Hydrogen 21 cm Constraints on the Photon's Spin Scale

We explore the fundamental but untested possibility that the photon is a continuous spin particle (CSP) with a small but non-zero spin Casimir $\rho$. When $\rho\neq 0$, the familiar polarization modes of the photon transform non-trivially under Lorentz boosts, leading to deviations from familiar QED. Surprisingly, these deviations are strongest at low energy, but smoothly vanish in the $\rho\rightarrow 0$ limit. In this letter, we compute corrections to the hydrogen 21cm transition rate, which is expected to be particularly sensitive given the small hyperfine energy splitting $\omega$. We find deviations from QED $\propto \rho^2 \alpha^2/\omega^2$ at leading order, suggesting experimental constraints $\rho\lesssim 1$ meV. Building on this work, we expect that a range of other atomic, molecular, or condensed matter systems could be used to provide even more stringent tests of $\rho$ in electromagnetic interactions.