Comment on time-variation of fundamental constants

TL;DR

The paper argues that only dimensionless fundamental constants can meaningfully vary over time, criticizing claims about varying dimensional constants and addressing recent debates and criticisms in the field.

Contribution

It clarifies the conceptual distinction between dimensionless and dimensional constants and refutes recent claims that dimensional constants' variation has physical meaning.

Findings

Dimensionless constants can vary meaningfully over time.

Claims about varying dimensional constants lack operational meaning.

The paper refutes specific recent claims and criticisms in the literature.

Abstract

The possible time variation of dimensionless fundamental constants of nature, such as the fine-structure constant $\alpha$, is a legitimate subject of physical enquiry. By contrast, the time variation of dimensional constants, such as $\hbar$, $c$, $G$, $e$, $k$,... which are merely human constructs whose number and values differ from one choice of units to the next, has no operational meaning. To illustrate this, we refute a recent claim of Davies et al that black holes can discriminate between two contending theories of varying $\alpha$, one with varying $c$ and the other with varying $e$. In Appendix A we respond to criticisms by P. Davies and two Nature referees. In Appendix B we respond to remarks by Magueijo and by T. Davis. In Appendix C we critique recent claims by Copi, A. Davis and Krauss to have placed constraints on $\Delta G/G$.} In Appendix D we provide extracts of a lecture by Dirac, of which we have only recently become aware, which includes the comment "Talking about whether a thing is constant or not does not have any absolute meaning unless that quantity is dimensionless".