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

The discovery of the Planck relation is generally regarded as the starting point of quantum physics. 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 use the Maxwell theory to directly calculate the energy and momentum of a radiation wave packet. We find that the energy of the wave packet is indeed proportional to its oscillation frequency. This allows us to derive the value of Planck's constant. Furthermore, we show that the emission and transmission of a photon follows the all-or-none principle. The “strength” of the wave packet can be characterized by ζ, which represents the integrated strength of the vector potential along a transverse axis. We reason that ζ 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 Planck's law.