New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass

Abstract

A high-frequency test of Coulomb's law is described. The sensitivity of the experiment is given in terms of a finite photon rest mass using the Proca equations. The null result of our measurement expressed in the form of the photon rest mass squared is ${\ensuremath{\mu}}^{2}=(1.04\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ ${\mathrm{cm}}^{\ensuremath{-}2}$. Expressed as a deviation from Coulomb's law of the form $\frac{1}{{r}^{2+q}}$, our experiment gives $q=(2.7\ifmmode\pm\else\textpm\fi{}3.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. This result extends the validity of Coulomb's law by two orders of magnitude.