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mfb

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In our current theories, the number of dimensions has to be fixed by hand, but it could be possible that it can be calculated in some more fundamental theory.

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julian

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Doesn't CDT (Causal dynamical triangulation) a background approach to quantum gravity appear to have a good semi-classical description - in that at large scales, it re-creates the familiar 4-dimensional spacetime, but it shows a dynamical reduction of spacetime to two dimensions at the Plank scale and a fractal structure of slices of constant time?

And the discovery that in the limit of short distances, spacetime becomes effectively two-dimensional may indicate the presence of a dynamically generated ultraviolet cutoff: "...quantum gravity may be "self-renormalizing" at the Planck scale, by virtue of a mechanism of dynamical dimensional reduction."

And the discovery that in the limit of short distances, spacetime becomes effectively two-dimensional may indicate the presence of a dynamically generated ultraviolet cutoff: "...quantum gravity may be "self-renormalizing" at the Planck scale, by virtue of a mechanism of dynamical dimensional reduction."

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Imho, there are sound hopes to expect that dimensionality of spacetime should eventually be understandable im terms of spontaneous decoupling of internal vs external information between interaction observers. Ie spacetime may be seen as the interconnecting structure between subsystems, and this structure is then by construction the result of a negotiation game - spacetime is simply what everyone that disagrees can agree about.

/Fredrik

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What do you mean by "dimension" of space and time? Do you mean the size? Or the fact that they are measured in dimensional units (meter, second)? Or the topological dimension (3 for space and 1 for time)?

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ohwilleke

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In principle, you could show that space-time is emergent by showing that a tiny share of space-time connections are non-local. Arguably, the need to include a small number of sub-luminal and super-luminal paths (at reduced weights with distance from "c") in photon path integrals is suggestive evidence of these kinds of pervasive, but slight non-local connections which would point to the emergent picture.

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julian

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http://arxiv.org/abs/1605.05694

Spontaneous Dimensional Reduction in Quantum Gravity

S. Carlip

(Submitted on 18 May 2016)

Hints from a number of different approaches to quantum gravity point to a phenomenon of "spontaneous dimensional reduction" to two spacetime dimensions near the Planck scale. I examine the physical meaning of the term "dimension" in this context, summarize the evidence for dimensional reduction, and discuss possible physical explanations.

http://arxiv.org/abs/1605.05979

On the UV dimensions of Loop Quantum Gravity

Michele Ronco

(Submitted on 19 May 2016)

Planck-scale dynamical dimensional reduction is attracting more and more interest in the quantum- gravity literature since it seems to be a model independent effect. However different studies base their results on different concepts of spacetime dimensionality. Most of them rely on the spectral dimension, others refer to the Hausdorff dimension and, very recently, it has been introduced also the thermal dimension. We here show that all these distinct definitions of dimension give the same outcome in the case of Loop Quantum Gravity. This is achieved by deriving a modified dispersion relation from the hypersurface-deformation algebra with quantum corrections. Moreover we also observe that the number of UV dimensions can be used to constrain the ambiguities in the choice of these Loop-Quantum-Gravity modifications of the Dirac spacetime algebra. In particular, we find that the the simplest polymerization of connections i.e. K→sin(δK)δK, which is much used in the literature, cannot reproduce the shared expectation of dUV=2.

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haushofer

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https://www.sns.ias.edu/ckfinder/userfiles/files/Reflections(3).pdf

However, string theory doesn't seem to give an explanation of why we have one time direction; also, it seems to allow for two spatial dimensions on top of the often quoted nine; we simply don't know how to 'decompactify' such a theory to three.

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