Kowalski path to entropic force

[marcus]

In my estimation the clearest path to entropic gravity has been shown by Jerzy Kowalski-Glikman. His 4 February paper has some definite advantages over anything that came out since. http://arxiv.org/abs/1002.1035

Kowalski-Glikman, you remember, was the organizer at Wroclaw of the July 2009 Planck Scale conference--probably that year's most successful QG/unification conference. I've been following his research beginning in 2004 and my impression is he rarely makes unnecessary moves---his output is consistently to the purpose. Credibility and track record are a plus.

Another advantage is that he points to where the underlying degrees of freedom should appear. Topological defects in the domain of a constrained topological field theory (BF).
So it's not some nebulous abstract entropy he's talking about. There are equations. There are arguments to support what in other papers may simply be assumed.

Another advantage is he gives a clear brief summary of the history---from its pre-1995 sources through Jacobson, Padmanabhan, Verlinde and Smolin to the present.

Another is that K-G was directly involved (with Laurent Freidel and Artem Starodubtsev) in developing a BF formulation of quantum gravity+matter---he knows the constrained topological field theory approach first hand. See
Freidel, K-G, Starodubtsev "Particles as Wilson lines of gravitational field" Physical Review D 2006; gr-qc/0607014

I expect we will see some further papers following this short note. So I want to start this thread to discuss K-G's 5 page note and whatever follows along the indicated path.

Again the link:
http://arxiv.org/abs/1002.1035
A note on gravity, entropy, and BF topological field theory
Jerzy Kowalski-Glikman
5 pages
(Submitted on 4 Feb 2010)
"In this note I argue that the expression for entropic force, used as a starting point in Verlinde's derivation of Newton's law, can be deduced from first principles if one assumes that that the microscopic theory behind his construction is the topological SO(4,1) BF theory coupled to particles."

 

[marcus]

I found some earlier comment by Kowalski-Glikman on Peter Woit's blog.
http://www.math.columbia.edu/~woit/wordpress/?p=330&cpage=1#comments

It was in a lively discussion with Laurent Freidel, Lee Smolin, Urs Schreiber, Aaron Bergman, and others.

An interesting point was where K-G explained why, in his version, DSR does not predict an energy-dependent speed of light.
http://www.math.columbia.edu/~woit/wordpress/?p=330&cpage=1#comment-7788
He has consistently maintained that view in his DSR papers, starting back in 2003:

Three K-G papers in 2003, that I commented on here:
https://www.physicsforums.com/showthread.php?t=11323
maintained that DSR does not involve an energy dependent speed of massless particles, contradicting Smolin's position on this.

We had a thread commenting on the 2006 discussion at Woit's
https://www.physicsforums.com/showthread.php?t=107417
but the link given there will no longer bring up the comments by Kowalski-Glikman. These were on "page 1" so to get them you have to click on "earlier comments". Which does work and gets you:
http://www.math.columbia.edu/~woit/wordpress/?p=330&cpage=1#comments

In February 2007, K-G gave a Perimeter talk, which a PF member, William Donnelly, attended and reported.
https://www.physicsforums.com/showthread.php?t=156193 Here's the Perimeter talk:
Gravity, Constrained BF theories, and DSR - Jerzy Kowalski-Glikman - 22/02/07 - 1:30 PM
Notice the overlap with his recent paper, three years later:
http://arxiv.org/abs/1002.1035
A note on gravity, entropy, and BF topological field theory
This is a propos of what I mentioned in the preceding post:
"...knows the constrained topological field theory approach first hand."

What I suspect is that, unlike some other people that Verlinde's paper started off on a new pursuit, Jerzy K-G already had in mind candidate degrees of freedom for entropic gravity to be based on. He was one those already prepared for this development.

The underlying degrees of freedom could possibly be topological, at least in part. There were those Freidel et al papers finding matter represented by filamentary topological defects, and this recent Misner business.

 

[czes]

Thank you Marcus for the links.
I think, there is also a thermodynamic arrow of time. When the entropy increases we say the time goes forth. Time stops when entropy is conserved. Therefore some physicists (Barbour, Zeh) say the time doesn't exist as a fundamental phenomenon.
Some people live healthy and the entropy of their body increases slowly - they have more time.
Unfortunately most processes are irreversible.

 

[marcus]

I see that Kowalski-Glikman has produced a couple of books

Towards Quantum Gravity (Springer 1999)
I'm not sure but his could be the first book on Quantum Gravity, aimed at introducing graduate students to this area of research. 1999. K-G edited it.
http://books.google.com/books?id=3OIEvmdMym4C&printsec=frontcover&dq=kowalski-glikman

Planck scale effects in astrophysics and cosmology (Springer 2005) Edited by Giovanni Amelino-Camelia and Jerzy Kowalski-Glikman.
http://books.google.com/books?id=RntpN7OesBsC&printsec=frontcover&dq=Kowalski-Glikman

CZES, I appreciate your comments and am glad you are finding some of the links useful.

A lot of people seem to share the perception of time as emergent and intimately related to thermodynamics.
Time isn't really understood (IMHO). It seems to have a kind of dual nature---geometric on the one hand, thermodynamic on the other.
Conventionally, time gets "geometrised" as just another axis, or coordinate. It gets incorporated as a feature of spacetime geometry. But that doesn't quite satisfy us because it leaves out thermodynamic aspects of time, like the arrow direction you mentioned.
So one can choose to treat time as emergent---basically not real, appearing only at macroscopic scale. Carlo Rovelli's essay "Forget Time" is an example---he presents a strong case for time being emergent.

Maybe this tension could be resolved by joining thermodynamics with geometry.
Bekenstein Hawking Unruh showed a connection in the 1970s. Certain kinds of geometry have temperature and entropy. Then Jacobson 1995 made a very strong connection deriving Gen Rel geometry from thermodynamics. Padmanabhan has written extensively on that in recent years. Verlinde, and Kowalski-Glikman are pushing in that direction.

At some point, in K-G's approach I want to stop calling it geometry and begin thinking of it as topology---still the thermodynamics of the shape of space, but a different deeper sort of shape.

 

[czes]

Hi Marcus
I am impressed. I thought the timelessness is a crazy idea of Barbour and some crazy philosophers. Carlo Rovelli is an excellent physicist and his example shows the timelessness become a scientific theory.
http://www.fqxi.org/data/essay-cont...f?phpMyAdmin=0c371ccdae9b5ff3071bae814fb4f9e9

All together suggests the space and time are emergent phenomena. A space-time is an usefull tool in General Relativity but in Quantum Gravity we have to find another tool. I think it could be a quantum information for example a non-local Compton wave length ?
Therefore I am interesting Cramer's Transactional Interpretation because it shows directly that space and time are created of the quantum information.
I am not a professional physicist but I read the links you write on the threads and I can learn a lot. Thank you for your work here.

 

[atyy]

BF+matter --> BF+constraint=LQG

Does this mean that LQG is emergent?

 

[marcus]

BF+matter --> BF+constraint=LQG

Does this mean that LQG is emergent?

Atyy, I'm interested in how you might answer this question yourself! I am sometimes not sure I understand how the word is being used. To me (just based on how I think of it) you can't always tell ahead of time whether the goal of a research program, like Loop, is emergent theory or fundamental---or for that matter effective. You can't always classify the endpoint of a research venture before it is reached.

To decide ahead of time whether a theoretical model that some group of people are fashioning is going to turn out to be this, that, or the other thing, seems to me like trying to foretell the future.

It's been said before: a quantum theory of geometry and matter is not meant to describe what nature IS, but rather to describe how it responds to measurement.

No mathematical theory can tell us what the world is made of, only how it behaves when subjected to experiment and observation. Two distinct theories could, I suppose, both be fundamental and both make exactly the same predictions---but employ entirely different mathematical gadgets and paraphernalia. The mathematical objects of our theories do not tell us what she is made of, but merely how she behaves.

So I am inclined not to call LQG's shots ahead of time but just wait and see how the community comes to regard it, if it achieves some testable formulation and passes some empirical checkpoints.

 

[marcus]

There's nevertheless a question lingering here.

Since I'd refrain from cataloging the goal of the LQG program as this that or the other type--with possibly-spurious finality since the program is in progress, with goals periodically reformulated--one natural question to ask how is it currently changing?

Something I'd like to understand better is this SO(4,1) BF trend in LQG. We have a bunch of papers on this topological field theory approach, by Krasnov, Freidel, Starodubtsev, Smolin, Kowalski-Glikman, and others. As I recall it goes back to around 2000 and the first spinfoam papers by John Baez. The plebanski action, that spinfoams are based on, is a BF theory.

The most recent goal statement I remember was Rovelli saying "to formulate quantum field theory without background spacetime [geometry]". That was at the strings 2008 conference. I also remember him saying something recently that I can't link to because I don't remember where or when exactly---he said the aim is not to quantize GR, but to construct a quantum theory that has GR as the appropriate limit. It is not important whether or not one arrives at the theory by way of some conventional quantization procedure, starting from GR. The important thing is to reach the quantum theory, not how you get there. And as he said at strings 2008, the problem is not that there are many such from which one must choose, rather at this stage it's to find even just one [backgroundless] quantum theory with the right behavior.

 

[marcus]

I made some extracts from the Kowalski-Glickman paper which may be useful here.
I guess part of the point is that what Verlinde needs to assume is already deduced from BF theory, by Kowalski.

These extracts give a kind of rough outline showing how the arguments in the paper are organized.

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

==quote Jerzy K-G==
The plan of this note is as follows. In the next section I will recall the formulation of gravity as a constrained SO(4, 1) BF theory and its coupling to particles.

These technical results will be needed for the derivation
of Verlinde’s entropic force... (page 2)
...

III. ENTROPY AND GRAVITY FROM TOPOLOGICAL FIELD THEORY
In the previous section I argued that if one couples the SO(4,1) topological BF theory (which after gauge breaking down to SO(3,1) is equivalent to General Relativity) to point particles, then the theory forces the particles to be accompanied by semi-infinite Misner strings... (page 3)

...
Knowing this let us turn to deducing the form of entropic force acting on the particle. Suppose the test particle of mass m is at distance R from the mass M, which we can assume to be also point-like. Consider now, as in Verlinde’s argument, ...(page 4)

Let me now turn to the main argument of this paper. It is well known that there is entropy associated with
Misner string, see [19], [20], [21], and [22] where it is argued that the entropy of Misner string ... (page 4)


...The entropy (3.2) adds to the original entropy of the screen, and since it is proportional to the test particle
displacement it leads to the emergence of the entropic force. Notice that since entropy increases when the test
particle moves towards the mass M this entropic force is attractive. Also when the test particle which was initially inside the screen moves outside, the entropy decreases...

Having (3.2) it is possible now to run the remaining part of the Verlinde’s argument essentially without modifications...(page 4)

IV. CONCLUSIONS AND OUTLOOK
In this note I argued that the form of entropic force being the starting form of the recent proposal of Verlinde
[6] to seek the origin of gravity in thermodynamics can be understood if one assumes that the fundamental degrees of freedom behind it are described by the topological BF theory coupled to particle(s). The reason for this is that, as shown in [16] and discussed in [17], a particle carrying the charge...

==endquote==

 

[atyy]

Atyy, I'm interested in how you might answer this question yourself! I am sometimes not sure I understand how the word is being used. To me (just based on how I think of it) you can't always tell ahead of time whether the goal of a research program, like Loop, is emergent theory or fundamental---or for that matter effective. You can't always classify the endpoint of a research venture before it is reached.

I don't follow the logic of this paper (where does the entropy of the Misner string come from?), but am pretty sure this paper intends gravity - or at least the constraint - to be emergent. The constraint term is not there in the fundamental theory, and emerges in some limit.

Loop is an interesting case. I believe it was intended to be fundamental (in Jacobson's and Verlinde's sense, not Smolin's) - eg. in the discussion on Peter Woit's blog you mentioned - Haelfix says LQG somehow surely requires a non-trivial fixed point, and Smolin agrees that it is interesting to work on LQG renormalization - ie. there should be a link with Asymptotic Safety, which is the definition on non-emergent gravity. However, I believe that LQG will turn out to be emergent. I was hoping through GFT. But recently I came across http://arxiv.org/abs/0907.2994. BTW, tensor networks are very "topological" http://arxiv.org/abs/1001.4517 (kidding, I don't know if this has anything to do with BF theory). More seriously, following Physics Monkey's lead, there is a relationship between BF theory and Kitaev's spin model http://arxiv.org/abs/0805.2536, which is related to Wen's string nets http://arxiv.org/abs/0809.2393 , http://arxiv.org/abs/0809.2821.

 

[marcus]

I don't follow the logic of this paper (where does the entropy of the Misner string come from?),...

I can't answer this right off, so let's look at the relevant part of Jerzy's paper:

==quote==
Let me now turn to the main argument of this paper.
It is well known that there is entropy associated with
Misner string, see [19], [20], [21], and [22] where it is
argued that the entropy of Misner string is intrinsically
defined. In particular, using methods of conformal field
theory Carlip [21] shows that the segment of the Misner
string of the length ∆x carries the entropy
∆S = (1/8πG) n ∆x = (1/8π) m ∆x . ...(3.1)
Although this result has not been rigorously established
in the present context of BF theory, it is unlikely that a
formula analogous to (3.1) does not hold in this case as
well. It seems clear that Misner string carries entropy, no
matter what is the theory describing local and/or topo-
logical degrees of freedom.
==endquote==

So he refers to [19] thru [22], in particular to Carlip's [21]


[19] S. W. Hawking and C. J. Hunter, “Gravitational entropy
and global structure,” Phys. Rev. D 59, 044025 (1999)
http://arxiv.org/abs/hep-th/9808085

[20] S. W. Hawking, C. J. Hunter and D. N. Page, “Nut
charge, anti-de Sitter space and entropy,” Phys. Rev. D
59, 044033 (1999) http://arxiv.org/abs/hep-th/9809035

[21] S. Carlip, “Entropy from conformal field theory at
Killing horizons,” Class. Quant. Grav. 16 (1999) 3327
http://arxiv.org/abs/gr-qc/9906126

[22] R. B. Mann, “Misner string entropy,” Phys. Rev. D 60
(1999) 104047 http://arxiv.org/abs/hep-th/9903229

The abstract of the first of these goes some way towards answering the question you raised:

Gravitational Entropy and Global Structure
S.W. Hawking, C.J. Hunter

"The underlying reason for the existence of gravitational entropy is traced to the impossibility of foliating topologically non-trivial Euclidean spacetimes with a time function to give a unitary Hamiltonian evolution. In d dimensions the entropy can be expressed in terms of the d-2 obstructions to foliation, bolts and Misner strings, by a universal formula. We illustrate with a number of examples including spaces with nut charge. In these cases, the entropy is not just a quarter the area of the bolt, as it is for black holes."

 

[atyy]

Yes, the reason I'm confused is that say in Carlip's and Mann's papers the entropy of the Misner string comes from underlying quantum degrees of freedom (in both cases a CFT, I think?). But in Kowalski-Glikman's paper, the Misner string is a fundamental quantum degree of freedom - or not?

 

[marcus]

Yes and it is appropriate to be confused at that point because (remember Jerzy's is a brief preliminary note) at that point he waves his hands!
As I recall he says, "well entropy is entropy. If they found it in their context, then it should be possible to find it in my context."

I should look back and find the quote. I think his expectation that that logical gap can be filled is not on-the-face unreasonable. Oh, the passage where he solemnly and deliberately waves his hands is something I already quoted:
Although this result has not been rigorously established
in the present context of BF theory, it is unlikely that a
formula analogous to (3.1) does not hold in this case as
well. It seems clear that Misner string carries entropy, no
matter what is the theory describing local and/or topo-
logical degrees of freedom.

In other words, "I still have to check this in the BF theory context, but entropy is entropy, a physical something that rises above the details of which math model, so I'm fairly sure it will check out."

You are quite right to point out the lacuna.

 

[marcus]

...
http://arxiv.org/abs/hep-th/9808085
Gravitational Entropy and Global Structure
S.W. Hawking, C.J. Hunter

"The underlying reason for the existence of gravitational entropy is traced to the impossibility of foliating topologically non-trivial Euclidean spacetimes with a time function to give a unitary Hamiltonian evolution. In d dimensions the entropy can be expressed in terms of the d-2 obstructions to foliation, bolts and Misner strings, by a universal formula. ..."

There's something interesting here that goes well beyond the AdS/CFT context, I think.

You recall that Hawking's Euclidean path integral approach to QG never worked out---Jan Ambjorn for one worked on it all thru the 1990s. Finally in 1998 Ambjorn and Loll cut the Gordian and FORCED there to be a foliation.
That is what "Causal Dynamical Triangulations" is. It is Hawking's path integral using the natural simplex regularization, with a timeslice foliation required, sort of ad hoc.

A vague dim intuition comes in here and points out that Loll CDT has so far not successfully dealt either with matter or with black holes. There are some papers but it didn't yet get off the ground in those departments.

So what is going on. Is there a connection between matter and obstructions to foliation, like Misner stringularities, the Misner defects that Jerzy K-G is mentioning?