Talk:Parameterized post-Newtonian formalism

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Title

Should this be Parametrized instead of Parameterised ? A google search reveals that both are used (albeit 145 for the former, 11,200 for the latter). MP (talk) 11:38, 17 April 2006 (UTC)

I am confused. Parameterized with three es and a z seems to be the most common spelling. The OED tells me that none of the others are acceptable. –Joke 15:37, 17 April 2006 (UTC)

Students beware

Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.

Good luck in your search for information, regardless!---CH 02:38, 1 July 2006 (UTC)

Hey, should the O(n) formalism actually be O(x^n)? AJRobbins 05:08, 12 November 2007 (UTC)

To AJRobbins: What is the "x" in the n-th order approximation? JRSpriggs 08:34, 12 November 2007 (UTC)
I have no idea. I just thought it was confusing. AJRobbins (talk) 02:40, 20 November 2007 (UTC)

I'm in the process of expanding this into a full article. The expansion will be finished on about 5 Sep 2006. In the meantime, please don't edit. Mollwollfumble 02:11, 2 September 2006 (UTC)

The spherically symmetric case?

Would someone knowledgeable comment on the spherically symmetric case, which parameters can be ignored, or other simplifications? And, for example, it appears that for GR that 4Φ1 + 4Φ2 + 2Φ3 + 6Φ4 + O(ε³) must add exactly to 2U² but this is very non-obvious. And if one had an alternate g00 for a symmetric metric, say either of the two common approximations g00 = -1/(1+U)^2 or g00 = -(1-U)^2, which parameters would these affect and by how much? I.e. how much suffers by our common approximations? Have we verified gravity that closely yet? Also, I personally feel this article should be raised in priority. Verification of gravity is a popular topic in the scientific press. But no one can get beyond superficial press talk, in part because the criteria, i.e. the PPN, are not given accessible explanations. Even Misner-Thorne-Wheeler text just says that calculating these is difficult and doesn't give, for example, ways to approximate the parameters. At one time 1st order was fine, but now we need accessibility to at least 2nd order in the PPN that is widely understood. Thanks. Rlshuler (talk) 21:57, 6 October 2015 (UTC)

The indexes of the metric tensor.

The old version of this sentence read: "${\displaystyle g_{\mu \nu }}$ is the 4 by 4 symmetric metric tensor and indexes ${\displaystyle i}$ and ${\displaystyle j}$ go from 1 to 3."

My version reads: "${\displaystyle g_{\mu \nu }}$ is the 4 by 4 symmetric metric tensor and indexes ${\displaystyle \mu }$ and ${\displaystyle \nu }$ go from 0 to 3."

Why the changes? First of all, ${\displaystyle \mu }$ and ${\displaystyle \nu }$ are the indexes, not ${\displaystyle i}$ and ${\displaystyle j}$. This is because ${\displaystyle \mu }$ and ${\displaystyle \nu }$ follow the "${\displaystyle g}$" for the metric tensor. That makes ${\displaystyle \mu }$ and ${\displaystyle \nu }$ the indexes by definition. See tensor index notation about this.

Secondly, metric tensors in GR apply to spacetime (a combination of both space and time) and not just space. This because space and time are interchangeable in relativity. See special relativity and relativity of simultaneity for details. In fact, the result of integrating the metric tensor over a world line ${\displaystyle W}$ via

${\displaystyle \tau =\int _{W}{\sqrt {g_{\mu \nu }dx^{\mu }dx^{\nu }}}}$

is the proper time ${\displaystyle \tau }$ experienced by an observer traveling along that world line, not a length as would be the case if this was done with a normal spatial metric. See metric tensor (general relativity) and proper time for more information. This is also touched on in Ricci calculus.

Finally, a 4x4 metric requires that the indexes have 4 possible values. "1 to 3" is only 3 possible values. The modern convention is to number the coordinate time index as 0. Hence my statement that the indexes go from 0 to 3. EMS | Talk 00:16, 30 December 2017 (UTC)

The text in the next section refers to ${\displaystyle g_{00}}$, ${\displaystyle g_{0i}}$, and ${\displaystyle g_{ij}}$. These mean the time-time component, the mixed time-space components, and the purely spatial components. See Ricci calculus#Space and time coordinates.
This article is not about Einstein's general relativity in its full generality with arbitrary curvilinear coordinates. It is about a quasi-classical approximation to any of large group of theories of which GTR is only one. It assumes that the coordinate system is nearly that of an inertial frame of reference, that is, a Cartesian coordinate system which is non-rotating and free-falling. JRSpriggs (talk) 06:12, 30 December 2017 (UTC)
Thank you. Your last edit improves on my edit and makes the whole article more cohesive. EMS | Talk 02:11, 20 January 2018 (UTC)

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