This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 fourvelocity in terms of a fourvector ( 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 fourvector ( 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 fourvector: 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 =...
View
Full
Document
This note was uploaded on 08/24/2011 for the course PHY 190 taught by Professor Bertoldi during the Fall '08 term at University of Toronto Toronto.
 Fall '08
 BERTOLDI
 Momentum, Special Relativity

Click to edit the document details