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Lecture12

# Lecture12 - 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 1 through 8 in Six Ideas that Shaped Physics, Unit R. Exam 1: Wednesday, October 5 at 8:00pm in WTHR 104

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The Aberration of Starlight As is often the case, care in choosing the coordinate system to represent a physical system can make it easier to predict and explain phenomena. In relativistic situations, one often has the added difficulty of dealing with two coordinate systems, S and S’ , at once. We require S’ to be in standard orientation relative to S so that we can use the standard form of the Lorentz transformation equations a to analyze situations Sun S : inertial frame in which the Sun is essentially at rest throughout the year. Earth location at t = 0 x y z Earth is moving in the x direction at speed V = 30 km/sec at t = 0. So, S’ in standard orientation and moving at speed V relative to S has the Earth momentarily at rest at the origin and is a good approximation to a coordinate system fixed in an observatory on Earth near t = t’ = 0. We are interested in observations of a star made near that time.
Sun x y z The star in question is located on the positive y axis of S, so a photon that arrives at the Earth’s location at t = 0 has traveled straight down the y axis. The red dots are events on its worldline. The time and space separations measured between them in S are Δ t 21 , Δ x 21 = 0 and Δ y 21 = - c Δ t 21 . 1 2 We use the Lorentz transformation equations to determine the time and space separations between events 1 and 2 measured in S’ . 21 21 t t γ = ∆ 21 21 x V t γ = - 21 21 y c t = - ∆ y x 2 1 21 y 21 x We conclude that the star will be observed in the direction inclined at an angle θ toward the x’ axis and away from the y’ axis with 4 21 21 | | tan 10 radians | | x V y c γ θ θ - = = This is a bit more than 20 seconds of arc and easily measured by astronomers.

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Sun S : inertial frame in which the Sun is essentially at rest throughout the year. Earth location at t = 0 x y z Earth location at t = 6 months V arrowrightnosp Six months later, the position of this star measured in the Earth’s frame will be inclined at the same angle but in the opposite direction from the y’ axis. Q1. The direction of a star located on the x axis measured in the Earth observatory at these two times would be A) inclined 20 arcseconds away from the x’ direction, toward y’ direction at t = 0 and away at t = 6 months B) inclined 20 arcseconds away from the x’ direction, away from y’ direction at t = 0 and toward at t = 6 months C) along x’ axis at both times.
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