Ciro Santilli @cirosantilli 37

In special relativity, it is impossible to travel faster than light.

One argument of why, is that if you could travel faster than light, then you could send a message to a point in Spacetime that is spacelike-separated from the present. But then since the target is spacelike separated, there exists a inertial frame of reference in which that event happens before the present, which would be hard to make sense of.

Even worse, it would be possible to travel back in time:

In the Galilean transformation, there are two separate invariants that two inertial frame of reference always agree on between two separate events:

However, in special relativity, neither of those are invariant separately, since space and time are mixed up together.

Instead, there is a new unified invariant: the spacetime-interval, given by:

Note that this distance can be zero for two events separated.