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prase comments on OPERA Confirms: Neutrinos Travel Faster Than Light - Less Wrong Discussion
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If Lorentzian relativity doesn't work, Galilean relativity is certainly not what replaces it. Moreover, I find it difficult to imagine how you could have photons transforming under Lorentz group and other particles transforming under Galilei (or whatever else) group. This will certainly produce inconsistencies, unless you managed to explain them away in some clever complicated way.
I would rather accept that neutrinos are indeed tachyons, whatever weird consequences it may have.
It only produces an inconsistency if you treat either one as fundamental and try to base the other one off of it. As stated, though, this is already withdrawn.
Edited to add: An explanation on the downvotes would be appreciated. I was wrong. I said so. Yet the post with the errors is sitting at zero, and the post explaining why I even ever made the error, and this one, are downvoted. Seems sort of weird.
Let's have a neutrino and a photon and assume that neutrinos transform under Galilei while photons transform under Lorentz. Adjust the impulse of the neutrino so that it moves exactly at v=c parallel to the photon. If they are fired towards the detector at the same time, they will be detected at the same time.
Now change the reference frame to one of an observer moving in the same direction at c/2 (or any other arbitrary velocity). With respect to this observer, the photon moves still at c according to Lorentz while the neutrino moves at c/2 according to Galilei. Therefore the photon will reach the detector before the neutrino does.
This is a paradox. Either the detection of the neutrino and the photon are one event or not, it cannot depend on reference frame.