Differences between the quantum mechanical and relativistic concepts of time are explained by applying the strong equivalence principle to the electron in an atomic clock. The resulting clock model calls for the microscopic equations of motion of the electron to be formulated in Minkowski space, and for the photon to be described relativistically as a four-dimensional localization of energy. The resulting Lagrangian formulation of quantum mechanics is completely analogous to the more familiar nonrelativistic Hamiltonian model based on the Schrödinger equation. It accounts for the 720 degree rotation of a wave function as the absorption of one 360 degree electromagnetic wave cycle and the emission of another, yielding two wave cycles to correspond with one clock cycle. Because the properties of energy are universal the equations are able to be extended to include galaxies in spite of vast differences in lifetime. They show that symmetry exists between the electromagnetic fields of atoms and the gravitational fields of galaxies due to the presence in both of radial and transverse fields. The description of galaxy structure is fundamentally distinct because it is based on the conjugate variables energy and time.
Published Date: 2022-12-27; Received Date: 2022-11-24