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Homework Help: A question on special relativity

  1. Oct 4, 2004 #1
    two events occur at the same place in a certain inertial frame and are separated by a time interval of 5 microseconds. What is the spatical separation ebtween these two events in an inertial frame in which the events are separated by a time interval of 13 microseconds?


    I must admit i am a a bit stumped on this one

    on one hand i think it has something to do with simultaneity. But then the frame which observes the longer time must be in motion.

    one the other hand i think that perhaps that the distance between the first and the second observer is so large that the doppler effect of light comes in to play. But i am not sure

    please help, thank you
     
  2. jcsd
  3. Oct 4, 2004 #2

    Doc Al

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    Make use of the fact that the spacetime interval between any two events is an invariant.
     
  4. Oct 4, 2004 #3
    what is an invariant? perhaps i know it as something else please describe
     
  5. Oct 4, 2004 #4

    jcsd

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    You know that I in the equation below does not change:

    [tex]I = dx^2 + dy^2 + dz^2 - dct^2[/tex]
     
  6. Oct 5, 2004 #5
    ok that blows my mind even more...

    someone suggested using a ratio between the two distances and times to get this answer but i was not usre about what he was saying
     
  7. Oct 5, 2004 #6

    jcsd

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    The Lornetz invariance of the interval is one of the most basic concepts in special relativity

    you know that for any Minkowskian coordiantes:

    [tex]dx^2 + dy^2 + dz^2 -dct^2 = dx'^2 + dy'^2 + dz'^2 - dct'^2[/tex]


    even if you haven't been given this it can be proved from the Lorentz transformation.

    so in the first inertial frame you know that dct = 5c and dx = dy = dz = 0, in the second frame dct' = 13c, so use the above equation to find: [itex]dx'^2 + dy'^2 + dz'^2[/itex] which by the Pythagorean theorum is the square of the distance between the two events in the primed frame.
     
    Last edited: Oct 5, 2004
  8. Oct 5, 2004 #7
    i understand this now, that light travls in a spherical front and the distnace travled by the light is given by ct (obviously)

    so the distnacei s 12c which is 12 micorseconds times c so distance is 3.6 e +3

    thank yo very much
     
    Last edited: Oct 5, 2004
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