*Originally posted by amolv06*

**From what I've heard, special relativity doesn't forbid faster than light travel, it only forbids travelling at the speed of light. I often hear people say that if one was to travel faster than light, one would go backwards in time. Where does this assertion come from? To me, it seems like that rather than going backwards in time, one would move in a sort of imaginary time dimension. What am I missing here?**

Interesting thought. I'm sure someone better versed in physics will come along and lay the smack down on me, but my boneheaded algebra approach seems consistent with your assertion that superluminal velocities do not, in fact, imply travel backwards through time.

Suppose v>c. Then let v = c+k, where k>0. Using the time dilation formula, we have:

dt* = dt / SQRT(1-(v/c)^2)

= dt / SQRT(1-((c+k)/c)^2)

= dt / SQRT((c^2 - c^2 - 2ck - k^2)/c^2)

= dt / SQRT((-2ck - k^2)/c^2)

= (1/i) * dt / SQRT((2ck + k^2)/c^2)

Now, using the fact that (1/i) = -i, we have:

dt* = -i * dt / SQRT((2ck + k^2/c^2)

This expression is an imaginary number with real part Re(dt*) = 0, and imaginary part Im(dt*) = -dt / SQRT((2ck + k^2/c^2). As amolv06 suggests, a preliminary reading of this result would indicate that at superluminal velocities the component of travel in "normal time" would be 0, while there would be some negative component of travel in "imaginary time", whatever that means. It doesn't seem to indicate travel backwards through time at all. So, as amolv06 asked, where does this assumption that superluminal velocity does imply travel backwards through time come from? Is it strictly sci-fi, or is there some physical basis for it?