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Spacetime Interval

  1. Jun 20, 2012 #1
    1. The problem statement, all variables and given/known data

    The spacetime interval between the origin in frame S and an event, A, is found to be r = 8
    lightseconds. In frame S' moving in Standard orientation with respect to S at speed v =
    0.5c event A is measured at a distance r' = 6 lightseconds from the origin.

    (a) What is the time interval between the origin in S' and event A?

    (b) Could an event at the origin and event A be causally related? Explain your answer


    2. Relevant equations


    3. The attempt at a solution

    I am studying for upcoming exam so the solution isnt as important as understanding the question, but as far as i know the spacetime interval is invariant which is throwing me way off here, I'm certain if i can get part a i understand part b but am completely at sea with part a) any help will be greatly appreciated, cheers.
     
  2. jcsd
  3. Jun 22, 2012 #2

    BruceW

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    Homework Helper

    Yes, the spacetime interval is invariant. Question (a) asks for the time interval, not spacetime interval.
     
  4. Jun 22, 2012 #3

    collinsmark

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    Gold Member

    Also, in addition to what BruceW mentioned,

    I suspect that when the problem statement said,
    "...distance r' = 6 lightseconds..."
    it's not asking for the spacetime interval to A, but really asking for the x' component of r. In other words, the distance from the origin to the projection of A onto the x' axis.

    It probably would have been clearer if the problem statement was worded, "measured at a distance x' = 6 lightseconds."

    In other words, the spacetime interval from the origin to A is 8 lightseconds (true whether one is in S or S', since spacetime intervals are invariant). And in S', the spacial distance (not spacetime distance) from the origin to A is 6 lightseconds. Still in other words, this "6 lightseconds" vector lies along the x' axis itself.

    That's my guess as to what the problem statement is trying to say.
     
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