I have question. Want to know time dilation for clock at negative coordinate in moving frame to reach origin of rest frame.
Let us use P' = ( -7/8ls,0,0 ). Use v =3/5c, then γ = 5/4. ls is light seconds.
Do you apply Lorentz Transforms like this
t' = ( t - vx/cē )γ
But, we do not have t yet.
Apply length contraction to know when P' reaches the rest origin. Distance is (7/8)/γ = (7/8)(4/5) = 7/10ls.
Now apply transform. Since at origin, x = 0
t' = ( 7/10s - (3/5c)(0/cē) )γ
t' = (7/10s) γ
This means moving clock beats faster.
What's wrong with this?