Physics Lecture Recap: Relativity Concepts and Violation of Simultaneity
In this lecture recap, we covered topics related to relativity, including length contraction, velocity addition, and the Doppler effect. We discussed the consequences of special relativity, such as violations of simultaneity, and explored scenarios involving light beams hitting moving walls. Theoretical calculations using Lorentz transformations were applied to demonstrate the non-simultaneous nature of events in moving frames of reference.
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Lecture Topics & Quiz: Sep. 6, 2019 1 PHY3101: Chapter 2
Lecture Topics Sep. 6 What we just finished Length contraction, velocity addition Doppler effect (mostly from reading document) Document 2C_SR_LT_consequences Today: LT examples (Chap. 2) Simultaneity violation, simultaneity examples Document 2C_SR_LT_consequences Document 2D_SR_simultaneity_examples Next 2-3 lectures Energy and momentum in SR Document 2E_SR_momentum_energy 2 PHY3101: Chapter 2
Programming Introduction We had excellent sessions Wednesday & Thursday Wednesday: Sep. 4 7:00pm 8:15pm Thursday, Sep. 5 7:00pm 8:15pm (repeat of Wed) Primary purpose: make sure you have tools Download python on your machine Very simple programs We will have bonus homework soon 3 PHY3101: Chapter 2
Relativity Question A room of rest length L moves at very high speed. A person at the center shoots laser beams at both walls simultaneously. As seen from someone on earth, which wall is hit first? 1. Wall 1 2. Wall 2 3. They are hit simultaneously 4 PHY3101: Chapter 2
Relativity Question A room of rest length L moves at very high speed. A person at the center shoots laser beams at both walls simultaneously. As seen from someone on earth, which wall is hit first? 1. Wall 1 2. Wall 2 3. They are hit simultaneously Speed of light is alwaysc. 1. Beam must catch up to Wall #2 2. Beam meets oncoming Wall #1 So Wall #1 is hit first. We can also show this from LT 5 PHY3101: Chapter 2
Consequences of SR: Violation of Simultaneity Moving room at velocity v Light beams launched simultaneously When do the beams hit the walls? Solve using Lorentz contracted length, light speed = c 6 PHY3101: Chapter 2
Violation of Simultaneity (2) 1 2L/g c+v ( 1 2L/g c-v ( 1 L t1= = ) 1+b ( ) 2g c 1 L t2= = ) 1-b ( ) 2g c =L b 1 1 L Dt = t2-t1= 1-b- 2g c 1+b g c 1-b2 1-b2 1-b2=gbL =Lb Not simultaneous! c c Let s calculate using LT directly 7 PHY3101: Chapter 2
Violation of Simultaneity (3) Use LT for time coordinate, using t = 0 =gbD z D t +bD z =gbL Dt =g c c c Same result, but nice to verify 8 PHY3101: Chapter 2
Simultaneity Example Two events (light beams?) occur at the same time 300 m apart on a rocket moving with a velocity = 0.6 =1.25 0.6 D t +bD z 300 3 108= 0.75 msec Dt =g c 9 PHY3101: Chapter 2
Simultaneity Violation: Snake Problem Snake of rest length 100 cm moves at v = 0.6c to the right Michelle holds 2 hatchets 100 cm apart, brings them down simultaneously. Left hatchet barely touches snake s tail As seen by Michelle, the snake is contracted to a length of 80 cm so the other hatchet lands 20 cm in front of snake s head. 100 cm 80 cm v = 0.6c zR = 100, tR = 0 zL = 0, tL = 0 What does snake see? 10 PHY3101: Chapter 2
Snakes Viewpoint Na ve point of view Length contraction: hatchets in snake s frame are contracted to 80 cm apart. But he is 100 cm long in his own rest frame, so when the hatchets land he should have his head cut off! Having your head cut must be relativistically invariant, i.e., it shouldn t depend on what frame it is observed So what is wrong here? Resolution: Hatchets are not simultaneous in snake s frame! 11 PHY3101: Chapter 2
Correct Analysis in Snakes Frame Let snake moves from left to right (along +z) Tail at zL = zL = 0, left hatchet lands at tL = tL = 0 tR=g tR-bzR/ c zR=g zR-bctR ( )= 0- 1.25 )= 1.25 ( ) 0.6 ( ) 1.00 )=125 cm ( )/3 108= -2.5 10-9sec ( ( )100-0 ( So the hatchets land at different times! Right hatchet lands first 25 cm in front of his head (he is 100 cm) Left hatchet lands afterwards at the edge of his tail 80 cm v = 0.6c v = 0.6c 100 cm O frame (snake) 25cm z R = 100, t R = -2.5ns 12 PHY3101: Chapter 2
Drug Dealer Problem Room of length L = 60 m moves to right at velocity v = 0.8c. (Agent, dealers, room all moving together in O frame) Dealers are shot simultaneously by Fed agent in his rest frame. What does a stationary observer see? 13 PHY3101: Chapter 2
View From Earth Frame (Frame O) =gbL D t +bD z Dthit= t2-t1=g c c 0.8 60 3 108= +267 nsec 1 = 0.6 Dealer 1 is hit first, then Dealer 2 But could someone standing on earth next to Dealer 1 when he is struck send a warning in time to Dealer 2 so that he could duck? From LT, length of room in earth frame is 0.6 60 = 36 m Time of warning light signal to reach Dealer 2 is 36 c-v= c 1-b ( 36 36 Dtwarn= = = 600 nsec ( )0.2 ) ( ) 3 108 So warning signal takes too long to get there in time! 14 PHY3101: Chapter 2
Relativistic Kinematics This is energy and momentum. We covered pages 1-3 of the note on relativistic kinematics 15 PHY3101: Chapter 2
