Spontaneous dimensional reduction of quantized spacetime

In summary, a few lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. This suggests a fascinating relationship between small-scale quantum spacetime and the behavior of cosmologies near an asymptotically silent singularity.
  • #1
tom.stoer
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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.
 
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  • #3
O damn; do you want me to understand this 11-dim. magic?
 
  • #4
tom.stoer said:
O damn; do you want me to understand this 11-dim. magic?

I was hoping you'd explain it to me :smile:
 
  • #5
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 .
 
  • #6
tom.stoer said:
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
 
Last edited:
  • #8
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 ?
 
  • #9
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.
 

What is spontaneous dimensional reduction of quantized spacetime?

Spontaneous dimensional reduction of quantized spacetime is a theoretical concept in physics that suggests that at extremely small scales, the fabric of spacetime may undergo a spontaneous reduction in the number of dimensions it has. This means that at the smallest levels of existence, our familiar 3-dimensional world may appear to be more like a 2-dimensional surface.

What is the evidence for spontaneous dimensional reduction of quantized spacetime?

Currently, there is no direct evidence for spontaneous dimensional reduction of quantized spacetime, as it is a theoretical concept that has not yet been observed or tested. However, some theories in quantum gravity, such as loop quantum gravity, suggest that this phenomenon may occur at the Planck scale, which is the smallest possible scale in the universe.

How does spontaneous dimensional reduction of quantized spacetime affect our understanding of the universe?

If proven to be true, spontaneous dimensional reduction of quantized spacetime would have a significant impact on our understanding of the universe. It would challenge our current understanding of space and time and could potentially lead to a new theory of quantum gravity that unifies the four fundamental forces of nature.

What are the implications of spontaneous dimensional reduction of quantized spacetime for practical applications?

At this time, there are no known practical applications of spontaneous dimensional reduction of quantized spacetime. However, further research in this area could potentially lead to new technologies and advancements in our understanding of the universe.

Are there any experiments or observations that could provide evidence for spontaneous dimensional reduction of quantized spacetime?

Scientists are currently exploring various ways to test the concept of spontaneous dimensional reduction of quantized spacetime. One possible method is to study the properties of particles at extremely small scales and look for any anomalies that could be attributed to a reduction in dimensions. Other experiments involve studying the behavior of gravity at the Planck scale to see if it exhibits any signs of dimensional reduction.

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