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Velocity Addition in Special Relativity

  1. Nov 23, 2012 #1
    Hi All,

    Pardon me if this question looks so silly.

    Trying to understand velocity addition in special relativity.

    Say velocity components as measured in stationary frame of reference S are u, v, w in x, y, Z directions respectively and those in moving frame S' are u', v', w' in x', y', z' directions respectively. Let the velocity of relative motion between the reference frames is V and the motion is along x(or x') direction. Then velocity addition equations are as follows

    u = (u'+V)/(1+(u'V/c^2)) -----(i)

    v = {v'[1-(v^2/c^2)]^(1/2)}/[1+(u'V/c^2)] -----(ii)

    w = {w'[1-(v^2/c^2)]^(1/2)}/[1+(u'V/c^2)] -----(iii)

    Now say if light is emitted in the moving frame S' in its direction of motion x' i.e u'=c, then an observer in S measure the speed as u=c according to the equation (i)

    But how do I check using eqn (ii) that light emitted in y' direction in frame S' has speed c in frame S. I substitute u'=0 and v'=c in eqn (ii), but that leads to v=c[1-(v^2/c^2)]^(1/2)

    Please help me in figuring out where I go wrong
  2. jcsd
  3. Nov 23, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Don't forget equation (i): The light will have a component of velocity in the x direction.
  4. Nov 23, 2012 #3
    Thanks for pointing out, Doc
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