Lecture09

# Lecture09 - Physics 344 Foundations of 21st Century Physics...

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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: Chapters 5 in Six Ideas that Shaped Physics, Unit R.

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Q1. An alien spaceship travels at a constant velocity as it covers a distance of 3 light-hours in a time of 5 hours as measured by observers on Earth. The time measured by the clock on board the ship during this part of its trip is A) greater than 5 hours B) 5 hours C) less than 5 hours * ( 29 2 2 2 2 2 2 2 2 ( ) (5 3 ) hours 4 hours s t t x y z t = ∆ = ∆ - ∆ + ∆ + ∆ = - ∆ = Let S be the Earth frame and S’ the ship frame, then When using the invariant squared-interval, it is not necessary that S’ be in standard orientation relative to S . Q2. Did either the Earth observers or the aliens measure a proper time lapse between the events at the beginning and the end of this portion of the aliens’ trip? A) No, neither of them did B) the Earth observers did, the aliens didn’t C) the aliens did, the Earth observers didn’t D) Yes, the both did *
Completing the Derivation of the Lorentz Transformation Equations We have been using the fact that coordinate separations between events measured in a frame S and in a frame S’ in standard orientation relative to S are related by ( ) x x V t γ = ∆ - ∆ 2 V t t x c ∆ = ∆ - y y = ∆ z z ∆ = ∆ but we still have to establish the validity of the final two equations. Those equations relate spatial separations measured in S and S’ between pairs of events in directions that the observers judge to be perpendicular to the direction of their motion relative to each other. The text’s discussion in chapter 4 assumes that a ruler at rest in S’ and lying on it y’ axis will be observed to be parallel to the y axis in S . Is this true?

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How would an S -frame observer measure the orientation of a moving ruler? Recall our most direct procedure for measuring the length of a ruler oriented parallel to its velocity. We had to mark the locations in S of the moving ruler’s ends at the same time in S and use rulers at rest in S to determine the distance between the marks in order to measure the length of the moving ruler. V a mark location of this end first mark location of this end later If we marked the location of one end first and the location of the other end a little later, the ruler would move in the meantime and the separation between the marks would be greater or less than the ruler’s length. This diagram depicts the situation in which the location of the back end of the
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## This note was uploaded on 12/09/2011 for the course PHYS 344 taught by Professor Garfinkel during the Fall '08 term at Purdue.

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Lecture09 - Physics 344 Foundations of 21st Century Physics...

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