Einstein-Nordström theory as a frame for a theory of quantum gravity

Abstract

The Einstein-Nordström theory is proposed as a framework for a theory of quantum gravity, dividing the space of physical reality into a part longer than the radius of a proton and described by Einstein’s classical field theory of gravitation and one smaller than the radius of a proton, for the Yang–Mills theories of elementary particles, with both of them separated by a common event horizon. This division of space is reflected into the division of classical Newtonian point particle dynamics and Helmholtz line vortex dynamics, leading to a non-dimensional number for stable vortex line configurations, as for the stability of the Karman vortex street in classical fluid dynamics, and here for the non-dimensional mass ratio, of the Higgs particle mass to the Planck mass. Setting the vortex core radius of the line vortices equal to the Planck length, Lorentz invariance is broken for energies larger than the Planck energy, whereby the underlying more fundamental symmetry is the Galilei group, establishing a preferred reference system. With the Hamiltonian operator there commuting with the particle number operator, this permits the existence of negative, as well as positive masses.