Constraining the photon mass via Schumann resonances

The photon is the paradigm for a massless particle and current experimental tests set severe upper bounds on its mass. Probing such a small mass, or equivalently large Compton wavelength, is chal-lenging at laboratory scales, but planetary or astrophysical phenomena may potentially reach much better sensitivities. In this work we consider the effect of a finite photon mass on Schumann resonances in the Earth-ionosphere cavity, since the TM modes circulating Earth have eigen-frequencies of order O (10 Hz) that could be sensitive to m γ ≈ 10 − 14 eV / c 2 . In particular, we update the limit from Kroll [Phys. Rev. Lett. 27 , 340 (1971)], m γ ≤ 2 . 4 × 10 − 13 eV / c 2 , by considering realistic conductivity profiles for the atmosphere. We find the conservative upper bound m γ ≤ 2 . 5 × 10 − 14 eV / c 2 , a factor 9.6 more strict than Kroll’s earlier projection.