Since we're Going There^TM, I propethisize that the reason time appears to stop at speed of light is that time is the ultimate measure of mass. It's like pressure in a body of water: if you swim upwards and reach lower pressure (slower passage of time form your perspective), you will eventually reach an event horizon where there is no more water to swim in. Reaching faster than light speeds shouldn't be impossible, but it wouldn't obey all of the rules we know to make acceleration in general possible. Technically to find out I think we would need to establish a colony that spends a few millenia inventing a new science by living permanently at the speed of light.