Talk:Stress-energy tensor
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[edit] Some Suggested Improvements
I think this article should link to a new article on conservation laws in general relativity, in which it should be stressed that the divergence law for the stress-energy tensor does not have quite the interpretation expected from flat spacetime. It is not really a conservation law anymore (because it does not account for energy/momentum exchanged between matter or nongravitational fields and the gravitational field itself).
Another point is that the stress-energy tensor plays a role in other metric theories of gravitation besides general relativity, so strictly speaking, I think this article really belongs in the category of things dealing with physical interpretation of Lorentzian manifolds. --CH
The article could certainly use a lot of additional content; some examples, some mention of the interpretation of its various matrix entries and why it's called the "stress-energy tensor", the ambiguity in its definition as a Noether current and the special role of the symmetric form in general relativity, etc. --Matt McIrvin 01:22, 9 August 2005 (UTC)
[edit] comment from energy-momentum density
I added a whole bunch of stuff to this article. I think this article should be merged with Stress-energy tensor. I was also going to move this article to Stress tensor (which I will still consider doing, after I have merged), but stress tensor is a redirect to Stress (physics) so i wonder if i should. -Lethe | Talk 00:03, Jan 20, 2005 (UTC)
Care to elucidate Noether procedure? --ub3rm4th 16:34, 23 Feb 2005 (UTC)
- Pleast note the spelling of 'Belinfante'. It is incorrect here, I believe.
[edit] Merge reproposed
Hi all, I just put in a merger template and discovered that Lethe had already independently made the same suggestion, but apparently the merger did not occur. Seems to me that this article is about the stress-energy tensor, so it should be called that, but there is already an existing article with some material worth keeping. Conclusion: the thing to do is to merge this article into the existing "stress-energy tensor" article.
FWIW, I am revising the gtr pages and plan to eventually have much better articles on Noether symmetry and all that.---CH (talk) 22:41, 11 August 2005 (UTC)
I added some stuff, but there really ought to be a separate article on plain old stress tensors as opposed to relativistic stress-energy tensors, as I know this is a pretty important subject in engineering, and the relativity stuff is completely irrelevant in that context. We could then refer to the stress tensor article when talking about the space-space components of the stress-energy tensor, which incorporates it. I'd even say that this is more important than beefing up the relativistic content, but unfortunately the relativity stuff is what I know a lot about. Are there any structural engineers out there? --Matt McIrvin 02:39, 17 August 2005 (UTC)
[edit] relativistic implies homogeneous?
it's not obvious to me. what about a fast bound particle? Also, this isn't particular to field theories, is it? -Lethe | Talk 11:55, August 15, 2005 (UTC)
[edit] Why symmetric?
I came to this article to learn why it is important or useful to have the stress-energy tensor be symmetric, but the author seems to assume that the tensor is always symmetric and ignores the fact that the stress-energy tensor can be asymmetric when defined in terms of a Lagrangian density. See for instance the chapter on continuum mechanics in Goldstein's Classical Mechanics. Tpellman 14:01, 19 October 2006 (UTC)
- In general relativity the stress-energy tensor has be symmetric to fit into the Einstein field equations. In other fields I think the reason why the asymetric forms are not studied so much is that any asymmetric stress energy tensor can be symmetrised by the addition of a physically irrelevant term. --Michael C. Price talk 14:38, 19 October 2006 (UTC)
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- If the stress-energy tensor is the result of varying the action with respect to the metric tensor, then it must be symmetric because the metric tensor is symmetric. Also, one can prove that the symmetry is equivalent to conservation of angular-momentum which is known to be a physical fact. JRSpriggs 03:39, 20 October 2006 (UTC)
- The points JRSpriggs and myself have made are further elaborated on pages 562/3 of Goldstein's Classical Mechanics. Perhaps this should be mentioned in the article. --Michael C. Price talk 07:56, 20 October 2006 (UTC)
