Einstein did not contribute significantly to the quantum mechanics we are familiar with, but he did contribute to its theoretical foundations. In a seminal theory on black body radiation, he used two physically distinct sets of coordinates, a classical set to describe the continuity of heat energy with Maxwell Boltzmann statistics and an atomic set to describe discrete energy states required by the Planck radiation law. His methods are extended here to reveal that matrix mechanics is an incomplete description of atomic structure. In addition to the discrete energy states of the diagonal matrix elements, classically derived components of kinetic energy are necessary. We conclude that the diagonalized matrix elements and eigenvalues of the Schrödinger equation both describe characteristics of the steady states, but the physical variables they describe are different, because they are measured with respect to different coordinate systems. Einstein’s assumptions lead to a resolution of the measurement problem by introducing statistical laws at the microscopic level.

Einstein showed in his seminal paper on radiation that molecules with a quantum-theoretical distribution of states in thermal equilibrium are in dynamical equilibrium with the Planck radiation. The method he used assigns coordinates fixed with respect to molecules to derive the A and B coefficients, and fixed relative to laboratory coordinates to specify their thermal motion. The resulting dynamical equilibrium between quantum mechanical and classically defined statistics is critically dependent upon considerations of momentum exchange. When Einstein’s methods relating classical and quantum mechanical statistical laws are applied to the level of the single quantum oscillator they show that matrix mechanics describes the external appearances of an atom as determined by photon-electron interactions in laboratory coordinates, and wave mechanics describes an atom’s internal structure according to the Schrödinger wave equation. Non-commutation is due to the irreversibility of momentum exchange when transforming between atomic and laboratory coordinates. This allows the “rotation” of the wave function to be interpreted as the changing phase of an electromagnetic wave. In order to describe the momentum exchange of a quantum oscillator the Hamiltonian model of atomic structure is replaced by a Lagrangian model that is formulated with equal contributions from electron, photon, and nucleus. The fields of the particles superpose linearly, but otherwise their physical integrity is maintained throughout. The failure of past and present theoretical models to include momentum is attributed to the overwhelming requirement of human visual systems for an explicit stimulus.

Einstein derived his coefficients of induced and spontaneous emission by assuming that electromagnetic radiation is directional, having the form of "needle radiation." That idea is extended here and shown to suggest that stimulated emission should be described as a three-body problem: nucleus, electron, and photon. The photon is conceived of as having a central core with localized momentum surrounded laterally by a continuous sinusoidal field; stimulated emission is due to the coupling of its field with the bound electrons of nearby molecules. Coupling is directly proportional to the density of oscillators so that starlight is predicted to have a different microscopic structure than artificial light. Noncommutation does not occur in the three-body model of emission because the conservation of momentum fixes the order of observables. This allows the mathematical formalism of quantum mechanics to be assigned a more precise physical interpretation. Evidence for the three-body model is described at the macroscopic level by using high-speed photographs of spark discharges. It is hypothesized that all forcesgravitational, electroweak, and nuclear-have independent structure and are thus in agreement with the three-body model.

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