The Zeldovich Number: A Universal Dimensionless Measure for the Electromagnetic Field

In this paper 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 both the classical and the quantum theory. In particular, we find that this number—called here the Zeldovich number—for macroscopic systems is very large, of the order of 1020. For the hydrogen atom in the ground state, the Zeldovich number is equal to 0.025 and for the xenon atom it is around 50.