Searching for Granularity of the Vacuum.pdf

Searching for Granularity of the Vacuum D.Eichler Ben-Gurion University, Beer-Sheva, 84105, Israel 9 9 The hypothesis is considered that the vacuum is a Lorentz non-invariant foam in which translational symmetry 9 1 is spontaneously broken at the Planck or grand unification scale. This could possibly be observed via Rayleigh r a scattering of ultrahigh energy quanta, and it appears to be ruled out for spin 1/2 leptons and independently testable M for photons. A weaker version of the hypothesis predicts (for otherwise massless neutrinos) irreversible neutrino 2 2 mixing over a length scale of lP lanck (Eν /EP lanck)−2 in comoving cosmic coordinates for a purely four dimensional 3 v universe, and, for neutrinos that have spin 3/2 in a higher dimensional manifold above the energy scale ηEP lanck , 0 −4 2 the mixing is predicted to take place over a scale of η times this length. Such neutrino mixing might also be 0 1 observable with atmospheric and solar neutrino experiments. 1 8 9 / h p - I. INTRODUCTION o r t s a Translational invariance of the vacuum is a sacred tenet of physics. One might suspect that, near the Planck : v i scale, space may be grainy due, say, to condensates, quantum black holes, a spatially varying θ parameter, or phase X r decorrelation of virtual modes. This raises the question of whether on such small scales translational symmetry is a preserved or spontaneously broken. A grainy vacuum would suggest that physics at macroscopic scales is to some (possibly small) degree unpredictable. Hawking 1,2 has suggest