Physical interpretation of the Planck's constant based on the Maxwell theory

TL;DR

This paper derives the physical meaning of Planck's constant using Maxwell theory, showing how wave packets relate to photon behavior and black-body radiation, providing a classical explanation for quantum phenomena.

Contribution

It offers a novel derivation of Planck's constant from Maxwell theory and explains photon emission as an all-or-none process, linking classical wave theory to quantum concepts.

Findings

Energy of wave packets proportional to frequency

Photon emission follows all-or-none principle

Wave packets can behave like particles

Abstract

The discovery of the Planck's relation is generally regarded as the starting point of quantum physics. The Planck's constant h is now regarded as one of the most important universal constants. The physical nature of h, however, has not been well understood. It was originally suggested as a fitting constant to explain the black-body radiation. Although Planck had proposed a theoretical justification of h, he was never satisfied with that. To solve this outstanding problem, we used the Maxwell theory to directly calculate the energy and momentum of a radiation wave packet. We found the energy of the wave packet is indeed proportional to its oscillation frequency. This allows us to derive the value of the Planck's constant. Furthermore, we showed that the emission and transmission of a photon follows the principle of all-or-none. The "strength" of the wave packet can be characterized by zeta, which represents the integrated strength of the vector potential along a transverse axis. We reasoned that zeta should have a fixed cut-off value for all photons. Our results suggest that a wave packet can behave like a particle. This offers a simple explanation to the recent satellite observations that the cosmic microwave background follows closely the black-body radiation as predicted by the Planck's law.