Question

What happens to time ABOVE the speed of light,theories?

Answer 1

Its really rather academic since physically nothing can exceed the speed of light. However, you can extend the the mathematics for speeds greater than that of light. Recall that relativity states that as an object approaches that of light, time slows down for it, until at the speed of light, time will stop for it , as viewed from an external rest frame. The equations for time dilation are \[t^{\prime}=\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}\]. Inspection of this equation shows that when \(v>c\), then you obtain the square root of a negative number, and hence enter teh realm of imaginary numbers. Indeed, the solution will then describe "imaginary time", and may relate to a particle going backwards in time. Such hypothetical particles have been investigated theoretically, and are known as Tachyons, but such entities have yet to be observed and not believed to exist.

Another reason why it is thought that faster than light speeds are not possible, is that it could potentially violate causality, that is to say, solutions permit the effect to occur before the event.

Answer 2

According to the geometry of Minkowski, if there were two observers, Let's call them W and U, and W sent a message (at an event labeled A) faster than the speed of light from his light cone (Refer to a scholarly article on the geometry of minkowski for an explanation of a light cone, I am only a physics major, not a professor) observer U will receive the message at event B. However! Observer U will perceive event B happening before event A. Now if there was a third observer (V) who sent a message faster than the speed of light at event b to observer W at a new event (called C), observer W would receive a response to his message before he sent the original message. Therefore, if the original message said that he burned his tongue on his coffee, V would be able to tell W that he would burn himself if he drank the coffee. But this creates a contradiction and is therefore impossible by logic and minkowski's geometry of light cones (The message would have left the light cone, which is impossible.)

(I take no credit for this explanation as it is from Roger Penrose's "The Emperor's New Mind" a book discussing physics, mathematics and computers.)