Tachyon paradox: The argument explaining that tachyons (should they subsist, of course) can’t carry an electric charge. For an imaginary-massed particle travelling faster than c, less energy the tachyon has, the faster it travels, till at zero energy the tachyon is travelling with unlimited velocity, or is transcendent. Now a charged tachyon at a specified (non-infinite) speed will be travelling faster than light in its own medium, and must emit Cherenkov radiation. The loss of this energy will obviously decrease the energy of the tachyon that will make it go faster, resultant in a runaway reaction where some charged tachyon will rapidly race off to the transcendence.
Though the above argument outcomes in a curious end, the meat of the tachyon paradox is this: In relativity, the transcendence of the tachyon is frame-dependent. That is, even as a tachyon may emerge to be transcendent in one frame, it would emerge to others to still have non-zero energy. However in this situation we have a condition where in one frame it would encompass come to zero energy and would stop emitting the Cherenkov radiation; however in the other frame it would still contain energy left and must be emitting Cherenkov radiation on its way to the transcendence. As they can’t both be true, by the relativistic arguments, tachyons can’t be charged.
This argument obviously does not make any account of the quantum mechanical treatments of tachyons that complicate the circumstances a huge deal.