An Actual Discussion of Einstein’s Early Fusion Picture for Photons and Classical Maxwell Fields

Abstract

This is the first part of a pair of companion papers devoted to an analysis of Einstein’s fusion picture for light-quanta (subsequently also referred to as “photons”) with classical electromagnetic fields that he formulated in 1909 via a purely verbal description. There, the overlap of many of the hypothetical local force fields, surrounding the photonic energy points, should produce the well–known classical Maxwell fields. We claim that, alone from such a logical connection, that apparently did not receive sufficient attention in the literature, one may draw essential conclusions on the photon states. In the present paper, we give a historical overview of Einstein’s photon conceptions until 1927. We extract hints from his formulations, that lead from his local force fields to Schrödinger wave functions, which reproduce the conserved integrals for energy, momentum, and angular momentum of Maxwell theory in form of Hilbert space expectations. Also a preliminary multi–photon theory, including Glauber states, is shown to be motivated by Einstein’s composite photons with possibly (incoherently!) overlapping force fields. In the resulting Fock space theory, gained by symmetrizing the many–photon states the goal of a fusion theory is, however, not realizable. In the subsequent companion paper “On sectorial photon theories reconstructing Einstein’s early fusion picture for light” (referred to as Rieckers 2025) our conclusions are extended to photon states that surpass Fock space theory by describing actual infinitely many photons. These are shown to cover also classical light states in terms of collective structures. Appealing to the more recent mathematical tools of convex state space approach and algebraic quantum field theory, we suggest there mathematical realizations of Einstein’s fusion program.