Comment on time-variation of fundamental constants

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".