Inconstant Planck's constant

TL;DR

This paper explores the hypothesis that Planck's constant varies randomly over time, affecting quantum system evolution, and discusses experimental bounds on such fluctuations based on quantum and electromagnetic experiments.

Contribution

It introduces a model where Planck's constant fluctuates randomly and analyzes its impact on quantum systems' dynamics, proposing experimental methods to constrain these fluctuations.

Findings

Time evolution of quantum systems is altered by Planck's constant fluctuations.

Interferometric and electromagnetic cavity experiments can set bounds on fluctuation parameters.

The model suggests potential observable deviations from standard quantum mechanics.

Abstract

Motivated by the Dirac idea that fundamental constant are dynamical variables and by conjectures on quantum structure of spacetime at small distances, we consider the possibility that Planck constant $\hbar$ is a time depending quantity, undergoing random gaussian fluctuations around its measured constant mean value, with variance $\sigma^2$ and a typical correlation timescale $\Delta t$. We consider the case of propagation of a free particle and a one--dimensional harmonic oscillator coherent state, and show that the time evolution in both cases is different from the standard behaviour. Finally, we discuss how interferometric experiments or exploiting coherent electromagnetic fields in a cavity may put effective bounds on the value of $\tau= \sigma^2 \Delta t$.