Special Relativity Quiz


Advanced search

Message boards : Science : Special Relativity Quiz

AuthorMessage
Profile Rod
Avatar
Send message
Joined: Jan 3 06
Posts: 4483
Credit: 811,266
RAC: 0
Message 102352 - Posted 3 Feb 2010 3:08:27 UTC

    Last modified: 3 Feb 2010 3:18:38 UTC

    A Special Relativity Quiz from
    Uncertain Principles Blog


    _____
    I am getting to apreciate sites designed for mobile devices..

    Profile Mike Hewson
    Forum moderator
    Avatar
    Send message
    Joined: Dec 1 05
    Posts: 3592
    Credit: 28,560,132
    RAC: 12,846
    Message 102354 - Posted 3 Feb 2010 4:00:08 UTC

      Last modified: 3 Feb 2010 4:59:59 UTC

      My stabs at it :

      Q : Two twins, named Alice and Bob in keeping with convention, get into identical rocket ships separated by a distance L, with Alice in front and Bob behind her. At a pre-arranged time, they each start their rocket, and accelerate for a pre-determined time. At the end of the acceleration, they are each moving at a relativistic speed-- 4/5ths the speed of light, say. Which of these twins is older at the end of the acceleration?

      A : Not enough info, poorly written question. What does 'in front' and 'behind' mean? They start and finish in inertial frames having been accelerated. But the pattern ( direction, magnitudes and time dependence ) of acceleration(s) is/are not specified - constant or what? As for who is older - from which frame ... etc. In any case all speeds are 'relativistic', just some ( alot ) more than others! :-)

      Q : A second question, which may or may not help you think about the answer: At the end of their acceleration, what is the spacing between their ships as measured by Alice and Bob?

      A : Ditto. Plus whose time is it that is pre-aranged or pre-determined and how, etc ....

      The sneaky underlying bit here is the method of knowing/assuring simultaneity. SR and GR rest upon clock synchronisation using signalling when separated not just making two clocks, synchronising 'in place' and then moving the clocks apart.

      Bet ya the author weasels out of all of this by undisclosed assumptions.

      Cheers, Mike.

      ( edit ) Caveat : the twin 'paradox' includes the re-union of the two participants back to a single ( original ) frame ie. a return to a close region of spacetime.
      ____________
      "I have made this letter longer than usual, because I lack the time to make it short." - Blaise Pascal

      Profile Rod
      Avatar
      Send message
      Joined: Jan 3 06
      Posts: 4483
      Credit: 811,266
      RAC: 0
      Message 102360 - Posted 3 Feb 2010 13:26:50 UTC

        The comments refine the questions a bit

        Both Alice and bob are traveling in the same direction.

        The Observer is in the final reference frame.

        Profile Chipper Q
        Avatar
        Send message
        Joined: Feb 20 05
        Posts: 1568
        Credit: 708,571
        RAC: 0
        Message 102367 - Posted 4 Feb 2010 3:06:30 UTC - in response to Message 102360.

          Last modified: 4 Feb 2010 4:00:00 UTC

          The comments refine the questions a bit

          Both Alice and bob are traveling in the same direction.

          The Observer is in the final reference frame.

          Not sure about the comments and it's hard for me to accept the terms characterizing the use of Google as cheating, especially after showing up a second day expecting to see the answer and now it says the answer will be given 'probably tomorrow'. So I cheated then, but failed to find a specific answer. I found enough (edit: see for example, Adding to the paradox: the accelerated twin is older) to hazard a guess, though – er, wait – it's up for a vote :))

          Not much to her dismay, Alice will be the older twin, and gravitational time dilation would be main the reason – clocks run slower in regions of lower gravitational potential (closer to the center of a massive object, assuming the earth (& sun) in this case if keeping with convention).

          Thanks for posting that one Rod, I hope I voted correctly! :)

          (edit again: if they accelerate towards the sun and the end of the acceleration is less than about 10 minutes after they started then Bob will be older. But if they accelerate away from the sun then Alice will be older, however long the acceleration lasts. Not sure I could give a general solution covering all angles & durations to give the distance L on a good day.)

          Profile Rod
          Avatar
          Send message
          Joined: Jan 3 06
          Posts: 4483
          Credit: 811,266
          RAC: 0
          Message 102368 - Posted 4 Feb 2010 3:38:45 UTC

            I apologise. I am intmate with the blog and the author. There is no strategy, just fun..

            I am on a mobile device so typing is a chore.

            Chipper has the right answer :)

            Today response

            Answer

            Profile hockeyguy
            Avatar
            Send message
            Joined: Aug 29 05
            Posts: 93
            Credit: 15,622
            RAC: 0
            Message 102703 - Posted 23 Feb 2010 1:11:01 UTC

              My first thought was, are they moving in the same direction? Apparently so.

              I don't understand how Alice is older. If they both accelerated for the same amount of time, and the same rate of acceleration, how is there any difference? In fact, relative to Bob, Alice never even moved! How did she age?

              If someone leaves earth, and ages during their journey, does the aging undo itself on the way home, or does it just get worse?
              ____________

              Profile Chipper Q
              Avatar
              Send message
              Joined: Feb 20 05
              Posts: 1568
              Credit: 708,571
              RAC: 0
              Message 102704 - Posted 23 Feb 2010 2:45:27 UTC - in response to Message 102703.

                My first thought was, are they moving in the same direction? Apparently so.

                I don't understand how Alice is older. If they both accelerated for the same amount of time, and the same rate of acceleration, how is there any difference? In fact, relative to Bob, Alice never even moved! How did she age?

                If someone leaves earth, and ages during their journey, does the aging undo itself on the way home, or does it just get worse?

                It's a lesson on the equivalence principle - acceleration is equivalent to being subject to a gravitational force - clocks will run at slightly different rates with the slower clocks being the ones that are subject to greater gravitational forces - the effect of gravitational time dilation.

                I guessed the right answer but I'm not sure it was for the right reasons :)

                Relative to both twins is the gravitational field they started out in and for the duration of the acceleration one twin (Bob) was always "lower" than the other (Alice) in that field, and so his clock would run slower. That was my reasoning, anyway.

                The relative rates of aging on the way back would depend on the motions of the rocket ships ...

                Post to thread

                Message boards : Science : Special Relativity Quiz


                Home · Your account · Message boards

                This material is based upon work supported by the National Science Foundation (NSF) under Grants PHY-1104902, PHY-1104617 and PHY-1105572 and by the Max Planck Gesellschaft (MPG). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the investigators and do not necessarily reflect the views of the NSF or the MPG.

                Copyright © 2014 Bruce Allen