Analogy between turbulence and quantum gravity: beyond Kolmogorov's 1941 theory

TL;DR

This paper explores the analogy between turbulence and quantum gravity, proposing an extension beyond Kolmogorov's 1941 theory to support the idea of a fractal quantum spacetime and introducing methods to analyze its scaling properties.

Contribution

It extends the turbulence-quantum gravity analogy beyond K41 theory, reconciling fractal quantum spacetime with recent quantum gravity models like Horava-Lifshitz.

Findings

Fractal quantum spacetime can be compatible with Horava-Lifshitz gravity.

Singular quantum wavefunctions are implied by this compatibility.

Operational procedures based on Extended Self-Similarity are proposed for analyzing quantum gravitational fluctuations.

Abstract

Simple arguments based on the general properties of quantum fluctuations have been recently shown to imply that quantum fluctuations of spacetime obey the same scaling laws of the velocity fluctuations in a homogeneous incompressible turbulent flow, as described by Kolmogorov 1941 (K41) scaling theory. Less noted, however, is the fact that this analogy rules out the possibility of a fractal quantum spacetime, in contradiction with growing evidence in quantum gravity research. In this Note, we show that the notion of a fractal quantum spacetime can be restored by extending the analogy between turbulence and quantum gravity beyond the realm of K41 theory. In particular, it is shown that compatibility of a fractal quantum-space time with the recent Horava-Lifshitz scenario for quantum gravity, implies singular quantum wavefunctions. Finally, we propose an operational procedure, based on Extended Self-Similarity techniques, to inspect the (multi)-scaling properties of quantum gravitational fluctuations.