> I have told Androcles the following many times, and I have
> always wondered if he really is so stupid that he doesn't understand it,
> or if he is only pretending not to:
>
>  x' is a point moving with the Greek frame.
> Thus x' = x - vt means that the Greek fame is moving in the positive
> x - direction.
>
> --------|---------------> xi   v ->
> --------|---------------> x
>
> The LT is then:
>   tau = (t - x*v/c^2)/sqrt(1-v^2/c^2)
>   xi = (x - v*t)/sqrt(1-v^2/c^2)
> which may be written:
>   t = (tau + xi*v/c^2)/sqrt(1-v^2/c^2)
>   x = (xi + v*tau))/sqrt(1-v^2/c^2)
>
> x' = x + vt obviously means that the the Greek frame is moving
> in the opposite direction:
> --------|---------------> xi  <- v
> --------|---------------> x
> or:
> --------|---------------> x   v ->
> --------|---------------> xi
>
> This is equivalent to interchanging the frames.

Of course.
But don't forget

> --------|---------------> xi   v->
> --------|---------------> x
> or:
> --------|---------------> x   <-v
> --------|---------------> xi

which is equivalent to putting the car into reverse gear.

>
> It should be blatantly obvious that the LT then becomes:
>   t = (tau - xi*v/c^2)/sqrt(1-v^2/c^2)
>   x = (xi - v*tau))/sqrt(1-v^2/c^2)
> which may be written:
>   tau = (t + x*v/c^2)/sqrt(1-v^2/c^2)
>   xi = (x + v*t)/sqrt(1-v^2/c^2)
>
> So what is it, Androcles?

> Are you really so incredible stupid that you don't understand this?

Not at all, Paul. I understand it completely and fully agree with you.
That's what I was explaining to Mike

When tau = (t - x*v/c^2)/sqrt(1-v^2/c^2) we call it time dilation.
When tau = (t + x*v/c^2)/sqrt(1-v^2/c^2) we call it time contraction.