Velocity Addition in Special Relativity

[rajark]

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

 

[Doc Al]

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)

Don't forget equation (i): The light will have a component of velocity in the x direction.

 

[rajark]

Thanks for pointing out, Doc