The Quantum Condition and the Non‐Euclidean Nature of Space‐Time

TLDR: The origin of the Bohr-de Broglie quantum condition for the stability of atomic and nuclear systems can be interpreted in terms of a locally high Gaussian curvature of space-time equivalent to a large value of the gravitational constant along the lines suggested by Motz.

Abstract: The origin of the Bohr-de Broglie quantum condition for the stability of atomic and nuclear systems can be interpreted in terms of a locally high Gaussian curvature of space-time equivalent to a large value of the gravitational constant along the lines suggested by Motz’ for the stability of the electron. Assuming the mass is purely electromagnetic in origin and that hadrons are composed of highly relativistic electron-positron pairs in “charmonium” or heavy, integrally charged, quarklike arrangements, and also by adopting a symmetrical definition of the electromagnetic force between two moving particles as proposed by Einstein in 1905, one arrives a t the existence of a minimum approach distance as well as a changing source size or rest mass for the electron and positron in highly relativistic orbits of pion mass that form the basis of all hadrons (FIGURE I).’ The existence of a minimum approach distance between the fundamental entities is equivalent to a non-Euclidean geometry with a high local G similar to that of Motz, except that this local G is found to increase inversely as the square root of the pair mass during the course of the evolution of the universe by internal pair-production. This process begins with the Newtonian value of G and increases up to a maximum value of e2/m2, starting with a single massive “Lemaitre-atom”-like electron-pair of mass equal to that of the universe, MU, a t the Planck density, c * / ~ G ’ . ~ As a result, the charges in equilibrium orbits move along geodesics of the local space so that they do not radiate, which is contrary to classical electromagnetic theory. In these orbits, the tangential Lorentz contraction of the field source is exactly equaled by the radial contraction produced by the local space-curvature, thus reducing the source to the spherical shape associated with a state of rest. This provides a simple physical or geometrical explanation of the Bohr-de Broglie quantum condition, which can be applied to the stability of electron orbits and, thus, to all matter. Because hadrons appear to be describable as molecular arrangements of highly relativistic electrons and positrons whose masses, sizes, and lifetimes can be accounted for in terms of the basic electromagnetic constants, e, m,, c, and h , without any other arbitrary constants or adjustable parameters: and because the electron and positron may in turn be regarded as self-stabilized, spinning sources of a single field’ analogous to “twisted geons,” “vortex rings,” or “strings” in a fluidlike space-time continuum or ether, the wave-particle nature of matter finds a simple physical explanation. In this model, there is no “hard” or “ponderable” matter. Instead, all matter “particles” consist of stable, spinning sources of electromagnetic fields of finite inner size, with the size of the source determining the rest mass. This explains the relation of heavy quarks to leptons, including their small, pointlike size and spin ‘/2. In this model, the strong force is explained as a relativistic form of the electromag-