Evidence that photons have extension in space


Abstract: Satyendra Nath Bose realized that there was a logical inconsistency in the derivation of Planck's radiation law since the derivation used to obtain the temperature-independent prefactor in the blackbody radiation law had been based in part on classical wave hypotheses, such as the number of degrees of freedom of the ether. Bose worked out a strictly quantum derivation by combining the quantum hypothesis with statistical mechanics to determine the number of states of each mode that would occupy a 6-dimensional phase space. Here I use the model of an extended photon to show that the temperature-independent prefactor of Planck's radiation law can be derived in an alternative manner by calculating how many extended photons of each mode would fill a 3-dimensional Euclidean space. By combining my derivation of the temperature-independent prefactor with Planck's temperature-dependent probability distribution, I show that all of the major equations that describe blackbody radiation can be derived from the assumption that the photon is an extended body in 3-dimensional Euclidean space. This derivation provides evidence for the suggestion that photons are neither mathematical points nor groups of infinite plane waves, but quantized and finite volume elements.

Keywords: Blackbody radiation, Planck's radiation law, photon

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