Diffusion in quantum gravity

Details Diffusion in quantum gravity Diffusion in quantum gravity

2012-04-11

arxiv.org/abs/1204.2550v1

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, 1 figure

Scientific paper

The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is controlled by a multiscale fractional diffusion equation, and physically interpreted as a composite stochastic process. The simplest example is a fractional telegraph process, describing quantum spacetimes with a spectral dimension equal to 2 in the ultraviolet and monotonically rising to 4 towards the infrared.

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