Animated Alfred and Brian

The animation at right shows the Alfred and Brian spacetime diagram with k = 2. Both Alfred and Brian send out pulses at t=1 on their own clocks, and both receive the echo back at t=4. The coordinate grid from Alfred's point of view is shown in light gray lines. The animation shifts from Alfred's point of view to Brian's point of view and then back again. It should be clear from this that the space-time diagram in Brian's frame of reference is exactly the same at the space-time diagram in in Alfred's frame of reference except for a right-left mirror image.

Both Alfred and Brian measure a time t=k=2 for the "echo event" on their own world line, but determine a time t=(1+k²)/2=2.5 for the "echo event" on the other world line. Both Alfred and Brian find a time dilation factor of gamma = (1+k²)/2k=1.25. Both Alfred and Brian determine the distance of the "echo event" on the other world line to be D=(k²-1)/2=1.5c so the relative velocity is (v/c)=(k²-1)/(k²+1)=0.6.