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Lecture15

# Lecture15 - 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: Chapters 9 and 10 in Six Ideas that Shaped Physics, Unit R. Exam 1: Wednesday, October 5 at 8:00pm in WTHR 104 One week from today!

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Consider events 1 and 2 whose spacetime coordinates in S are t 1 = 2 seconds, x 1 = 3 seconds, t 2 = 4 seconds and x 2 = 2 seconds. Q1. What is the separation 4-vector ? A) B) C) D) 21 s 21 ˆ ˆ (1second) (3seconds) s t x = + 21 ˆ ˆ (2seconds) (1second) s t x = + 21 ˆ ˆ (2seconds) (1second) s t x = - 21 ˆ ˆ (6seconds) (4seconds) s t x = + * Q2. Could this separation 4-vector be a segment of a particle’s worldline? A) Yes B) No * Q3. What proper time lapse would a clock moving at constant speed from event 1 to event 2 measure? A) 2 seconds B) 5 seconds C) 3 seconds D) seconds E) seconds 5 3 * What is the clock’s 4-velocity during the trip? ˆ ˆ (2/ 3) (1/ 3) u t x = -
Particle Dynamics and 4-Momentum Conservation We showed last time that at any event along the worldline of a particle the 4-vector equation , net d P F d τ = with particle 4-momentum vector tangent to the particle’s worldline and with magnitude m , the particle’s mass, has spatial components in an inertial frame instantaneously co-moving with the particle that express the Newtonian form of the Momentum Principle, P mu = net dp dv m F dt dt = = a a a By adopting it as the relativistic version of the Momentum Principle we accomplish several essential things. 1. We have a frame-independent fundamental principle. Consistent with the Principle of Relativity, the form of its representation in every inertial frame will be the same. 2. We guarantee that the relativistic principle has the correct Newtonian limit. 3. We combine the Energy and Momentum Principles into a single 4-Momentum Principle.

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Of course, the components of the 4-momentum vector of a particle of mass m in an inertial coordinate system S are the relativistic energy and momentum components you’ve used before. In conventional units they are 2 E m c γ = p m v = a a and Our analysis has shown how we explain these particular forms, they are singled out by the demand for a frame-independent fundamental principle that assures consistency with the Principle of Relativity and the need to make the correct predictions in the experimentally well-tested Newtonian limit. As you saw yesterday in recitation, when using the 4-momentum conservation
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Lecture15 - Physics 344 Foundations of 21st Century Physics...

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