Pascual Jordan's resolution of the conundrum of the wave-particle duality of light

Abstract

In 1909, Einstein derived a formula for the mean square energy fluctuation in black-body radiation. This formula is the sum of a wave term and a particle term. In a key contribution to the 1925 Dreimaennerarbeit with Born and Heisenberg, Jordan showed that one recovers both terms in a simple model of quantized waves. So the two terms do not require separate mechanisms but arise from a single consistent dynamical framework. Several authors have argued that various infinities invalidate Jordan's conclusions. In this paper, we defend Jordan's argument against such criticism. In particular, we note that the fluctuation in a narrow frequency range, which is what Jordan calculated, is perfectly finite. We also note, however, that Jordan's argument is incomplete. In modern terms, Jordan calculated the quantum uncertainty in the energy of a subsystem in an energy eigenstate of the whole system, whereas the thermal fluctuation is the average of this quantity over an ensemble of such states. Still, our overall conclusion is that Jordan's argument is basically sound and that he deserves credit for resolving a major conundrum in the development of quantum physics.