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Unformatted text preview: PHY190 Lecture #15 November 23, 2007 R9.4 Properties of Four Momentum On a spacetime diagram d R d is tangent to the worldline as an object moves time coordinate is treated on equal footing with the three space coordinates By defining four-velocity in terms of a four-vector ( d R ) and an invariant ( d ) we can calculate d R d in other frames (once we know it in one frame). Do this with the Lorentz transformations that we already know Similarly P is also the ratio of a four-vector ( d R and two invariants ( m and d ) P t = mdt /d = m ( dt- vdx ) d = m dt d- dx d = ( P t- vP x ) In general, P t = ( P t- vP x ) P x = ( P x- vP t ) P y = P y P z = P z These are the same transformations as ( t ; x ) ( t ; x ) In general if you have any four-vector: A = ( A t ; A x , A y , A z ) Can transform them to another frame with: A = - v- v 1 1 A A t A x A y A z =...
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