Physics in one dimension with perpendicular non-locality

Abstract

Abstract A single momentum-carrying dimension connected by Lorentz transformations to a perpendicular non-local dimension having time but lacking spatial measures is applied to electromagnetic radiation, thermal radiation, the Schrödinger equation, Kepler’s 3:rd law, the rotation curve of spiral galaxies, and the universe as a whole represented by the linear part of its apparent expansion. This is made possible by identifying and making local terms equal to non-local ones as prescribed by the geometry. For example, 1-D momentum, the oscillating orbited radius of a system and baryonic mass are local whereas field components, oscillation periods and the electron cloud of an atom are non-local. Accordingly, in thermal radiation the physical process of a single quantum transfer replaces field radiation intensity as a function value. The Schrödinger equation can be rearranged and split into factors of circulating current carried by electrons surrounding magnetic charge. The latter result derives from a suitable factorization of the Bohr atom. Based on the assumption that the geometrical framework is valid generally for the rest frame the so-called ‘dark matter’ of galaxies can be identified by analogy with black body radiation and with the electron cloud as being non-local as might be expected of a ‘massive field’. The basic theory yields a radius that is the inverse of a line increment per unit length and per unit time as in Hubble’s constant. A tentative numerical value of this line increment appears as a residue when the Bohr atom is factorized for the purpose of providing a circular current to the Schrödinger equation.