Talk:Stress–energy tensor

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)

I do not understand the title of the section As a Noether current. I would expect a derivation of the energy-momentum tensor from a space-time transformation of a field, and I would pose it in the context of field theory, not general relativity. I would name this section under its current content something like "stress-energy momentum conservation in curved spacetime" or something like that. --Daniel 25 feb 2008 —Preceding unsigned comment added by 80.26.142.131 (talk) 18:02, 25 February 2008 (UTC)

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.

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)

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)

That a theory is symmetric under certain group doesn't mean that their states are invariant. The group of special relativity is generated by translations, rotations and boosts, but the state of, say, an atom, is obviously not invariant. For your example, translation invariance means that the bound solutions are the same no matter where you place the center of mass. Do not confuse "relativistic" in the sense of "in the framework of special relativity" with in the sense of "moving really fast".-Daniel —Preceding comment was added at 16:42, 2 March 2008 (UTC)

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)

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)

When one defines the tensor $t^{\mu \nu }$ as the current leading to the conserved "charges" $P^{\mu }$ there remain an ambiguity since any tensor of the form $\partial _{\sigma }A^{\sigma \mu \nu }$ with $A^{\sigma \mu \nu }$ antisymmetric can be added to $t^{\mu \nu }$ leading to a divergenceless tensor whose spatial integral is still $P^{\mu }$. The noether-theoretic tensor obtained assuming an invariant lagrangian density is just one of the possible tensors, but it is not the most usefull, because it does not reflect the Lorentz symmetry. When one takes into account the full Poincarè group then the symmetric (Belinfante) tensor arises. Its generalization to curved spaces is the Hilbert tensor, and it is this tensor the one used in general relativity. So I think that the article cannot leave for the end the "many stress-energy tensors" without explaining why, while using them without distinction in the body of the article. It should be stated all of this at the vey beggining of the article. --Daniel —Preceding comment was added at 17:09, 2 March 2008 (UTC)

Notation

In the section As a Noether current, I'm unclear on the notation used in the expression

$\nabla _{b}T^{ab}=T^{ab}{}_{;b}=0$

I've never seen notation with the subscript ;b and I would have written the expression as

$\partial _{\mu }T^{\mu \nu }=0$

Jeodesic 13:16, 23 October 2007 (UTC)

The semi-colon indicates a covariant derivative. The covariant derivative is used frequently in general relativity. See mathematics of general relativity for further enlightenment (possibly). :) MP ^{(talk•contribs)} 15:27, 23 October 2007 (UTC)

I've added the statement $\partial _{\mu }T^{\mu \nu }\neq 0$ to the section to make it clearer that we are not talking about the ordinary, non-covariant derivative. --Michael C. Price ^talk 07:02, 25 October 2007 (UTC)

Pressure? Viscosity??

I am confused with the interpretation of some of the tensor elements. Pressure and viscosity? Aren't they just macroscopic manifestations of microscopic properties of matter? When you work witl viscous liquid, viscosity is the result of strong (..er than in e.g. water) bonds between molecules, it is not a property of the region of space where that liquid is currently located.

IOW: on microscopic level (atom....proton scale) there is no "viscosity" as a physical reality. Same goes for pressure.

Please, if you can clear up my confusion, please do so somewhere in the article. Thanks. 89.102.207.196 (talk) 00:17, 12 May 2008 (UTC)

See clarification in lead -- the s-e tensor describes matter. --Michael C. Price ^talk 09:25, 12 May 2008 (UTC)

Actually, it is the image which is wrong — it should say "shear stress" where it says "viscosity". Unfortunately, I cannot change the image. As Mike said, the components of the stress-energy tensor measure non-gravitational properties, that is, not properties of spacetime itself but of its contents. The Einstein field equations connect the curvature of spacetime to this attribute of its contents. JRSpriggs (talk) 19:55, 12 May 2008 (UTC)