- #1

Pi-Bond

- 302

- 0

## Homework Statement

(Not homework, just a textbook question I'm confused about)

Two photons travel along the x-axis of S, with a constant distance L between them. Prove that in S' (moving at velocity v w.r.t S) the distance between these photons is [itex]L\sqrt{\frac{c+v}{c-v}}[/itex]

## Homework Equations

The Lorentz transforms

## The Attempt at a Solution

I don't understand why the length does not simply contract by the gamma factor, i.e. why the distance in S' is not [itex]\gamma L[/itex]. To obtain this I used the Lorentz transform for the coordinates of the positions of the photons. Setting the first at x=0 and the second at x=L yielded the coordinates in S' for the first as [itex]x'=-\gamma vt[/itex] and the second as [itex]x'=\gamma(L-vt)[/itex]. Subtracting these two yielded the above result. What am I doing wrong?