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Gravitational time dilation and distance

Discussion in 'Physics' started by Jeroen D Stout, Oct 8, 2018.

  1. If I have a light clock in the centre of the earth, and one at a distance from the earth, two observers at the clocks will agree that the inner-earth clock runs slower.

    But if we'd look with a magic telescope at each-other's clock, we'd agree that the photons bouncing between the mirrors are travelling at c.

    As far as I can work out, that implies that either:

    1. From the far-away clock's perspective, the inner-earth clock is larger, so that it takes photons longer to bounce between mirrors. I.e., dropping a clock to the centre of the earth makes it 'bigger' from the dropper's perspective.
    2. From the far-away clock's perspective, the inner-earth clock has mirrors which are constantly moving (like velocity time dilation).

    I have seen the Schwarzschild metric quite often as an answer to this sort of question. I certainly understand that the inner-earth clock would tick less frequently. But that is not really the question.

    If I looked with the magic telescope at the inner-earth clock the path of the photons must be different in some way for us to agree on c. Is either of my two implications above correct?

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