Quest for time variation of Planck constant

Emilio Fiordilino

doi:10.1140/epjp/s13360-020-01031-1

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2024 Impact factor 2.9

EPJ PLUS - Condensed Matter and Complex Systems

Eur. Phys. J. Plus (2021) 136: 54
https://doi.org/10.1140/epjp/s13360-020-01031-1

Regular Article

A new time standard and parametric chaos

Emilio Fiordilino^a

Dipartimento di Fisica e Chimica - Emilio Segré, Università degli Studi di Palermo, Via Archirafi 36, 90123, Palermo, Italy

^a emilio.fiordilino@unipa.it

Received: 23 September 2020
Accepted: 16 December 2020
Published online: 7 January 2021

Abstract

Recent observations suggest a time variation of the fine structure constant $α = e^{2} / ħ c$ $\alpha =e^2/\hbar c$ on a time scale of the age of the Universe. We conjecture that the dependence is to be attributed to the Planck constant $ħ \to ħ_{0} f (t)$ $\hbar \rightarrow \hbar _0f(t)$ , define the cosmological time $τ = \int_{0}^{t} f (t^{'}) d t^{'}$ $\tau = \int _0^t f(t') \mathrm{d}t'$ and derive a form of the Schrödinger equation which takes into account the variation of $ħ$ $\hbar$ . As a first result, the solution of the equation for an atom interacting with a long resonant laser field predicts a sizeable variation of the population of the atomic levels. As a second result, we find that the time dependence of the Planck parameter introduces a new form of chaotic behaviour which is not due to the initial conditions.