Fractional quantum mechanics meets quantum gravity phenomenology

TL;DR

This paper links fractional quantum mechanics with quantum gravity phenomenology, suggesting experiments in fractional quantum systems could model quantum gravity effects, including nonlocal behaviors and fractal dimensions.

Contribution

It establishes a novel connection between fractional quantum mechanics and quantum gravity phenomenology, providing a new framework for experimental exploration of quantum gravity effects.

Findings

Fractional quantum mechanics can model deep infrared quantum gravity regimes.

Experiments with Bose-Einstein condensates can simulate quantum gravity phenomena.

Nonlocal behaviors in fractional systems suggest similar effects in quantum gravity.

Abstract

This letter extends previous findings on the modified Schr\"odinger evolution inspired by quantum gravity phenomenology. By establishing a connection between this approach and fractional quantum mechanics, we provide insights into a potential deep infrared regime of quantum gravity, characterized by the emergence of fractal dimensions, similar to behaviors observed in the deep ultraviolet regime. Additionally, we explore the experimental investigations of this regime using Bose-Einstein condensates. Notably, our analysis reveals a direct implication of this analogy: general experiments probing fractional quantum mechanics may serve as equivalent models of quantum gravity. We identify instances of nonlocal behavior in such systems, suggesting an analogous phenomenon of nonlocality in quantum gravity.