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Special relativity - frames of reference

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data
    We have two frames of reference: K (x,y,t) and K' (x',y',t') such that initially x=x'=y=y'=t=t'=0. Now let K' move with a velocity [tex]\vec{v} = v [\tfrac{1}{\sqrt{2}},\tfrac{1}{\sqrt{2}}][/tex]
    Write Lorentz transformations in such a case.

    2. Relevant equations

    3. The attempt at a solution
    My try is:
    [tex]t' = \frac{t - (\vec{v} \circ (x, y))/c^2}{\sqrt{1 - \frac{v^2}{c^2}}}, \; x' = \frac{x - v_x t}{\sqrt{1 - \frac{v^2}{c^2}}}, y' = \frac{y - v_y t}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]

    where [tex]v_x = v_y = \frac{v}{\sqrt{2}}[/tex]
    Last edited: Feb 25, 2009
  2. jcsd
  3. Feb 26, 2009 #2


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    Science Advisor
    Gold Member

    Looks good to me.
  4. Feb 26, 2009 #3
    Great, thank you!
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