Gravity is not entropic force ?

[qsa]

Ok that point is well taken. You're right that's the specific question here. And I admit that if we define the question as such, it's probably false. But my only point was that I feel that's somehow a too simple question & conclusion.

My point is that, although Verlindes idea seems imperfect, I think it's more interesting to try to discuss how it can be improved, rather than trying to just proove that it's false.



I disagree. I merely question that then notions of entropy is more complex than verlinde admits, but I think the underlying idea is not wrong. It may be wrong because the measures of information and the holographic principle is wrong. Both these things are IMHO related to the careless treatment of the observer, because the observer is also the home of the theory in my view.

So while it seems probably that the specific attempt of verlinde is flawed, there is something about the idea that I think is right. And since ideas in this direction are unfortunately rare, I show my support even though his first attempt is wrong. I see more than a flawed theory here - I see a way of reasoning that can generate theories.

/Fredrik

the paper by joakim helps to clarify many issues, it should be a very interesting read. It has been listed before in PF but I think a close examination is warranted here.

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

 

[CHIKO-2010]

Quantum Mechanics is not a local theory so you will have to look for boundary values and sum over all space if you want to do it right. For example,the operator U is expanded linearly as its border conditions at the holographic screen were irrelevant. In reality, U should be written like U=Aexp(...), where A is a function that makes U goes smoothly to 0 at the screen and to the maximum value of entropy at r=0.

What are you talking about? U as it is defined in the paper is the standard operator of translations which is valid in quantum mechanics! acting on a state \psi(z) it transforms the state into a new state \psi(z+\delta z) (\delta z can be counted as infinitesimally small). Again, it is completely irrelevant what are the entropies of these two states \psi(z) and \psi(z+\delta z). what is relevant is an entropy difference. QM is nonlocal theory in ceratin sense but in this particular case we are talking about gravitational potential energy of neutron-Earth system which depends only on local coordinate z.

 

[CHIKO-2010]

P.S. The only physical boundary condition on the wave-function of neutron is \psi(z=0)=0 (if the mirror is treated as a perfect reflector)

 

[MTd2]

U as it is defined in the paper is the standard operato

A standard operator that is non unitary...

 

[CHIKO-2010]

A standard operator that is non unitary...

It is not unitary only for the specific problem: neutron-earth system where the gravitational interactions are treated according to Verlinde. This follows from the entropic description of gravity and falsified by the observations. your heroic attempts to modify U on cosmological scales etc are wrong. well, you could try to modify quantum mechanics also -- the claim in the paper is only valid if the usual quantum mechanical description of the given problem is correct, of course.

 

[MTd2]

well, you could try to modify quantum mechanics also -- the claim in the paper is only valid if the usual quantum mechanical description of the given problem is correct, of course.

This is what is done in the paper too, it is set up its own axioms to modify quantum mechanics. There are other ways too, like, I sugested, setting up a kappa modification dependent on space and/or time.

 

[MTd2]

An holographic surface is a remain from a very limited attempt to see common aspects of GR and QM, which is the surface of a black hole quantized by a discreet quantity. This was later generalized by Wald (past cone only) and Bousso to any surface that represented causal discontinuity.

So, if one is claiming an holographic surface within a Newtonian context, that person is imposing quite artificially a causal discontinuity. For low gravitational fields, that's ok, but if one is trying to get a quantization in this same context, some GR low energy limit must be taken or considered. The reason for this it is that the integration will include places where gravitational distortions are very important, like the particle horizon or apparent horizon.

 

[CHIKO-2010]

This is what is done in the paper too, it is set up its own axioms to modify quantum mechanics. There are other ways too, like, I sugested, setting up a kappa modification dependent on space and/or time.

Your suggestion of nullifing kappa in eq. 13 would mean that the gradient of entropy for free falling neutron in the gravitational field of Earth is zero. According to Verlinde this means that neutron does not gravitate at all (i.e. free fall acceleration g=0) -- you will end up contradicting the experiments anyway

 

[CHIKO-2010]

P.S. The parameter kappa is entirely determined by the entropy gradient which is a constant (see e.q. 3.6 of Verlinde) i.e. it does not depend on space and time

 

[MTd2]

What I meant it is that the deficit in the non unitarity does not have to be equal to the gradient of entropy.

 

[CHIKO-2010]

What I meant it is that the deficit in the non unitarity does not have to be equal to the gradient of entropy.

Well, non unitarity is due to the fact that netron states have different entropy at different positions, and the entropy gradient in turn defines the strength of gravity. I do not see any way how you can avoid this.

 

[Fra]

the paper by joakim helps to clarify many issues, it should be a very interesting read. It has been listed before in PF but I think a close examination is warranted here.

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

Thanks, I'll print and read that during the week. Just judging from the title though, what I personally think is not quite that "gravity and holograhpy follows from QM". What I think is that gravity follows from a interacting inference systems. Which can be thought of as a more generalized form of "measurement theory".

If we characterize QM as inference containing non-commutative structures, then the additional constraint we need to add, is the complexity bound. QM as it stands more corresponds to either a static non-interacting observer, or possibly an equilibrium condition. When an observer gains or looses mass at a rate that is significant relative to the observed processes, QM as we know breaks down IMO. This is why I think the framework needs to allow evolving observers. Real observing systems aren't static. And of course there is neither a static description of their dynamics expcet as partial descriptions by a third observer interacting with it.

Part of this also means that two observers generally rate the "entropy" differently. And there is no observer-invariant transformation except as local equilibrium conditions. Therefor I think the ultimate entropic interactions necessarily must reflect the observes action and evolution as well, not just be an objective false description of two interacting subsystems.

It's indeed popular to dismiss these problems as metaphysical but that's IMO just like sticking the head in the sand for a difficult problems. No progress will be made unless we try to face the problems.

/Fredrik

 

[czes]

Your suggestion of nullifing kappa in eq. 13 would mean that the gradient of entropy for free falling neutron in the gravitational field of Earth is zero. According to Verlinde this means that neutron does not gravitate at all (i.e. free fall acceleration g=0) -- you will end up contradicting the experiments anyway

Does it mean that according to Verlinde gravity is entropic force but gravitational field is not quanized because there are not gravitons ?
Therefore due to Verlinde the slit can't be opaque for neutrons ?

 

[CHIKO-2010]

Does it mean that according to Verlinde gravity is entropic force but gravitational field is not quanized because there are not gravitons ?
Therefore due to Verlinde the slit can't be opaque for neutrons ?

It is true that in Verlinde's gravity there are no gravitons as fundamental degrees of freedom. However, the contradiction with the experiments discussed in the paper is not due to the fact that gravity is not quantized. This is a problem of quantum-mechanical particle moving in the CLASSICAL gravitational field of Earth. The probelm is due to the fact that this classical gravitational force acting on neutron has intrinsically entropic origin, i.e. its emerges only due to the change in the entropy of neutron states at different positions. That is a neutron state \psi(z) and \psi(z+\delta z) do not "match" unitarily, loosely speaking something gets lost/gained going from \psi(z) to \psi(z+\delta z). Solutions which reflect this changes compared to the usual description of the problem are obviously different, so that the predictions are not agree with observations. The experiments, in turn, are in reasonably good agreement with the standard description.

 

[czes]

It is true that in Verlinde's gravity there are no gravitons as fundamental degrees of freedom. However, the contradiction with the experiments discussed in the paper is not due to the fact that gravity is not quantized. This is a problem of quantum-mechanical particle moving in the CLASSICAL gravitational field of Earth. The probelm is due to the fact that this classical gravitational force acting on neutron has intrinsically entropic origin, i.e. its emerges only due to the change in the entropy of neutron states at different positions. That is a neutron state \psi(z) and \psi(z+\delta z) do not "match" unitarily, loosely speaking something gets lost/gained going from \psi(z) to \psi(z+\delta z). Solutions which reflect this changes compared to the usual description of the problem are obviously different, so that the predictions are not agree with observations. The experiments, in turn, are in reasonably good agreement with the standard description.

I think, a neutron continually absorbs and emits the virtual particles-antiparticles from the gravitational field. If the virtual p-a are just non-local quantum information interactions between the massive object and the rest of the Universe. Each massive particle absorbs and emits (oscillate) due to its Compton wavelength. Therefore the density of the appearing and disappearing virtual p-a is inversely proportional to the distance from the massive object.

The neutron increases the frequence of the oscillation when it approaches the Earth because it absorbs more than emits due to the density of the virtual p-a. It becomes accelerate towards the massive object because it gains more information in this direction.
The fundamental information could be Planck length contraction and Planck time dilation for each non-local quantum information due to Compton wavelength of each particle.

Graviton would be here just a shift of the spacetime of the Planck length and time due to interaction with this non-local information due to Compton wavelength.

I have calculations for gravitational time dilation using the Compton wavelength structure.
Personally I do not use entropy in that calculation but Verlinde's calculations shows a similar effect.

 

[CHIKO-2010]

I think, a neutron continually absorbs and emits the virtual particles-antiparticles from the gravitational field. If the virtual p-a are just non-local quantum information interactions between the massive object and the rest of the Universe. Each massive particle absorbs and emits (oscillate) due to its Compton wavelength. Therefore the density of the appearing and disappearing virtual p-a is inversely proportional to the distance from the massive object.

The neutron increases the frequence of the oscillation when it approaches the Earth because it absorbs more than emits due to the density of the virtual p-a. It becomes accelerate towards the massive object because it gains more information in this direction.
The fundamental information could be Planck length contraction and Planck time dilation for each non-local quantum information due to Compton wavelength of each particle.

Graviton would be here just a shift of the spacetime of the Planck length and time due to interaction with this non-local information due to Compton wavelength.

I have calculations for gravitational time dilation using the Compton wavelength structure.
Personally I do not use entropy in that calculation but Verlinde's calculations shows a similar effect.

Frankly speaking, I cannot make any sense from your post. you seems have your own theory of gravitational interactions, which is hard to comprehand (at least for me) from your short writing. If your work is available on-line/published please give a reference and I'll read it. Thanks

 

[CHIKO-2010]

P.S. Did Verlinde calculate time dilation in his theory?

 

[czes]

Frankly speaking, I cannot make any sense from your post. you seems have your own theory of gravitational interactions, which is hard to comprehand (at least for me) from your short writing. If your work is available on-line/published please give a reference and I'll read it. Thanks

GRAVITATIONAL TIME DILATION
My calculations are based on an equation:
lp / l x ) * (lp / l y ) = -a Fg / Fe

where:
lp * lp – Planck length squared = hG/c3
l x , l y –Compton wave length of two interacting particles x,y l= h/mc
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 = ke^2 /r^2


Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential (closer to the center of a massive object), the more slowly time passes. Albert Einstein originally predicted this effect in his theory of relativity and it has since been confirmed by tests of general relativity.

In quantum gravity time is created by a number of quantum events. Each event results with a Planck's time dilation and therefore we perceive a flow of the time. Time doesn't exist as an independent fundamental property or phenomenon.

We measure a distance and a time by a constant speed of light as a constant number of the quantum events which are passed by a photon N= R/lp.

A distance and time become contracted by the number of Planck's units when there is an additional non-local information from a real massive particle with its Compton wave length l= h/mc . We calculate the interference of the information from the direction of the observer and from the direction of the massive particle as a vector sum in a triangle.

As we showed above N=M/m particles cause (M/m) [(lp /(ly/2) )] length contraction and proportional time dilation where ly is a Compton wave length information of the massive particle perpendicular to the information of the observer in vacuum.

Therefore time is a sum :

t(f)^2 (R/lp) = t(0)^2 (R/lp) + t(f)^2 (M/m) [(lp /(ly/2) )]

t(0)^2 (R/lp) = t(f)^2 {(R/lp) - (M/m) [(lp /(ly/2) )]}

where:
lp * lp – Planck length squared = hG/c^3
Compton wave length lp=h/mc
After substitution we receive a well known equation for gravitational time dilation:
t(0)^2= (1-2GM/Rc^2 )

http://www.hlawiczes1.webpark.pl/gravastar.html

I didn't see Verlinde calculated time dilation but he received Holographic Principle resolution
S=A/4 l(p)^2

 

[MTd2]

Well, non unitarity is due to the fact that netron states have different entropy at different positions, and the entropy gradient in turn defines the strength of gravity.

Yes, one has to define a dependence on entropy for k. It does not have to be linear, one can define k in whatever way you want, with the following constrains: map 0 at the cosmological horizon to maximum entropy at the origin, smoothly increasing until. It will not affect the potential, since both have different dependencies on the entropy.

 

[CHIKO-2010]

Yes, one has to define a dependence on entropy for k. It does not have to be linear, one can define k in whatever way you want, with the following constrains: map 0 at the cosmological horizon to maximum entropy at the origin, smoothly increasing until. It will not affect the potential, since both have different dependencies on the entropy.

Why one has to map something on the cosmological horizon when describing neutron-earth system? Besides, it is just against the holographic conjecture to assume that the entropy on the cosmological horizon is 0 and entropy "at the origin" (center of earth?!) is maximum! Do you really think that these "boundary conditions" are natural?

Do you agree that the generator of z-translation P must be non-hermitian? If yes, the rest
of the derivation given in the paper is actually very simple. First you parameterize non-hermitian operator P as P=p+ix, where both p and x are hermitian operators. then use eq.12, the definition of entropy eq (7) and Verlinde's equation (11). you will get x=2Im\kappa given by eq. (15).

If you want to use instead of linear operators non-linear operators and all that kind of nonsense, be my guest. But note that the algebraic structure of QM in the paper is not modified, that is [z,p]=ih, [p,p]=[z,z]=0, while with your proposal I am sure you will get even more dramatic modification of QM. If you have a concrete proposal of such a modification please let me know and we can discuss it further. If not, it does not make sense to continue.

 

[MTd2]

Why one has to map something on the cosmological horizon when describing neutron-earth system? Besides, it is just against the holographic conjecture to assume that the entropy on the cosmological horizon is 0 and entropy "at the origin" (center of earth?!) is maximum! Do you really think that these "boundary conditions" are natural?

For Verlinde's gravity they surely natural. As I explained above, the holographic screen is a reminiscent of quantum theory using an asymptotic spatial region with a causal discontinuity. It doesn't exist in Newtonian regime, so if one wants to quantize, a necessary step is a suitable function which works well in a reasonable cosmology.

The entropy of an object of the bulk goes to zero when it approaches the holographic screen, not the holographic screen itself. The object needs less bits to represent it.

 

[CHIKO-2010]

F

The entropy of an object of the bulk goes to zero when it approaches the holographic screen, not the holographic screen itself. The object needs less bits to represent it.

Ok. I somehow thought you are talking about the entropy of holographic screens in your previous post. Your objection does not make sense to me anyway. I am repeating again - the net result depends on the entropy gradient, \partial S/\partial z which is constant throught space and time, according to Verlinde.

I simply cannot "digest" your remark that for the quantization of neutron in the classical gravitational field of Earth you necessarily need to consider cosmological model. I do not want to argue about this anymore, I won't be able to understand your arguments anyway.

 

[MTd2]

It is not possible to affirm that the relation between kappa and the entropy is linear. It must be considered the general relativistic for that given that, the integration domain goes to the holographic screen, where gravitational effects are strong, and so entropy. Linearity is not expected. One thing is certain, unitarity goes to one as one gets close to the observer, but how it goes to one, it is another story. It could very well to 1 a few inches from the holographic screen and remain constant from billions of light years.

 

[CHIKO-2010]

It is not possible to affirm that the relation between kappa and the entropy is linear. It must be considered the general relativistic for that given that, the integration domain goes to the holographic screen, where gravitational effects are strong, and so entropy. Linearity is not expected. One thing is certain, unitarity goes to one as one gets close to the observer, but how it goes to one, it is another story. It could very well to 1 a few inches from the holographic screen and remain constant from billions of light years.

For the derivation of Newton's law there is no need to consider strong gravity. A holographic screen in Verlinde's theory can be any equipotential surface that embodies the gravitating mass M. Agan, to describe classical gravitational field produced by Earth at a distance R+r from the center of Earth you need to consider holographic screen at R+r. This is how Verlinde derives his gravitational potential. Now drop in this potential a neutron (a test particle). If you consider the neutron as a classical particle everything follows Verlinde.

However, when one considers neutron as a quantum mechanical particle you are start saying that now we have to move screen to the cosmological horizon. then you suggest that \kappa is non-zero only "a few inches" from the screen and zero (or almost zero) everywhere else. The straightforward conclusion from your theory is: since \kappa is 0 near Earth, the translation operator is unitary, and, as a result, there is no gradient of entropy and hence nor gravitational field acting on neutron (near Earth). your theory fails to explain experiments, it looks like it does not have a classical limit as well.

I think your confusion boils down to a very simple fact -- you resist to recognize that classical gravitational field of Earth acting on neutron states is a local field

 

[CHIKO-2010]

P.S. And aslo, please be a little bit more accurate in your definitions, it sometimes very hard to underdtand what are you talking about. E.g., what does it mean "unitarity goes to 1"?

 

[MTd2]

If one is looking for the deficit in unitarity, one is surely questioning the limits of "information processing". That is given by the biggest holographic screen possible, the one given by the apparent horizon of the observable universe. This is a consequence of QM taking all possible combinations, paths, etc, which is limited by the holographic screen, which is always an asymptotic surface with causal discontinuity. The classical problem does not have this issue, which is why one can work with the holographic screen that most suits the problem.

since \kappa is 0 near Earth, the translation operator is unitary, and, as a result, there is no gradient of entropy and hence nor gravitational field acting on neutron (near Earth). your theory fails to explain experiments, it looks like it does not have a classical limit as well.

Not quite, since the depedey of kappa of the entropy is sligh. For example: K= exp(-constant*((radius of the earth)/radius of the observable iniverse))*(gradient of entropy)). May not be quite this, but this is the idea.

 

[MTd2]

P.S. And aslo, please be a little bit more accurate in your definitions, it sometimes very hard to underdtand what are you talking about. E.g., what does it mean "unitarity goes to 1"?

It means that your lab experiments conserve quantum probabilities to amazing accuracy, where as those near the holographic screen might vanish or creates states or whole particles, which means crossing the horizon.

 

[CHIKO-2010]

Not quite, since the depedey of kappa of the entropy is sligh. For example: K= exp(-constant*((radius of the earth)/radius of the observable iniverse))*(gradient of entropy)). May not be quite this, but this is the idea.[/QUOTE]


Ok. let's be more specific. Could you please answer the questions below, just want to exclude that we have disagreement on the level of technicalities:

1. Do you aregree with eq. (7)?
2. Do you agree with eq. (13)?
3. I suppose you agree with (11).

If 1,2,3 are yes, then why do you doubt in 15? it just follows from the above eqs. if you do not agree with eather 1,2,3 please explain how do you think they must be modified.

 

[CHIKO-2010]

It means that your lab experiments conserve quantum probabilities to amazing accuracy, where as those near the holographic screen might vanish or creates states or whole particles, which means crossing the horizon.

Sorry, but probabilities are conserved (in time of course) in the paper -- the time evolution is unitary (hamiltonian hermitian). The type of unitarity conservation you are talking about has been addressed very carefully by Verlinde, at classical (thermodynamical) level it is related with the reversability of the underlying thermodynamic process that ensures the derived Newton's force is conservative

 

[MTd2]

1. Do you aregree with eq. (7)?
2. Do you agree with eq. (13)?
3. I suppose you agree with (11).

Yes, yes, yes. For 15, mc*logistic function, with 0 at r=0, and a non zero value at r=holographic screen. But one very steep, quite a step function.

"The type of unitarity conservation you are talking about has been addressed very carefully by Verlinde, at classical (thermodynamical) level it is related with the reversability of the underlying thermodynamic process that ensures the derived Newton's force is conservative"

Indeed, precisely these that I am talking about. If you release an object near the ground, you will see it unitarity, but not if you observe a similar experiment, from earth, done a few seconds or so after the big bang, which is near the holographic horizon in our past cone. You will get the results similar to yours. He did not address precisely the question of how much unitary would change.