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

TL;DR

This paper revisits Pascual Jordan's 1925 work demonstrating that wave and particle aspects of light's energy fluctuations can be explained within a unified quantum framework, defending his conclusions against criticisms and clarifying their significance.

Contribution

It clarifies and defends Jordan's original argument that wave-particle duality in light can be explained by a single quantum model, addressing previous criticisms and emphasizing its validity.

Findings

Jordan's model recovers both wave and particle terms in energy fluctuations

The fluctuation in a narrow frequency range is finite and well-defined

Jordan's argument is fundamentally sound and historically significant

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.