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Lecture05

# Lecture05 - 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 TA: Dan Hartzler Office: PHYS 7 Grader: Fan Chen Office: PHYS 222 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.

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Measuring the Length of a Moving Object (Method Two) Step 1: Send observers to closely spaced locations along the x axis of the coordinate system S and synchronize their clocks. Step 2: At a pre-arranged time, say t = 0, have the observers who happen to have the ends of the rod at their locations record this fact. The x-coordinates of events e1 and e2 are the x-coordinates of those observers. The length of the moving rod measured in S is simply the distance between the events, t e2 x e1 21 2 1 . L x x x = ∆ = - Alternatively, we could consider the locations of those two observers as marking the locations in S of the events e1 and e2 and use rulers at rest in S to measure the distance between them at a later time. This distance is just x 21 again and, so, determines the rods moving length. It is important to recognize the role that synchronized clocks and simultaneity play in both methods for measuring the length of a moving object along the direction in which it is moving. In method 1 synchronized clocks are used to measure the object’s velocity. In method 2 they are used to determine where the ends of the object are at the same time .
Measuring the Time Interval Between Ticks of a Moving Clock t x e1 e2 This spacetime diagram depicts the worldline of a clock moving at constant speed V along the x axis of an inertial coordinate system S . The events e n are ticks of the moving clock. e3 e0 t1 t0 t2 t3 One way to measure the time interval between these ticks in the inertial frame S is with the help of a set of observers with synchronized clocks at rest at locations closely spaced along the axis, much as we did to measure the length of a moving ruler. v S -frame clock worldlines In this case, each observer that happens to have the moving clock at their location when it ticks record the time of this event read from their own S-synchronized clocks. In this way, the observer at the location of the moving clock when its n th tick happens directly measures the S-frame coordinate time t n at which that event happened.

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t e2 x e1 Space-like and Time-like Spacetime Displacements The separation between a pair of events measured to determine the length of a moving ruler in a frame S purely spatial (the events are simultaneous) in that frame. They are an example of what are called space-like
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Lecture05 - Physics 344 Foundations of 21st Century Physics...

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