Effective Photon Mass Suppression by Path-Ensemble Averaging: A Phenomenological Hypothesis.

We examine the phenomenological hypothesis that the photon effective mass entering macroscopic propagation is a suppressed value $\tilde m = m_0/N$, where $m_0$ is an experimental upper bound and $N$ a dimensionless suppression factor associated with a path ensemble. We state explicitly that this relation is an ansatz: it is not derived from the path integral and no mechanism for $N$ is proposed. We compute the Compton length and the dispersion delay as functions of $N$ and show that, under the model-dependent galactic bounds on the Proca vector-potential energy, the ansatz requires $N \gtrsim 3\times10^{8}$–$10^{9}$. The associated time-of-flight signature is many orders of magnitude below any foreseeable sensitivity, so the hypothesis is at present consistent but not falsifiable by dispersion tests.