Lect10_[Compatibility_Mode]

Lect10_[Compatibility_Mode] - Physics 344 Foundations of...

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Shuo Liu Office: PHYS 283 [email protected] Office Hours: If you have questions, just email us to make an ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Reading: Chapter 7 of the text. Notices: Homework is due Thursday at the beginning of recitation. Exam I will be at 8:00pm Thursday, October 7 in MTHW 210
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We have been focused on the relationship between coordinate time and position measurements made by observers using Home- and Other-frame coordinate systems in standard orientation relative to each other. Last lecture we finally completed our derivation of the inverse Lorentz transformation equations () xx V t γ = + 2 V tt x c ⎛⎞ ′′ =+ ⎜⎟ ⎝⎠ y y = zz = recitation last week you established that the corresponding Lorentz V t = V x =− y y = = In recitation last week you established that the corresponding Lorentz transformation equations are 2 c t t Notice that when using SR units they imply that the angles between the t and t’ x axes and the x and x’ axes in a two-frame spacetime diagram are equal. tan / Vc θ= x θ
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t t’ This two-frame spacetime diagram A event 1 depicts an event 1, say, the decay of a muon. uestion 1: Which of the other events x B C D Question 1: Which of the other events shown occurs at the same location as event 1 in the Home (unprimed) frame? x O Question 2: Which of the other events shown occurs at the same location as event 1 in the Other (primed) frame? Question 3: Which of the other events shown occurs at the same time as event 1 in the Other (primed) frame?
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Lorentz Contraction and Time Dilation are Frame-Symmetric Two specific predictions of the Lorentz transformation equations are Lorentz contraction: For any object moving through my frame at speed V measure a length along the direction of its motion that smaller than the I measure a length along the direction of its motion that smaller than the length I measure for an identically constructed object at rest in my frame, 22 00 /1 / . L LL V c γ == Time dilation: For a clock while moving through my frame at speed V I measure a period between ticks that is longer than the period I measure for an identically constructed clock at rest in my frame, . 1/ T TT Vc Δ Δ= Δ Note well, not all spatial and time separations between pairs of events transform in these ways. These are special cases. The Lorentz contraction result holds only because the events defining the length of the moving object are simultaneous in my frame.
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue.

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Lect10_[Compatibility_Mode] - Physics 344 Foundations of...

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