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

[marcus]

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."

 

[arivero]

Have you seen that I wrote the same 2 days earlier (18 Jan) but without high mathematic ?
They start to use Compton wave length but still do calculate by Shannon entropy using Boltzmann constant. Compton wave length does it much easier.

Compton wave length? Do you mean the the radius for a Newtonian gravitational orbit around a body of mass M to sweep one Planck Area in one unit of Planck time?

 

[atyy]

"The proportionality is given by a fudge factor f, which we adjust to make m exactly into the passive gravitational mass".

"It is important to emphasize that I have not shown here that classical spacetime emerges from loop quantum gravity, as we have assumed that there is a classical spacetime in the exterior region where we make measurements. What has been shown is that if there is a classical spacetime that emerges then Newton’s law of
gravity is necessarily satisfied."

 

[marcus]

Inertial mass and gravitational mass are two different things. I suppose in any theory where the two arise and are shown to be proportional, one has the choice of setting them equal.

The issue about splitting the universe into two regions is more interesting, I think.

There is a school of thought which holds that Quantum Mechanics is inherently about information which a classical observer has about a quantum system.
It only applies where the observer is OUTSIDE the experimental setup, or system.

The Hilbert space is in essence a property of the boundary: the box containing the experiment, the interface through or across which observations are made.

According to that view, one cannot have a comprehensive QM that embraces the whole universe, because it would not have room for the outside observer.
One has to divide the universe into two parts: a box containing what is to be observed and studied, and a classical outside.

At least that is a simplified sketch. Does it fit with any views of QM that you have encountered?

I recall Smolin stressing this and related foundational issues in a couple of PIRSA video talks, I can get the links if anyone is interested.

 

[atyy]

Hmmm, I finally succumbed and glanced at Verlinde's paper! So if you assume that entropy scales with area, you get gravity?

So any gravity here: http://arxiv.org/abs/0704.3906 ?

Interestingly that is cited by http://arxiv.org/abs/0907.2939 , which does reference Crane, Rovelli, Smolin and Markopoulou "The mathematical structure that we observe in section 2 shares some features with an approach to quantum gravity called “relational quantum cosmology” [11]".

 

[arivero]

Just a thinking.

Set [c]=1. Then

$[G]=L / M$ and
$[h]=L . M$

So a lot of relationships can be just naive dimensional analisis when M=1 or when you can somehow disregard masses or lenghts. This is a peril in this kind of papers, and so they are more careful than usual about doing all the steps explicit.

Related question: if we were to live in an universe with more than 3 spatial dimensions, which should be the shape of Newton's Gravity Formula? which the units of [G]? I got worried because Smolin seems to say that his paper does not depend of the number of dimensions.

 

[Fra]

The issue about splitting the universe into two regions is more interesting, I think.

There is a school of thought which holds that Quantum Mechanics is inherently about information which a classical observer has about a quantum system.
It only applies where the observer is OUTSIDE the experimental setup, or system.

The Hilbert space is in essence a property of the boundary: the box containing the experiment, the interface through or across which observations are made.

According to that view, one cannot have a comprehensive QM that embraces the whole universe, because it would not have room for the outside observer.
One has to divide the universe into two parts: a box containing what is to be observed and studied, and a classical outside.

At least that is a simplified sketch. Does it fit with any views of QM that you have encountered?

I am starting to feel that there is good hope for substantial progress, when good questions appear from many directions.
I think the dark ages are soon over and unavoidable conclusions await us.

The point marcus raises is a key one to me as well.

But I do not feel it's necessary to consider one side to be "classical". The abstraction should works even when the observer side is non-classical with respect to a second observer. It's just IMO a matter of conditional probabilities, and it doesn't matter as I see it wether the prior condition is classical or quantum. The action of the observing system is I think _as if_ it was classical.

It's somewhat analogous to the action of a player, where the action is executed from the point of view of the player with the full confidence in that the observed expectation is correct - even if it's wrong! Yet this is completely rational. This IMO also relates to a question Dmitry raised some time ago about the role of "false information"; in my view/interpretation at least the observer can not have an independent view of wether it's own expectations is right or wrong, so from the point of view of intrinsic action, right or wrong doesn't matter. Wether it matters to another observer, is a completely different question and relates to the action of that observer.

I think this deeper connection that everbody, smoling, bekenstein and verlinde are now fishing for is going to take us yet on entire level away from realism. I think we will eventually think of "hilbert space" as about as up to date as we once thought of Newtons absolut spacetime

/Fredrik

 

[MTd2]

Related question: if we were to live in an universe with more than 3 spatial dimensions, which should be the shape of Newton's Gravity Formula? which the units of [G]? I got worried because Smolin seems to say that his paper does not depend of the number of dimensions.

Well, to make gauss law work, you should need that the power law fell with the inverse the number of dimensions minus one...
So, in 10 dimensions it would be 1/r^9.

Edit:
Hmm, he meant the method is valid. Because at least in the citation he gave, it looks like so.

http://arxiv.org/abs/hep-th/9901069

I guess it was just an unfortunate choice of words.

 

[marcus]

Recent comment on Verlinde's paper:
http://arxiv.org/abs/1001.3808

 

[ensabah6]

"The proportionality is given by a fudge factor f, which we adjust to make m exactly into the passive gravitational mass".

"It is important to emphasize that I have not shown here that classical spacetime emerges from loop quantum gravity, as we have assumed that there is a classical spacetime in the exterior region where we make measurements. What has been shown is that if there is a classical spacetime that emerges then Newton’s law of
gravity is necessarily satisfied."

What is needed to show classical spacetime emerges from LQG?

 

[marcus]

What is needed to show classical spacetime emerges from LQG?

*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.

 

[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.

He could revise his paper by stating "classical spacetime in LQG has been shown in this paper" and cite reference. i.e Ashketar Friedal 2009.

 

[marcus]

I see no reason for anyone to do what you suggest.
In this paper Smolin is not discussing who else has proved what. He is not giving a status report! For his purposes all he needs to do is to point out the facts about his own proof, namely that his particular proof has such and such assumptions. Proves this and not that. He has to tell the reader clearly what HE is doing.

It would be great if someone well versed in the current situation would write a review paper this year, saying who has proven what. In what cases, with what assumptions. In which versions of Lqg and so on. Review papers are different from research papers.

Last year Laurent Freidel gave a review talk (about the semiclassical limit) at the Marcel Grossmann meeting in Paris. It's a lot of work to prepare a review talk or review paper.
You don't expect every individual research paper to provide a review

 

[ensabah6]

I see no reason for anyone to do what you suggest.
In this paper Smolin is not discussing who else has proved what. He is not giving a status report! For his purposes all he needs to do is to point out the facts about his own proof, namely that his particular proof has such and such assumptions. Proves this and not that. He has to tell the reader clearly what HE is doing.

It would be great if someone well versed in the current situation would write a review paper this year, saying who has proven what. In what cases, with what assumptions. In which versions of Lqg and so on. Review papers are different from research papers.

Last year Laurent Freidel gave a review talk (about the semiclassical limit) at the Marcel Grossmann meeting in Paris. It's a lot of work to prepare a review talk or review paper.
You don't expect every individual research paper to provide a review

Given Smolin writes ""It is important to emphasize that I have not shown here that classical spacetime emerges from loop quantum gravity, as we have assumed that there is a classical spacetime in the exterior region where we make measurements. What has been shown is that if there is a classical spacetime that emerges then Newton’s law of
gravity is necessarily satisfied."

Does classical spacetime emerge from LQG?

 

[oldman]

The issue about splitting the universe into two regions is more interesting, I think.

So do I. Here are some off-the-wall remarks:

Both Verlinde and Smolin seem to distinguish quite sharply between the macroscopic and the
microscopic --- the macroscopic milieu that we live in, where spacetime has emerged and gravity rules as an entropic force arising from happenings inside surfaces enclosing the microscopic quantum milieu. On such separating surfaces, they propose, holographic information exists about the microscopic milieu; details about the microscopic degrees of freedom (in principle including gravity itself?) are not needed to derive Newton’s law of gravity.

Our familiar Newtonian gravity is thus suggested to be a consequence of this proposed distinction.

It seems to me that the only way one can quantitatively distinguish between the microscopic and macroscopic domains is via Planck’s constant, h, by choosing a scale based on a length defined by h, like the Compton wavelength of an object. But Verlinde argues that:

...one may wonder why we needed to introduce Planck's constant in the first place, since the only aim was to derive the classical laws of Newton. Indeed, h eventually drops out of the most important formulas. So, in principle one could multiply it with any constant and still obtain the same result. Hence, h just serves as an auxiliary variable that is needed for dimensional reasons. It can therefore be chosen at will, and defined so that (3.5) is exactly valid. The main content of this equation is therefore simply that there is an entropy change perpendicular to the screen proportional to the mass m and the displacement delta x. That is all there is to it.

If this means that the macroscopic-microscopic distinction is a movable feast, as it were, which can be done away with once it has been used to derive Newton’s gravity, it makes me wonder if said gravity might not be MONDified by the heirarchical inhomogeneity of our universe (strings-quarks-baryons-atoms-fluids-planets-stars-galaxies- voids and sheets).

 

[Fra]

associations

Hmm... when I skimmed Smolins paper "Newtonian gravity in loop quantum gravity" as well as skimming his [38]"Holography in a quantum spacetime" http://arxiv.org/abs/hep-th/9910146 referenced to in the first paper during

"Nonetheless, it is intriguing to wonder if the relationship between area and entropy
is even more fundamental than the notion of geometry itself. Could there be a more
fundamental picture, before spacetime emerges in which area has the fundamental
meaning of the capacity of a quantum channel by which information flows[38]?"

there is a touch of a new interpretation of LQG that remotely smells a little bit like what I thought it was, before I got rovelli's book and started to read. My original idea, that motivated me to look into rovelli's thinking and get the book, is that I originally associate the spin networks to microstructure of an observer. As such, a finite microstructure always has a boundary. The idea I had was that if this is true, then one can consider an interaction of two spin networks. Their interaction would eventually have to evolve a connection - connecting the two networks. In a similar sense eventually a whole environment would _emerge_ relations.

But my impression of rovelli's reasoning from his book and old papers was that this was not really how He thought of it, and I felt I had to REinterpret everything to make sense out of, so I lost interest.

But just like I see some angles to string theory that is promising (where string are emergent), this also sounds like one possible angle into LQG that might restore my interest.

If what I envision work, I would also see no reason why LQG could not also unify all forces. There would probably be a more complex "network" that represents all degrees of freedom, not only space.

/Fredrik

 

[tom.stoer]

Does classical spacetime emerge from LQG?

I haven't seen any paper claiming this has been achieved - but of course I cannot claim that I know all relevant papers :-)

What I miss is a review paper on the new results from the last two years!

Questions:
1) A propagator can somehow tell you a lot about long-distance limits, dimensionality etc., but it is not clear to me whether this sufficient. What happens to dimensionality in strong gravitational fields / inside a BH horizon but away from the "singularity"?
2) What does the "new-look-LQG" mean in terms of en emerging 4D spacetime? What does it mean in terms of Lorentz violation? (or - to be more precise - deformation)? What does it mean for light propagation, GZK cutoff, etc.? Are there already hints how to copmplete the canonical approach (the Hamiltonian)? I expected something like that from Thiemann's papers, but either this project is still incomplete, or I completely miss something.
3) What is the current status regarding the Immirzi-Parameter? What's its meaning (theta angle in LQG), what's it's value? Is it a field?
4) What is the current status regarding q-deformation / framing of graphs (and braiding)?
5) Is the cc an input (as for q-deformation) or a result?

A couple of years ago both Smolin and Ashtekar (and others) invested some time to present the current status in quite regular review papers. Unfortunately nothing like that has been done for the last years.

 

[qsa]

I am starting to feel that there is good hope for substantial progress, when good questions appear from many directions.
I think the dark ages are soon over and unavoidable conclusions await us.

/Fredrik

Indeed.

The only conclusion I see is that there must be some rays going from a particle to another one in the other side of the universe instantly. I think I know what it is, but I can't tell you. Path integral gives a hint I guess , since a particle sniffs all of the universe as it moves,even tiny bit.

maybe entropy is caused by gravity rays, entropy is an amount of change of state after all.

so if entropy is due to gravity so time should be due to gravity( i.e. change of state), should'nt it?

 

[marcus]

...

What I miss is a review paper on the new results from the last two years!

...A couple of years ago both Smolin and Ashtekar (and others) invested some time to present the current status in quite regular review papers...

I also am impatient to see a 2010 review paper.

The most recent review paper for LQG is the May 2008 Rovelli, published online by the AEI in their Living Reviews series. ( http://relativity.livingreviews.org/Articles/lrr-2008-5/ )

This is a well-thought-out list of questions, IMHO. Thanks for compiling it:
==quote==

Questions:
1) A propagator can somehow tell you a lot about long-distance limits, dimensionality etc., but it is not clear to me whether this sufficient. What happens to dimensionality in strong gravitational fields / inside a BH horizon but away from the "singularity"?
2) What does the "new-look-LQG" mean in terms of en emerging 4D spacetime? What does it mean in terms of Lorentz violation? (or - to be more precise - deformation)? What does it mean for light propagation, GZK cutoff, etc.? Are there already hints how to copmplete the canonical approach (the Hamiltonian)? I expected something like that from Thiemann's papers, but either this project is still incomplete, or I completely miss something.
3) What is the current status regarding the Immirzi-Parameter? What's its meaning (theta angle in LQG), what's it's value? Is it a field?
4) What is the current status regarding q-deformation / framing of graphs (and braiding)?
5) Is the cc an input (as for q-deformation) or a result?
​

==endquote==

I was motivated by your comment to look around for the LQG review papers that came before Rovelli 2008.
I found

1. Ashtekar and Lewandowski 2004 ( http://arxiv.org/abs/gr-qc/0404018 )

2. Smolin 2004 ( http://arxiv.org/abs/hep-th/0408048 , arxiv only. )

3. Rovelli 1998 ( http://arxiv.org/abs/gr-qc/9803024 comparative survey of several qg incl. string)

4. Rovelli 1997 ( http://arxiv.org/abs/gr-qc/9705059 invited Living Reviews LQG article predecessor to current 2008 one)

This doesn't count books---for example Thiemann's book would serve some of the same purposes as a review article. Also there was a conference talk by Ashtekar (to Marcel Grossmann 2006) that could serve at least in part as a review or status report
( http://arxiv.org/abs/0705.2222 ).

 

[ccdantas]

i'm not following this closely, but what about Padmanabhan's previous work? No citations or relations to it?

Thanks.

 

[marcus]

i'm not following this closely, but what about Padmanabhan's previous work? No citations or relations to it?

Thanks.

Verlinde's reference [14]

Smolin's reference [10]

Both citations are to Padmanabhan's most recent (and I think most complete) presentation of his ideas for basing gravity on thermodynamics.
http://arxiv.org/abs/0911.5004
Thermodynamical Aspects of Gravity: New insights

This most recent Padmanabhan has fairly complete references to his earlier work

I see Ted Jacobson and Thanu Padmanabhan as both very much in the middle of this stir about a thermodynamic origin of the geometry of the universe. One or both ought to be responding to recent papers this year in some way or other. It will be interesting to see what they say.

Perhaps you found Padmanabhan's "A Dialogue" intuitive and stimulating, as I did. The more recent "Thermodynamical Aspects" paper is more technical and scholarly but I thought that "Dialogue" was an entertaining useful way of making the ideas accessible.
Do you remember his recalling Boltzmann's insight? Namely: if it has temperature, it must have atoms I oversimplify. From there, Padma argues that we know space has temperature (deSitter temp, Hawking temp, Unruh temp) and these are temperatures of geometry, and therefore geometry must rest on discrete degrees of freedom. It must have "atoms". Have I misinterpreted what he said? I haven't checked back.

 

[czes]

Just a thinking.

Set [c]=1. Then

$[G]=L / M$ and
$[h]=L . M$

So a lot of relationships can be just naive dimensional analisis when M=1 or when you can somehow disregard masses or lenghts. This is a peril in this kind of papers, and so they are more careful than usual about doing all the steps explicit.

Related question: if we were to live in an universe with more than 3 spatial dimensions, which should be the shape of Newton's Gravity Formula? which the units of [G]? I got worried because Smolin seems to say that his paper does not depend of the number of dimensions.

I thought about it. There are different relations but all of them has its meaning. The question is to find a proper meaning.
For example I studied Planck lengt and Compton length. I assume it has something to do with a space curvature but is it really ?
We calculate in 3 spatial dimensions. What are the 3 dimensions. Do they exist on the fundamental quantum level ?
I assume the space for our observation is made of the information. How many dimensions are between two quantum informations ? Do they need any dimension at all ?

 

[marcus]

Just a thinking.

Set [c]=1. Then

$[G]=L / M$ and
$[h]=L . M$

So a lot of relationships can be just naive dimensional analisis when M=1 or when you can somehow disregard masses or lengths. This is a peril in this kind of papers, and so they are more careful than usual about doing all the steps explicit.
...

I thought about it. There are different relations but all of them has its meaning. The question is to find a proper meaning.
For example I studied Planck length and Compton length. I assume it has something to do with a space curvature but is it really ?
We calculate in 3 spatial dimensions. What are the 3 dimensions. Do they exist on the fundamental quantum level?
I assume the space for our observation is made of the information. How many dimensions are between two quantum informations? Do they need any dimension at all?

Czes, I don't want you to be put at a disadvantage by not knowing some relevant background which is familiar to the rest of us. Other people here are aware of an interesting paper on arxiv that touches on elementary dimensional analysis, involving the Planck and Compton lengths, because some of the contributory material was worked on here at PhysicsForums, back in 2005 and 2006.
http://arxiv.org/abs/gr-qc/0603123

Another thing Czes, do you normally use Tex in your writing? Tex is available here at PF. Just write a formula like L^2 or M_{Planck}
and put symbols "tex" and "/tex" around it. except use square brackets [...] instead of quotes "..."
In other words, copy this without the underline
[tex]L^2[/tex]
and you will get

$$L^2$$

Copy this without the underline
[tex]M_{Planck}[/tex]
and you will get

$$M_{Planck}$$

 

[czes]

Thank you Marcus. I am newbe here but I would like to learn as soon as possible.

 

[ccdantas]

(...)Both citations are to Padmanabhan's most recent (and I think most complete) presentation of his ideas for basing gravity on thermodynamics. (...)

Thanks, Marcus. Yes, I have followed those papers by Padmanabhan. Along with Verlinde's, I have also seen that recent one by Smolin, but have not read them in detail yet, so I was wondering where Padmanabhan's work fit in, if at all.

I suppose you may have also seen this comment today:

Notes Concerning "On the Origin of Gravity and the Laws of Newton" by E. Verlinde [http://arxiv.org/abs/1001.3808" ]; by Jarmo Mäkeä

Now, of course, there will be a flow of papers on the subject... Hopefully with a way to effectivly test these ideas.

 

[ccdantas]

(...)
I suppose you may have also seen this comment today:
(...)

Ok, sorry, I've just seen your previous post.

 

[ccdantas]

"My idea is that in a theory in which space is emergent forces are based on differences in the information content, and that very general random microscopic processes cause inertia and motion." --- Verlinde --- see http://staff.science.uva.nl/~erikv/page18/page18.html" .

I'd hypothesize that one could retrive similar results without using holography arguments for bit staturation but a more fundamental basis such as supposing that microscopic processes are concurrent -- this leads directly to deadlock (spacetime singularity) and deadlock avoidance (inertial effects) (E.g. search my blog under the term "concurrent" for speculations on this).

 

[qsa]

Indeed.

The only conclusion I see is that there must be some rays going from a particle to another one in the other side of the universe instantly. I think I know what it is, but I can't tell you. Path integral gives a hint I guess , since a particle sniffs all of the universe as it moves,even tiny bit.

maybe entropy is caused by gravity rays, entropy is an amount of change of state after all.

so if entropy is due to gravity so time should be due to gravity( i.e. change of state), should'nt it?

The World as a Hologram
Authors: L. Susskind
(Submitted on 15 Sep 1994 (v1), last revised 28 Sep 1994 (this version, v2))
Abstract: According to 't Hooft the combination of quantum mechanics and gravity requires the three dimensional world to be an image of data that can be stored on a two dimensional projection much like a holographic image. The two dimensional description only requires one discrete degree of freedom per Planck area and yet it is rich enough to describe all three dimensional phenomena. After outlining 't Hooft's proposal I give a preliminary informal description of how it may be implemented. One finds a basic requirement that particles must grow in size as their momenta are increased far above the Planck scale. The consequences for high energy particle collisions are described. The phenomena of particle growth with momentum was previously discussed in the context of string theory and was related to information spreading near black hole horizons. The considerations of this paper indicate that the effect is much more rapid at all but the earliest times. In fact the rate of spreading is found to saturate the bound from causality. Finally we consider string theory as a possible realization of 't Hooft's idea. The light front lattice string model of Klebanov and Susskind is reviewed and its similarities with the holographic theory are demonstrated. The agreement between the two requires unproven but plausible assumptions about the nonperturbative behavior of string theory. Very similar ideas to those in this paper have been long held by Charles Thorn.
ok, susskind does use light rays, but he uses light rays to represent a parton(particle) on the screen. Not far enough. I propose a ray from every point in space-time to every other point in space-time. The number of connections(two way) per two points(A,B) will represent the entropy(information) that passes between those two points. the entropy at those points is related to the probability of finding a particle at those points. The entropy at A will affect B and vis=versa in such way to change their probabilities(entropies) to indicate attraction(by lowering the pobabilities at those points, forcing an increase in probabilties in the neighbouring points). This technique works for all forces

just a suggestion.

 

[tom.stoer]

This is a well-thought-out list of questions ...

Questions:
1) A propagator can somehow tell you a lot about long-distance limits, dimensionality etc., but it is not clear to me whether this is sufficient. What happens to dimensionality in strong gravitational fields / inside a BH horizon but away from the "singularity"?
2) What does the "new-look-LQG" mean in terms of en emerging 4D spacetime? What does it mean in terms of Lorentz violation? (or - to be more precise - deformation)? What does it mean for light propagation, GZK cutoff, etc.? Are there already hints how to copmplete the canonical approach (the Hamiltonian)? I expected something like that from Thiemann's papers, but either this project is still incomplete, or I completely miss something.
3) What is the current status regarding the Immirzi-Parameter? What's its meaning (theta angle in LQG), what's it's value? Is it a field?
4) What is the current status regarding q-deformation / framing of graphs (and braiding)?
5) Is the cc an input (as for q-deformation) or a result?
​

...

I was motivated by your comment to look around for the LQG review papers that came before Rovelli 2008. ...

Not well-thought-out, just some ideas what I am missing. Anyway - thanks a lot!

Regarding your list of papers: I would add

http://arxiv.org/abs/hep-th/0303185
How far are we from the quantum theory of gravity?
Lee Smolin
(Submitted on 20 Mar 2003 (v1), last revised 11 Apr 2003 (this version, v2))
Abstract: An assessment is offered of the progress that the major approaches to quantum gravity have made towards the goal of constructing a complete and satisfactory theory. The emphasis is on loop quantum gravity and string theory, although other approaches are discussed, including dynamical triangulation models (euclidean and lorentzian) regge calculus models, causal sets, twistor theory, non-commutative geometry and models based on analogies to condensed matter systems. We proceed by listing the questions the theories are expected to be able to answer. We then compile two lists: the first details the actual results so far achieved in each theory, while the second lists conjectures which remain open. By comparing them we can evaluate how far each theory has progressed, and what must still be done before each theory can be considered a satisfactory quantum theory of gravity. We find there has been impressive recent progress on several fronts. At the same time, important issues about loop quantum gravity are so far unresolved, as are key conjectures of string theory. However, there is a reasonable expectation that experimental tests of lorentz invariance at Planck scales may in the near future make it possible to rule out one or more candidate quantum theories of gravity.

Strictly speaking it's not a review of LQG but it tries to compare several approaches to QG. Nevertheless it summarizes the status of LQG as of 2003.

 

[qsa]

I take back what I said about Verlinde earlier, he has hit a nerve. But I am still not happy about him not reaching the right conclusion, given his knowledge; not that I don't understand the magnitude of the problem. It is said that bernoulli (1700 something) almost hit on light's nature, but he missed it by a notch. I hope we don't have to wait 200 years. So it is not about fancy equations, it is about insight.

 

[marcus]

Verlinde's blog of 15 January is simple and important. I will copy and comment.

I think the example of (entropic) polymer elasticity looks in the direction of LQG. That a polymer in a heat bath will contract just by assuming random zig-zag. There are more angle states at the joints which result in a short molecue than a long one. It gets the energy to do work as it contracts from the random bumps it receives in the heat bath. I may be mistaken but it seems to me that in LQG the spinnetworks can evolve in a way that is distantly analogous to Verlinde's polymer. In any case his 15 January blog post is very simple, and it clarifies the idea of an "entropic force":

==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 )

 

[atyy]

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

 

[marcus]

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

Quick to try conclusions! Please explain.
What the Loop people normally mean by "background independent" is that you don't have to provide a fixed initial geometry for things to happen in. No prior metric.

Have you glimpsed a prior background metric in Verlinde's approach? I doubt not that you have, but please spell it out for me. Exactly what background metric is he dependent on?

 

[atyy]

Quick to try conclusions! Please explain.
What the Loop people normally mean by "background independent" is that you don't have to provide a fixed initial geometry for things to happen in. No prior metric.

Have you glimpsed a prior background metric in Verlinde's approach? I doubt not that you have, but please spell it out for me. Exactly what background metric is he dependent on?

I am thinking something like "background independence" = "diff invariance" = "most general generally covariant" (like in http://arxiv.org/abs/0911.3165). So that's AS. AS also means the gravitational field is not emergent. So no emergence=AS=background independence. So emergence=not AS=not background independent.

But I guess there are some ways round it. AS I think would be local and fixed topology. So presumably one could have emergent background independent theories which are maybe non local or sum over topologies - like GFT hopes to be.

 

[marcus]

Your bringing in AS (asymptotic safety) confuses me. To keep thoughts clear I stick to one meaning of background independence (no fixed assumed metric).

Diffeo invariance is normally stated separately in LQG papers.

And background independence is extremely difficult to show in AS. Reuter has been obsessed with trying to do this, and never satisfied. He was already struggling to show that AS was BI when he talked at Loops 2007 in Morelia. He was working even harder at Loops 2008 in Nottingham.

The point is that on the face of it, AS is obviously not BI---it uses an initially specified metric. Reuter's method cannot get started without an initial metric. So on the face of it AS is not BI and everybody can see this. (How he tries to work around this is another matter.)

So let's set aside the discussion of AS, which doesn't really enter here I think, and just look at Verlinde's concept. Please tell me how it is NOT background independent, in the normal LQG usage of the term.
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?