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Velocity Addition in Special Relativity 
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#1
Nov2312, 09:35 AM

P: 16

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
Nov2312, 09:59 AM

Mentor
P: 41,309




#3
Nov2312, 11:18 AM

P: 16

Thanks for pointing out, Doc



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