Not sure if this is cranky or not, but when I was youthful I noticed that the Lorentz transformation of space-time due relativistic effects, square root of one minuc v squared over c squared, implies an imaginary solution for an v greater than c, that is for traveling faster than the speed of light. Now, most sci fi stories suggest that one would go backwards in time if one exceeded the speed of light, but I deduced that one would go into a second time dimension.

Of course the problem is that as long as Einstein is right, it is simply impossible to exceed the speed of light, thereby making the entire speculation irrelevant.