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Chapter2_4

# Chapter2_4 - cp E p ~ ′ ′ ′ ′ = ′ z y x p c p c p...

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PHY3063 R. D. Field Department of Physics Chapter2_4.doc University of Florida Consider two frames of reference the O-frame (label energy and momentum according to E,p x ,p y ,p z ) and the O'-frame (label energy and momentum according to E',p x ',p y ',p z ') moving at a constant velocity V, with respect to each other at let the origins coincide at t = t' = 0. The Lorentz transformations tell us how the frames are related. z z y y x x x p c cp p c cp E p c cp p c E E = = + = + = ) ( ) ( β γ z z y y x x x cp p c cp p c E cp p c cp E E = = = = ) ( ) ( where 2 1 / 1 / = = c V . The following are Lorentz 4-vectors: = z y x cp cp
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Unformatted text preview: cp E p ~ ′ ′ ′ ′ = ′ z y x p c p c p c E p ~ and = z y x cdp cdp cdp dE p d ~ ′ ′ ′ ′ = ′ z y x p cd p cd p cd E d p d ~ Invariant Mass: 2 2 2 2 ) ( ) ~ ( ~ ~ ~ ~ ~ c m p p p p p p = ′ = ′ ⋅ ′ = ⋅ = y x z y' z' x' V Object O: (E,p x ,p y ,p z ) O': (E',p x ',p y ',p z ') O O' differentials Same in all frames!...
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