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

TL;DR

This paper extends the Zeldovich formula to provide a universal, dimensionless measure of electromagnetic field strength applicable across classical and quantum regimes, revealing vastly different values for macroscopic and atomic systems.

Contribution

The authors generalize the Zeldovich formula to create a universal measure of electromagnetic field strength applicable to various systems in classical and quantum physics.

Findings

Zeldovich number for macroscopic systems is about 10^{20}

For hydrogen atom in ground state, Zeldovich number is 0.025

For xenon atom, Zeldovich number is around 50

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.