h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Im a bit of a fanatic, and i've always liked this:

dt = (2Lo)/c

Where dt = change in time
Lo = Length 0 or the distance between the observer and the thing in motion relative to the observer.
c = speed of light (3.0 x 10^8 m/s^-1 about...)

The observer sees the clock moving with speed v. This will make a triangle exemplified in the following equation:

((dt1 x c)/2)^2 = Lo^2 + ((dt1 x v)/2)^2)

(dt1)^2 x ( (c^2)/4) - (v^2)/4) ) = Lo^2

(dt1)^2 = ((4Lo^2)/(c^2 - v^2))

Then, taking the first equation and substituting it in we get:

==> (dt1) = dt / (root(1-((v^2)/(c^2))))

dt1 seems be the same as dt (they are in the same dimention after all).

Because v^2 can never be greater than c^2 (see Einstein's theory of relativity) dt1 must be greater than dt.

Therefore t would always be less than t1, and time would be different for those travelling at different speeds.