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JoshuaZ comments on Particles break light-speed limit? - Less Wrong
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Neutrinos not neutrons (very different particles. Neutrons are much better understood and easier to work with.)
There's work in the US at Fermilab which could reasonably measure things at this level of accuracy. I don't know much about the Japanese work by stuff related to SK might be able to do similar things. Other than those issues your analysis seems accurate. None of these points detract from the general thrust of your argument.
Edited- Neutrinos, obviously. Brain fart.
I think Fermilab-MINOS can measure such things but I believe I read they have to update and recalibrate a bunch of things to get more accuracy, first. (Recall MINOS already saw this same effect but not at a statistically significant level. Obviously, they now have an incentive to improve their accuracy.)