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I remember reading that a tachyon is faster than light, but am still confused as to how and if they could exist in our universe?

Qmechanic
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If there were a particle that traveled faster than $c$, we would call it a tachyon. Such a particle would indicate that we fundamentally misunderstand the structure of spacetime, since travel faster than $c$ is forbidden in special and general relativity. There is no experimental evidence for any such particle.

More realistically, tachyons indicate problems with a theoretical model. I have had discussions with string theorists who are working to modify the such-and-such model so that it no longer predicts tachyons.

rob
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    Such a particle would indicate that we fundamentally misunderstand the structure of spacetime, since travel faster than c is forbidden in special and general relativity. Not true. There are specific issues with FTL in SR, but this is not a correct statement of any of them. –  Aug 14 '14 at 02:49
  • @BenCrowell I always appreciate your high standards for rigor and I look forward to your more careful answer. My point was mostly that tachyons are generally considered symptoms of a sick theory. – rob Aug 14 '14 at 03:21