Authors: John L. Haller Jr.
With super-luminal neutrinos being observed in 2011 then refuted in 2012 we present an argument, based on Jensen’s inequality, that they might still exist only with a smaller excess speed than initially thought. Specifically, the quantity measured by OPERA and ICARUS is the average of the length of the displacement over time which is greater than the length of the average velocities - which determines and does not break Lorenz invariance. We examine quantum diffusion to explain the physics behind the particle’s variance resulting in an excess average velocity of ℏ⁄(mc^2 (t+τ) ), where t is the baseline and τ is the coherence time. We examine the experimental setup at OPERA to estimate the excess velocity and show it is within the error as observed in the tighter re-run. We also show consistency with Fermilab 1979 and supernova 1987A. In conclusion we comment on arguments refuting superluminal neutrinos and note a similar consequence of quantum mechanics that conservation of energy can be violated, if only for a short time.
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