Classical «quantization» of the free electromagnetic field: A puzzling solution to Maxwell’s equations

Abstract

It is shown that, as a consequence of a speculative adaptation of the concept of vacuum polarization, as introduced in quantum electrodynamics, Maxwell’s equations for the free electromagnetic field admit solutions suggesting lumped distributions of energy in space-time which allow introducing, in an entirely classical way, the concept of photon as a particlelike perturbation of vacuum. The corpuscular and wavelike features of the electromagnetic radiation are then reconciled and emerge in a natural and non-conflicting way. It appears then possible to interpret outside quantum mechanics and quantum electrodynamics such experimental results as the Compton effect, the photoelectric effect and others, calling for discretized distributions of electromagnetic energy. «Quantized» solutions of Maxwell’s equations are presented for plane and spherical propagations, with arbitrary polarization directions. The Compton effect is discussed in the framework of these solutions, as well as Young’s two-slit optical experiment and Aspect’s 1982 correlated-photon experiment. Equating tohv the electromagnetic (E/M) energy in the volume characterizing the space-time localization of energy, we obtain a numerical value for the electric charge polarizing the vacuum according to the proposed model. This charge happens to amount approximately to a multiple of the numerical value of the electron charge. This result could lend some support to the suggested speculative adaptation of the concept of vacuum polarization. It gives rise to a different fashion of approaching optics and its neighbouring fields.