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Unformatted text preview: Today: Review of SR Exam1: Tomorrow, 7:30-9:15pm, MUEN E050 You can bring 1 paper (Letter format) written on both sides with whatever you think might help you during the exam. But you cannot bring the textbook or lecture notes. Bring your calculators (but no PCs or cell phones please). Today: one extra office hour from 3-4pm in F-527. Yummy! Review of SR: The cast Peep? Chicken for Lunch! What exactly did we do during the first few weeks? • Galileo transformation: Classical relativity • Michelson-Morley 'c' is same in all inertial frames • Einstein's postulates: Incompatible with Galilean relativity! • Consequences were 'time dilation' and 'length contraction' Lorentz transformation Velocity transformation • Spacetime interval: Invariant under Lorentz transformation Chapter 1: Spacetime Re-definition of important physical quantities to preserve conservation laws under LT:- Momentum- Force- Kinetic Energy- Rest Energy- Total Energy Chapter 2: Relativistic Mechanics Let's start with a few important concepts Einstein’s Postulates of Relativity #1: If S is an inertial frame *) and if a second frame S’ moves with constant velocity frame S’ moves with constant velocity relative to S, then S’ is also an inertial frame. #2: The speed of light in vacuum is the same in all inertial frames of reference. *) An inertial frame is a reference frame that is not accelerating. Event • Where something is depends on when you check on it and on the movement of your own reference frame. • Time and space are not independent quantities; they are related by Lorentz Tr. • Definition: An event is a measurement of where something occurs at what time. ) , , , ( t z y x Events are not invariant under Lorentz transformation! In fact the LT converts the coordinates of an event from one frame to another; such as from S: ( x,y,z,t ) to S' ( x',y',z',t' ) What does the Lorentz tr. do? The the Lorentz (and Galileo) transformation converts the coordinates x,y,z,t of an event (x,y,z,t) in frame S to the corresponding coordinates x',y',z',t' of another frame S' . The way LT is presented here requires the following: The frame S is moving along the x axes of the frame S The frame S' is moving along the x-axes of the frame S with the velocity v (measured relative to S) and we assume that the origins of both frames overlap at the time t=0. S x z y S' x' z' y' v (x,y,z,t) (x',y',z',t') Transformations If S’ is moving with speed v in the positive x direction relative to S, then the coordinates of the same event in the two frames are related by: Galilean transformation (classical) Lorentz transformation (relativistic) t t z z y y vt x x = ′ = ′ = ′- = ′ ) ( ) ( 2 x c v t t z z y y vt x x- = ′ = ′ = ′- = ′ γ γ Remark: This assumes (0,0,0,0) is the same event in both frames....
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This note was uploaded on 08/24/2010 for the course PHYS 2130 taught by Professor Staff during the Spring '08 term at Colorado.
- Spring '08