Physical interpretation of the Planck’s constant based on the Maxwell theory
Donald C. Chang Macro-Science Group, Division of LIFS Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Email: bochang@ust.hk
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 ζ , which represents the integrated strength of the vector potential along a transverse axis. We reasoned 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 the Planck’s law.
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