Lecture06

Lecture06 - Physics 344 Foundations of 21 st Century...

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Unformatted text preview: Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Fan Chen Office: PHYS 222 [email protected] Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: Sections 3.1, 3.2, 3.3, 6.1 and 6.2 in Six Ideas that Shaped Physics, Unit R. The Relativity of Simultaneity Observers in relative motion through a relativistic Universe can disagree about whether or not pairs of events they observe occur at the same time or not. This was the case for the events E and 2 in the physical situation that we analyzed last lecture. This most basic relativistic phenomenon is the reason that the x’ axis of the inertial coordinate system S’ is inclined relative to the horizontal surfaces of simultaneity of the system S in this spacetime diagram drawn from the perspective of S . The two coordinate systems are shown in standard orientation relative to each other. 2 3 t 2 x 2 t t ’ x E x ’ Jack stands near a long straight section of track as a train car passes at constant speed V . Jill is sitting in the middle of the train car. Lighting strikes the front and back of the train leaving marks on both the train and the ground, events 1 and 2. Jack’s measurements indicate that these lighting strikes both happened at time t = 0, the same time as Jill passes him, event 3. In other words, he finds that all three events are simultaneous. x z Jill Jack V a Spatial diagram Jack’s frame t = 0 event 2 event 1 event 3 John Q1. Jill’s measurements of when these events happen indicate that A) 1 occurred after 2 B) 1 and 2 were simultaneous C) 1 occurred before 2 Q2. John happens to be standing at rest near the location on the track where lighting strikes the back of the train when it strikes, event 2. His measurements indicate that A) 1 occurred after 2 B) 1 and 2 were simultaneous C) 1 occurred before * * Completing the 2-Frame Diagram Last time we showed that the S-frame spacetime coordinates of the events 2 and E are 2 3 t 2 x 2 t t ’ x E x ’ 3 2 2 / 2 (1 / ) E t L c t V c = =- 3 2 2 / 2 (1 / ) E x LV c x V c = =- 2 / (1 / ) L c t V c =- 2 (1 / ) L x V c =- and . For SR units set c = 1. 2 2 2 2 2 / (1 / ) (1 / ) (1 / ) E L LV c L x V c V c V c ⇒ ∆ =- =--- 2 2 2 2 2 2 / / / (1 / ) (1 / ) (1 / ) E L c L c LV c t V c V c V c ∆ =- =--- 2 E t ∆ 2 E x ∆ θ θ So, since our 2-frame diagram is drawn using SR units, the angle θ between the x and x’ axes has...
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Lecture06 - Physics 344 Foundations of 21 st Century...

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