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Relativity Quiz

  1. Jun 10, 2005 #1
    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:

    - Relativity: The Special and General Theory, Section 20

    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. :confused: 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?
     
    Last edited: Jun 10, 2005
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  3. Jun 11, 2005 #2

    James R

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    Ellipse:

    I agree with you. You are right. The quiz answer is wrong.

    Anybody can declare himself to be at rest. Everybody has a "rest frame".

    The differences in final elapsed times in the twin paradox depend on whose frame of reference is inertial, and whose is not. Stella's is a non-inertial frame. Terrance's frame is inertial.
     
  4. Jun 11, 2005 #3
    Question 9

    If Stella then stops, turns around, and very slowly returns to Earth, can she be said to have aged less than Terrance?


    I thought the answer should be not until she is reunited with Terrance, (the clocks can not be compaired) but how the answer is written, it is an unquallified "yes," because when she is reunited she will be seen to be younger.???
     
    Last edited: Jun 11, 2005
  5. Jun 11, 2005 #4
    James R: I agree with you. You are right. The quiz answer is wrong.

    Anybody can declare himself to be at rest. Everybody has a "rest frame".

    The differences in final elapsed times in the twin paradox depend on whose frame of reference is inertial, and whose is not. Stella's is a non-inertial frame. Terrance's frame is inertial.


    But since Stella felt a change in acceleration, she must recognize she is not at rest.
     
  6. Jun 11, 2005 #5

    learningphysics

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    Yes. I made the exact same mistake. Once she is reunited with Terrance then she can be said to have aged less.

    The explanation seemed to presume that they compare the clocks once they are reunited... but it seemed to me that the question suggested that Stella was on the return trip, not that she had arrived at Earth.
     
  7. Jun 11, 2005 #6
    learningphysics: Yes. I made the exact same mistake. Once she is reunited with Terrance then she can be said to have aged less.

    Good! Then we are outvoting any other explanation. #9 was the only one I missed!
     
    Last edited: Jun 11, 2005
  8. Jun 11, 2005 #7
    James R,

    The quiz answer is right. Everybody does not have a "rest frame".

    If you're in a rest frame then experiments done in your frame will match the results of those done in any other rest frame. But if Stella starts an experiment on her way out and finishes it after she starts to turn around, she won't get the same result as she would have in a rest frame.
     
  9. Jun 11, 2005 #8
    Can you explain why Einstein calls the chest at rest? Experiments in the chest will not be the same if the chest is inertial.
     
    Last edited: Jun 11, 2005
  10. Jun 11, 2005 #9
    ellipse,

    Yes, because, in the case described by E, the guy in the chest concludes that he is in a g field "which is constant with regard to time..." Stella can't come to that conclusion.
     
  11. Jun 12, 2005 #10

    James R

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    robert Ihnot:

    No. She recognises that she is at rest, but something weird is going on with her local gravity.

    jdavel:

    Of course they do. Every person is always at rest relative to him or herself. The definition of "rest frame of an object" is the "reference frame in which the object is at rest".

    Replace "rest frame" with "inertial frame", and you're right.

    There's nothing in physics which says the laws of physics are the same in all rest frames. They are the same in all inertial frames, though. Not every rest frame is inertial, but some inertial frames are also rest frames.
     
  12. Jun 12, 2005 #11

    pervect

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    The quiz is right.

    While everyone is at rest relative to him or herself, the definition of a rest frame given above is incorrect.

    A 'frame' is a very special sort of coordinate system, one in which there are no pseudo-forces (to use Newtonian language), or in which the Christoffel symbools are all zero (to use more precise but less generally understood GR language).

    A coordinate system in which an accelreated observer is at rest is not a frame, because it does have pseudo-forces (and non-zero Christoffel symbols).

    There are other difficulties with the coordinate system of an accelerated observer besides the fact that it is not a frame. Such a coordinate system only covers a small local region of space and not all of space-time as a truly well behaved coordinate system should.

    There are two reasons for this - one reason is the existence of an event horizon in the coordinate system of an accelerated observer, and another is the fact that coordiante lines cross each other, giving rise to an unacceptable situation in which one event has multiple coordinates when the coordinate system is made too large.
     
  13. Jun 12, 2005 #12
    James R.,

    You said: "....The quiz answer is wrong. Anybody can declare himself to be at rest. Everybody has a "rest frame"."

    To which I said: 'The quiz answer is right. Everybody does not have a "rest frame"."

    To which you said: "Of course they do. Every person is always at rest relative to him or herself. The definition of "rest frame of an object" is the "reference frame in which the object is at rest"."

    To which I say: Touche!

    However....I still think the quiz answer is wrong! But to make my point, I should have argued with the quiz answer "Anybody can declare himself/herself to be at rest". Instead of your translated version "Everybody has a rest frame" (even though pervect has now said they're the same thing).

    Stella can not declare herself to have been at rest the whole time. She knows otherwise! Constant (wrt time) acceleration is indistnguishable from constant gravity. But time varying acceleration (what we have here) is not. Gravity alone can not produce time varying acceleration that is detectable without reference to the mass that's causing the gravity. Even if some huge mass suddenly appeared outside Stella's space ship, she wouldn't know it; she'd just be moving in free fall instead of at constant velocity. Until she crashed into the huge mass, all her experiments would continue to give the same results.
     
    Last edited: Jun 12, 2005
  14. Jun 12, 2005 #13

    learningphysics

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    The question made no mention of "rest frame".

    Can Stella say that she's at rest during the entire trip?
     
  15. Jun 12, 2005 #14

    pervect

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    Perhaps not - but the answer offered sure did, and it made a hash of it, I'm afraid.

    The original question was, IIRC

    I will assume that this is the question you had in mind (the thread has diverged a lot).

    The answer to this question is no. The issue of whether or not Stella can consider herself to be "at rest" in some general philosophcial sense is not really releveant to the answer.

    What you need to do to prove that Terrance has aged more than Stella is to prove that the twins cannot be reunited in such a way that Terrance is younger than Stella. (The question was a little vague, that's the way I interpreted it, however).

    But there is at least one way to re-unite the twins in which Terrance is the older. This is for Stella to change her mind, and re-accelerate to her original velocity, and for Terrance to accelerate to an even faster velocity to rejoin Stella.
     
  16. Jun 12, 2005 #15

    learningphysics

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    This was the question I was referring to:

    "Question 10

    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?"
     
  17. Jun 12, 2005 #16

    pervect

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    Ah, OK. In the context of special relativity, the answer is "no". A person who is "at rest" doesn't feel any accelerations or other pseudo-forces. Stella does feel these things, sho she can't be considered to be "at rest".

    You can consider in this context that "at rest" means "in an inertial frame of reference", which means that acceleration is not allowed.
     
    Last edited: Jun 12, 2005
  18. Jun 12, 2005 #17
    same here...i got question #9 wrong because I thought stella hadn't reached Earth yet :frown:
     
  19. Jun 12, 2005 #18
    Isn't the question referring to general relativity though? There are GR related questions before Question 10, so I think it's meant to take into context both SR and GR.
     
  20. Jun 12, 2005 #19
    Really, I don't care about the semantics of the question. I just wanted to know what the correct view was. From reading these responses, it seems Stell can call herself at rest, which is all I really wanted to know.
     
  21. Jun 12, 2005 #20
    Nope. A lot of the responses say she can't, and they're right.
     
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