Time is frozen at light speed. You arrive at your destination instantaneously, not even experiencing a tick of Planck time. To an outside observer it takes you time. From the perspective of a photon from the sun, there is no time or distance passing between its genesis in the sun and it landing on your face. From an observer on earth it took 8 minutes and millions of miles.
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I mean if we're already violating physics by having objects with mass going the speed of light, I don't see what's wrong with also assuming the thing we have for going light speed can't also instantaneously accelerate.