A ratio-locked radio signature of a universal shift in the electron mass

Abstract

A universal fractional shift ε in the electron mass would imprint fixed relative shifts across radio bands, with ratios set by atomic physics and independent of ε itself. That multi-band pattern — and the falsification it enables — is the content of this paper, not a competitive bound on the amplitude. Methanol absorption already constrains |Δμ/μ| at the few×10^{-7} level, some thirty-five times tighter than the best 21 cm reinterpretation quoted below; a single molecular comparison cannot, however, test whether a shift lies in m_e rather than in a coupling, nor whether every band shares it. We derive how such a shift would propagate: +2 for the hydrogen 21 cm hyperfine frequency, +1 for radio recombination lines, −1 for a dispersion-measure reconstruction (degenerate with the fitted column unless an independent electron column is supplied), −1 or −3 for synchrotron characteristic frequency according as the emitting population is labelled by Lorentz factor or by energy, and −2 for Faraday rotation. Only the 21 cm and Faraday rows are presently usable in a Gaussian multi-band fit; the other three are theoretical propagation channels, not simultaneous precision measurements available today. The pattern separates a varying electron mass from a varying fine-structure constant by sign structure, and the hydrogen-to-deuterium hyperfine ratio is an internal control on universality. We treat ε as a free amplitude to be fitted, not predicted, and commit to no mechanism. The construction is a theoretical template for multi-band programmes, not a new observational bound or an end-to-end survey forecast. A single band deviating from its assigned weight falsifies the pattern.