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Spacetime Interval

  1. Jan 23, 2009 #1
    The spacetime interval s between two events is s^2 = c^2*t^2 - x^2 where t is the time between the 2 events and x is the distance between the 2 events in a given frame of reference.


    What is the general condition on s such that two events cannot be simultaneous in any
    frame?

    I don't really understand the question..
    What am i supposed to do?
    I mean...the shortest possible time between 2 events is 0, so picking a reference frame in which they are simultaneous, the spacetime interval between them would simply be the distance x between them
    or
    s = root (-x^2)
    which is not a real number....(even though I think the spacetie interval can be imaginary)
    So if the time between any 2 events is more than 0, then the spacetime interval would be greater than root (-x^2) since we'd be substracting -x^2 from a number larger than zero....so is the restriction that if s is less than root (-x^2), then 2 events can' tbe simultaneous in any frame?
    Can someone please tell me if im on the right track at all??
     
  2. jcsd
  3. Jan 23, 2009 #2
    Does this make sense?

    The spacetime interval between two events doesn't change when you change from one inertial frame to another, although x and t do. If s^2 = 0, the measured time between events (t) is equal to the time required for light to travel the measured distance between the events (x/c). So only if x=0 could the events be simultaneous.

    If s^2 < 0, the measured time between events is less than the time required for light to travel the measured distance between events; so a frame can be found in which the events are simultaneous. In this frame x^2 = -s^2.

    If s^2 > 0 , |t| > |x/c|. Since the distance between the events can't be negative in any frame, t must be greater than 0. There is no frame in which the events are simultaneous.
     
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