# Velocities as seen by different observers.

## Main Question or Discussion Point

You have two frames (A & B) with each having velocity v with respect to one another. To make things easier, A is at rest with you, and B is moving to the right at v. Also, in frame B, it observes a particle moving to the right at speed u'. We can then find the velocity of this particle as observed by A, u via u = (u'+v)/(1+u'v/c^2).

From this, we can then calculate the velocity difference of the particle and B as observed by A. This velocity is not what is observed by B, that would be u'.

Now have u' to the left in B (it is now implicitly "negative").

Once again calculating the velocity difference in A to find the velocity that A observes the particle to have with respect to B, I find that its magnitude is not equal to that of the first case where the particle was moving to the right in B.

I can see why this is the case mathematically, but it doesn't seem intuitive. That is, there is only a change in direction of u' in B, but A observes two different velocities with respect to B.

Can anyone offer me some intuition on this? I have a feeling it has to do with clocks not being synchronized from frame to frame.

Thanks.