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Show Light Has The Same Velocity in S and S'

  1. Sep 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the velocity transformation equations. Find the x and y components of the velocity in the frame S of a light ray that has speed c along the y′axis of frame S′ where S and S′are the usual frames we have been considering with S′ moving with speed v with respect to S along the common x − x′ axes. Show that the light ray has speed c in the frame S.


    2. Relevant equations
    1. u'_x = (u_x-v)/{1-(v*u_x/c^2)}
    2. u'_y = u_y/{gamma(1-(v*u_x/c^2))}
    3. u'_z = u_z/{gamma(1-(v*u_x/c^2))}
    3. The attempt at a solution
    u_z = u'_z = 0, obviously. I'm looking for u_x and u_y, so I need to start with u_x. I set u'_x to 0 and solved, getting u_x = v. I'm not sure if that's right, or if I should've gotten c, but I tried to plug u_x = v into equation 2, and did not get that u_y was c.
     
  2. jcsd
  3. Sep 6, 2012 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Welcome to PF.

    Think about how to get speed from the x and y components of velocity.
     
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