- #1
insynC
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Homework Statement
Derive the Lorentz transformation for the x component of momentum, i.e.
Px' = [tex]\gamma[/tex] (Px - vE/(c[tex]^{}2[/tex]))
I've used Px = x component of momentum (not very good with latex, sorry!)
Homework Equations
I thought the best place to start was the Lorentz transformation for velocity (which was given):
ux' = [ux - v] / [1 + v ux/(c[tex]^{}2[/tex])]
The Attempt at a Solution
Applying this, I used the fact Px = [tex]\gamma[/tex] m0 ux - where m0 is rest mass - and then fiddled around with it.
I was able to almost get the answer, except on the RHS I got what is required multiplied by a factor of:
1 / [ [tex]\gamma[/tex] - [tex]\gamma[/tex] ux v /(c[tex]^{}2[/tex]) ]
Unfortunately I couldn't show this was equal to 1 and am not even convinced it is. Was the approach I took the easiest way to the answer? I've tried it again and got the same problem, so maybe there is a better way to tackle it.