The Zeldovich number: A universal dimensionless measure for the electromagnetic field

Abstract

In this work we extend the Zeldovich formula, which was originally derived for the free electromagnetic field and was interpreted as the number of photons. We show that our extended formula gives a universal dimensionless measure of the overall strength of electromagnetic fields: free fields and fields produced by various sources, in classical and in quantum theory. In particular, we find that this number (the Zeldovich number) for macroscopic systems is huge, of the order of $10^{20}$. For the hydrogen atom in the ground state it is equal to 0.025 and for the xenon atom it is around 50.