Duncan, Anthony; Janssen, Michel: Pascual Jordan's Resolution of the Conundrum of the Wave-Particle Duality of Light

In 1909, Einstein derived a formula for the mean square energy fluctuations in a small subvolume of a box filled with black-body radiation. This formula is the sum of a wave term and a particle term. Einstein concluded that a satisfactory theory of light would thus have to combine aspects of a wave theory and a particle theory. In the following decade, various attempts were made to recover this formula without Einstein’s light quanta. In a key contribution to the 1925 Dreimännerarbeit with Born and Heisenberg, Jordan showed that a straightforward application of Heisenberg’s Umdeutung procedure, which forms the core of the new matrix mechanics, to a system of waves reproduces both terms of Einstein’s fluctuation formula. Jordan thus showed that these two terms do not require separate mechanisms, one involving particles and one involving waves. In matrix mechanics, both terms arise from a single consistent dynamical framework.