Searching for Granularity of the Vacuum

Abstract

The hypothesis is considered that the vacuum is a Lorentz non-invariant foam in which translational symmetry is spontaneously broken at the Planck or grand unification scale. This could possibly be observed via Rayleigh scattering of ultrahigh energy quanta, and it appears to be ruled out for spin 1/2 leptons and independently testable for photons. A weaker version of the hypothesis predicts (for otherwise massless neutrinos) irreversible neutrino mixing over a length scale of $l_{Planck}(E_{\nu}/E_{Planck})^{-2}$ in comoving cosmic coordinates for a purely four dimensional universe, and, for neutrinos that have spin 3/2 in a higher dimensional manifold above the energy scale $\eta E_{Planck}$, the mixing is predicted to take place over a scale of $\eta^{-4}$ times this length. Such neutrino mixing might also be observable with atmospheric and solar neutrino experiments.