#### Re: But faster than light time becomes imaginary

The Lorentz formula for relativistic time dilation, which is basically just the summing of space and time movement vectors using Pythagoras's right-angle triangle formula, tells us an awful lot of really interesting things about space-time.

Perhaps the most important thing it tells us is that it shows that our movement through space and our movement through time are similar enough phenomena that the two vectors can actually be summed: space and time are not two entirely different things, for if they were then the vectors couldn't be summed to reach a meaningful answer. Relativistic time dilation has been proved to work in accordance with the Lorentz formula, probably the best known example being the timing allowances that need to be built in to the GPS satellites to account for both gravitational and relativistic time dilation.

The nature of the Pythagorus/Lorentz formula is such that there is no scope for discontinuities in the curve produced with the consequence that it sets upper and lower bounds for the rates of movement through both space and time: we term the fastest you can go as 'c' and the slowest is zero. This means that your individual vectors through space or time can't exceed 'c', or go slower than zero within the dimensions being summed, or in other words, you can't exceed 'c' in this universe because, as far as we can tell, Pythagorus/Lorentz always applies.

For anyone who's interested, take the Lorentz formula, simplify it to produce a factor by removing the relative terms, and then, using normalised values (0 = 0, 'c' = 1), punch it in to a spread sheet and plot the results - you'll get a quarter-circle arc of radius 1 ('c'). So whilst Lorentz proves to be true we exist only on that one-dimensional arc, curved through space-time; never inside or outside.

Once you've done that, you can then start speculating about the rest of the circle ;-)