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What will be the consequence (severe ones) on laws of physics if a particle that travels faster than light is discovered?

I am looking for a more general answer so that a high school student would be able to understand. Or is it not possible to explain a high school student without bringing special relativity into context?

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According to Günter Nimtz, we've already measured superluminal velocities.

Many (most?) physicists disagree with Nimtz' interpretation of his experimental results, probably mostly due to the fact that tachyons potentially violate causality (remember that according to special relativity, faster-than-light means backwards in time when looked at from a different frame of reference!).

However, according to Recami, special relativity can be extended to include tachyons without violating causality (see this PDF if you can stomach the physics).

I haven't really looked into the problem in detail (I've been planning to read through this issue of Annalen der Physik for some time, but never got around to it), but my gut feeling is that tachyonic interactions might indeed be real (I hesitate to call them tachyonic particles because they'll necessarily have some pretty strange features to be consistent with special relativity).

If Recami's analysis is correct, tachyons cannot be used to do anything useful like committing the perfect murder (Bell paradox) or answering questions before they are asked when using an anti-telephone (Tolman-Regge paradox). So even if they do exist, the implications might be far from earth-shattering.

The situation might turn out similarly to the 'spooky action at a distance' due to entanglement: When first discovered, there was a lot of controversy, but in the end the physics community just shrugged, accepted that the world is a bit stranger than we formerly assumed and moved on.

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The reason I didn't add your pdf only because he asked a general (not too complicated) answer ;-) –  Waffle's Crazy Peanut Mar 31 '13 at 17:52
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@CrazyBuddy Hm, it does not hurt, if the question gets some answers for people who can stomach a bit more complicated physics too :-). The OP can still choose what he likes best to accept. –  Dilaton Mar 31 '13 at 18:50
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@Dilaton: correct me if I'm wrong, but imo fields with imaginary mass (QFT tachyons) do not lead to superluminal particles (SR tachyons) - they are just called by the same name for hysterical raisins and because you can (but need not) describe the latter via imaginary mass as well –  Christoph Mar 31 '13 at 19:03
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A more complete exposition by Recami, which seems to be what other people in the field have been referencing, is Riv Nuovo Cimento 9 (1986) 1, available at dinamico2.unibg.it/recami/scientific.htm . Recami references an earlier paper by V. Gorini, "Linear Kinematical Groups," Commun Math Phys 21 (1971) 150, which is available here: projecteuclid.org/… . Gorini proves a no-go theorem that says you can't extend the Lorentz transformations to superluminal speeds, while maintaining a desired list of 6 properties... –  Ben Crowell Mar 31 '13 at 21:29
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...summarized in sec. 3.2 of Recami. In sec. 14 of Recami, he catalogs a whole bunch of possible ways of making viable theories by violating one of these 6 properties. However, there doesn't appear to be anything in the catalog that is attractive or has borne fruit since 1986. –  Ben Crowell Mar 31 '13 at 21:32
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Though, we haven't observed any particle traveling faster than light, we've already hypothesized a particle. Through this assumption, we do know several properties that such a particle should have like, it must have an imaginary mass, should never slow down below $c$, etc.

Neither Einstein's nor Newton's theories will get affected by such a particle. Well, SR helped us in calculating those properties. But, there will be serious implications of such particles. Because, they have an imaginary mass and from the energy-momentum relation, we can see that their velocity increases with decrease in energy. They can violate causality, etc. , etc...

There will be a lot of advantages like time-travel, faster than light communication, etc. I'm quite sure that such particles have no place in classical mechanics. Who knows? We may introduce a new theory for such particles or revise SR (which is quite strange)

I think this is enough. Maybe, you can read the Wiki article on FTL and Tachyons.
You can ignore strange terms if you want, but you can still read it...

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according to Recami, SR+tachyons does not lead to causal paradoxa - see dinamico2.unibg.it/recami/erasmo%20docs/… (PDF) –  Christoph Mar 31 '13 at 16:49
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@Christoph: But (a) this seems to be highly contoversial, and (b) Recami cheerfully admits the existence of Gorini's no-go theorem, which calls into question the self-consistency of the whole picture of FTL frames of reference in 3+1 dimensions. –  Ben Crowell Apr 1 '13 at 4:22
    
@BenCrowell: personally, I don't think this no-go theorem is a deal breaker: while you cannot extend the principle of relativity to include both sub- and superluminal observers, (and considering that tachyons are delocalized by necessity, I don't find that particularly surprising), do we really need to do so? Does SR treat light-like observers on the same footing as time-like ones? If not, why should extended SR do so for space-like ones? –  Christoph Apr 1 '13 at 8:07
    
@Christoph: "considering that tachyons are delocalized by necessity, I don't find that particularly surprising". Could you amplify on this? Delocalized in space according to a bradyonic obsever's notion of what's a spatial dimension? In one spatial dimension? All three? Why? There are clear reasons why zero-mass particles can't be used to build observers (conformal invariance, can't make a clock out of photons). But it's not obvious to me in the case of tachyons. If delocalization makes tachyonic observers implausible, why doesn't that appy to 1+1 dimensions, where Gorini doesn't apply? –  Ben Crowell Apr 2 '13 at 14:59
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