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

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 ${\mu }^2=(1.04\mathrm{}\pm 1.2)\times {10}^{-19\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$. Expressed as a deviation from Coulomb's law of the form $\frac{1}{r^{2+q}}$, our experiment gives $q=(2.7\mathrm{}\pm 3.1)\times {10}^{-16\mathrm{}}$. This result extends the validity of Coulomb's law by two orders of magnitude.