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

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.

Version to appear in the December 2005 Special Issue of Int. J. Mod. Phys. D

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• The deformation-stability fundamental length and deviations from c
• Space-time: Commutative or noncommutative ?
• Possible polarisation and spin dependent aspects of quantum gravity
• Electroweak symmetries from the topology of deformed spacetime with minimal length scale
• Entropy in the Present and Early Universe
• Free Massless Particles, Two Time Physics and Newtonian Gravitodynamics
• Soft singularity and the fundamental length