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

[atyy]

No, AS is central to the discussion - AS is the case where gravity is not emergent.

So diff invariance is *not* background independence in LQG? I thought that was the whole point of LQG.

"Diffeomorphism invariance is the technical implementation of a physical idea, due to Einstein. The idea is a modification of the pre-general-relativistic (pre-GR) notions of space and time. In pre-GR physics, we assume that physical objects can be localized in space and time with respect to a fixed non-dynamical background structure." http://relativity.livingreviews.org/Articles/lrr-2008-5/

 

[atyy]

You must mean that in order to get his concept of gravity going and build his theory, Verlinde has to start by postulating some fixed metric, some particular chosen geometry.

That may be the case, but what is it? Where does it come in?

OK, let's try this. The Bekenstein/Hawking/Unruh temp is a result of QFT on fixed curved spacetime.

BTW, my argument must not be entirely correct, since there is AdS/CFT which is a working theory of quantum gravity, which is pretty background independent, but not entirely.

 

[Fra]

So Verlinde thinks AS is wrong. AS has diffeomorphism invariance or background independence. So QG cannot be background independent. Or Verlinde is wrong.

I can not speak of Verlinde reasoning yet but I personally do not see diff invariance as fundamental. The reason is simple. It's not that I am suggesting that there exists a preferred background or observer - on the contrary, I am taking it a step further, since to me diff invariance contains information; and this information can physically only be a result of an interaction. So diff invariance is inferred by a physical observing system, and if we do not believe on bird view observer with unconstrained information capacity and processing power, then it is impossible to make a completely confident inference of diff invariance.

This is why I think this invariance is emergent as well. In fact I think all symmetries are emergent in the same sense. Other symmetry groups are subject to the same constraint as I see it.

So in my view, realist type of the diff invariance between observers, is replaced but each observer "seeing" (inference by interaction history) different symmetries, this in turn implies interactions between them, which causes a selective pressure and ultimately the classical invariance emerges as an equilibrium condition only.

This reaching of equilibrium and "consensus-symmetries" is also how all interactions could emerge.

So to start with diff invaraince as a god given, realist constraint that is unquestionable is IMO in direct conflict with some of the principles that guide me. But I would argue that it is not in conflict with the basic idea of "background independence", it is rather a deepened version of it.

/Fredrik

 

[marcus]

...since there is AdS/CFT which is a working theory of quantum gravity, which is pretty background independent, but not entirely.

Please spell it out for me. In what way is it not entirely BI? I would have thought anything based on Anti-deSitter (AdS) space would be entirely based on that background geometry.
Indeed as far as I'm aware, the conjectured AdS/CFT correspondence seems to require a rather elaborate geometric setup. Presumably I'm mistaken about this, so I would be grateful if you could explain.

In what way is AdS/CFT pretty background independent, but not entirely so?

 

[marcus]

OK, let's try this. The Bekenstein/Hawking/Unruh temp is a result of QFT on fixed curved spacetime.
...

Atyy, surely that does not prove what you suggest. Just because someone uses a fixed curved geometry to prove a result does not imply that a fixed curved geometry is required and that similar results cannot be proven in more general context.

Black holes exist in General Relativity, which is a background independent theory. Verlinde can take for granted that black holes very generally have horizons and the horizons have temperature and entropy---and he can use that assumption (should he need to) without even a hint of dependence on a fixed geometric background.

I don't think you have shown that Verlinde has any need to fix on a particular metric to set up his theory (although it is still just a pup, not even half-grown, so we'll have to wait and see.)

 

[Fra]

So to start with diff invaraince as a god given, realist constraint that is unquestionable is IMO in direct conflict with some of the principles that guide me. But I would argue that it is not in conflict with the basic idea of "background independence", it is rather a deepened version of it.

I think the "mistake" to start assuming diff invariance in a context where you want to explain not only geometry, but the entire manifold is analogous to the mistake that the entropy ALWAYS increase, when the truth is that it's only an expectation, given a equipartition premise, and that it's further only a statistical statement.

I think it's the same with diff invariance. We expect it, but it can not be fundamental, even the symmetry is only statistical and rather corresponds IMO to an evolutionary steady state, that even doesn't have an independent evaluation.

/Fredrk

 

[atyy]

Please spell it out for me. In what way is it not entirely BI? I would have thought anything based on Anti-deSitter (AdS) space would be entirely based on that background geometry.
Indeed as far as I'm aware, the conjectured AdS/CFT correspondence seems to require a rather elaborate geometric setup. Presumably I'm mistaken about this, so I would be grateful if you could explain.

In what way is AdS/CFT pretty background independent, but not entirely so?

In AdS/CFT the metric is dynamical (which is why it's a theory of gravity), except at the boundaries (so it should be "asymptotically-AdS/CFT").

 

[marcus]

Please spell it out for me. In what way is it not entirely BI? I would have thought anything based on Anti-deSitter (AdS) space would be entirely based on that background geometry.
Indeed as far as I'm aware, the conjectured AdS/CFT correspondence seems to require a rather elaborate geometric setup. Presumably I'm mistaken about this, so I would be grateful if you could explain.

In what way is AdS/CFT pretty background independent, but not entirely so?

In AdS/CFT the metric is dynamical (which is why it's a theory of gravity), except at the boundaries (so it should be "asymptotically-AdS/CFT").

Thanks, that's somewhat as I imagined. So the holographic principle is far more general and could apply to a realistic cosmology.
The Maldacena conjecture is not quite applicable in the real world because, as far as we know, we have a boundaryless universe with accelerating expansion---bearing more resemblance to the deSitter picture---rather than some asymptotically Anti-deSitter case.

So perhaps we could characterize the AdS/CFT by saying that the background dependence is concentrated on the boundary. The spacetime is required to have a boundary and there must be a fixed geometry, a fixed metric of a certain type, set up on this boundary (that being where the conformal field theory lives.)

It seems to me (I hope I'm not mistaken) that Verlinde (and Jacobson and Padmanabhan as well) do not require the AdS/CFT setup---they appeal only to the more general holo principle. The question for me is then whether the holographic principle is happy with background independence. I think it must be. Jacobson and Padmanabhan are dyed-in-the-wool (general) relativists. Would they be messing with it, if it weren't? Not a serious argument, but I've seen no hint otherwise.

 

[atyy]

Thanks, that's somewhat as I imagined. So the holographic principle is far more general and could apply to a realistic cosmology.
The Maldacena conjecture is not quite applicable in the real world because, as far as we know, we have a boundaryless universe with accelerating expansion---bearing more resemblance to the deSitter picture---rather than some asymptotically Anti-deSitter case.

So perhaps we could characterize the AdS/CFT by saying that the background dependence is concentrated on the boundary. The spacetime is required to have a boundary and there must be a fixed geometry, a fixed metric of a certain type, set up on this boundary (that being where the conformal field theory lives.)

Yes, that's my understanding. Well, inadequate as it is, given AdS/CFT is our best toy model for the moment - I wonder whether one can say that gravity is an "entropic force" in it?

 

[marcus]

... Well, inadequate as it is, given AdS/CFT is our best toy model for the moment ...

Wait, whose best toy model of what?

 

[atyy]

Wait, whose best toy model of what?

Quantum gravity.

 

[atyy]

The question for me is then whether the holographic principle is happy with background independence. I think it must be. Jacobson and Padmanabhan are dyed-in-the-wool (general) relativists. Would they be messing with it, if it weren't? Not a serious argument, but I've seen no hint otherwise.

Yeah, I think Visser must be excommunicated from the church of general relativity?

 

[Physics Monkey]

You must mean that in order to get his concept of gravity going and build his theory, Verlinde has to start by postulating some fixed metric, some particular chosen geometry.

That may be the case, but what is it? Where does it come in?

With all due respect to Verlinde's attempt, I think there is background dependence everywhere in his paper.

I will be quite specific about what I mean. He certainly makes several statements about being able to define geometry from information content. For example, he suggests that the screen should contain information about the emergence of space on both sides of the screen. But I don't really know what "sides" means in a world without geometry. A good example of an honest, in my opinion, attempt to make sense of these things comes from Fotini's causal quantum histories, but her approach is much more primitive (suggestive of how hard this game is). 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.

As for the geometry of the screen, he suggests we define the area of the screen by its maximum information content, but he doesn't address the emergence of locality or curvature. Why does it mean anything at all to say a particle is close to one part of the screen and not another? A good example illustrating how this isn't a given comes from Fotini's quantum graphity setup. In a certain non-geometric phase of quantum graphity it doesn't mean much to talk about locality on a screen (everything is near everything else in a sense).

Furthermore, I think its fair to say that he doesn't make it plausible from these definitions that the emergent geometry looks anything like flat space, yet he uses flat space intuition to relate the radius of a sphere to its area. For that matter, even the dimension of the emergent space is assumed, but the dynamical triangulations people have taught us that this need not be so. My personal opinion is that none of his claims are obtainable from the very vague "definitions" he gives of emergent geometry. Perhaps with some additional work the definitions could be sharpened, but I suspect this would require more physics input. And again, this is not to say that he hasn't said something interesting, but I don't think its close to being really background independent.

 

[marcus]

Yeah, I think Visser must be excommunicated from the church of general relativity?

This is straying from topic (we were discussing Verlinde and Smolin's recent papers) but relativity strikes me more like the opposite of a religion---one declines to believe that the universe has a pre-ordained geometry.

Gen rel entails a sort of skepticism: one rejects the idea of a "god-given" geometry, either here around us or off in the distance fixed on an eternal boundary. Somewhat like an ordinary garden-variety atheist one assumes that geometry, like everything else, evolves and has some provisional/tentative explanation. One doubts absolutes. It's just a pragmatic attitude not a consistent philosophy. One doubts those absolutes one can---those which are, so to speak, handy within reach. Explanatory laws are an onion with ever deeper layers, I admit. So this is not meant to be persuasive, I'm just describing a skeptical attitude about the world.

Surely you meant the Visser comment as a joke, but it shows a contrasting attitude which allowed me to reply. In any case Visser is not the topic.

If we look at Verlinde's change of course---it looks like he has come closer to the kind of skepticism I described.

He is dealing with a 4D spacetime.
He is probing into how geometry might evolve, what might underlie general relativity.

I see this more as pragmatic realism---not a religious-like faith in revealed truths such as invisible dimensions and borders at infinity.

 

[marcus]

If I'm not mistaken someone who used to post here at PF Beyond fairly regularly has just contributed some acute comments at N.E.W. blog:

==quote==

Frank says:
January 23, 2010 at 12:49 pm
Peter is right to criticize that the entropic formulation by Jacobson and Verlinde is not deep, because describing space-time as a thermodynamic limit does not tell (almost) anything about the microscopic constituents.

When Bernoulli deduced the ideal gas law from atoms, he was able to show that gases are made of atoms whizzing around. But as suggested by many, almost any microscopic degree of freedom at Planck scale will give the proper thermodynamic limit: loops, ribbons, etc. all yield a limit that then leads to Jacobson’s and Verlinde’s argument.

It is highly probable that the Jacobson/Verlinde argument is not able to distinguish between different microscopic models of quantum gravity. There is one exception though: the argument eliminates all theories with higher dimensions. 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.

Quantum gravity people will say: we knew this since (at least) 15 years. And they are right. However, if the exploration of quantum gravity were the right path to find the microscopic degrees of freedom, they would have been found long ago. In fact, quantum gravity does not allow to deduce much about the microscopic degrees of freedom.

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:
January 23, 2010 at 1:06 pm
I think that Lubos is wrong. Unruh’s proportionality between acceleration and temperature implies that gravity can be seen as an thermal/entropic effect. There is little doubt about it. If you want to get rid about the gravity-entropy relation, you must get rid of Unruh radiation – and that is impossible.

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

 

[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.