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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.

Feynman referred to interference as “the only mystery,” and we continue to pursue that idea here by examining the theory behind it with heightened scrutiny. Three interpretations are described: The standard model, Feynman’s sum-over-paths, and Einstein’s photon model. The standard model bases its arguments on the wave function and its subsequent collapse. The sum-over-paths model is equivalent to the standard model, but it explains interference by avoiding use of the wave function and its conceptual problems due to collapse. The Einstein model is the most challenging for it is revolutionary and intuitively demanding. We critique the three models by studying their treatment of polarized light. In Part II, the interference of low intensity light will be discussed.

It is demonstrated how the choice of a reference system origin influences our interpretation of the natural laws. Instead of placing it arbitrarily as is customary in mechanics, we locate it at an energy minimum, or zero point of material systems. In an example from celestial mechanics, the sun defines the point of minimum gravitational potential and preferred origin for the planetary system. As a comparison, Heisenberg's derivation of quantum kinematics is shown to be deficient, because microscopes do not define the point of minimum energy of an atomic system. To improve upon it, new interpretations of quantum kinematics and mechanics are proposed by locating the reference system origin at the zero point of an atomic system, where the Hamiltonian, H = T + V, equals zero. Experiments with atomic clocks are cited in support of the new physical model. The Schwarzschild solution relative to a mass point is proposed as the preferred interpretation of a general relativity theory due to the location of the origin at a zero point. These interpretations of long-standing theories provide new points of view to familiar problems.

Dirac noted in his first paper on quantum electrodynamics [Proc. Roy. Soc. A 114, 243 (1927)] that, “The theory is non-relativistic only on account of the time being counted throughout as a c-number [classically], instead of being treated symmetrically with the space coordinates.” His suggestion for a relativistic theory of quantum mechanics is carried out here by describing the atom in configuration space as the action integral of a Lagrangian. Atomic structure is described with discrete coordinates in Minkowski space, while the atom itself resides in the curved space-time continuum of the gravitational field, the background space of quantum gravity. Although it does not meet the more ambitious goals of a string theory or loop quantum gravity, it is the first successful theory. In other words, it is the first theory to describe how gravitational fields interact with quanta at the microscopic level. This paper is dedicated to the thousands of theoretical physicists who have defended nonrelativistic theory since its inception in 1926 without questioning its limitations even as it lost touch with reality and became ever more difficult to believe.

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 forces — gravitational, electroweak, and nuclear — have independent structure and are thus in agreement with the three-body model.

Existing derivations of uncertainty for single-particle interactions violate complementarity because they require that the photon exhibit wave and particle behavior simultaneously, and thus singularly. In order to restore physical consistency to quantum theory, a model of the photon is proposed with spatial extension equal to the wavelength. As a result, uncertainty and indeterminacy must be assigned independent meanings. Uncertainty describes the limit in measurability for instantaneous exchanges of momentum and is due to a photon’s particle properties. It is causal in origin and provides a model for the kinematics of quantum theory. Indeterminacy, however, is statistical in nature and is attributed to the exchange of momentum by time-averaged fields. The need for two limitations on measurability is seen as an extension of the duality principle to measurement theory.