Probing the speed of light with radio waves at extremely-low frequencies

The speed of light, a fundamental physical constant and thought to be independent of frequency, is tested here with naturally occurring radio waves from lightning discharges in the atmosphere at extremely-low frequencies. It is shown that the speed of light in the frequency range \mbox{5-50 Hz} is known with an accuracy determined by perturbations of the ionospheric reflection height associated with space weather phenomena, which place an upper limit on the photon rest mass $m_\gamma$\mbox{$\stackrel{\scriptscriptstyle <}{\scriptscriptstyle \sim}$4\cdot 10^{-52}$ kg} to date.\\