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phy190_l16

# phy190_l16 - PHY190 Lecture#15 R9.4 Properties of Four...

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PHY190 Lecture #15 November 23, 2007 R9.4 Properties of Four Momentum On a spacetime diagram d R 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 ( ) we can calculate d R 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 ) P t = mdt /dτ = m γ ( dt - vdx ) = γm dt - dx = γ ( P t - vP x ) In general, P t = γ ( P t - vP x ) P x = γ ( 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 = γ - γv 0 0 - γv γ 0 0 0 0 1 0 0 0 0 1 A A t A x A y A z = γ - γv 0 0 - γv γ 0 0 0 0 1 0 0 0 0 1 A t A x A y A z

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phy190_l16 - PHY190 Lecture#15 R9.4 Properties of Four...

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