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Lorentz Boost of a photon

  1. Feb 25, 2009 #1
    hi there!

    Just wondering... if i have a photon moving in the z direction 4 momentum given by (0,0,1,1)

    and I lorentz boost it in the z direction... would I get the same original 4 momentum (0,0,1,1) cuz i thought that boosting something at the speed of light means that it remains at the speed of light right?

    in the case of the x direction (1,0,0,1) the lorentz boost in the x direction gives (cosh, -sinh, 0,1)... which isn't the original 4 momentum

    could somebody kindly explain what exactly i'm getting wrong here?

    Thank you!
     
  2. jcsd
  3. Feb 25, 2009 #2

    Dale

    Staff: Mentor

    The magnitude (Minkowski norm) of the photon's 4 momentum is invariant, but the components of the 4 momentum do change. When you boost it in the z direction you will get a 4 momentum of the form (0,0,E/c,E/c) where E/c is not in general equal to 1 in all frames.
     
  4. Feb 25, 2009 #3

    jtbell

    User Avatar

    Staff: Mentor

    The energy and momentum are not invariant between reference frames. The speed of the photon is invariant, nevertheless.

    In general, v/c = pc/E. For a photon in the original reference frame, E = pc so v/c = 1. In the new reference frame, after the transformation, you should be able to show that E' = p'c so v'/c = 1 also.
     
  5. Feb 25, 2009 #4
    ok... so am i getting this right? ... since E/c can change then lorentz boosting of a photon in the direction of its travel changes its energy therefore changing its frequency/colour only? the velocity remains at c
     
  6. Feb 25, 2009 #5

    Dale

    Staff: Mentor

    Correct.
     
  7. Feb 25, 2009 #6

    jtbell

    User Avatar

    Staff: Mentor

    Note that the change in frequency and wavelength between two reference frames is just the longitudinal relativistic Doppler shift.
     
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