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A neutrino could not exceed or reach the speed of light, given that it has mass (2.2 ev). Unless of course relativity was altered in some fundamental way (or discarded).
If for example the faster than light neutrinos were anti-neutrinos and were going backwards in time they would appear to be travelling faster than light. Would this violate relativity? I know nothing is supposed to travel faster than light but relativity does allow for the possibility of antimatter time reversal. Time reversal may look the same as going faster than the speed of light but the speed of light is still a cosmic speed limit for matter in a matter universe.
An anti-particle should still travel at the same velocity, but from point B to A rather than A to B. Correct me if im wrong