As per in the title. If it turns out that neutrinos do travel faster than the speed of light, how will the success of special relativity be explained? My apologies if this has been asked before; I've just browsed through few questions, and I couldn't find one that matches (although it was slightly touched on in one answer).
Answer
The various theoretical options are very different in nature, and the answer to this question almost defines the option.
1) Relativity is wrong, there is objective absolute time, Lorentz symmetry is emergent (as in electrodynamics before Einstein), and going faster than light doesn't create any time-loop paradoxes.
2) Relativity is valid, but neutrinos, not photons, travel at the actual relativistic speed-limit; photons have a small mass, or photons are confined to a braneworld while neutrinos can take shortcuts through hyperspace.
3) Relativity is valid, neutrinos are tachyons (or the OPERA result manifests some other sort of spacelike correlation), and something (Deutsch's multiverse, Hawking's CTC instability, weakness and/or uncontrollability of the effect, QM itself actually comes from CTCs...) prevents it from creating a time-loop paradox.
It should be extremely difficult to turn any of these 3 options into a fully working theory capable of reproducing the standard model. The odds are still heavily against OPERA having actually observed FTL neutrinos.
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