Authors: Tim Joslin
The CERN-OPERA neutrino experiment at the Gran Sasso Laboratory obtained a measurement, vn, of the muon neutrino velocity with respect to the speed of light, c, of (vn-c)/c = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) x10-5. The neutrino flight path from CERN to OPERA was established using distances and timings based on "round-trip" light speed signals. These are incommensurate with the reference frame dependent "one-way" flight times of neutrinos over the same path. We perform a Lorentz transformation to demonstrate the frame-dependence of the result. We conclude that an Earth system (ES) reference frame defined by a timing system which assumes isotropic light speed, such as the UTC, is not able to support experiments requiring accurate one-way light speed measurement. We hypothesise that vn = c and consider the 2.7K CMB as a possible candidate for the isotropic frame of reference where round-trip and one-way light speeds are equal. On this basis we find that the CERN-OPERA experiment would be expected to measure deviations in neutrino arrival times compared to the expected light speed transmission of up to ±~2ns/km of neutrino flight path, but usually of less magnitude and with a bias towards early arrival. Only the N-S component (relative to the Earth's axis) of the motion of the neutrino flight path relative to the isotropic frame would be statistically significant in the CERN-OPERA experiment. Assuming no bias in the mean of the other components of the experiment's motion against the isotropic frame in the neutrino timing, because of the Earth's rotation and orbit, we find a mean early neutrino arrival time of ~113ns would be expected were the CMB the isotropic frame. That is, the potential error is of the same order as the early arrival time of the neutrinos of (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) ns, suggesting further analysis of possible sources of deviation from our theoretical estimate may be worthwhile. We propose further statistical methods to test the hypotheses that vn = c and that the CMB represents the isotropic frame, using the existing OPERA neutrino velocity measurement data.
Comments: 10 pages
[v1] 10 Nov 2011
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