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Special Relativity simultaniety

  1. Sep 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Two events occur in an inertial system K as follows.
    Event 1: x1 = a, t1 = 2a/c, y1 = 0, z1 = 0
    Event 2: x2 = 2.6a, t2 = 1.9a/c, y2 = 0, z2 = 0

    What is the velocity of the frame K' in which these events appear to occur at the same time? Express the velocity vector using the variables a and c and the unit vectors, i, j, and k; for example, 2*i + 2*j is a vector which bisects the x and y axes.
    2. Relevant equations
    Lorentz equations

    3. The attempt at a solution

    First I assumed that I could use the time dilation, T0=T/Ɣ with T (the observed time) being zero but that obviously will not work. I likewise tried it with length contraction.

    I dont know where else to go from here.
     
  2. jcsd
  3. Sep 18, 2016 #2

    Simon Bridge

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    HInt: "simultaniety" and "Lorentz transformation".
     
  4. Sep 18, 2016 #3
    So the K' would have to travel the distance between event 1 and 2, in the amount of time between the events?
     
  5. Sep 18, 2016 #4

    TSny

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    Wouldn't this make the two events occur at the same place in K' rather than occur at the same time in K'?
     
  6. Sep 18, 2016 #5

    Simon Bridge

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    You know the space-time coordinates for the events in K.
    Use the Lorentz transformation to get equations for the space-time coordinates in another reference frame.
     
  7. Sep 19, 2016 #6
    PhysicsInNJ: Please write down for us the Lorentz equations for ##\Delta x'## and ##\Delta t'## in terms of ##\Delta x## and ##\Delta t##.
     
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