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.
Blackbody radiation, Planck's radiation law, photon
"Evidence that photons have extension in space,"
Turkish Journal of Physics: Vol. 38:
1, Article 3.
Available at: https://journals.tubitak.gov.tr/physics/vol38/iss1/3