In dealing with Grand Unification/supergravity/superstring/M theories, theoretical physicists will discard a theory which proposes the existence of tachyons, the theoretical…and so far, unobserved…with, IIRC, negative imaginary mass.
I like my universe with symmetry and balance; massless luxons in the middle of the velocity scale going at c, massive particles on one side always going slower than light, why NOT tachyons on the other side, always going faster than c?
Anything that can travel faster than light (including that famous Bright young lady) can also travel back in time. This doesn’t necessarily mean that it does travel back in time in any particular reference frame, but it can.
And tachyons are not a particularly big problem, so long as they can’t be detected by any means. But if they can’t be detected by any means, then what does it mean to say that they exist?
Well, actually even that’s not such a big deal. It hinges on a technicality you’d appreciate (and may well know about).
Remember that what we’re talking about in the bradyon/luxon/tachyon trichotomy is the phase velocity of the waves, while signals must propagate with the group velocity. That is, in order to send a signal through any field (photon, electron, gravitino…), you have to put together a bunch of the basic waves to say what you want. The basic waves may each move at one speed, but the shape of the group as a whole may travel at a different speed, due to how the waves interact with each other.
So, what happens for tachyons? Well, there are two different kinds of groups, it turns out. One propagates (and carries signals) slower than light, so it’s no problem at all for causality. The other propagates faster than light, but it cannot be compactly supported. That means that in order to send a signal from here to there, you’d have to be there – and pretty much everywhere else – already to set up the message.