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The argument reveling that tachyons (must they exist, of course) cannot carry an electric charge. For a (imaginary-massed) particle travelling quicker than c, the less energy the tachyon has, the quicker it travels, till at zero energy the tachyon is travelling along with infinite velocity, or is transcendent. Now charged tachyon at a given (non-infinite) speed will be travelling quicker than light in its own medium, and must emit Cherenkov radiation. The loss of this energy will decrease naturally the energy of the tachyon that will make it go faster; resulting in a runaway reaction where any charged tachyon will race off to transcendence promptly.
Even though the above argument results in a curious conclusion, meat of the tachyon paradox is this: In relativity, the transcendence of tachyon is frame-dependent. i.e., wheraes a tachyon might seem to be transcendent in one frame, it would seem to others to still have a nonzero energy. But in this case we have a condition where in one frame it would have come to zero energy & would stop emitting Cherenov radiation, however in another frame it would have energy left still and must be emitting Cherenkov radiation on its way to transcendence. As they cannot both be true, through relativistic arguments, tachyons cannot be charged.
Naturally this argument does not make any account of quantum mechanical treatments of tachyons that complicate the condition a great deal.
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