Lect18_[Compatibility_Mode]

Lect18_[Compatibility_Mode] - Physics 344 Foundations of...

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 haugan@purdue.edu TA: Dan Hartzler Office: PHYS 7 dhartzle@purdue.edu Grader: Shuo Liu Office: PHYS 283 liu305@purdue.edu Office Hours: If you have questions, just email us to make an ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Reading: Re-read chapters 1 through 10 as necessary. Notices: Begin thinking about questions you would like to ask during the view session during recitation Thursday review session during recitation Thursday. Exam I is this Thursday, October 7 at 8:00pm in MTHW 210

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As we finished on Friday we were discussing a physical situation with features somewhat analogous to those in the pole-barn puzzle we considered earlier. The Puzzle of the Identically Accelerated Rockets Two identical rocketships are initially at rest in your (Home) inertial coordinate system, one in front of the other. Each has an antenna on its cockpit and there is a thread connecting the tips of these antennae. You measure the length of this thread and, thus, the initial distance between the rocketships to be L . The rocketships are under computer control. Their computers are programmed so that their engines will both fire at your coordinate time t = 0, and so that the rockets’ engines will have identical settings when the rockets’ clocks read the same time. The rockets move straight ahead in the x direction in which they were originally pointing. a) The computer control programs eventually shut off the rockets’ engines. Explain why you, in the Home frame, will or will not observe the rockets’ engines shut off yy , , g simultaneously, and why you will or will not measure their final velocities to be equal. If they are not, will the rocket in front be moving faster or slower relative to you than the rocket behind? b) Explain why the thread initially connecting the rocketships does or does not break during their trip.
Solving The Identically Accelerated Rockets/Twins Puzzle This Home-frame diagram shows the worldlines of the two rockets before their engines are fired at t = t F . Do the engines shut off at the same Home- t t’ frame time? Yes. The rocket’s computers run at rates governed by proper time aboard the rockets, but since the their speeds at any Home frame time will be the same, the rocket’s clocks will shut off at the same Home-frame time, t = t S . After that, the rockets ove on at the same constant speed relative to the x’ t F t S move on at the same constant speed relative to the Home frame. Did the thread break? The explanation in the Home frame relies on x sense of mechanism. The rockets are the same distance apart, so, a Lorentz contracted thread couldn’t span the gap.

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Lect18_[Compatibility_Mode] - Physics 344 Foundations of...

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