Slide 1If you want to know your progress so far, please send me an email request at [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 probeSlide 15Alternate 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 Earth. You take a long voyage traveling at a speed near that of light. Upon your return to Earth, your paycheck will be: (a) smaller than if you had remained on Earth, (b) larger than if you had remained on Earth, or (c) the same as if you had remained on Earth.The Twin Paradox – The SituationThe Twins’ PerspectivesThe Twin Paradox – The ResolutionLength ContractionLength Contraction – EquationRelativistic DefinitionsRelativistic MomentumRelativistic Addition of Velocities1101/13/1901/13/19General Physics (PHY 2140)Lecture 25Lecture 25 Modern PhysicsRelativityTime dilation, length contractionChapter 26http://www.physics.wayne.edu/~apetrov/PHY2140/2201/13/1901/13/19If you want to know If you want to know your progressyour progress so far, please so far, please send me send me an email requestan email request at [email protected]@physics.wayne.edu3301/13/1901/13/19Lightning ReviewLightning ReviewLast lecture: 1.1.Modern physicsModern physicsThe Michelson-Morley experimentThe Michelson-Morley experimentEinstein 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 2mv V ftp fD =D +4401/13/1901/13/19Reminder (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…5501/13/1901/13/19Simultaneity: SummarySimultaneity: SummaryTwo events that are Two events that are simultaneous in one reference framesimultaneous in one reference frame are in are in general general not simultaneous in a second referencenot simultaneous in a second reference frame 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 there is In the thought experiment, both observers are correct, because there is no preferred inertial reference frameno preferred inertial reference frame6601/13/1901/13/1926.6b Time Dilation: setup26.6b Time Dilation: setupThe concept of The concept of time intervaltime interval is also is also not absolutenot absolute To 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 ground7701/13/1901/13/1926.6b Time Dilation26.6b Time DilationA 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 systemsystem holds 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)Imagine an experiment:8801/13/1901/13/19Time 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 (ΔΔttpp))She observes the events to occur She observes the events to occur at the same placeat the same placeΔΔttpp = distance/speed = (2d)/c = distance/speed = (2d)/c9901/13/1901/13/19Time Dilation, Time Dilation, Stationary ObserverStationary ObserverObserver O is a Observer O is a stationary observerstationary observer on the earth on 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 mirror has By the time the light from the laser reaches the mirror, the mirror has moved to the rightmoved to the rightThe light must travel farther with respect to O than with respect to O’The light must travel farther with respect to O than with respect to O’101001/13/1901/13/19Time 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 fartherfarther for O for OThe time interval, The time interval, ΔtΔt, for O is longer than the , for O is longer than the time interval for O’, time interval for O’, ΔtΔtpp111101/13/1901/13/19Time Dilation, Time ComparisonsTime Dilation, Time Comparisons Observer O measures a longer Observer O measures a longer time interval than observer O’time interval than observer O’22cv11p22pwheretcv1tt121201/13/1901/13/19Time Dilation, SummaryTime Dilation, SummaryThe time interval The time interval Δt between two events measured by an observer Δt between two events measured by an observer moving with respect to a clock is longer than the time interval Δtmoving with respect to a clock is longer than the time interval Δtpp between the same two events measured by an observer at rest with between the