By exploiting Einstein’s rate-equation approach [A. Einstein, Phys. Z. 18, 121 (1917)] to Planck’s law of blackbody radiation [M. Planck, Ann. Phys. 309, 553 (1901)], we obtain a simple relation between the population densities of the two energy levels of the atomic oscillators in the walls of the black body, as assumed by Einstein in his paper from 1917, and the occupation numbers in a photonic excited and ground state. This relation establishes a quantum principle for photons and, more generally, all bosons, which has the same physical relevance as Pauli’s exclusion principle [W. Pauli, Z. Phys. 31, 765 (1925)], which is the quantum principle for fermions. We demonstrate the equivalence of these two quantum principles by inserting either of them into the Boltzmann distribution, thereby transforming the Boltzmann distribution into either the Fermi-Dirac [E. Fermi, Rendiconti Lincei 3, 145 (1926)] and Bose-Einstein [Bose, Z. Phys. 26, 178 (1924)] distribution.