Pete, Okay, let's try to apply Lorentz transformation for the exercise I gave to depict MacM's wrong view. Say, you are in a spaceship moving at v=0.6c from earth to moon. If earth-moon distance is 1.2c second, according to earth observer you need (1.2c second)/0.6c=2 seconds to reach moon. Now, from your point of view. You see earth-moon distance as 0.8*1.2c second = 0.96c second. According to MacM's interpretaion, you still need 2 second (instead of 1.6second suggested by standard SR) to complete the trip and therefore you will find that your velocity relative to earth (or moon) is (0.96c second)/2 = 0.48c. This cannot be right (Correct only based on MacM's relativity, which is the wrong version of relativity).Based on standard SR you will still see the relative velocity as (0.96c second)/1.6 = 0.6c! There is nothing to talk about on MacM's view on this matter, seriously, because his view is WRONG. I believe you agree that for this case, the spaceship observer measures the time for the trip as 1.6 second and the earth-moon distance as 0.96c second, while earth observer measures them as 2 second and 1.2c second respectively. Applying LT for spaceship passing earth event gives us t=t'=0 and x=x'=0. Now, apply LT for t=2 seconds and x=0 that is an event occuring on earth at the time the spaceship arrives to the moon. This is the result: x' = 1.25*(0-0.6c*2) = 1.5c second t' = 1.25*(2-0) = 2.5 secondNext, apply LT for t=2 seconds and x=1.2c second that is an event occuring on the moon at the time the spaceship arrives to the moon. This is the result: x' = 1.25*(1.2c-0.6c*2) = 0 t' = 1.25*(2-0.6*1.2) = 1.6 secondYou can see that the correct result is obtained by applying LT for the spaceship arriving the moon event, which occurs at x'=0 at the same position as the spaceship passes earth event. The distance covered by the spaceship during the 1.6 second trip, according to the spaceship observer, is 0.6c*1.6 = 0.96c second. You can verify using other method that event at D occurs at t=0 in earth reference frame and event at E occurs at t=2sec in earth reference frame, say, by first synchronize clocks at D and E to ensure that they both tick simultaneously.