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Homework Help: Conceptual Question on General Relativity

  1. Feb 1, 2012 #1
    1. The problem statement, all variables and given/known data
    A thought experiment. Imagine ants living on a merry-goround,
    which is their two-dimensional world. From measurements
    on small circles they are thoroughly familiar
    with the number pi. When they measure the circumference
    of their world, and divide it by the diameter, they
    expect to calculate the number pi=3.14159. . . . We
    see the merry-go-round turning at relativistic speed.
    From our point of view, the ants’ measuring rods on the
    circumference are experiencing Lorentz contraction in
    the tangential direction; hence the ants will need some
    extra rods to fill that entire distance. The rods measuring
    the diameter, however, do not contract, because their
    motion is perpendicular to their lengths. As a result, the
    computed ratio does not agree with the number . If you
    were an ant, you would say that the rest of the universe is
    spinning in circles, and your disk is stationary. What possible
    explanation can you then give for the discrepancy,
    in view of the general theory of relativity?

    2. Relevant equations

    None needed.

    3. The attempt at a solution
    My friends and I have tried to answer this problem using the curvature of space. We tried to explain how the outer edges of the merry-go-round bend inward from an observer outside the merry-go-round and so the diameter calculated from the measure of the circumference will be different than measure the diameter directly. However, we think the entire outside of the merry-go-round will bend inwards equally.
  2. jcsd
  3. Feb 2, 2012 #2
    the ants that are moving around at relativistic speed, see their x and y axis rotated with respect to the stationary axis, such that the ruler extends more after going around by 2 pi radians in the moving frame than 2 pi in the stationary frame
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