Macroscopically-Discrete Quantum Cosmology

Milne’s Lorentz-group-based cosmological spacetime and Gelfand-Naimark unitary Lorentz-group representation through transformation of Hilbert-space vectors combine to define a Fock space of ‘cosmological preons’—quantum-theoretic universe constituents. Lorentz invariance of ‘age’–global time– accompanies Milne’s ‘cosmological principle’ that attributes to each spatial location a Lorentz frame. We divide Milne spacetime—the interior of a forward lightcone– into ‘slices’ of fixed macroscopic width in age, with ‘cosmological rays’ defined on (hyperbolic) slice boundaries. The Fock space of our macroscopically-discrete quantum cosmology (DQC) is defined only at these exceptional universe ages. Self-adjoint-operator expectations over the ray at any spacetime-slice boundary prescribe throughout the following slice a non-fluctuating continuous ‘classical reality’ represented by Dalembertians, of classical electromagnetic (vector) and gravitational (tensor) potentials, that are current densities of locally-conserved electric charge and energy-momentum. The ray at the upper boundary of a slice is determined from the lower-boundary ray by branched slice-traversing stepped Feynman paths that carry potential-depending action. Path step is at Planck-scale; branching points represent preon creation-annihilation. Each single-preon wave function depends on the coordinates of a 6-dimensional manifold, one of whose ‘extra’ dimensions associates in Dirac sense to a self-adjoint operator that represents the preon’s reversible local time. Within a path, local-time intervals equal corresponding intervals of monotonically-increasing global time even though, within a (fixed-age) ray, the local time of a preon is variable. The operator canonically conjugate to a preon’s local time represents its (total) energy in its (Milne) ‘local frame’. A macroscopically-stable positive-energy single-preon wave function identifies either with a Standard-Model elementary particle or with a graviton. Within intermediate-density sub-Hubble-scale universe regions such as the solar system, where ‘reproducible measurement’ is meaningful, physical special relativity—‘Poincaré invariance’—approximates DQC for spacetime scales far above that of Planck. c © Electronic Journal of Theoretical Physics. All rights reserved.