Opera's neutrinos and the Robertson test theory of the Lorentz transformations

Abstract

The difference in light's travel time from CERN to GPS to Gran Sasso, on the one hand, and light going the direct route in vacuum (mimicked by neutrinos), on the other hand, is analyzed with a modified Robertson test theory of the Lorentz transformations. The modification consists simply in removing the restriction of what Robertson referred to as agreement to equate the to and from speeds of light. For reasons that will be contained in a paper to soon follow, we restrict ourselves, within the new freedom, to the case of preferred frame kinematics with absolute simultaneity. At the level of not assuming any concomitant dynamical changes in this alternative, the analysis yields \QTR{it}{zero effect}, i.e. no change with respect to special relativity (to be expected). The 60 ns would thus remain unexplained. However, a gravitation related effect that would likely accompany an alternative kinematics yields that value up to uncertainties due to the need to simplify the experimental set up for analysis. The effect amounts to $(\lambda /2)(D/c)(V/c)^{2}$, where $D$ is distance to GPS, $V$ is speed with respect to the frame of isotropy of the cosmic background radiation and $\lambda$ is a factor greater than 1, but likely not greater than 1.2 or 1.3, that reflects lack of precise knowledge of the average distance to the common view GPS satellite. A $\lambda $ factor of \ 1.2 yields 60 ns.