ABC of multi-fractal spacetimes and fractional sea turtles

Gianluca Calcagni

doi:10.1140/epjc/s10052-016-4021-0

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arXiv · 1602.01470

ABC of multi-fractal spacetimes and fractional sea turtles

Gianluca Calcagni

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Abstract

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with $q$-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

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Gianluca Calcagni. 2016-04-06. ABC of multi-fractal spacetimes and fractional sea turtles. https://doi.org/10.1140/epjc%2Fs10052-016-4021-0

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