Einstein's clock experiment. What would happen if you were to travel at the speed of light or faster than the speed of light towards the clock? Can we translate this into traveling large distances in space? By that I mean, if light is traveling towards us while we are traveling towards it at the speed of light or faster, shouldn't we be able to arrive at that Galaxy (Sun/planet) in no time at all? Meaning that we would be able to reach a Star before their light has even hit our planet or hit us.
The equations in special relativity for time dilation show that if you go faster than the speed of light, time begins to move backwards from your reference frame. This means that the clock would tick backwards, and that from your reference frame, you would travel to the star in no time if you were moving at exactly the speed of light, or, you would end up at the star before you started moving towards it, due to time dilation. However, from the reference frame of an observer at rest, you would end up at the star after you began. Since Lorentz transformations don't allow for this, you cannot actually travel at the speed of light or faster.