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relativity_10-1 - ′ ′ = ′ ′ ′ ′ = ′ ′ ′...

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PHY2061 R. D. Field Department of Physics relativity_10.doc University of Florida Force Transformations Consider a particle moving with velocity v' in the x' direction in the the O' frame . Let β = V/c and β ' = v'/c. Hence, β ' = p x 'c/E' and t d p d c t d p d p d E d t d E d c E p c p d E d c m p c E x x x x x x = = = = + = β β 2 2 2 0 2 2 ) ( In the O-Frame In the O'-Frame dt dp F dt dp F dt dx v y y x x = = = t d p d F t d p d F t d x d v y y x x = = = Lorentz Transformations: 2 1 / 1 / β γ β = = c V ) ( ) ' ( x d t cd cdt y d dy cdt x d dx + = = + = β γ β γ ) ( ) ( x y y x x p cd E d dE p d dp E d p cd cdp + = = + = β γ β γ Forces: ( ) ( ) y y y y y y x x x x x x x F t d p d t d x d c t d p d c x d t d p d dt dp F F t d p d t d p d t d x d c t d E d c t d p d c x d t d c E d p d dt dp F + = + = +
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Unformatted text preview: ′ ′ = ′ ′ ′ + ′ + = ′ ′ + ′ ′ + ′ ′ = ′ + ′ ′ + ′ = = ) 1 ( 1 ) 1 ( 1 1 / ) / ( 1 1 1 ) / ( ) / ( ⊥ ⊥ ′ ′ + = ′ = F F F F ) 1 ( 1 || || y x z y' z' x' V Particle O: (E,p x ,p y ,p z ) O': (E',p x ',p y ',p z ') O O' v' PHY2060 Review...
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