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

[atyy]

Surely you meant the Visser comment as a joke,

Of course! Besides, I'm protestant, so being excommunicated is a good thing to me!

but it shows a contrasting attitude which allowed me to reply. In any case Visser is not the topic.

Actually I think Visser's ethos is very relevant. The topic at hand is "emergent or not?". I would say AS and LQG (non-Oriti, non-Thiemann LQG) explore the possibility that gravity is not emergent, while strings, Volovik, Visser, Wen, Horava and Markopoulou are emergent - with really only strings and AdS/CFT providing a concrete and working example of emergence so far.

So is gravity "entropic" in strings or AdS/CFT? The comment about "entropic forces" brings to mind the Casimir effect, which is a "fluctuation driven" force, like an "entropic force" except the fluctuations are quantum, not thermal. One of the oldest "emergent" viewpoints is Sacharov's, in which gravity is induced by quantum effects. I'm not sure whether induced gravity is really "fluctuation driven", but I remember an interesting comment about this from Strominger "If gravity is induced [9], which means that Newton’s constant is zero at tree level and arises as a one loop correction, then the entanglement entropy is responsible for all of the entropy, and reproduces the area law with the correct coefficient [7,10]. This might in fact be the case in string theory, where the Einstein action is induced at one loop from open strings, but this notion has yet to be made precise. Recent progress [11] has revealed a rich holographic relation between entanglement entropy and minimal surfaces including horizons." Ref [9]=Sacharov, [7]=Jacobson http://arxiv.org/abs/0906.1313

 

[ensabah6]

*shrug* Some people say this has already been shown.

Note that Smolin did not say that the correct largescale limit had not been shown. He said that using his particular thermodynamics argument he did not show it.

You could write a simple email letter to two people: Lee Smolin and his associate at Perimeter, Laurent Freidel. You could ask:

"Has it been shown that classical spacetime emerges from LQG?"

I don't know what they would answer. They might both say Yes, or they might both say No, or they might hold different opinions. I wonder.

They are both busy people. It would not be fair to ask for more than a Yes/No answer.
One would have to be courteous and keep it simple.

I see no reason for anyone to do what you suggest.
In this paper Smolin is not discussing who else has proved what.

I see that Wolfgang basically shared my concern

wolfgang says:
January 23, 2010 at 6:14 am

I do not find Lee Smolin’s argument very convincing.

Verlinde considers the change in entropy dS for displacements dx assuming a holographic principle. But in his calculation he implicitly assumes the geometry of a smooth and indeed flat geometry.

There is of course nothing wrong about that, but if Lee Smolin wants to use this argument, then he has to first show that there is a reasonable limit of loop quantum gravity, which reproduces this smooth and (almost) flat spacetime and I don't see that.​

 

[marcus]

... The topic at hand is "emergent or not?". I would say AS and LQG (non-Oriti, non-Thiemann LQG) ...

Atyy that is not the topic and what you mean by "emergent" appears to be somewhat strange--vague possibly, or ill-defined.

The word "emerge" taken out of the context of a specific model is used in so many senses by the community that, in the abstract, it is almost meaningless.

Our topic of discussion is Verlinde's paper and some of the immediate reaction to it (such as Smolin's response).

As for "emergence", it is a big issue to a lot of people whether or not it can be shown that the geometry of classical spacetime emerges from the spinnetwork and spin foam descriptions. For the LQG program to be successful, it must be shown that classical geometry is emergent from LQG descriptors or degrees of freedom.
LQG is very similar to the CDT approach of Renate Loll's group. They recently showed that in fact a de Sitter universe is emergent from the CDT path integral.

You seem to have sorted different approaches out in an arbitrary almost frivolous way! You put Thiemann-LQG on one side of an imaginary fence and some other undesignated LQG (Lewandowski-LQG? Freidel-LQG?) on the other side. Your classification of Horava I can make no sense of. His approach seems closer to Reuter's Asymptotic Safety than to, say, XG Wen. Wen, on the other hand, seems closer to Loll, Oriti, and Rovelli.
===================

As I see it, your distinction "emergent or not" is not clear and not relevant to the events we are watching. The primary distinction that is operating here is 4D versus extra dimensions.

That's what's causing the shock waves. Horava used to stringify, his new approach is 4D.
Verlinde used to stringify, his new approach is 4D.

Most of the other approaches you mentioned (Wen, Thiemann, Oriti, LQG in general with it's spinnetwork spinfoam and GFT formalisms, Reuter...) plus the Loll CDT approach you didn't mention, are all focused on 4D.

I think that's the first cut you need to make, in order to parse the situation. (But I'll keep thinking about the "emerge-or-not" distinction and see if I can make sense of it.)

 

[atyy]

Atyy that is not the topic and what you mean by "emergent" appears to be somewhat strange--vague possibly, or ill-defined.

I'm just reacting to the part you highlighted in blue in your post #31.

You seem to have sorted different approaches out in an arbitrary almost frivolous way! You put Thiemann-LQG on one side of an imaginary fence and some other undesignated LQG (Lewandowski-LQG? Freidel-LQG?) on the other side. Your classification of Horava I can make no sense of. His approach seems closer to Reuter's Asymptotic Safety than to, say, XG Wen. Wen, on the other hand, seems closer to Loll, Oriti, and Rovelli.

Well, you may disagree, but this is definitely not frivolous.

 

[marcus]

wolfgang says:
January 23, 2010 at 6:14 am
... But in his calculation [Verlinde] implicitly assumes the geometry of a smooth and indeed flat geometry...​

Verlinde's paper is heuristic. It is frankly preliminary and handwaving---to get the ideas across, not to be rigorous. I see no indication that a rigorous proof would NEED to assume flat geometry. The future will tell.

It's common practice to present new ideas with sketchy proofs, and then fill in the gaps later. If you want to make predictions, you are free to prophesy that Verlinde will forget this idea and will not write followup papers filling in the gaps and expanding and generalizing.
You could prophesy that, but I think you'd turn out to be wrong.
I think he will fill in, make rigorous, extend results.It sounds to me like Wolfgang is just miffed about something. Should Smolin have waited and not pointed to some interesting implications of Verlinde's idea? Should he have waited until Verlinde dotted eyes and crossed tees? Of course not! Smolin's paper is ALSO preliminary and heuristic and he is quite frank about its assumptions and limitations. Wolfgang appears displeased that Smolin did not justify one of his assumptions. Smolin simply made the assumption and moved ahead to see where it led. Fair enough, I'd say. Too bad Wolfgang didn't like it.

 

[ensabah6]

There is one exception though: the argument eliminates all theories with higher dimensions[/B]. In my view, the only conclusion about new physics that can be drawn from the Jacobson/Verlinde argument is: space-time is emergent and is made of microscopic degrees of freedom that fluctuate in 3+1 dimension.

The paper by Verlinde does not change the situation at all. Except that it confirms that superstrings are not the right microscopic degrees of freedom, because they do not live in 3+1 dimensions. But Peter would not call this a new result

Frank says:
On the other hand, this does not tell anything new, as I argued in my previous comment. The reason that Lubos is against the connection between gravity and entropy is clear: he understands that the Jacobson/Verlinde argument undermines string theory, because it excludes higher dimensions. Worse, through Verlinde’s simplification for Newtonian gravity, EVERY physicist now understands that higher dimensions are out! This is Lubos’ nightmare: a simple argument that suggests that string theory is wrong. Even worse, the argument is made by one of the world’s most distinguished string theorists! We can all guess what will happen: Lubos will start discrediting the argument with the same anger with which he discredits global warming. Watch the show.

==endquote==

http://www.math.columbia.edu/~woit/wordpress/?p=2673&cpage=1#comment-52658
http://www.math.columbia.edu/~woit/wordpress/?p=2673&cpage=1#comment-52659

This result, and the earlier paper below seem to be providing strong evidence against higher dimensions -- perhaps string theory is physically wrong. More research is obviously needed, and I'm open to LHC finding evidence of SUSY and maybe protons do decay. http://arxiv.org/abs/0811.1614
Dark Energy, Inflation and Extra Dimensions
Paul J. Steinhardt, Daniel Wesley
26 pages, Physical Review D
(Submitted on 11 Nov 2008 )
"We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of compactifications; and a dark energy phase consistent with observations is only possible if both Newton's gravitational constant and the dark energy equation-of-state vary with time. If the theory violates the NEC, inflation and dark energy are only possible if the NEC-violating elements are inhomogeneously distributed in the compact dimensions and vary with time in precise synchrony with the matter and energy density in the non-compact dimensions. Although our proofs are derived assuming general relativity applies in both four and higher dimensions and certain forms of metrics, we argue that similar constraints must apply for more general compactifications."

He works both in the NEC case and in the NEC-violating case. Gets interesting results either way.

 

[marcus]

I'm just reacting to the part you highlighted in blue in your post #31...

Thanks for explaining. I will look back at my post #31:

Verlinde's blog of 15 January ...

==quote==
Entropic forces and the 2nd law of thermodynamics
15/01/10 02:21
Let me address some other confusions in the blog discussion. The fact that a force in entropic does not mean it should be irreversible. This is a complete misunderstanding of what it means to have an entropic force. This is why I added section 2 on the entropic force. For a polymer the force obeys Hooke's law, which is conservative. No doubt about that.

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

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

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

By the way, it is true that the total energy of a system of two masses is given by the total mass. But if one then takes the entropy gradient to be proportional to the reduced mass, one again recovers the right force. I thought of putting that in the paper, but I think it is kind of trivial. This confusion was not to difficult to solve.

Another point that may not be appreciated is that the system is actually taken out of equilibrium. If everything would be in equilibrium, the universe would be a big black hole, or be described by pure de Sitter space. Only horizons, no visible matter. If a system is out of equilibrium, there is not a very precise definition of temperature. In fact, different parts of the system may have different temperatures. There is no problem also with neutron stars. In fact, physical neutron stars do not have exact zero temperature. But the temperature I use in the paper is one that is associated with the microscopic degrees of freedom, which because there is no equilibrium, is not necessarily equal to the macroscopic temperature.

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

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

Similarly, gravitons can be useful, and in that sense exist as effective "quasi" particles. But they do not exist as fundamental particles.
==endquote==
(from blog http://staff.science.uva.nl/~erikv/page18/page18.html )

Yes! His example illustrates how gravitons are in LQG! In LQG gravitons do not exist on a fundamental level. There is no mathematical object in the LQG corresponding to a graviton. But by taking special care, one can calculate the graviton propagator. The propagator/n-point function that applies in situations where the concept is applicable.
This was done by Rovelli's group around 2006-2007 to show that gravitons are emergent in LQG.

Gravity is emergent in LQG by your own definition of "emergent", it would seem.

That was partly why I highlighted that part of post #31. It shows, among other things, that Verlinde and LQG are in the same boat, or on the same page...however you want to say it

 

[marcus]

This result, and the earlier paper below seem to be providing strong evidence against higher dimensions -- perhaps string theory is physically wrong...

Yes possibly it is physically wrong. I was glad to be reminded of the Steinhardt-Wesley paper. It is another trouble-maker for extra dimensions. After all we observe accelerated expansion. They argue that inflation (which cosmologists tend to rely on) as well as accelerated expansion are both incompatible with extra dimensions, under reasonable assumptions and without extensive fine-tuning. I'll just quote your post:

http://arxiv.org/abs/0811.1614
Dark Energy, Inflation and Extra Dimensions
Paul J. Steinhardt, Daniel Wesley
26 pages, Physical Review D
(Submitted on 11 Nov 2008 )
"We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of compactifications; and a dark energy phase consistent with observations is only possible if both Newton's gravitational constant and the dark energy equation-of-state vary with time. If the theory violates the NEC, inflation and dark energy are only possible if the NEC-violating elements are inhomogeneously distributed in the compact dimensions and vary with time in precise synchrony with the matter and energy density in the non-compact dimensions. Although our proofs are derived assuming general relativity applies in both four and higher dimensions and certain forms of metrics, we argue that similar constraints must apply for more general compactifications."

He works both in the NEC case and in the NEC-violating case. Gets interesting results either way.

I agree, Ensabah. The results in Steinhardt-Wesley are quite interesting. What leaves a question in my mind is that they did not continue with a follow-up paper. It has been over a year now. I wonder if we will eventually get a follow-up.

The dilemma for Steinhardt is that his own pet cosmology is based on extra dimensions and was intended as an alternative to inflation. It was supposed to be string-friendly because it dispensed with the need for inflation.
To the extent that he still cherishes his own brain-child (the ekpyrotic or cyclic Steinhardt-Turok universe from around year 2000) it must not feel good to be proving no-go theorems that many people take as discrediting extra dimensions.

 

[ensabah6]

Thanks for explaining. I will look back at my post #31:



Yes! His example illustrates how gravitons are in LQG! In LQG gravitons do not exist on a fundamental level. There is no mathematical object in the LQG corresponding to a graviton. But by taking special care, one can calculate the graviton propagator. The propagator/n-point function that applies in situations where the concept is applicable.
This was done by Rovelli's group around 2006-2007 to show that gravitons are emergent in LQG.

Gravity is emergent in LQG by your own definition of "emergent", it would seem.

That was partly why I highlighted that part of post #31. It shows, among other things, that Verlinde and LQG are in the same boat, or on the same page...however you want to say it

I take it that in string theory, gravitons ARE fundamental particles. I'ved asked a similar question about composite particles, but if SUSY is true, and gravitons are only quasi-particles, not fundamental particles, would there be a SUSY-analogue of graviton, the gravitino fermion?

If gravitons are not fundamental particles but string theory says they are, does this mean string theory is wrong?

 

[ensabah6]

Yes possibly it is physically wrong. I was glad to be reminded of the Steinhardt-Wesley paper. It is another trouble-maker for extra dimensions. After all we observe accelerated expansion. They argue that inflation (which cosmologists tend to rely on) as well as accelerated expansion are both incompatible with extra dimensions,
under reasonable assumptions and without extensive fine-tuning. I'll just quote your post:
I agree, Ensabah. The results in Steinhardt-Wesley are quite interesting. What leaves a question in my mind is that they did not continue with a follow-up paper. It has been over a year now. I wonder if we will eventually get a follow-up.

The dilemma for Steinhardt is that his own pet cosmology is based on extra dimensions and was intended as an alternative to inflation. It was supposed to be string-friendly because it dispensed with the need for inflation.
To the extent that he still cherishes his own brain-child (the ekpyrotic or cyclic Steinhardt-Turok universe from around year 2000) it must not feel good to be proving no-go theorems that many people take as discrediting extra dimensions.

The only experimental predictions I've heard extra dimensions might suggest is deviations of Newton's law below the milimeter scale, which is hard to show. I do wonder if these no-go theorems affect braneworlds to KKLT compactification schemes.

 

[atyy]

Gravity is emergent in LQG by your own definition of "emergent", it would seem.

That was partly why I highlighted that part of post #31. It shows, among other things, that Verlinde and LQG are in the same boat, or on the same page...however you want to say it

Perhaps you are right. My definition of emergent is not AS. I've typically put LQG with AS since that seems to be the ethos of LQG, but I do think the mathematics of LQG (Oriti, Thiemann) is heading away from AS, so perhaps the graviton is emergent in LQG in the sense that LQG and AS will turn out to be radically different theories.

 

[marcus]

... I've typically put LQG with AS since that seems to be the ethos of LQG, ...

It's odd you should see it that way, Atyy. I have never seen LQG as in any way similar to AS!
As far as ethos, the two seem to me quite alien to each other.

It's a major unmet challenge to reconcile them.

 

[atyy]

It's odd you should see it that way, Atyy. I have never seen LQG as in any way similar to AS!
As far as ethos, the two seem to me quite alien to each other.

It's a major unmet challenge to reconcile them.

The reason I've put them together is that LQG emphasizes diffeomorphism invariance, and to me the most general generally covariant Lagrangian of AS (eg. Weinberg's paper) is the very embodiment of diffeomorphism invariance.

 

[marcus]

The reason I've put them together is that LQG emphasizes diffeomorphism invariance, and to me the most general generally covariant Lagrangian of AS (eg. Weinberg's paper) is the very embodiment of diffeomorphism invariance.

Ah! That is a point of similarity.

For me what stands out is that AS is totally about the renormalization group. The running of constants with scale. LQG has never come to grips with renormalization, or running. It almost does not even recognize these (which are at the heart of AS).

That, and the fact that Reuter's AS---which unlike Weinberg's you can actually CALCULATE with---is not manifestly background independent. Something that annoys and obsesses Reuter so that he is always trying to fix it. But LQG starts with background independence.

So prima facie (first sight, on the face) each approach fails to encompass the foremost principle of the other. Bridging and reconciling is going to take a lot of work, which has been discussed but IMO hasn't been done yet.

Loll tends to be rather complacent about the fact that her CDT has explicit diffeomorphism invariance and is also somehow OK with renormalization (I don't completely understand why.) And yet it seems to me that even with Loll CDT the ethos is entirely different from Reuter AS. Loll's mainstay a path integral over simplicial geometries. Reuter has neither simplicial geometries nor a path integral. He has a metric, which of course Loll does not.

Offhand I would say that diffeomorphism invariance is too widely shared among disparate approaches to serve as a one-shot classifier tool.

 

[atyy]

Loll tends to be rather complacent about the fact that her CDT has explicit diffeomorphism invariance and is also somehow OK with renormalization (I don't completely understand why.) And yet it seems to me that even with Loll CDT the ethos is entirely different from Reuter AS. Loll has a path integral over geometries. Reuter does not.

Loll is very close to AS. The only difference is that Loll uses gauge invariant variables, while Reuter works in a specific gauge. Loll has also tended to interpret her results as evidence of a fixed point in the renormalization flow. Essentially, if there is a fixed point, then the fixed point controls the scaling of various properties near it. Loll looks at the scaling of some properties, and thinks these are due to the influence of a fixed point. This is rather handwavy, and Loll admits that maybe the fixed point isn't that of AS, but maybe of Horava or Shaposhnikov - which are actually emergent, by definition of emergent=not AS.

But why do you think LQG and AS should be reconciled? If the graviton is emergent in LQG, then surely LQG and AS should not be reconciled (I believe Verlinde's definition of emergent is not AS, since the graviton - or more accurately, a field with diffeomorphism invariance, whose quanta in the linear approximation are called gravitons - is fundamental in AS).

 

[ensabah6]

Using Verlinde's argument, Smolin shows Loop implies Newton's law of gravity in the appropriate limit.

Verlinde's recent paper has thus supplied LQG with a missing piece of the puzzle.
Smolin's paper presents his perspective on the significance of the Jacobson 1995 paper and of Verlinde's recent contribution---the basing of spacetime geometry on thermodynamics (basing gravity on entropy.)

http://arxiv.org/abs/1001.3668
Newtonian gravity in loop quantum gravity
Lee Smolin
16 pages
(Submitted on 20 Jan 2010)
"We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity when boundaries are imposed on a quantum spacetime."

What would additional work would Smolin or Verlinde need to show that GR can be recovered in appropriate limit and setting?

 

[marcus]

...

But why do you think LQG and AS should be reconciled? If the graviton is emergent in LQG, then surely LQG and AS should not be reconciled (I believe Verlinde's definition of emergent is not AS, since the graviton - or more accurately, a field with diffeomorphism invariance, whose quanta in the linear approximation are called gravitons - is fundamental in AS).

This post #65 is very interesting. You are again opening up questions for me or causing me to look at something differently. Of the top of my head, I'd say that I would not expect LQG to be reconciled with Reuter's AS specfically (warts and all). I would be interested to know if it could be made compatible with the running of G with scale.
Can the renormalization flow be somehow made meaningful in the LQG context?

I am happy that LQG has no gravitons (or rather that their propagator only emerges with a lot of work, and only in a certain limited controlled case). If I want the theory to make contact with renormalization, scale-dependence, do I have to buy the graviton to get that? If so, no deal.

Just a superficial reaction, and of course it isn't up to me---my subjective preference counts for nothing.

 

[marcus]

What would additional work would Smolin or Verlinde need to show that GR can be recovered in appropriate limit and setting?

If you are interested in recovering GR you might look back at Ted Jacobson's paper. He concerned himself with recovering GR starting from thermodynamics and holo.

In your case I wouldn't bother with either Smolin or Verlinde's papers. I'm not sure they are even relevant. I think in both of them are non-relativistic and aim at getting Newton's Law. I don't see any point to your question. It's like trying to "add something" in order to "fix" something that aims to prove X, in order to make it prove Y. Maybe I'm wrong, but it doesn't seem to make sense.

I think it's great that they can prove Newton's law of gravity in a non-relativistic setting! Shouldn't everybody should be able to do this, quite separately from recovering GR? It's a worthy goal.

 

[atyy]

I am happy that LQG has no gravitons (or rather that their propagator only emerges with a lot of work, and only in a certain limited controlled case). If I want the theory to make contact with renormalization, scale-dependence, do I have to buy the graviton to get that? If so, no deal.

It'll be interesting to see. Oriti, Gurau, Freidel, Rivasseau are working on GFT renormalization, which I think is pushing in a direction away from AS (I don't think the GFT fixed point will be related to an AS fixed point, if it exists - Rivasseau himself said in his talk that any such link is not obvious). A separate development is that Thiemann's latest view seems to be that diffeomorphism invariance is not exact. On the other hand, Bahr and Dittrich have pointed out that if AS is true in Regge theory, then the Hamiltonian constraint in the corresponding canonical formulation can be solved. If this lesson extends to LQG, then LQG requires AS.

 

[ensabah6]

I don't see any point to your question. It's like trying to "add something" in order to "fix" something that aims to prove X, in order to make it prove Y. Maybe I'm wrong, but it doesn't seem to make sense.

I think it's great that they can prove Newton's law of gravity in a non-relativistic setting! Shouldn't everybody should be able to do this, quite separately from recovering GR? It's a worthy goal.

If Verlinde or Smolins results do not apply in the non-relativistic setting, strong gravitational field, but instead gives results that are completely at odds with what GR predicts and has been experimentally confirmed, then his insights have very limited applicability. Spin-2 gravitons can also reproduce Newton's gravity in the weak field limit.

 

[tom.stoer]

One has to make very clear what is meant by gravitons:
- physical particles that can be detected experimentally?
- certain states in a Hilbert space?
- idealized plane wave states in a Feynman diagram used to do pertutbation theory?
- ...

One must not mix the plane-wave concept with something like physical existence. The plane waves are a mathematical tool that does not directly fit to experiments. In experiments you detect localized particles, whereas planes waves are certainly not localized. So the problem you observe in QG is implicitly there in ordinary QFT as well, but you are used to hide it behind hand waving arguments going back to the Kopenhagen interpretation.

I don't think that renormalization group theory depends on the existence of plane wave solutions! Neither do Feynman diagrams; they can e.g. be formulated with distorted waves, even if this is less well-known and more complicated.

Look at QCD: you can formulate QCD (at least in a certain regime - e.g. deep inelastic scattering) based on gluons, but that concepts FAILES completely when it comes to hadron physics.

So I don't see why we should insist on a theory that relies on a perturbative concept only. If string theory can be completed non-perturbatively then I expect that something different from plane wave state must emerge.

 

[atyy]

One has to make very clear what is meant by gravitons

Yes, that's why I take language about a theory in which gravitons are fundamental to be shorthand for a theory whose fundamental high energy action is based on the metric field and has the property of general covariance.

 

[tom.stoer]

so if we agree that plane wave states are useless in quantum gravity ... what are gravitons?

 

[marcus]

Yes, that's why I take language about a theory in which gravitons are fundamental to be shorthand for a theory whose fundamental high energy action is based on the metric field and has the property of general covariance.

This is somewhat of a hodgepodge of criteria. You are trying to say "non-emergent" I think. But general covariance does not belong in the list.
Lots of very different theories can have diffeo invariance aka general covariance. Not a very discriminating criterion.

In LQG, for example, gravitons are definitely not fundamental, you have to artificially "flatten" the theory to force a graviton propagator to appear. LQG is kind of a paragon of an emergent spacetime theory. Which is why the LQG community is already all over the Verlinde paper.

We already have a paper by Smolin and a new one by Modesto that came out today And Verlinde's paper has not even been out 3 weeks.

There is a backlog of LQG stuff having to do with holography black holes and thermodynamics, Smolin, Ted Jacobson, Kirill Krasnov, Rovelli. Modesto draws on this and on his own work with the LQG black hole.

so if we agree that plane wave states are useless in quantum gravity ... what are gravitons?

I think you may be suggesting gravitons are a useful mathematical convention. Useful in certain limited circumstances. Sometimes a good way to think about propagating disturbances in the field.

Not sure what you have in mind, so I will state that as my opinion only. In any case we don't have to include gravitons in the discussion.

 

[Physics Monkey]

Should we really think of LQG of a theory of emergent spacetime? I already argued that Verlinde has background dependence in much of his paper. LQG is considerably more background independent that Verlinde's proposal at this point, but even LQG is deeply rooted in the mathematics of manifolds (without a prior metric of course). I'm skeptical of calling a theory that starts from manifolds a theory of emergent spacetime. Perhaps we will understand later that manifolds weren't essential, that it the manifold will fall away as physically irrelevant, but I don't think anyone is in a position to claim that right now in LQG. Or am I wrong?

 

[Physics Monkey]

so if we agree that plane wave states are useless in quantum gravity ... what are gravitons?

I wouldn't say plane wave states are useless. On a conceptual level they allow you to see that a string coupled to a non-trivial background metric is like a string moving in a coherent state of its own flat space gravitons. The graviton vertex operator is precisely a plane wave state as is appropriate in flat space. I'm not claiming that this is the only way to see the connection, only that this way is simple and useful. Of course, one has to be careful about the difference between an exact plane wave state and a sharply peaked (in momentum) wavepacket, but I think this subtle distinction is understood.

 

[marcus]

Should we really think of LQG of a theory of emergent spacetime? I already argued that Verlinde has background dependence in much of his paper. LQG is considerably more background independent that Verlinde's proposal at this point, but even LQG is deeply rooted in the mathematics of manifolds (without a prior metric of course). I'm skeptical of calling a theory that starts from manifolds a theory of emergent spacetime. Perhaps we will understand later that manifolds weren't essential, that it the manifold will fall away as physically irrelevant, but I don't think anyone is in a position to claim that right now in LQG. Or am I wrong?

The theory starts with a manifold but moves on to dispense with it. It does not assume the physical existence of a continuum. Nor does it assume the physical existence of loops, spin networks, foams, 4-simplices or tetrahedra.
This is an interesting and fairly high-level question which Rovelli gave the definitive word on last summer in about twelve slides of a May 2009 seminar talk.
http://relativity.phys.lsu.edu/ilqgs/panel050509.pdf

This file begins with a dozen or so slides from Ashtekar, and then a series from Carlo, and finishes with some from Laurent Freidel. It was not prepared for wide distribution but is primarily a discussion among a small group of colleagues about issues of ontology and interpretation which arose two weeks earlier when John Barrett (Nottingham, UK) gave a talk to the same group.

My crude summary: LQG is not talking about what Nature is "made of" but about how Nature responds to measurements.
It uses various formalisms---the simplices of Group Field Theory (GFT), the networks and foams of the canonical and covariant versions of LQG---as alternative ways of imagining and calculating which the researchers have discovered are consistent.

So one is looking for deeper systems of description, a deeper layer of degrees of freedom from which familiar spacetime emerges. But one does not re-ify these deeper d.o.f.
In LQG the geometry of spacetime is certainly emergent, but in LQG one does not, at least as yet, say from what it is emergent.

The best is to read the dozen or so slides, because they say more than the one-slide summary at the end. But I will quote the summary slide:

==Rovelli 5 May 2009 seminar slide 12==
Summary

1. “Loopy, polymer, triangulated” spaces are helps for intuition, not descriptions of reality. No incompatibility between them.

2. In quantum gravity, flat space is neither many small Planck scale things not few big large-spin 4 simplices. It is a process with a transition amplitudes. We can represent it with different pictures, according to the measurements we are considering, the calculation scheme, and the approximation scheme.

3. We must compute diff-invariant amplitudes, including when dealing with excitations over a flat space. The only way of doing so that I know is to code the background into the boundary space. (Boundary formalism.)

4. We need an approximation scheme. For scattering amplitudes, we can truncate degrees of freedom to a finite number, very much like is done in computing in QED and QCD. (Vertex expansion.)

5. Regime of validity of the vertex expansion: processes whose size L is not much larger than the minimal relevant wavelength λ. Includes the large distance behavior of the scattering amplitudes in coordinate space.

6. At given ratio λ/L, the Large-spin Limit captures processes at scales larger than the Planck length. It gives the semiclassical limit.
→ This does not mean that flat space is “made out of large 4-simplices”!
→ It means that we describe measurements performed at scales larger that the
Planck scale, at low order.
==endquote==

Some of these points specifically address questions raised in the discussion of John Barrett's talk, two weeks earlier.

 

[atyy]

Should we really think of LQG of a theory of emergent spacetime? I already argued that Verlinde has background dependence in much of his paper. LQG is considerably more background independent that Verlinde's proposal at this point, but even LQG is deeply rooted in the mathematics of manifolds (without a prior metric of course). I'm skeptical of calling a theory that starts from manifolds a theory of emergent spacetime. Perhaps we will understand later that manifolds weren't essential, that it the manifold will fall away as physically irrelevant, but I don't think anyone is in a position to claim that right now in LQG. Or am I wrong?

One of the LQG-related formalisms I find fascinating is group field theory. Apparently, all spin foams are related to some GFT - Rovelli likens this to the Maldacena duality http://relativity.livingreviews.org/Articles/lrr-2008-5/ .

A GFT has a manifold and fixed metric. "Quantum Gravity is described by an (almost) ordinary QFT, although with peculiar structure, and one that uses even a background metric "spacetime" (although here interpreted as an internal space only), given by a group manifold ... http://arxiv.org/abs/0903.3970 "

 

[marcus]

A GFT has a manifold and fixed metric...

That could be misleading if one gets the impression that the manifold used in GFT somehow represents spacetime.

The manifold is the cartesian product of N copies of a Lie group G. Think of a fixed geometrical structure like a simplex, or a spin network with N edges. To complete the specification of a geometry this structure needs to be labeled with, say, elements of G.
One can represent "all the possible labelings" by the cartestian product G^N.

One way to think of quantizing "all the possible labelings" is to construct a quantum field theory on G^N. That is a field theory defined on a group manifold---called a group field theory or GFT.

The GFT construction is widely applicable---to covariant LQG (spin foams) and to simplicial quantum gravity (e.g. Regge) and I forget what else. LQG papers use GFT for calculation.
Obviously the group manifold of all possible labelings has no direct relation to what we live in and move around in and experience as space and time.

The fact that GFT techniques of calculation are applied to simplicial QG, and that Rovelli for example, uses GFT uses GFT for spin foam calculations, does not mean that any theory thinks the world is made of simplices, or that the a cartesian product of groups exists in nature. I tried to suggest this a couple of posts back, where I quoted a seminar talk slide in blue bold. The idea, one which LQG can serve as paradigm or prime example, is of emergence from unspecified degrees of freedom---a number of ways of calculating which are shown to be equivalent.
In other words, don't say what the world is made of (whether spin networks or simplices or whatnot). Try to describe how it responds to measurement.

 

[tom.stoer]

I wouldn't say plane wave states are useless. On a conceptual level they allow you to see that a string coupled to a non-trivial background metric is like a string moving in a coherent state of its own flat space gravitons. The graviton vertex operator is precisely a plane wave state as is appropriate in flat space. I'm not claiming that this is the only way to see the connection, only that this way is simple and useful.

You are right, string theory provides already in its perturbative formulation interesting hints regarding the nature of gravity.

Nevertheless I would claim that perturbative string theory is doomed to fail, especially as there is no hint that the perturbation series is finite (there are other reasons as well); therefore one needs a non-perturbative concept. And I am pretty sure that this non-perturbative theory will not be based on "gravitons" or "plane-waves". Instead I expect that "gravitons" will emerge in some limit only. But to be honest I don't think that this limit is physically relevant.

So in contradistinction to QCD there will be no regime in QG where you have experimental access to gravitons.

 

[czes]

You are right, string theory provides already in its perturbative formulation interesting hints regarding the nature of gravity.

Nevertheless I would claim that perturbative string theory is doomed to fail, especially as there is no hint that the perturbation series is finite (there are other reasons as well); therefore one needs a non-perturbative concept. And I am pretty sure that this non-perturbative theory will not be based on "gravitons" or "plane-waves". Instead I expect that "gravitons" will emerge in some limit only. But to be honest I don't think that this limit is physically relevant.

So in contradistinction to QCD there will be no regime in QG where you have experimental access to gravitons.

I looked for a forum where the background independent ideas are discussed and I found it here. I am not a professional physicist and I just walk between Loop Quantum Gravity, Cramer's Transactional Interpretation and Quantum Decoherence approach.
I did some trivial transformations of the equations of gravity and quantum mechanics which suggest the space is created of the interactions (cross product) of the quantum information.

Since some days I repeat my question:

Each particle oscillate (Schrodinger's Zitterbewegung) due to Compton wave length and its frequency. If the information of the oscillation is non-local it has interact with the information from another particles and create a spatial lattice like a quantum network in LQG. The space would be there just a standing wave made of emitted and absorbed information. A graviton might be derived here as a distortion in the network (a mathematical picture of the quantum vacuum density), something like a photon.
What creates a space in LQG if not an information of the oscillating particle ?

 

[Haelfix]

You are right, string theory provides already in its perturbative formulation interesting hints regarding the nature of gravity.

Nevertheless I would claim that perturbative string theory is doomed to fail, especially as there is no hint that the perturbation series is finite (there are other reasons as well); therefore one needs a non-perturbative concept. And I am pretty sure that this non-perturbative theory will not be based on "gravitons" or "plane-waves". Instead I expect that "gravitons" will emerge in some limit only. But to be honest I don't think that this limit is physically relevant.

So in contradistinction to QCD there will be no regime in QG where you have experimental access to gravitons.

Kind of preaching to the choir I think. Most of the advances in string theory since the mid 90s are nonperturbative in nature. Whether its dualities, Ads/Cft or matrix theory. It's far from complete, but the whole 'emergent spacetime' concept very much comes from work done there.

 

[Hans de Vries]

Since some days I repeat my question:

Each particle oscillate (Schrodinger's Zitterbewegung) due to Compton wave length and its frequency.

The Zitterbewegung is a rather outdated concept, that is, there is nothing physically
vibrating and certainly not at c. It is the propagation which is composed out of two
light-like propagators, The Left and Right Chiral components.

Both these components do propagate individually at c but they are coupled together
via the mass term m. Each field is a source of the other enabling propagation speeds
anywhere between 0 and c.

To understand this better one can linearize the Klein Gordon equation, which is possible
in 1+1d, into a Left and Right moving component which are both moving at c but are
coupled via the mass term allowing propagation speeds lower than c.

I did this here: (in sections 16.1 through 16.4)
http://physics-quest.org/Book_Chapter_Dirac.pdf

There are computer simulations shown in figures 16.4 and 16.5. which obtain the
propagation of a Klein Gordon particle's wave-packet in this way.Regards, Hans

 

[MTd2]

My crude summary: LQG is not talking about what Nature is "made of" but about how Nature responds to measurements.
It uses various formalisms---the simplices of Group Field Theory (GFT), the networks and foams of the canonical and covariant versions of LQG---as alternative ways of imagining and calculating which the researchers have discovered are consistent.

You should see the paper I pointed out a few days ago:

http://arxiv.org/abs/1001.4364

Quantum Tetrahedra

Mauro Carfora, Annalisa Marzuoli, Mario Rasetti
(Submitted on 25 Jan 2010)
We discuss in details the role of Wigner 6j symbol as the basic building block unifying such different fields as state sum models for quantum geometry, topological quantum field theory, statistical lattice models and quantum computing. The apparent twofold nature of the 6j symbol displayed in quantum field theory and quantum computing -a quantum tetrahedron and a computational gate- is shown to merge together in a unified quantum-computational SU(2)-state sum framework.

 

[Orbb]

The Zitterbewegung is a rather outdated concept, that is, there is nothing physically
vibrating and certainly not at c.

Just a note: the recent paper

http://www.nature.com/nature/journal/v463/n7277/abs/nature08688.html
Quantum Simulation of the Dirac equation
"[...]We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, [...]"

where Zitterbewegung is experimentally observed.

 

[Hans de Vries]

Just a note: the recent paper

http://www.nature.com/nature/journal/v463/n7277/abs/nature08688.html
Quantum Simulation of the Dirac equation
"[...]We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, [...]"where Zitterbewegung is experimentally observed.

They did a "quantum" simulation of the 1d Dirac equation in a physical system which
they assume to be equivalent in behavior. Certainly they did not experimentally
observe the position of an electron while "Zittering" at c.

If you do a simple computer simulation of the 1d Dirac equation (which is the same
as the 1d linearized Klein Gordon equation) then there is no zittering at all but just
a wave packet moving at a constant speed. This is what is shown in figure 16.4.Regards, Hans

 

[Hans de Vries]

I shouldn't lead this thread into an off-topic direction. (sorry)
Maybe I should give my personal feelings about Erik Verlinde's paper instead.The first thing what game to my mind were the Neutron interference experiments
under gravity (Apparently Lubos Motl did so as well)
(http://motls.blogspot.com/2010/01/erik-verlinde-why-gravity-cant-be.html#more) Acceleration from force is to be understood as wave behavior, phase change
rates, Huygens principle, Wilson loops. Not only in field theory but also in gravity
as the neutron experiments prove. I did put quite some effort in the visualization
the EM case step by step in the following chapter of my book here:

"The Lorentz force derived from the interacting Klein Gordon equation"
(via Wilson Loops) see for instance images 11.3 through 11.6
http://www.physics-quest.org/Book_Lorentz_force_from_Klein_Gordon.pdf

It may be me but I can't find anything in the idea of "entropic force" which fits
into a wave behavior picture...Regards, Hans

 

[tom.stoer]

... I can't find anything ... which fits
into a wave behavior picture...

Why do you think it should fit into the material wave interpretation?

 

[Hans de Vries]

Why do you think it should fit into the material wave interpretation?

Well, the material wave interpretation is proven experimentally...

because of the success of molecular modeling software which threats
the wave function as a continues distribution of charge/current density
and spin density. \bar{\psi}\gamma^\mu\psi and \bar{\psi}\gamma^5\gamma^\mu\psiRegards, Hans

 

[ccdantas]

Good point on neutron interferometer.

At some point, I still believe that one should use a generalization of quantum concurrence for computing microstates. Information should not be equally "available", but under causality should be locally constrained by "shared resources"; concurrence should appear in the calculation.

(...) my book(...)

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

 

[MTd2]

It may be me but I can't find anything in the idea of "entropic force" which fits into a wave behavior picture...

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.

 

[czes]

The Zitterbewegung is a rather outdated concept, that is, there is nothing physically
vibrating and certainly not at c. To understand this better one can linearize the Klein Gordon equation, which is possible
in 1+1d, into a Left and Right moving component which are both moving at c but are
coupled via the mass term allowing propagation speeds lower than c.
I did this here: (in sections 16.1 through 16.4)
http://physics-quest.org/Book_Chapter_Dirac.pdf

There are computer simulations shown in figures 16.4 and 16.5. which obtain the
propagation of a Klein Gordon particle's wave-packet in this way.
Regards, Hans

Thank you Hans for the link of your book. I have printed it for me.
I agree there isn't a motion on a quantum fundamental level but there is a wave function which is an information any way. We do not observe a wave function alone as we do not observe an information alone either. We observe an interaction between wave functions. It is shown as a probable information of the particle due a squared wave function in Copenhagen. In other interpretations wave function is more real. This information shows a Compton wave length L=h/mc shown in Klein -Gordon equation.

A. We observe the indirect effects of the wave function as the existence of the particle so it has interact with an environment.
B. If the Compton wave length is a quantum information it has to be non-local due to Bell's theory

If the wave functions interact with each other and are non-local it has to represent something.
I assume it is distributed inversely proportional to the distance from a source of the oscillation represent a background information space.

 

[marcus]

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

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.

 

[marcus]

Ted Jacobson's 1995 paper is in some sense seminal here---at the root of all this discussion.
I thought it would be good for people to have a glimpse of the actual person:
http://math.ucr.edu/home/baez/marseille/jacobson_rovelli.jpg

This is Jacobson at the first Loops conference, Loops 2004, having a quiet conversation with Carlo Rovelli.

 

[czes]

Ted Jacobson wrote yesterday an article:
Extended Horava gravity and Einstein-aether theory
http://arxiv.org/abs/1001.4823

I think, we may use here a non-local information of the particles oscillation as a physical example of a matter field in Jacobsons theory.

 

[MTd2]

Hi Marcus, check your PMs! :)

 

[Fra]

I share some of these objections/comments...

Fwiw, I'll interject some of my personal views on this.

But I don't really know what "sides" means in a world without geometry.

Good point. One certainly wonders what "distance" means.

In my a the screen can be loosely defined informationally by means of what's predictable and what's not. I envision it like this. Prediction relate to a an observing system, making a prediction. This observer has a complexity. At some point, the predictability of constructed events are so small that it can not be distinguished from zero by a code of limited complexity - here is a natural "relative" horizon of measureable events.

This relates to the problem of how to conceptually handle the meaning of events with zero probability happen? - as I see it, yes then can, but that's irrelevant from the point of view of the ACTION of the observing system, the _expected_ action is invariant with respect to zero probability events, this is am abstract form of "locality". Instead this is where undecidability comes in. Part of the action is always undecidably as I see it - this is where the evolutionary parts comes in. This certainly limits the possibility of making certain predictions of anything. But I still think acknowledging this may improve our undertanding.

He also seems to assume that one side has "already emerged", but how did this happen? Smolin assumes the same thing in his paper, which is quite strange in my opinion.

I can't accept that either. But, I like to "read it" as a temporary working premise in order to show the implications.

I've encounted this exact problem in my own thinking, and the best resolution out of it I have found is to complement this "statistical information view" with an evolutionary view in darwinian style.

So this is why I think we need to start a the smallest complexity scale - which should be unique, and then ponder how higher order organization emerges as complexity increases.

I think his starting points, must in a satisfactoty future treatment be a result of such a process. It's that process I I also need to understand. I think there is a more information theoretical possibility to this than smolins CNS. Something that is formulated in terms of more abstraction "information channels" or screens, rather than explicit black holes.

/Fredrik

 

[Physics Monkey]

I can't accept that either. But, I like to "read it" as a temporary working premise in order to show the implications.

I certainly agree with you here. I have no logical problem with taking some of the space as emergent and trying to show that more "emerges". I'm not sure how natural a starting point this is, but regardless of my opinion, it indicates that Verlinde and Smolin both use background notions to make progress.

One place where your discussion of minimal complexity, etc strikes me as especially relevant is the case of our own universe (roughly de Sitter). A de Sitter spacetime contains a horizon that apparently limits the size of the physical HIlbert space available to observers in the space. Similarly, observers in de Sitter have limitations on how precisely they can measure various physical quantities. A classic reference is the article of Witten http://arxiv.org/abs/hep-th/0106109

 

[atyy]

Similarly, observers in de Sitter have limitations on how precisely they can measure various physical quantities. A classic reference is the article of Witten http://arxiv.org/abs/hep-th/0106109

"For life itself is only an approximation, valid in the limit of a complex organism or civilization." He means this to be true in any physics, not just in asymptotically ds Sitter spacetimes, right?

 

[Physics Monkey]

"For life itself is only an approximation, valid in the limit of a complex organism or civilization." He means this to be true in any physics, not just in asymptotically ds Sitter spacetimes, right?

Haha, yes, I would assume so. It's a pretty vague comment though, so who knows what he really means.