Absence of Quantum-Electrodynamic Corrections to the Charge of the Electron as Measured in Josephson Junction Experiments

The ac Josephson effect enables one to measure the ratio $\frac{\Delta \mu }{h}$, where $\Delta \mu$ is the electrochemical potential difference between two weakly coupled superconductors. Combined with an independent measurement of the electrostatic potential difference $V$, this measurement determines the ratio $\frac{e}{h}$. This determination rests on the fact that a voltage difference is defined so that the electrochemical potential difference is $\Delta \mu =eV$, where $e$ is the charge on the free electron. Further, while we argue that it is not directly relevant to the determination of $\frac{e}{h}$, there are no quantum-electrodynamic corrections to the electrostatic term in the chemical potential difference $\Delta \mu$.