Spacetime Quantization, Elementary Particles, and Cosmology

Relativistic quantum mechanics is generalized to account for a universally constant quantum of length a. Its value depends on the total convertible energy content of our universe: Eu = hc/2a. The eigenvalues of all (x,y,z,ct) coordinates are integer or half-integer multiples of a in every particular inertial frame. There are thus several spacetime lattices of lattice-constant a: the “normal lattice” contains the origin of the chosen frame, while “inserted lattices” are displaced by a/2 along one or several reference axes. States of motion are defined by possible variations of ψ-functions on any one of these lattices. Particle states are defined by their relative phases, specified by four new quantum numbers, ux, uy, uz, uct = 0, ±1, ±2,.... They account for all known elementary particles and yield a natural extension of the standard model. Spacetime quantization solves also the EPR paradox and other difficulties that subsisted in the usual continuum theories. It defines inertial frames and is related to cosmology.