Spontaneous dimensional reduction of quantized spacetime

[tom.stoer]

Interesting paper:

http://arxiv.org/abs/1009.1136v1
The Small Scale Structure of Spacetime
Steven Carlip
(Submitted on 6 Sep 2010)
Abstract: Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the strong-coupling limit of the Wheeler-DeWitt equation. If this description proves to be correct, it suggests a fascinating relationship between small-scale quantum spacetime and the behavior of cosmologies near an asymptotically silent singularity.

 

[atyy]

Do you think BKL and Kasner spaces are mentioned in a related way in http://arxiv.org/abs/0912.0854 ?

 

[tom.stoer]

O damn; do you want me to understand this 11-dim. magic?

 

[atyy]

O damn; do you want me to understand this 11-dim. magic?

I was hoping you'd explain it to me

 

[atyy]

I guess Carlip is trying to get it even without a classical spacelike singularity.

But the point of view expressed in http://arxiv.org/abs/0705.2643 "It is noteworthy that all reference to space and time has disappeared in (6). ...More succinctly, taking the quantum coset dynamics (6) as a guiding principle, the correct theory of quantum gravity may well turn out to be background independent in the sense that near the singularity, the theory — rather than ‘quantizing’ the spatial geometry, or some other spatially extended background structure — simply does away with the background altogether, whence the whole issue would become moot!" - seems pretty close to Carlip's.

The other question would be whether the E11 thing holds away from such highly symmetrized conditions. I remember seeing an argument for that somewhere, but can't remember right now. I listed some reviews of the E11 thing here https://www.physicsforums.com/showthread.php?t=424902 .

 

[marcus]

Interesting paper:

http://arxiv.org/abs/1009.1136v1
The Small Scale Structure of Spacetime
Steven Carlip
(Submitted on 6 Sep 2010)
Abstract: Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the strong-coupling limit of the Wheeler-DeWitt equation. If this description proves to be correct, it suggests a fascinating relationship between small-scale quantum spacetime and the behavior of cosmologies near an asymptotically silent singularity.

There's a video of Carlip giving this talk, in July 2009, about "spontaneous dimensional reduction" (in CDT, AsymSafe, Loop, String, and finally in a kind of suggestive classical imitation).
http://www.ift.uni.wroc.pl/~planckscale/movie/

You may have seen it already. It was at the (Breslau) Wroclaw XXV Max Born conference on the Planck scale.

Later in 2009 I saw Carlip give the very same talk in a Berkeley seminar, with the audience being mostly Dr. Hozhava and his postdocs/grad students. For some reason Horava seemed irritable and snippy. It seemed to me that Carlip was being nice and mentioning String along with the other approaches but apparently he didn't show enough respect for String to satisfy his host.

In the Wroclaw presentation he talked about "asymptotic silence". It was in a Kasner/BKL/Mixmaster context. With curvature going chaotically to infinity, things got so hectic that adjacency began to break down. Neighbor points couldn't talk to each other. Lightcones shrank effectively down to timelike lines.

So 4D space begins to "lose touch with itself" and in a way it "goes numb". He did not say this. He simply said "asymptotic silence" and described things geometrically. The other words are my impressions from his Wroclaw and Berkeley talks.

I can see how dimensionality could be reduced, then,
1. if adjacency/accessibility is so badly damaged that the spatial volume does no longer grow as the cube of the radius
2. or a heat kernel random walker does not get lost so easily (because he can hardly get anywhere in the cramped lightcones) and is more likely to accidentally return home. This is the "spectral dimension" measure.

So Carlip is encouraging the QG people to believe, by telling them "look, even in certain limited situations, classical itself imitates in a limited way what you all, in your various ways, have found happening."

Carlip's paper will be chapter in the George Ellis Festschrift:
http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521114400

The Ellisfest was meant to bring Loop, CDT, String and other QG together and get them talking, maybe even sharing ideas.
Ellis thought constructive dialog should be encouraged, so he made his 70th birthday celebration a chance for that kind of thing.
Many of the paper from that 2009 conference are already on line as preprint. I have a thread about it here:
https://www.physicsforums.com/showthread.php?p=2872109#post2872109

 

[marcus]

Spontaneous dimensional reduction was the subject of a recent popular article in New Scientist
http://www.newscientist.com/article/mg20727793.400-dimensions-vanish-in-quantum-gravity.html

It gave some intuition and made conversation with Renate Loll and Steve Carlip. Not great science journalism, but still might be of interest.

 

[czes]

There is an article of Gerard 't Hooft Dimensional Reduction in Quantum Gravity http://arxiv.org/abs/gr-qc/9310026
If we consider the matter and the space are emergent from a quantum information relations, the dimensions are not needed then in such a holographic universe.
A vacuum is a pure relation between virtual particles-antiparticles as a two dimensional network and observer's relation creates third dimension in an empty vacuum.
Particle with a rest mass needs more relation to define it and there is 11-dimensional chromodynamics.
Carlip and Loll didn't wrote about holographic universe, I think, but may be it will be a reason ?

 

[czes]

Marcus found an interesting article of K.H.Knuth
http://arxiv.org/abs/1009.5161
In the modern physics the space seems to be emergent and not fundamental. Therefore dimensions are the minimum number of the relations we need to define empty space, space with a mass or space in a complex particles.