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"null geodesic" - Dirac

  1. Jan 30, 2015 #1
    In Dirac's book on relativity, he begins and ends his section on proving the stationary property of geodesics with references to "null geodesics". His last sentence is: "Thus we may use the stationary condition as the definition of a geodesic, except in the case of a null geodesic."

    What is a null geodesic? Does he mean a null interval, like for a photon, with ds^2 = 0?
     
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  3. Jan 30, 2015 #2

    George Jones

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  4. Jan 30, 2015 #3
    So what path does a photon take then, if not those geodesic equations?
     
  5. Jan 30, 2015 #4

    George Jones

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    Dirac doesn't say that light does not follow a geodesic; Dirac writes "Thus we may use the stationary condition as the definition of a geodesic, except in the case of a null geodesic."

    Dirac's writing has to be unpacked very carefully. Just my personal opinion, but I think that Dirac's book is not a good book to use to teach oneself general relativity.
     
    Last edited: Jan 30, 2015
  6. Jan 30, 2015 #5

    PeterDonis

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    I think you mean "doesn't" here, correct?
     
  7. Jan 30, 2015 #6

    George Jones

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    Yes. I have edited my post to reflect this.
     
  8. Feb 3, 2015 #7
    OK, are you saying that a photon DOES follow those geodesic equations? Please be explicit.

    I see in the derivation - Hamilton's principle, stationary property, etc. - that I divided through by ds. Since ds equals zero for a photon, it seems to me that thus a photon would NOT follow the geodesic equations that result. I can't make sense of them for a photon, which is why I asked the question in the first place.

    If I minimize the component time (provided there are no off-diagonal terms for the time degree of freedom in the metric, static, etc.) then I get some different geodesic equations. Haven't managed to integrate them yet to check against the empirical data, but they are different.

    BTW, what is the latest and greatest / most accurate / data for the photon grazing the sun problem?
     
  9. Feb 3, 2015 #8

    PeterDonis

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    Not in the form you're using them. See below.

    That's not because photons don't follow geodesics; it's because "path length" ##ds## is not a good parameter along null geodesics, because it doesn't uniquely label each point on the geodesic with a different parameter value (it can't, since ##ds^2 = 0## everywhere on a null geodesic). You have to choose some other parameter that does uniquely label each event on the geodesic with a different parameter value. (Coordinate time in a suitable coordinate chart will be such a parameter.)
     
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