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Special relativity fundamental question

  1. Aug 3, 2009 #1
    I'm very new to special relativity and have a very basic question.
    A and B are moving from each other at a speed of [tex] v [/tex]
    at some instant a light flashes in the space.
    A records: At time [tex] t [/tex] a light flashed at [tex] x [/tex]
    B records: At time [tex] t' [/tex] a light flashed at [tex] x' [/tex]

    Here is what I understood from SR theory,
    A, at time [tex] t [/tex] sees what B records (instantly, forgetting the delay to see B's record) and writes the relationship to match what he records [tex] (t, x) [/tex] and B records [tex] (t', x') [/tex]

    [tex]x' = \gamma (x - vt)[/tex]
    [tex]t' = \gamma (t - v/c^2 x)[/tex]
    [tex]\gamma = 1/\sqrt{1 - v^2/c^2 }[/tex]

    Is my understanding correct?

    I am reading the wikibook http://en.wikibooks.org/wiki/Special_Relativity (hope that'll help me in all of special relativity)

    Thanks in advance
  2. jcsd
  3. Aug 3, 2009 #2


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    Yes, that is correct. The equations you have written (the first two specfically) are the Lorentz Transformation which relates position and time coordinates of an event as measured by the observers A and B, provided that one event has [itex]x = 0, t = 0[/itex] and [itex]x^{\prime} = 0, t^{\prime} = 0[/itex]. That is, the two coordinate systems are set up so their origins coincide.
  4. Aug 3, 2009 #3
  5. Aug 3, 2009 #4


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  6. Aug 3, 2009 #5
    thanks for correcting
  7. Aug 4, 2009 #6
    One more question related to the same scenario from wikibook

    1) How do you interpret the leaning forward of the time and x axis?
    Can you give some hints from the attached image?

    The book says (Bill and John are moving from each at [tex]v[/tex])
    Eq. 2 is from the Lorentz tranform and Eq. 1 is from the space-time interval definition
    But why does Eq. 1 has only [tex] T[/tex] from B's frame but not [tex] t[/tex] from John's frame?

    Can u pls give some advice?

    Actually I'm a bit confused as to how the interpretation that a moving objects are out of phase by [tex] T = (v/c^2) X[/tex] is derived. From that onwards I tend to wonder whether
    the wikibook is correct and questioning everything... really sorry if this is a silly question...

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    Last edited: Aug 4, 2009
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