Answer 1:
When doing a field theory that comes out with a
tachyonic solution (such as bosonic string theory,
which is not a valid theory in itself), the
tachyon has negative rest mass squared. The rest
mass is imaginary (the rest mass is an imaginary
number like the sqrt(1)*m, where m is a
real number, since rest mass =
sqrt(m^{2}). That is why we
consider these to be bad theories and they're
unstable (i.e. even if such a solution existed the
universe wouldn't stay in that state, like a ball
sitting at the top of a very narrow hill: given
even the tiniest push or gust of wind it would
roll down to a state where there were no
tachyons). But in those nonvalid theories, the
speed of a tachyon would depend on how much energy
you gave it. It is much like our own massive
particles here; the mass and speed depend on how
much energy that has.
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