Special relativity and Lorentz factor problem

[RealKiller69]

Homework Statement

There are 2 particles(1,2) separated ∆x=L moving with the same velocity u_x in frame of reference S , there's an other reference S' moving at v .
I have to calculate ∆x'. GAMMA(LORENTZ'S FACTOR)

Homework Equations

The Attempt at a Solution

I have done x1=0 when t=0
So for particle 1 x1=ut
Particle 2 x2=L+ut
So ∆x=L=gamma(∆x') , and it's not correct
The solution I have got from class is
X1=x0+ut1
X2=x0+L+ut2
So when I measure the distance between them in S' the solution is completely different, the thing I don't understand is , how t2=\t1 and not t2=t1.

 

[Orodruin]

You measure $\Delta x'$ by measuring the difference in $x'$ at the same $t'$, i.e., simultaneous events in $S'$. Since the particles are separated, relativity of simultaneity comes into play and what is simultaneous in $S'$ is not simultaneous in $S$, i.e., you will have different $t$ coordinates if you have the same $t'$ coordinate.