Thank you for this elaborate answer, but this does not seem right. I am not very well versed in the StarTrek lore, but they use warp drives, which are alcubierr

Thank you for this elaborate answer, but this does not seem right. I am not very well versed in the StarTrek lore, but they use warp drives, which are alcubierre drives, so they expand and fold space to move, thus never actually achieving an FTL speed themselves. If we don't move at relativistic speeds, there would be no time dilation effects, so we'll always have t == t'. Next off, I feel that this backwards inertial frame of reference is not right. But I'm too lazy to get into actual math so let's put this matter to rest until we get means of FTL travel or information transfer.