remain decoherence-free and evolve unitarily throughout.

As I've pointed out in my previous your analogy with the system 1 atom + bulk gas is wrong, simply because a subsystem consisting of 1 atom is not statistical, it does not make sense to talk about entropy of 1 atom. A particle in Verlinde's description does not correspond to 1 atom system. in fact it carries n~m/t bits of information (see 3.14 of Verlinde)

 

[S.Daedalus]

Don't you agree with this?

Well, I don't disagree, I'm just puzzled: if the neutron's entropy at height z is different from its entropy at height z + dz, and it propagates from z to z + dz, that must mean that it undergoes non-unitary evolution, it seems to me. Right?

But then, the solution to the modified quantum bouncer derived from this assumption, as shown in the paper, leads to real energy eigenvalues, and thus, unitarity. Those two statements seem to be at odds with each other, and I'm not sure how to resolve that tension.

As I've pointed out in my previous your analogy with the system 1 atom + bulk gas is wrong, simply because a subsystem consisting of 1 atom is not statistical, it does not make sense to talk about entropy of 1 atom.

Yes, pointing that out was the purpose of the analogy; the argument being, that in the system neutron + screen, it may make just as little sense to talk about the entropy (gain) of the neutron, which both Motl (in discussing the number of microstates available to the neutron rising) and the paper (in talking about the non-unitariness of the z-translation operator, or alternatively the different entropy of the neutron at different z's) seem to be doing. And if there's no entropy gain in the neutron, there doesn't seem to be a problem for Verlinde's reasoning -- there's no decoherence due to rising number of microstates, nor is there any need to modify the quantum bouncer.

 

[CHIKO-2010]

Yes, pointing that out was the purpose of the analogy; the argument being, that in the system neutron + screen, it may make just as little sense to talk about the entropy (gain) of the neutron, which both Motl (in discussing the number of microstates available to the neutron rising) and the paper (in talking about the non-unitariness of the z-translation operator, or alternatively the different entropy of the neutron at different z's) seem to be doing. And if there's no entropy gain in the neutron, there doesn't seem to be a problem for Verlinde's reasoning -- there's no decoherence due to rising number of microstates, nor is there any need to modify the quantum bouncer.

if you do not assume that the neutron carries entropy in quantum bouncer you will arrive at a wrong classical limit, which is approached as number of bounds states is large n (large z_n). In that limit neutron behaves as a classical particle which according to Verlinde must carry entropy (again see eq.3.14).

 

[S.Daedalus]

if you do not assume that the neutron carries entropy in quantum bouncer you will arrive at a wrong classical limit, which is approached as number of bounds states is large n (large z_n). In that limit neutron behaves as a classical particle which according to Verlinde must carry entropy (again see eq.3.14).

3.14 just describes the entropy gained by the screen as the particle merges with it; besides, it should be fine if the neutron carries some fixed entropy, it's just problematic if its entropy increases.

 

[czes]

The particle increases the entropy of 1 bit when it approaches at 1 Compton wavelength to the sphere.
Does it mean the entropy of the whole spherer = sum of the number of the wavelengthes of all particles inside the sphere ?
S=n R/l(c)

 

[CHIKO-2010]

3.14 just describes the entropy gained by the screen as the particle merges with it; besides, it should be fine if the neutron carries some fixed entropy, it's just problematic if its entropy increases.

Yes, but please also note that n bits in 3.14 specifically describes a particle of mass m on the screen (see, e.g., the discussion just above 3.14 and just below 3.15).

I think the fact that the entropy of neutron must be x-dependent is pretty clear from Verlinde's paper. Again, consider a holographic screen that suurounds a mass M, say at distance x from M. This microstates on this holographic screen carry information (entropy) concerning the object M. let us put now a test particle of mass m at a distance x+\delta x from M. The total entropy of test particle + screen is

S_{\particle}(x+\delta x) + S_{screen}(x)

which can be equated with the entropy os a screen at distance x+\delta x, that is screen with a test particle on it, S_{screen}(x+\delta x). Since \delta S_{sceen} is proportional to \delta x, S_{\particle} CAN NOT be x-independent. I think this is trivial.

The equation I have highlighted, assumes that neutron states and the microstates on the screen are uncorrelated which is perfectly OK, since the creen contains only the information in the surrounded volume. If you assume that neutron states are entangled with microstates on the screen, than you will get even in bigger troubles -- to describe a neutron in quantum bouncer you have to sum up screen microstates at each x. you will certainly get decohered picture.

 

[S.Daedalus]

I think this is trivial.

I may just be dense, but I don't see it. I agree that the entropy of the system screen + particle must be greater the closer the particle gets to the screen, but this only translates to an entropy increase in the particle if you assume irreversible, non-unitary dynamics, which I think is neither necessary, nor appropriate, if you want the particle's evolution to be describable by ordinary quantum mechanics.

The equation I have highlighted, assumes that neutron states and the microstates on the screen are uncorrelated which is perfectly OK, since the creen contains only the information in the surrounded volume.

What do you make of this quote from Verlinde's paper: "Eventually the particle merge [sic] with the microscopic degrees of freedom on the screen, but before it does so, it already influences the amount of information stored on the screen."?

Besides, assuming that the screen microstates and the neutron state are uncorrelated seems at odds with your proposal to replace the neutron by a screen containing it: for then, microstates on neither screen (not the Earth's nor the neutron's) would change with their respective position, and hence, the total entropy would be independent of location -- leading to no entropic gravity at all.

 

[czes]

I agree with CHIKO-2010 here.
Due to Holographic principle the screen contains only the information in the surrounded volume. When the particle is far away from the surface of the massive body you have 2 Horizon Events. One is of the massive body with a radius R where is higher entropy and another is of the particle where is the radius (R+x).

The maximum entropy is when the body collapses into a Black Hole. The lower entropy is for the body of radius R and the lowest is for the system with a distant particle (R+x).

The gravity as entropic force acts toward the higher entropy (the future Black Hole).

 

[CHIKO-2010]

What do you make of this quote from Verlinde's paper: "Eventually the particle merge [sic] with the microscopic degrees of freedom on the screen, but before it does so, it already influences the amount of information stored on the screen."?

Besides, assuming that the screen microstates and the neutron state are uncorrelated seems at odds with your proposal to replace the neutron by a screen containing it: for then, microstates on neither screen (not the Earth's nor the neutron's) would change with their respective position, and hence, the total entropy would be independent of location -- leading to no entropic gravity at all.

I do not see contradictions here -- holographic description of both masses m and M, being at "positions" x+\delta x and x=0, requires a screen at x+\delta x, so this screen has an entropy S(x+\delta x). Note that, space has not yet emerge for region < x+\delta x, so the position of m and M are encoded in microstates on the screen.

You perhaps did not noticed but there is NO total dependence of entropy S on x. The explicit dependence on x (gradient of S) is compensated by the change in the energy due to the work of an entropic force, that is total derivative of S wtr to x IS indeed 0. That is how the entropic force is defined in the first place!

 

[Fra]

The kind of analysis I would like to see to move forward is to define in terms of an inference abstraction, the notion that Verlinde thinks is "independent".

"Starting from first principles, using only space independent concepts like energy, entropy and temperature, it is shown..."

Energy, entropy and temperature are all different measures and their definition in terms of constructable measures are far from clear enough IMHO. In particular does it seem quite obvious that each of these measures are observer dependent, and the nature of a possible observer-covariant view is not clear either.

But of course you have to start somewhere and apply the admitted heuristic arguments, so did Verlinde.

In the end he notes

"This brings us to a somewhat subtle and not yet fully understood aspect. Namely, the
role of h-bar"

I think this is connected to how the measures are really somehow discrete.

In my opinion the weakest part of the whole argument isn't that the idea is all misguided, it's that it's heuristic and MIXING baggage notions the we well understand in classical setting, but not so in the general setting, with the holograpic conjecture which is also a bit unclear. I think he is not radical enough.

Can we reconsider how the measures energy, entropy and temperature are supposedly to be rationally constructed without relying on classical concepts, or fictious ensembles etc and instead only use the state of the observer as constructing tools and see how space and gravity is emergent along with the construction?

Since all horizons are observer dependent, that also seems to hint the duality that there may be two descriptions of the same thing, one with gravity one w/o.

Even in GR we have that. The free falling oberver does not see gravitation, it's just doing a random walk. So it seems clear that gravity seems simpler from the inside perspective. Only to an outside observer, does the mysterious gravity reveal itself. To the free fall observer it's just a random walk.

So it seems what we need to understand is why two observers, both doing a random walk - attract, right?

That is pretty close to asking, why two observers that are communicating, will have a tendency to negotiate agreements. And if space; is simply a measure of disagreement, then the connection is clear.

This is the obvious rational I see behind verlindes idea, but to make it clear, the notions of entropy, energy and temperature and the spacetime structure and the distance metric etc needs to be reconstructed.

/Fredrik

 

[czes]

So it seems what we need to understand is why two observers, both doing a random walk - attract, right?

That is pretty close to asking, why two observers that are communicating, will have a tendency to negotiate agreements. And if space; is simply a measure of disagreement, then the connection is clear.

This is the obvious rational I see behind verlindes idea, but to make it clear, the notions of entropy, energy and temperature and the spacetime structure and the distance metric etc needs to be reconstructed.
/Fredrik

I would like to refer everything from holographic point of view.
The ordinary hologram is made of the interfered waves of the coherent light rays. If we assume each that interference encodes a constant time dilation we get the space-time as in General Relativity. Each object will follow the curvature of that space. An inner observer is doing random walk in his space.

There are naturally more interferences and time dilations close to a massive object. The object absorbs more interferences toward the higher density closer to massive object and accelerates. it is the Unruh effect.

Therefore gravity may be shown as an entropic force (object moves toward the Event Horizon with higher entropy)
or
also as the result of the computer program where each point of interference has encoded a constant time dilation.