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Homework Help: Special relativity and Lorentz factor problem

  1. Jun 14, 2018 #1
    1. The problem statement, all variables and given/known data

    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)
    2. Relevant equations


    3. 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.
     
  2. jcsd
  3. Jun 14, 2018 #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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