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I just took the relativity quiz here: https://www.physicsforums.com/quiz.php?quizid=28 and I goofed on question 10. Could someone explain it to me? Below I've posted what the review of the quiz said about question 10 along with some of the previous questions for context.
This seems to conflict with what I've read about GR. In one of Einstein's thought experiments he imagined a man in a chest with a rope tied to the top being pulled with a constant acceleration in one direction. Einstein said:
This seems to support that Stella can call herself at rest. The only argument I can think of is that Stella's acceleration would generally be thought to not be constant and maybe that's why we can't call her at rest. Although it is possible for Stella to go from moving away from Earth, come to a stop, and return to Earth with a constant acceleration, maybe the question was taking the most likely situation in which Stella changes her acceleration multiple times during the course of the trip, and this is why she can't call herself at rest. The only other reason I can think of why Stella can't call herself at rest is if modern physics has replaced the conclusions of Einstein's acclerated chest thought experiment, and it's more acceptable now to call such "gravitational fields" that aren't the result of matter an indication of change in motion. Can someone clear this up for me?
Question 8
Assume Stella leaves Earth and travels exactly one light-year away (as measured by Terrance) at 0.99 c (as measured by Terrance), sending laser flashes every second back to Terrance.
In that time, Terrance's watch has ticked off an entire year. Since Stella is sending periodic flashes to Terrance, and he has received fewer than a year's worth of flashes, Terrance concludes that Stella's clock has elapsed less time than his own.
Can it now be said that Terrance has aged more than Stella?
...
Question 9
If Stella then stops, turns around, and very slowly returns to Earth, can she be said to have aged less than Terrance?
...
Question 10
The question was:
Can Stella argue that she's been at rest the whole time in her rocket ship, while it was Terrance who flew away for a light-year at 0.99 c?
Your answer was: Yes, because anyone can declare him/herself at rest.
Correct answer: No, because Stella felt accelerations while Terrance did not.
Your answer was: wrong
Explanation of the correct answer:
There are many ways to explain why Stella and Terrance did not take symmetric trips, but the easiest is just to consider the accelerations. If Stella felt accelerations at the appropriate times, then her velocity must have been changing, and she must have been the one who left Earth, turned around, and came home.
In more advanced mathematical discussions of this "twin paradox," it can be easily shown that the so-called "proper time," the time elapsed on clocks that Terrance and Stella carry around with them, is smaller along the path that Stella takes through space-time than along the path taken by Terrance.
This seems to conflict with what I've read about GR. In one of Einstein's thought experiments he imagined a man in a chest with a rope tied to the top being pulled with a constant acceleration in one direction. Einstein said:
- Relativity: The Special and General Theory, Section 20Relying on his knowledge of a gravitational field (as it was discussed in the preceding section), the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time...
...Ought we to smile at the man and say that he errs in his conclusion? I do not believe we ought to if we wish to remain consistent; we must rather admit that his mode of grasping the situation violates neither reason nor known mechanical laws. Even though it is being accelerated with respect to the "Galileian space" first considered, we can nevertheless regard the chest as being at rest.
This seems to support that Stella can call herself at rest. The only argument I can think of is that Stella's acceleration would generally be thought to not be constant and maybe that's why we can't call her at rest. Although it is possible for Stella to go from moving away from Earth, come to a stop, and return to Earth with a constant acceleration, maybe the question was taking the most likely situation in which Stella changes her acceleration multiple times during the course of the trip, and this is why she can't call herself at rest. The only other reason I can think of why Stella can't call herself at rest is if modern physics has replaced the conclusions of Einstein's acclerated chest thought experiment, and it's more acceptable now to call such "gravitational fields" that aren't the result of matter an indication of change in motion. Can someone clear this up for me?
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