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 in the atmosphere at extremely low frequencies. It is shown that the speed of light in the frequency range 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 $m_{\gamma }\lesssim 4\times {10}^{-52}\mathrm{k}\mathrm{g}$ to date.

Figure 1

The experimentally observed fractional accuracy of the speed of light (●) derived from theoretical modeling with Maxwell’s equations can be constrained by a maximum ionospheric reflection height perturbation $\sim \pm 1.5\mathrm{k}\mathrm{m}$ (dashed lines).

Figure 2

The photon rest mass as a function of frequency and ionospheric reflection height perturbations (solid line). The smallest upper limit of the photon rest mass (●) is determined by the smallest radio wave frequency and compared to virtual photon rest mass determinations from the Earth’s (dash-dotted line) and Jupiter’s magnetic field (dashed line).