Résumé
We present an exact statistical formulation of the inverse of the fine-structure constant, [Formula: see text], based on Planck’s law for a photon gas in a black body. This formulation is based on a relationship between [Formula: see text] and the statistical properties of the photon gas, specifically the variance and the average value of the photon number. The result is obtained through an analysis that connects the fine-structure constant to thermodynamic parameters of the black body, that is temperature and volume. The accuracy of the model is limited only by the precision of the fundamental physical constants used. Finally, we discuss the implications of the theory on the shot-noise associated with fluctuations of the photon particle-number.