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prase comments on OPERA Confirms: Neutrinos Travel Faster Than Light - Less Wrong Discussion
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Any reason to suggest this hypothesis? (And by relativity you mean Lorentz invariance?)
1) if neutrinos can beat lightspeed, relativity could simply not apply to them, rather than applying in some weird twisted way.
2) Neutrinos are nearly perfectly exempt from photon interactions (the simplest diagram is to pop out a virtual W and electron).
3) This could be the reason for 1.
4) How, then, do other charged particles get all relativized? Well, photons get entangled with just about everything just by virtue of most things having electrical charge. That's what the renormalization theory is about - including all of the recursing interaction effects that a particle can't get rid of into its basic description.
So, if you have, say, innate Galileian relativity for most particles but not for light, which has a constant speed in a preferred rest frame, charged particles are going to act at least a little bit like relativity predicts - as the particle approaches light speed, the bow wave part of its E-field gets stronger and stronger, accumulating energy... as it approaches the speed of light the photon energy would diverge like on a jet about to go supersonic, except that unlike the jet, you simply can't get the photons out of the way fast enough.
Hmm. That really doesn't work, because it suggests that the mass dilation would vary proportional to charge, not to mass. So I withdraw the first notion too.
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 As stated, though, this is already withdrawn.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.
The problem is that neutrinos can carry information. And if you carry information faster than light, you either have "time travel", or you screw up the whole framework of relativity. So... it's an easy claim that "relativity could simply not apply to them".
Well, what's so bad with "time travel" after all?
That it leads to paradoxes like "two people kill each other, each one being killed by the other before he pulls the trigger" in the case of a tachyon duel. And that kind of paradoxes (unlike the "I killed my grandfather" paradox) can't even be explained by alternative histories/Everett branches.
Existence of tachyons doesn't necessarily imply that paradoxes would be instantiated. Of course, even if there were tachyons, the world would still be consistent with itself. In the tachyon duel, perhaps the classification of the state of duellists (whether alive or dead) could depend on the reference frame, or perhaps the duel could not happen for some specific reason. Once you can write consistent equations of motion for elementary particles that allow for tachyons - and I think this is possible (although I don't know much about tachyons, maybe there are some problems which I am unaware of) - complex stories about killing grandfathers and shooting people with neutrinos must add up to normality, even if they seem weird at the beginning.