It is physically possible to travel faster than the speed of light by invoking general relativity, that is by either warping or ripping space-time. Think about it if we rip or warp space time so that an object is closer to us, it's going to take us a shorter amount of time to reach it, and therefore we're going to travel faster than light (if we want to). Similarly the shortest distance between two points is a worm hole rather than a straight line, so it is possible to travel faster than light this way aswell. However both these methods require elusive negative energy of which I know very little about, and is way beyond anything we can achieve in the foreseeable future. With regards to traveling through space faster than light, its handy to look at the highly theological Alcubierre drive (he dreamt it up via star trek) which uses negative energy rather than postive energy to power the body, as opposed to the positive energy used today to travel at lower than speed of light speeds. What you would effectively see, traveling faster than the speed of light according to Alcubierre is this "In front of the ship, stars would become long lines, streaks. At the back, nothing would be seen as light from previous stars wouldn't be traveling fast enough to keep up". Basically like the millenium falcon out of star wars.
How true that is I don't know, just out of this Kaku book I've been reading
