# Relativity and Transformations

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1. Mar 18, 2015

### john morrison

1. Show that if we transform first in the x-direction and then in the minus x direction with the same speed (v), we end up with the original space-time coordinates. Note: For this problem you will need to apply the transformation equation twice. You will also need to apply the transformations to both x and t.

2. Relevant equations

x' = \gamma(x-Vt)
y' = y
z' = z
t' = \gamma(t-(Vx)/c^2))

3. The attempt at a solution

I attempted to plug in -x into the x for x' and then plug in x' whenever I found an x. However, this didn't get me far.

Last edited by a moderator: Mar 18, 2015
2. Mar 19, 2015

### Orodruin

Staff Emeritus
The problem is asking you to apply the Lorentz transformation once with velocity v and once to the resulting coordinates with velocity -v (you can call the coordinates resulting from this t'' and x''). Your task is then to show that x'' = x and t'' = t. The problem does not tell you to switch the directions of the x or t axes.