Inconstant Planck’s constant

Abstract

Motivated by the Dirac idea that fundamental constants are dynamical variables and by conjectures on quantum structure of space–time at small distances, we consider the possibility that Planck constant [Formula: see text] is a time depending quantity, undergoing random Gaussian fluctuations around its measured constant mean value, with variance [Formula: see text] and a typical correlation timescale [Formula: see text]. 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 behavior. Finally, we discuss how interferometric experiments or exploiting coherent electromagnetic fields in a cavity may put effective bounds on the value of [Formula: see text].