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Relativity along an axis in an inertial frame

  1. Jun 6, 2013 #1
    Suppose that two events occur on the x axis of an inertial frame, Δx apart with a time interval between the events of Δt.
    a) the proper time interval between the events is...?
    b) the proper distance between the events is...?

    I think I'm just getting confused by the wording. I imagined that I was in the same frame of reference, and therefore the answers are Δt and Δx. But evidently, I'm wrong. Do I need to set the speed of the frame to 'v' and do something with simultaneous equations to remove that variable?

  2. jcsd
  3. Jun 6, 2013 #2
    OK, so I defined a stationary reference frame as S, and defined the frame in the question as S'. S' is moving wrt S at a velocity v.
    So the proper time is the Δt observed in S', and the proper length is the Δx observed in S'.

    I think I've worked out a, but struggling with b. I'm using the length contraction formula as one equation, and the Lorentz coordinate transformation as the second equation, but when I solve them simultaneously I can only achieve v=0.
  4. Jun 6, 2013 #3
    Start with definitions. What are proper time and distance?
  5. Jun 6, 2013 #4
    Proper length is measured distance in the FOR where the objects are at rest, i.e. in frame S'.

    I'm using the equations L' = L/gamma and x' = gamma(x-vt) and trying to solve these simultaneously, am I on the right track?
    I can't determine whether L' = x' and L = x, or L' = x and L = x', though...
  6. Jun 6, 2013 #5
    What are the "objects" in the case? Are they at rest as stated? In what reference frame are they at rest?
  7. Jun 7, 2013 #6
    The objects are two arbitrary points situated along the x axis of S', and are at rest in frame S', thus always separated by delta x.
  8. Jun 7, 2013 #7
    If you measure distance between two arbitrary points, you get arbitrary results. I do not think this is what the problem is about. Connect "objects" with the description of the problem.
  9. Jun 7, 2013 #8


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    Given the information as stated, with everything motionless in an inertial frame, why would the "proper time interval" not be [itex]\Delta t[/itex] and the "proper distance" [itex]\Delta x[/itex].
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