Talk:Mathematics of general relativity

Axiomatization

As far as I know, there has historically been attempts to axiomatize GR mathematically. These attempts have failed, as far as I know. [The failures have been of the type that the possible axioms are (possibly) true only if they do not falsify GR, i.e., Axiom -> no GR <=> Axiom false, sort of reversing the role of theorems and axioms.] I can't remember exactly where I read this, but it was definitely in an expensive, somewhat hard core, physics text, perhaps MTW? Does axiomatazation attempts warrant a section in the article? YohanN7 (talk) 15:18, 22 January 2013 (UTC)

Another thing: The $g_{ab}\,dx^{a}\,dx^{b}$ versus $g_{ab}\,dx^{a}\otimes dx^{b}$ issue is not always a matter of notation. Many authors use juxtaposition to mean the result of symmetrization. Since g is symmetric to begin with, the two potentially different objects are equal. YohanN7 (talk) 11:49, 23 January 2013 (UTC)

Recent discussions have changed the very definitions of things like the role of theorms and axioms. What we mean by things like infinity, infinities, infinitesimals especially as regards quantum mechanics, dimensions, relativity, and the reality of the historic discussion make it necessary to ask if motion constitutes a fourth dimension.

In the Time of Queen Elizabeth Ludolph Van Ceulen Ludolph van Ceulen 28 January 1540 – 31 December 1610) was a German-Dutch mathematician from Hildesheim. He emigrated to the Netherlands to state "Mathematics includes the study of such topics as quantity, structure (algebra), space (geometry), and change. It has no generally accepted definition."

Her response was to ask "why are there twice as many seconds in a century as inches in the circumference of the Earth at the equator"

2604:6000:1513:4FFD:A939:BB52:DBF7:A16C (talk) 22:07, 6 August 2020 (UTC)

Blunder-level egregious error and a very bad effort all round

This entire article is disaster. I'll confine myself to one item. In the section "Energy-Momentum Tensor", there are two gigantic errors. One, the "rule of thumb" only works in one direction - when going to flat space, you can replace covariant by ordinary derivatives. It most certainly does not work in the other direction. In particular, if we have a flat space conservation law Tmn,n = 0, we certainly do not necessarily have Tmn;n = 0 for the covariant derivative. If we impose such an equation by force, then it absolutely does not represent a conservation law for *any* symmetric tensor whatsoever. Only totally antisymmetric tensors lead to conservation laws via covariant divergence. On a test, such a blunder would be marked wrong, and so wrong that no partial credit would be awarded. In order to have a local conservation law in any connected manifold, you still need ordinary derivatives to convert an integral over a domain into an equivalent integral over the boundary. This is not even physics, it is basic tensor analysis.

It is ESSENTIAL that Wikipedia get a grip on the editors of these fundamental articles. They are almost uniformly terrible, as they are written by mediocre grad students who likely will never have an original idea. It is a terrible shame to have these people vandalizing these articles with what amounts to scientific graffiti.

Antimatter33 (talk) 00:17, 15 November 2019 (UTC)

Yes, I agree. So it goes. Until someone steps up to the challenge of fixing this, the issues will remain. Although, FWIW, "just replace , by ;" is something I heard more than once in class. Teachers love to say that, students repeat what they hear. Blame the teacher. It's a bad rule of thumb. 67.198.37.16 (talk) 03:08, 12 June 2023 (UTC)