Lecture11 - 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 (note change of location!)
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Events and Spacetime Separations We’ve developed a basic understanding of how observations made in different inertial frames are related by focusing on what happens in physical situations at specific locations and times, i.e., on events, and on spacetime separations between pairs of events. Coordinate time and spatial separations between a pair of events are frame-dependent measures of their spacetime separation. In the case of one inertial coordinate system, S’ , in standard orientation relative to another, S , the time and spatial separations measured between a pair of events in each are related by these Lorentz transformation equations, ( ) x x V t γ = ∆ - 2 V t t x c γ = ∆ - y y = ∆ z z = ∆ By considering a pair of events which are ticks of a clock at rest in S , a purely timelike separation in S , we see that these equations account for the basic phenomenon of time dilation. In this case, time that elapses between the ticks of the clock, moving relative to S’ , measured in S’ is 2 V t t x t c γ γ = ∆ - = ∆
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( ) x x V t γ = ∆ - 2 V t t x c γ = ∆ - y y = ∆ z z = ∆ By considering a pair of events which are the locations of the ends of an object at rest in S’ at the same time in S , a purely spacelike separation in S , we see that the transformation equations also account for the basic phenomenon of Lorentz contraction along the direction of an object’s motion. In this case, the x separation measured between the ends of the object in S is ( ) x x x V t x x γ γ γ = ∆ - = ∆ = We’ve also seen that the Lorentz transformation equations account for the relativity of simultaneity. Events that are simultaneous in S , purely spacelike separation in S , are not necessarily simultaneous in S’ , 2 2 V V t t x x c c γ γ = ∆ - = - The relativity of simultaneity plays an essential role in the reciprocity of time dilation and Lorentz contraction. Observers in S and S’ can both measure the other observer’s moving clocks to be ticking slow and moving rulers to be contracted along their direction of motion because of it.
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The invariant interval between a pair of events is a frame-independent measure of their spacetime separation. The “squared” interval separating a pair of events is invariant because it has the same value when computed in the same
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