Fractional quantum mechanics meets quantum gravity phenomenology

Abstract

This letter extends previous findings on the modified Schrödinger 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.

7 pages, two columns, 3 figures. Updated version with extended discussion on Barrow entropy, fractional powers of the Planck scale, temperature regime of validity and enhanced discussion on the analog optics model. Matches published version

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• The 300 TeV photon from GRB 221009A: a Hint at Non-linear Lorentz Invariance Violation?
• Gravitational Foundations and Exact Solutions in $n$-Dimensional Fractional Cosmology
• Fractional entropy of the Brown-Kuchař dust in fractional anti-de Sitter quantum gravity
• Emergent $\Lambda$CDM cosmology from a measure-induced deformation of the Newtonian action
• Coherence and Entanglement in a Non-commutative Spacetime