Special relativity and Lorentz factor problem

  • #1

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.
 

Answers and Replies

  • #2
Orodruin
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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.
 

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