Understanding Null Geodesics in Relativity: Insights from Dirac's Book

  • Context: Graduate 
  • Thread starter Thread starter exmarine
  • Start date Start date
  • Tags Tags
    Dirac Geodesic
Click For Summary

Discussion Overview

The discussion revolves around the concept of null geodesics in the context of general relativity, specifically referencing Dirac's treatment of the topic. Participants explore the implications of null intervals for photons and how these relate to geodesic equations, raising questions about the definitions and interpretations presented in Dirac's book.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions the definition of null geodesics, suggesting it relates to a null interval for photons where ds² = 0.
  • Another participant asserts that Dirac does not explicitly state that light does not follow geodesics, but emphasizes the need for careful interpretation of his writing.
  • A participant expresses skepticism about the suitability of Dirac's book for self-study in general relativity.
  • There is a discussion about whether photons follow geodesic equations, with one participant arguing that since ds equals zero for a photon, it implies that photons do not follow the resulting geodesic equations.
  • Another participant clarifies that the issue is not that photons do not follow geodesics, but rather that the parameterization using ds is not appropriate for null geodesics, suggesting the need for an alternative parameter.
  • One participant inquires about the latest data regarding the photon grazing the sun problem, indicating an interest in empirical validation.

Areas of Agreement / Disagreement

Participants express differing views on whether photons follow geodesic equations, with some arguing that the mathematical treatment leads to confusion due to the nature of null intervals. The discussion remains unresolved regarding the implications of Dirac's statements and the interpretation of geodesic behavior for photons.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about parameterization along null geodesics and the interpretations of Dirac's text. The discussion also highlights the potential for different mathematical approaches to yield varying geodesic equations.

exmarine
Messages
241
Reaction score
11
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?
 
Physics news on Phys.org
Yes.
 
So what path does a photon take then, if not those geodesic equations?
 
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:
George Jones said:
Dirac doesn't say that light does follow a geodesic

I think you mean "doesn't" here, correct?
 
PeterDonis said:
I think you mean "doesn't" here, correct?

Yes. I have edited my post to reflect this.
 
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?
 
exmarine said:
are you saying that a photon DOES follow those geodesic equations?

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

exmarine said:
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.

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.)
 

Similar threads

  • · Replies 76 ·
3
Replies
76
Views
4K
  • · Replies 42 ·
2
Replies
42
Views
6K
  • · Replies 50 ·
2
Replies
50
Views
4K
  • · Replies 14 ·
Replies
14
Views
8K
  • · Replies 30 ·
2
Replies
30
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K