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Synge: optical observations in GR

  1. May 21, 2014 #1

    pervect

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    A couple of questions about this paper, which, unfortunately, I can't access in is entirety
    http://link.springer.com/article/10.1007/BF02923262#page-1

    1) Re: optical coordinates. From what I've read (here and some other sketchy sources), these are similar to fermi-normal coordinates, but one uses an affine parameterization along null geodesics passing through a point, rather than affine parameterizations along spacelike geodesics at a point. I was wondering if there was anyone out there who could tell me if I was on the right track here.

    2) I'm rather curious about the bouncing-photon idea, which apparently can apparently do fermi-walker transport, but I haven't been able to find enough on the idea to figure it out.
     
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  3. May 21, 2014 #2

    WannabeNewton

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  4. May 21, 2014 #3

    Bill_K

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    These topics are both discussed in Synge's book, "Relativity: The General Theory", in which he devotes about 10 pages to each. Essentially he beats them both to death, in a power series expansion.

    You're right about the definition of optical coordinates, and he goes on to calculate a power series approximation to the metric and the geodesics. For the bouncing photon, he shoots a photon out in some direction. In the small distance limit, if it's reflected and comes back to us in the "same" direction, then we are using Fermi-Walker transport to define "same". Once more he expands the results far enough to see the Riemann tensor and the curvature of the base line.
     
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