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 As stated, though, this is already withdrawn.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.
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 As stated, though, this is already withdrawn.
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 ...
Link: nextbigfuture.com/2011/11/faster-than-light-neutrinos-opera.html
Link: science20.com/quantum_diaries_survivor/opera_confirms_neutrinos_travel_faster_light-84763
Paper: kruel.co/paper-neutrino-velocity-JHEP.pdf
Previously on LW: lesswrong.com/lw/7rc/particles_break_lightspeed_limit/