Quantum Electromagnetic Zero-Point Energy and Retarded Dispersion Forces

Abstract

In a manner quite analogous to the demonstration of a connection between nonrelativistic Schr\"odinger quantum mechanics and classical particle theory in the presence of a random force, it is shown that free-field quantum electrodynamics bears a close resemblance to classical electrodynamics in the presence of a randomly fluctuating transverse field. In particular, the energy eigenvalues and eigenfunctions of the quantum theory are found to be exactly the field energies and probability densities for the stationary probability distributions of randomly fluctuating normal coordinates. The result provides the direct connection between Casimir's zero-point energy calculations and Lifshitz's general theory for retarded dispersion forces between macroscopic obejcts. As an illustration of the connection, the attractive force between two conducting parallel plates is calculated from a single physical point of view, but by two alternative methods, one running through to Casimir's zero-point energy ideas, and the other following a calculation via the Maxwell stress tensor in analogy with Lifshitz's procedure.