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If you want to know your progress so far, please send me an email request [email protected] ReviewReminder (for those who don’t read syllabus)Simultaneity: Summary26.6b Time Dilation: setup26.6b Time DilationTime Dilation, Moving ObserverTime Dilation, Stationary ObserverTime Dilation, ObservationsTime Dilation, Time ComparisonsTime Dilation, SummaryIdentifying Proper TimeProblem: a deep-space probeAlternate ViewsTime Dilation – GeneralizationTime Dilation Verification – Muon DecaysImagine that you are an astronaut who is being paid according to the time spent traveling in space as measured by a clock on EThe Twin Paradox – The SituationThe Twins’ PerspectivesThe Twin Paradox – The ResolutionLength ContractionLength Contraction – EquationRelativistic DefinitionsRelativistic MomentumRelativistic Addition of Velocities1111/7/0311/7/03General Physics (PHY 2140)Lecture 25Lecture 25¾ Modern Physics9Relativity9Time dilation, length contractionChapter 26http://www.physics.wayne.edu/~apetrov/PHY2140/2211/7/0311/7/03If you want to know If you want to know your progressyour progressso far, please so far, please send me send me an email requestan email requestatatapetrovapetrov@[email protected]/7/0311/7/03Lightning ReviewLightning ReviewLast lecture:1.1.Modern physicsModern physics99The MichelsonThe Michelson--Morley experimentMorley experiment99Einstein relativity principle, simultaneityEinstein relativity principle, simultaneityReview Problem:Consider the oscillating emf shown below. Which of the phasor diagrams correspond(s) to this oscillation:1. all but (b) and (c) 2. all 3. (e), (f), and (g) 4. (d) 5. (e)6. none()sin 2mvV ftπφ∆=∆ +4411/7/0311/7/03Reminder (for those who don’t read Reminder (for those who don’t read syllabussyllabus))Reading Quizzes (bonus 5%):It is important for you to come to class prepared, i.e. be familiar with the material to be presented. To test your preparedness, a simple five-minute quiz, testing your qualitative familiarity with the material to be discussed in class, will be given at the beginning of some of the classes. No make-up reading quizzes will be given.There could be one today…… but then again…5511/7/0311/7/03Simultaneity: SummarySimultaneity: SummaryTwo events that are Two events that are simultaneous in one reference framesimultaneous in one reference frameare in are in general general not simultaneous in a second referencenot simultaneous in a second referenceframe moving frame moving relative to the firstrelative to the firstThat is, That is, simultaneity is not an absolute conceptsimultaneity is not an absolute concept, but rather one that , but rather one that depends on the state of motion of the observerdepends on the state of motion of the observerIn the thought experiment, both observers are correct, because tIn the thought experiment, both observers are correct, because there is here is no preferred inertial reference frameno preferred inertial reference frame6611/7/0311/7/0326.6b Time Dilation: setup26.6b Time Dilation: setupThe concept of The concept of time intervaltime intervalis also is also not absolutenot absoluteTo see this, imagine another boxcar experimentTo see this, imagine another boxcar experimentTwo observers, one in the car, another on the ground Two observers, one in the car, another on the ground7711/7/0311/7/0326.6b Time Dilation26.6b Time DilationImagine an experiment:A mirror is fixed to the ceiling A mirror is fixed to the ceiling of a vehicleof a vehicleThe vehicle is moving to the The vehicle is moving to the right with speed vright with speed vAn observer, An observer, O’,O’,at rest in this at rest in this systemsystemholds a laser a holds a laser a distance d below the mirrordistance d below the mirrorThe laser emits a pulse of light The laser emits a pulse of light directed at the mirror directed at the mirror (event 1)(event 1)and the pulse arrives back and the pulse arrives back after being reflected after being reflected (event 2)(event 2)8811/7/0311/7/03Time Dilation, Time Dilation, Moving ObserverMoving ObserverObserver O’ carries a Observer O’ carries a clockclockShe uses it to measure the time between the events (She uses it to measure the time between the events (∆∆ttpp))She observes the events to occur She observes the events to occur at the same placeat the same place∆∆ttpp= distance/speed = (2d)/c= distance/speed = (2d)/c9911/7/0311/7/03Time Dilation, Time Dilation, Stationary ObserverStationary ObserverObserver O is a Observer O is a stationary observerstationary observeron the earthon the earthHe observes the mirror and O’ to He observes the mirror and O’ to move with speed vmove with speed vBy the time the light from the laser reaches the mirror, the mirBy the time the light from the laser reaches the mirror, the mirror has ror has moved to the rightmoved to the rightThe light must travel farther with respect to O than with respecThe light must travel farther with respect to O than with respect to O’t to O’101011/7/0311/7/03Time Dilation, ObservationsTime Dilation, ObservationsBoth observers must measure the speed of the Both observers must measure the speed of the light to be clight to be cThe light travels The light travels fartherfartherfor Ofor OThe time interval, The time interval, ∆∆tt, for O is longer than the time , for O is longer than the time interval for Ointerval for O’’, , ∆∆ttpp111111/7/0311/7/03Time Dilation, Time ComparisonsTime Dilation, Time Comparisons22cv11p22pwheretcv1tt−=γ∆γ=−∆=∆Observer O measures a longer Observer O measures a longer time interval than observer Otime interval than observer O’’121211/7/0311/7/03Time Dilation, SummaryTime Dilation, SummaryThe time interval The time interval ∆∆t between two events measured by an observer t between two events measured by an observer moving with respect to a clock is longer than the time interval moving with respect to a clock is longer than the time interval ∆∆ttppbetween the same two events measured by an observer at rest withbetween the same two events measured by an observer at rest withrespect to the clockrespect to the clockA clock moving past an observer at speed v runs more slowly thanA clock moving past an observer at speed v runs more slowly thanan an identical clock at rest with respect to the observer by a factoridentical clock at rest with respect to the


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WSU PHY 2140 - Lecture notes

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