Minimal spatio-temporal extent of events, neutrinos, and the cosmological constant problem

TL;DR

This paper proposes that adopting a stabilized Poincare'-Heisenberg algebra introduces a minimal spatio-temporal extent to particles, potentially resolving the cosmological constant problem and explaining neutrino mass coincidences within an extended physics framework.

Contribution

It introduces the stabilized Poincare'-Heisenberg algebra as a fundamental structure for quantum gravity, linking minimal particle extent to solutions of major cosmological and particle physics problems.

Findings

Point particles are replaced by objects with minimal spatio-temporal extent.

Potential resolution of the cosmological constant problem.

Provides a first-principles explanation for neutrino mass and vacuum energy coincidence.

Abstract

Chryssomalakos and Okon, through a uniqueness analysis, have strengthened the Vilela Mendes suggestion that the immunity to infinitesimal perturbations in the structure constants of a physically-relevant Lie algebra should be raised to the status of a physical principle. Since the Poincare'-Heisenberg algebra does not carry the indicated immunity it is suggested that the Lie algebra for the interface of the gravitational and quantum realms (IGQR) is its stabilized form. It carries three additional parameters: a length scale pertaining to the Planck/unification scale, a second length scale associated with cosmos, and a new dimensionless constant. Here, I show that the adoption of the stabilized Poincare'-Heisenberg algebra (SPHA) for the IGQR has the immediate implication that `point particle' ceases to be a viable physical notion. It must be replaced by objects which carry a well-defined, representation space dependent, minimal spatio-temporal extent. The ensuing implications have the potential, without spoiling any of the successes of the standard model of particle physics, to resolve the cosmological constant problem while concurrently offering a first-principle hint as to why there exists a coincidence between cosmic vacuum energy density and neutrino masses. The main theses which the essay presents is the following: an extension of the present-day physics to a framework which respects SPHA should be seen as the most natural and systematic path towards gaining a deeper understanding of outstanding questions, if not providing answers to them.