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Lecture14

# Lecture14 - 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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Particle Dynamics and 4-Vectors One of the reasons we began our study of relativity was to develop a better understanding of the concepts and principles that we use to predict and explain the motions of interacting particles. For example, why are the momentum and velocity of a particle measured in a frame S related in this particular way, 2 2 ? 1 mv p m v v c γ = = - arrowrightnosp arrowrightnosp arrowrightnosp Since this is framed as a question about the representation of physics in inertial coordinate systems, we initially focused on how measurements made by observers in different frames, S and S’ , are related. The laws of physics work the same way in every inertial frame, we used it to show that the Lorentz transformation equations relate measurements of the spacetime coordinates of events made by observers in S and S’ . We also introduced spacetime diagrams as a way of representing the results of such measurements. After discussing evidence that supports the validity of the Principle of Relativity,
x t t O x E ˆ ˆ E EO x x x x = ∆ ˆ ˆ E EO t t t t = ∆ ˆ ˆ E EO t t t t ′ ′ = ∆ ˆ ˆ E EO x x x x = ∆ EO s It was the geometric representation of sequences of events in spacetime diagrams that eventually made it natural for us to introduce spacetime separation 4-vectors as an observer- independent way of referring to the way in which one event is situated relative to another in spacetime. The spacetime coordinates of an event E in any frame S are simply the components of the separation 4-vector extending from the frame’s origin event O to the event E . A frame S’ in standard orientation relative to S has the same origin event, so, the same separation 4-vector represents E in S’ . It’s components in S’ are, therefore, related to its components in S by the Lorentz transformation equations ( ) EO EO EO x x t γ β = + ( EO EO EO t t x γ β = - EO EO y y = ∆ EO EO z z = ∆ The invariance of the interval implied by the Lorentz transformations allowed us to introduce a (psuedo-)dot product that defines a geometrical structure of spacetime.

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Lecture14 - Physics 344 Foundations of 21st Century Physics...

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