Lagrangian Quantum Mechanics: A Fully Relativistic Theory of Atomic Structure

A fully relativistic formulation of quantum mechanics is derived by introducing a Lagrangian density of the fields between the excited and ground states and taking the action integral. The change in action, or photon, is a four-dimensional localization of fields that is defined symmetrically with respect to the field boundaries. Due to this photon model, we interpret the three mathematical formulations of atomic structure, matrix mechanics, wave mechanics, and path integrals, as different mathematical methods of describing the superposed physical components of an excited state: nucleus, electron, and photon. Recent experiments with slow and stopped light are shown to support this theoretical interpretation. The derivation of quantum theory with respect to fields requires new interpretations of the uncertainty principle, correspondence principle, complementarity, and force.

Part of the book: Metastable, Spintronics Materials and Mechanics of Deformable Bodies

Application of Einstein’s Methods in a Quantum Theory of Radiation

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.

Part of the book: Quantum Chromodynamic