What is the Distance Between Two Photons in Different Reference Frames?

[noblegas]

Homework Statement

two photons travel along the x-axis of S , WITH A CONSTANT DISTANCE L betweenthem. Prove that in S's the distance between these photons is L(c+v)^1/2/(c-v)^1/2.

Homework Equations

x'=gamma*(x-vt), x=gamma*(x'+vt), t=gamma*(t'+vx'/c^2), t=gamma*(t'-vx'/c^2)

The Attempt at a Solution

L(c+v)^1/2/(c-v)^1/2=L((c+v)/(c-v))^.5=L((+v/c)/(1-v/c))^.5. So will the two photons reach a midpoint along the x-axis. I think I should either find the difference between x_2 and x_`1 or the difference between x'_1 and x'_2. I thinkl in one reference frame , the time would be dilated with the moving frame for both photons . Is my line of thinking correct?

 

[diazona]

or the difference between x'_1 and x'_2.

That is the quantity you should be looking for, keeping in mind that the definition of simultaneity is not the same in S' as in S - so you need to calculate the difference between x_1' and x_2' as measured at the same time in S', not at the same time in S.

Consider drawing a spacetime diagram. I find that doing that helps with these kinds of problems.

 

[noblegas]

That is the quantity you should be looking for, keeping in mind that the definition of simultaneity is not the same in S' as in S - so you need to calculate the difference between x_1' and x_2' as measured at the same time in S', not at the same time in S.

Consider drawing a spacetime diagram. I find that doing that helps with these kinds of problems.

In order to calculate x_2' and x_1' should I calculate t_1 and t_2 first?

 

[pieterdb]

I'm trying to teach myself special relativity (using the book 'Introduction to Special Relativity' by Wolfgang Rindler). I'm currently working on the problem stated above.

My first approach was : x1=ct ; x2=L+ct.
Then using x'=gamma(x-vt) and t'=gamma(t-vx/c²) I calculate x1' and x2'. However I'm always arriving at L'=gamma(L) which is the formula for Length contraction.

Where is my mistake ? There obviously is a difference between the length contraction (of a rod in S seen from S') and the 'length contraction' in this problem (the distance between 2 moving photons).