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Lorentz Transformation in New Coordinates

  1. Sep 19, 2009 #1
    I know the Lorentz transformation in rectangular coordinates

    [tex]
    ct' = \gamma (ct - \beta x)
    [/tex]
    [tex]
    x' = \gamma (x - \beta ct)
    [/tex]
    [tex]
    y' = y
    [/tex]
    [tex]
    z' = z
    [/tex]

    I want to do this same transformation, but from cylindrical coordinates [tex](r,\theta,z)[/tex] to [tex](r',\theta',z')[/tex].

    Any ideas?
     
  2. jcsd
  3. Sep 19, 2009 #2
    To make things straightforward, I just want the new frame to be moving along one dimension, say z. My guess is

    [tex]
    ct' = \gamma (ct - \beta z)
    [/tex]
    [tex]
    r' = r
    [/tex]
    [tex]
    \theta' = \theta
    [/tex]
    [tex]
    z' = \gamma (z - \beta ct)
    [/tex]
     
  4. Sep 19, 2009 #3

    DrGreg

    User Avatar
    Science Advisor
    Gold Member

    Yes, that is exactly right. If the motion is in the z direction, the x and y coordinates do not change, and the r and θ coordinates depend only on x and y (and vice-versa).
     
  5. Sep 19, 2009 #4
    Awesome, I understand, Thanks!
     
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