How Does Verlinde's Theory Link LQG with Newtonian Gravity?

[marcus]

http://pirsa.org/06090001/

Ted Jacobson gave a 1-hour video lecture on his 1995 paper deriving the Einstein equation from thermodynamics (essentially the Clausius relation) and
including some more recent results, as of 2006.
He gives some conjectures about possible meanings.
I hadn't watched this talk before, for some reason didn't know it existed.

 

[Hans de Vries]

Nice! I'll take a look at your book.


Christine

Hi, Christine (Obrigado!)

Impressive work in progress, Hans!
Online introduction to relativistic quantum field theory with lots of illustrations, aids to intuition.
It looks like your plan is to cover the subject in 30 chapters, and you already have 14 chapters (all or part) filled in.
In case anyone didn't check it out already, the main chapter menu is here:
http://physics-quest.org/
This has links to the 14-or-so chapters which are all or part completed.

Thank you Marcus.

It's more work as I expected I'm currently at 700 pages including the
unfinished chapters and suspect to end up with something like 1100..

 

[Hans de Vries]

There is no equivalence principle issue here because in the paper by Verlinde, is about Newtonian gravity. So equivalence principle IS violated. But the quantum corrections due entropy that makes Newtonian gravity in the problem arise are of much larger magnitude or relevance than GR or interference patterns of neutrons.

And even so, I don't really see any issue here. In this set up, gravity is not a force, there is no particle to create gravity, if this were a paper on GR, you could say that geometry is bent by entropy. So, there is not an interference from gravity, because there is simply no gravity. It is exactly like if you used mirrors inside experiments to study coherence. The path is changed, but not the other states of the particle.

Let me put in other way. Entropy, here, is more like a new kind of mass.

Question: Why do things fall down according to General Relativity?

Answer: Elementary Wave behavior!

Gravitational time dilation causes the higher part of the wavepacket to oscillate
faster as the lower part and as a result the vertical spatial frequency increases,
corresponding to a continuous increasing momentum and (according to Fourier)
a downward accelerating wave packet.

Regards, Hans

 

[MTd2]

That doesn't look like general relativity, but some sort of argument to put quantum mechanics, with resort to wave mechanics, in the context. In general relativity gravity is caused because locally the shortest path between two points is parametrized by, and equated to, the momentum energy tensor. In the entropic case, by Jacobson, that is not equated with the energy tensor, but to where entropy is minimized.

Perhaps, here, you could apply your reasoning given that the highest part would be "hotter" than the lower and thus pushing the object.

 

[MTd2]

I still don't see why any interference pattern would be destroyed of the neutron experiment would be destroyed, given that no state relevant to the particles, in the experiment, was changed. Geometry follows the difference of perceived entropy in the environment, not the entropy in the object, in this case, the particles.

 

[Hans de Vries]

That doesn't look like general relativity, but some sort of argument to put quantum mechanics, with resort to wave mechanics, in the context. In general relativity gravity is caused because locally the shortest path between two points is parametrized by, and equated to, the momentum energy tensor. In the entropic case, by Jacobson, that is not equated with the energy tensor, but to where entropy is minimized.

Perhaps, here, you could apply your reasoning given that the highest part would be "hotter" than the lower and thus pushing the object.

It is General Relativity nevertheless.

(notwithstanding all the hand waving rubber sheet and "squeezing/sucking" divergent
coordinate lines metafores used to 'explain' why objects fall)

The behavior of matter is entirely determined by the Propagators/Green's functions and
the resulting wave behavior. Concepts like mass, energy and momentum (and thus the
momentum - energy tensor) become linked to space-time via wavelength and frequency.

Regards, Hans

 

[Hans de Vries]

Question: Why do things fall down according to General Relativity?

Answer: Elementary Wave behavior!

Gravitational time dilation causes the higher part of the wavepacket to oscillate
faster as the lower part and as a result the vertical spatial frequency increases,
corresponding to a continuous increasing momentum and (according to Fourier)
a downward accelerating wave packet.

Regards, Hans

This is closely identical to the acceleration resulting from the EM Lorentz force due
to a potential energy gradient. See for instance figure 11.4 which handles this
component of the Lorentz force derived from the Interacting Klein Gordon equation.

http://www.physics-quest.org/Book_Lorentz_force_from_Klein_Gordon.pdf

Figures 11.3 11.5 and 11.6 handle the other 3 components of the EM Lorentz force.Regards, Hans

 

[MTd2]

If you are talking about wave packets, you are attributing point matter a non local aspect . Maybe you can think like this in a small neighborhood of the particle, where space is flat, and you can approximate about the usual QFT or classical fields with potential. But, strictly talking about this about GR, you are already making extensions to concepts beyond it.

Anyway, that wouldn't change the experiment with the neutron interference.

 

[Hans de Vries]

If you are talking about wave packets, you are attributing point matter a non local aspect . Maybe you can think like this in a small neighborhood of the particle, where space is flat, and you can approximate about the usual QFT or classical fields with potential. But, strictly talking about this about GR, you are already making extensions to concepts beyond it.

Anyway, that wouldn't change the experiment with the neutron interference.

There is no problem extending propagators (in position space) to curved space time.
Massless propagators follow the curved coordinates. Yes it is not generally possible
to do this in an equivalent Fourier transformed coordinate system but one can derive
the wave behavior (in curved position space) in just the same way.

Regards, Hans

 

[MTd2]

Sure, you can, if the curved space is fixed. But if you are considering that such fields significantly change the background, you'd have to consider interactions with gravitons. If this thread was about Asymptotic Safety, I'd have no quarrels about this, and I'd agree with you, but this is about an "entropic force" that serves as the source of "gravity". But "gravity" here is just the shortest path to the lowest value of entropy, there is no graviton here.

 

[marcus]

MTd2 thanks for spotting this 5-page note by Jerzy Kowalski-Glikman
http://arxiv.org/abs/1002.1035
He's a major figure (co-organizer with Chris Meissner of the 2009 Planck Scale conference) and this note is, I believe, more important than its brevity would make you think.
Another chapter in the gravity-as-entropic-force story

A note on gravity, entropy, and BF topological field theory
Jerzy Kowalski-Glikman
5 pages
(Submitted on 4 Feb 2010)
"In this note I argue that the expression for entropic force, used as a starting point in Verlinde's derivation of Newton's law, can be deduced from first principles if one assumes that that the microscopic theory behind his construction is the topological SO(4,1) BF theory coupled to particles."

SO(4,1) is the deSitter group. John Baez contributed a thread on the deSitter group here at PF two or three years back. Connections with a lot of things. At that time I think Kowalski-Glikman was at Perimeter working on DSR. Just saw this, but have to run. I'll get back to it later.

EDIT: Been reading it. It involves a type of *topological defect* (occurring in GR along a curve) discovered by Misner in 1962 and called a "Misner string". This Misner string (not a string-theory string) can be thought of as a singularity, and is analogous to a "Dirac string" a defect which occurs in electromagnetism. The Misner string has associated with it an entropy, proportional to length---as if the entropy were distributed uniformly along the curve. This was unfamiliar to me. Have to look it up. Steve Carlip has a paper about the entropy of the Misner string.

 

[marcus]

You may remember all the Laurent Freidel and Etera Livine work around 2005 on spinfoams in 3D (Ponzano-Regge revisited) where they found that in that simplified situation matter was behaving as topological defects. E.g. like a conical singularity in space that persists thru time.

Apparently the "Dirac string" in electromagnetism is a singularity or defect where a gauge potential cannot be defined. The concept emerged in 1931. A dirac string does not have a definite location---sometimes described as a "fictitious curve". I think all that means is that it represents a topological defect in domain of definition of the potential.

There is a more natural mathematical description in terms of fiber bundles. I just looked at the Wikipedia
==quote http://en.wikipedia.org/wiki/Dirac_string ==
In physics, a Dirac string is a fictitious one-dimensional curve in space, conceived of by the physicist Paul Dirac, stretching between two Dirac magnetic monopoles with opposite magnetic charges, or from one magnetic monopole out to infinity. The gauge potential cannot be defined on the Dirac string, but it is defined everywhere else. The Dirac string acts as the solenoid in the Aharonov-Bohm effect, and the requirement that the position of the Dirac string should not be observable ...
<snippety snip>... can be understood in terms of the cohomology of the fibre bundle representing the gauge fields over the base manifold of space-time...
<snipsnip>... Informally, one might say that the Dirac string carries away the "excess curvature" that would otherwise prevent F from being a closed form, as one has that dF = 0 everywhere except at the location of the monopole.P.A.M. Dirac, "Quantized Singularities in the Electromagnetic Field", Proceedings of the Royal Society, A133 (1931) pp 60–72.
==endquote==

What I gather from several sources is that the Misner string (1962) is the GR analog of the Dirac string. What the Dirac string is to electromagenetism, the Misner string is to gravity.

This all comes (at least to me) as a slight shock. I wasn't expecting to be confronted by the topology of fiber bundles, not this week, at least. However I have been watching Jerzy Kowalski-Glikman since in 2004 and he has a lot of credibility with me. He's steady and doesn't hare about. I'm betting that this topological defect thing will not go away and that this short paper is so-to-speak opening the next chapter of this Jacobson-Verlinde story.

 

[qsa]

What I gather from several sources is that the Misner string (1962) is the GR analog of the Dirac string. What the Dirac string is to electromagenetism, the Misner string is to gravity.

another quote from
Jerzy Kowalski-Glikman
http://arxiv.org/abs/1002.1035


""In fact it turns out that a pointlike source must be
accompanied by a string extending from the source to
infinity.""

here is a quote from my post #28

ok, susskind does use light rays, but he uses light rays to represent a parton(particle) on the screen. Not far enough. I propose a ray from every point in space-time to every other point in space-time. The number of connections(two way) per two points(A,B) will represent the entropy(information) that passes between those two points. the entropy at those points is related to the probability of finding a particle at those points. The entropy at A will affect B and vis=versa in such way to change their probabilities(entropies) to indicate attraction(by lowering the pobabilities at those points, forcing an increase in probabilties in the neighbouring points). This technique works for all forces

In fact Dirac string and misner strings are the same and they represent ENERGY (very important statement). Moreover, all particles are made of them.

arXiv:hep-th/9903229v2 31 Mar 1999

I show that gravitational entropy can be ascribed to spacetimes containing Misner strings (the
gravitational analogues of Dirac strings), even in the absence of any other event horizon (or bolt)
structures. This result follows from an extension of proposals for evaluating the stress-energy of a
gravitational system which are motivated by the AdS/CFT correspondence.


I am glad that people are zeroing in. My Idea will eventually clear up all this mess. Funny, it is going to be in the sprit of Misner,Wheeler Thorne.. Gravitation (and everything ) as pre-calculus.

 

[Berlin]

another quote from
Jerzy Kowalski-Glikman
http://arxiv.org/abs/1002.1035


""In fact it turns out that a pointlike source must be
accompanied by a string extending from the source to
infinity.""

Sounds like C. Schiller to me..
Could it be, yes It could, something's coming, something good.

berlin

 

[tom.stoer]

I did not follow this blog in detail, so perhaps simply I overlooked it: Verlinde wrote a long comment regarding the logic of his paper in Lubos' blog: http://motls.blogspot.com/2010/01/erik-verlinde-comments-about-entropic.html

 

[ensabah6]

I did not follow this blog in detail, so perhaps simply I overlooked it: Verlinde wrote a long comment regarding the logic of his paper in Lubos' blog: http://motls.blogspot.com/2010/01/erik-verlinde-comments-about-entropic.html

If gravity is not a fundamental force, is quantizing it ala LQG the wrong approach to get the fundamental degrees of freedom?

 

[atyy]

If gravity is not a fundamental force, is quantizing it ala LQG the wrong approach to get the fundamental degrees of freedom?

Yes. However, it does not follow that if gravity has a temperature that it is not a fundamental force - I believe Ted Jacobson was in error in his final conclusion of his seminal paper - although that is the view I subscribe to on personal aesthetics.

 

[ensabah6]

Yes. However, it does not follow that if gravity has a temperature that it is not a fundamental force - I believe Ted Jacobson was in error in his final conclusion of his seminal paper - although that is the view I subscribe to on personal aesthetics.

String theory and LQG both model gravity as fundamental force, not emergent.

 

[atyy]

String theory and LQG both model gravity as fundamental force, not emergent.

Gravity is emergent in string theory. See the last slide where "AdS/CFT" is linked to "Emergent gravity" http://dao.mit.edu/~wen/talks/10IPMU.pdf.

 

[ensabah6]

Gravity is emergent in string theory. See the last slide where "AdS/CFT" is linked to "Emergent gravity" http://dao.mit.edu/~wen/talks/10IPMU.pdf.

In followup papers to Verlinde, it's been argued that Verlinde's derivation works only for 3 spatial dimensions, is this correct interpretation?

 

[atyy]

In followup papers to Verlinde, it's been argued that Verlinde's derivation works only for 3 spatial dimensions, is this correct interpretation?

I don't know. I don't really understand Verlinde's argument. I mainly think about this from Jacobson's and Padmanabhan's papers.

 

[ensabah6]

I don't know. I don't really understand Verlinde's argument. I mainly think about this from Jacobson's and Padmanabhan's papers.

THe claim that it implies 3D does exist, true or not I don't know

i.e
http://arxiv.org/abs/1002.0488

Hidden symmetries for thermodynamics and emergence of relativity

Liu Zhao

 

[tom.stoer]

If gravity is not a fundamental force, is quantizing it ala LQG the wrong approach to get the fundamental degrees of freedom?

Yes. However, it does not follow that if gravity has a temperature that it is not a fundamental force - I believe Ted Jacobson was in error in his final conclusion of his seminal paper - although that is the view I subscribe to on personal aesthetics.

I don't think so. If you want to make the entropic mechanism work there must be some degrees of freedom. Smolin uses Verlindes approach in the LQG context.

 

[Fra]

I don't think so. If you want to make the entropic mechanism work there must be some degrees of freedom. Smolin uses Verlindes approach in the LQG context.

IMHO, entropic arguments can be constructed even without observer independent degrees of freedom. As I see it, an observer indepedenent measures of disorder doesn't make sense. An entropic force (in my view) is just another word for an "expected tendency", and all expectations are biased. But as systems interact, one would expect equilibration of expectations encoded, so that objectivity is emergent. But the existence of this implies established equiblirum.

I think to complete this picture, one needs to understand in more detail the full emergence of spacetime in the sense of negotiations of difference expectations.

As I understand LQG, they are violating a mandatory intrinsic measurement perspective when trying to make a regular "quantum theory" of a reformulation of gravity - because where did the observer go? I've always understood that rovleli's idea is to do away with the observer, rather than understand how a generic observer evolves. His trick to do so, is to first acknowledge the observer, but then state that the relations between observers can only be communicated, and this communication structure is given by QM. I think this is a quite doubtful usage of QM formalism conceptually.

/Fredrik

 

[tom.stoer]

IMHO, entropic arguments can be constructed even without observer independent degrees of freedom.

...

As I understand LQG, they are violating a mandatory intrinsic measurement perspective ... - because where did the observer go?

I don't like reasoning that uses an observer like the Kopenhagen interpretation b/c you run into trouble with with Wigner's friend(s). LQG (as I understand Smolin's idea) implements the holographic principle, that means you have some fundamental degrees of freedom (SU(2) spin networks), they are inducing a holographic quantum theory on a surface (Chern-Simons gauge theory) which is what is observed in principle and from that you derive entropy and eventually force, the latter one being the new part of the story. So you replace the observer by a generic holographic argument. That's nice.

Now you can ask "why fundamental degrees of freedom?" As I said you need them simply b/c w/o them you are not able to produce entropy at all.

The next question is "why SU(2) spin networks?" That's a rather tricky question - to be honest I don't know how to motivate them w/o referring to symmetry structures of the 4-dim. manifold from which they are constructed (and which you want to derive eventually). If you want to try SU(3) spin networks, I guess the story regarding entropy would be essentially the same. The difference is of course the smooth spacetime which should emerge.

I think you should forget about the history of LQG and the construction of spin network states based on the Ashtekar / LQG approach. Starting point would simply be a spin network Hilbert space. What are the artefacts coming from GR?
- SU(2) symmetry: see above; to be explained
- Gauss constraint G: done; implemented in the phys. Hilbert space
- diffeo. / vector constraint D: the same
- Hamiltonian / scalar constraint H: ?

The Hamiltonian constraint is the only artifact knowing about the details of the Einstein-Hilbert action. So I would expect that it will emerge in some appropriate limit; higher order corrections etc. are definately allowed. Most of the results from LQG do not use H at all as it is still purely inderstood. So the whole framework is rather robsut and works w/o H or with a different H.

If this is reasoning is true the main question is: why SU(2)?

 

[atyy]

I don't think so. If you want to make the entropic mechanism work there must be some degrees of freedom. Smolin uses Verlindes approach in the LQG context.

Why can't the degrees of freedom be those of a quantized metric field?

 

[tom.stoer]

Why can't the degrees of freedom be those of a quantized metric field?

?

They are essentially a "quantized metric field".

There are some details like Ashtekars formulation, spin network states, induced Chern-Simons gauge theory on the horizon, ... but essentially the spin network is what remains from GR

 

[atyy]

?

They are essentially a "quantized metric field".

There are some details like Ashtekars formulation, spin network states, induced Chern-Simons gauge theory on the horizon, ... but essentially the spin network is what remains from GR

Yes, that's what I thought. I was saying Jacobson's conclusion is wrong, and Verlinde's too - I believe that by "emergent" they meant that it could not be a quantized metric field. If you read the end of Smolin's discussion, he acknowledges that this is what they meant, but that he disagrees with it, and that their work does not rule out that the degrees of freedom could be a quantized metric field, which would be "emergent" in a Smolin sense, but not a Jacobson or Verlinde sense.

 

[tom.stoer]

I have to check Verlindes reasoning. I would say that there must be "something". Perhaps his approach is generic enough not to specify "something", but w/o "something" there would be nothing at all :-)

I would say that Verlindes idea is to get rid of gravity as a fundamental entity b/c it always causes trouble. So perhaps his argument is viable with fundamental degrees of freedom (regradless what they are in detail), especially if the are not related to gravity.

If you look at it from a particle physics perspective there are enough degrees of freedom to carry entropy. If you look at it from Smolins LQG perspecive it's clear that he needs gravity b/c w/o gravity LQG simply fades away:-)

 

[Fra]

I don't like reasoning that uses an observer like the Kopenhagen interpretation b/c you run into trouble with with Wigner's friend(s).
...
So you replace the observer by a generic holographic argument. That's nice.
...
Now you can ask "why fundamental degrees of freedom?" As I said you need them simply b/c w/o them you are not able to produce entropy at all.
...
If this is reasoning is true the main question is: why SU(2)?

I stand by my position, and maybe I could expand later. But I certainly do not think the oldest copenhagen view is enough, since there the observer is a given classical realist structure. Wigner's friend is not a problem for what I have in mind. All I ask is that the action of the observer is entering the abstractions. The observer is not an inert information sink that can ask unlimited kinds and amounts of questions, and encode unlimited information.

With objecting to rovelli I'm not suggesting that the original classical realist observer is the way, I am thinking of a different way but which is closer to the measurement ideal that is the idea of doing away with the observer. To me, it's not possible to do away with the observer.

What one needs to define a measure of missing information, is distinguishable degrees of freedom. But if the distinguishable degrees of freedom are dependent on the observer, the constructed measure is intrinsically relative. I'm not saything there are no degrees of freedom.

About Smolins ideas, he seems to have had more than one. Some of smolins reasoning (I'm thinking CNS and reality of time, evolution of law), are at least in my interpretation in stark contrast to rovelli's RQM ideas.

Questions like why SU(2) are exactly the thinks that I think we could answer if we see it as an evolved equilibrium - rather than as a fixed eternal realist fact. I can't do this, but a possible pathway to doing it is at least visible to me.

I think the symmetries, that more or less are the signatures of the SM might be explainable as self-organising memory structures interact and where the invariants are preferred during different conditions. This means that maybe these symmetries are not fundamental, in the observer indepedent way. I rather think that they are (at best) uniqely expected in the statistical sense for a very constrained class of observers.

/Fredrik

 

[Fra]

About wigners friend, here is my simple reasoning of this.

For simplicity let's consider wigners friend to be somehow soldered onto the mesurement device, so that wigners friend and the apparatous are "one" :)

Then we have two observers.

Wigner and his friend/apparatous.

The fact that wigner doesn't know what has happened (until he speaks to his friend) means his ACTION reflects this. This means we predict an interaction between wigner and his friend. Ultimately this interaction is canceled when they reach an agreement.

This is an analogt but I mean this in a deeper sense, not just that wigner and his friend enter an intermittent argument, but that in a general example wigner and his friend could simply be system A and system B, both interacting with system C.

The idea here, predicts that there is an interaction even between observers!

/Fredrik

 

[czes]

In 1968 Sakharov wrote the the gravity isn't a fundamental force and it is a secondary effect.
Marcus sent me a good link of 2010:
http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.5004v2.pdf
It is a long paper but it is good to read a summary.

It seems for me that there isn't volume nor surface either. It is just a product of the information and a product seem to show an area.
I prefer probability ρ(x) = |ψ(x, t)|*|ψ(y, t)| instead of ρ(x) = ψ (x, t)^ 2
as in Copenhagen Interpretation.
This product of the wave functions shows interesting properties:
Tp / T(x) * Tp / T(y) = -a Fg / Fe
(lp / l x ) * (lp / l y ) = -a Fg / Fe
where Tp is a Planck time, lp is Planck length, lx, ly are Compton wave lengths , a (alfa) is fine structure const. Fg -gravitational interaction, Fe -electromagnetic interaction.

In a computer the information creates a program of the image just in an interaction not in a define space.

 

[tom.stoer]

Let's use an even simpler approach - "shut up and calculate".

We agree that every observer making measurements does not "see" the subsystem itself but only the 2-dim. screen of the subsystem. I don't care how the observer itself is represented as he is located outside the subsystem :-)

 

[Fra]

We agree that every observer making measurements does not "see" the subsystem itself but only the 2-dim. screen of the subsystem. I don't care how the observer itself is represented as he is located outside the subsystem :-)

Would it be unreasonable to assume that the representation of the observer, would impose constraints on possible inferred theories about the subsystem itself? - and hence constrains on it's possible actions?

Although the 2-dim screen defines the distinguishable events, further structure can emerge on the observer side of the screen as histories of events accumulate and organise.

Maybe one can find an argument where certain representations are simply more likely to be preserved, and that these represtations have certain symmetries. This is the kind of first principle explanation of the symmetries I seek.

So the inconsistencies of the observer bias, that cricits points out, are turned around and used as interactions that work as a selective pressure to evolve the observer. Then consider that even a particles can be thought of as an observers, one could understand the appearance of preferred particle hierarchies in this sense as expected "optimal representations" rather than "fundamental representations".

/Fredrik

 

[czes]

Let's use an even simpler approach - "shut up and calculate".

We agree that every observer making measurements does not "see" the subsystem itself but only the 2-dim. screen of the subsystem. I don't care how the observer itself is represented as he is located outside the subsystem :-)

And each measurement located on the screen blocks the entropy of the subsystem. Isn't it ?

 

[czes]

A system is in an equilibrium if it absorbs and emits the same energy.
For example:
A planet surface is a sphere and if we go deeper the subspheres are smaller proportionally to a squared distance from the surface. Therefore the entropy dS=Q/T might be balanced if the temperature T increases proportional to the squared distance from the surface according to dS=kA/4 L^2
A=area of the subsystem
L= Planck length

It seems strange how the systems with different temperature may be in thermal balance but it is in our Earth and we use it by pumping cold water into thermal deep hole and taking a warm water.

 

[Hans de Vries]

Question: Why do things fall down according to General Relativity?

Answer: Elementary Wave behavior!

Gravitational time dilation causes the higher part of the wavepacket to oscillate
faster as the lower part and as a result the vertical spatial frequency increases,
corresponding to a continuous increasing momentum and (according to Fourier)
a downward accelerating wave packet.

Regards, Hans

A sort of coincidence but this role of the wave behavior in gravitational acceleration is
now proved with a 10,000 fold improvement: better as one part in 100 million (7x10-9)

Atom Interferometer Provides Most Precise Test Yet of Einstein's Gravitational Redshift

http://www.sciencedaily.com/releases/2010/02/100217131125.htm

http://www.sciencedaily.com/images/2010/02/100217131125.jpg

It's pure Mathematics: A wave packet in a potential field (which causes different
frequencies at different places) will accelerate in the direction were the frequency
is lower. This is just the same as the acceleration of a charged wave packet in
an electric potential field (see my book Section 11.6 and shown in figure 11.4)

EM Lorentz force derived from Klein Gordon's equation

http://www.physics-quest.org/Book_Lorentz_force_from_Klein_Gordon.pdf


Regards, Hans