Talk:Electromagnetic stress–energy tensor

CGS or SI units

This article is non-standard since it uses CGS instead of SI and an arrow to symbolize a vector instead of boldface (it's not even the right arrow). 88.154.158.95 13:10, 25 November 2006 (UTC)

SI units are now included as well as CGS units. JRSpriggs (talk) 06:00, 11 April 2008 (UTC)

Rename

The page name should reflect the fact that the article is limited to the energy-momentum tensor for electromagnetic fields. Saligron 04:54, 29 January 2007 (UTC)

I moved this article from "Energy momentum tensor" to "Electromagnetic stress-energy tensor" which is a more accurate description of the contents. I hope that this is acceptable to you. JRSpriggs 09:34, 29 January 2007 (UTC)

The name fits much better. Thanks. Saligron 10:43, 29 January 2007 (UTC)

I think you should re-redirect "Energy momentum tensor" to "Stress-energy tensor". Hwasungmars 19:53, 30 May 2007 (UTC)

Good idea. Done. JRSpriggs 08:31, 31 May 2007 (UTC)

The relativistic formula for the tensor

I am not sure at present what is the correct formula in each system of units. However, I am sure that some of these formulas are wrong. There should be a factor of 1/4 in the first formula which is missing, for example. JRSpriggs 10:13, 20 April 2007 (UTC)

Well, c=1 unit is of the so-called "geometric units" or "standard relativistic units" which has no relation with Planck units at all. You might mix them up. Nevertheless, the formula as what I keyed in is correct for c=1 unit convention, and $\epsilon _{o}={\frac {1}{\mu _{o}}}$ holds, which can further simplify the tensor. All of these come from James Hartle's General Relativity textbook[1]. --KasugaHuang 14:45, 24 April 2007 (UTC)

As for the first formula, if you mean this: $T^{\alpha \beta }=\epsilon _{o}[-F^{\alpha \gamma }F_{\gamma }^{\beta }+g^{\alpha \beta }F_{\gamma \delta }F^{\gamma \delta }]$, this is not what I keyed in, and further confirmation may be required. :) --KasugaHuang 14:52, 24 April 2007 (UTC)

I have never heard of "geometric units" or "standard relativistic units", if those are different from Planck units. If you want to have a separate section giving the formulas in those units, that would be fine. But please do not mix them up with SI units or cgs units.
As to the formula you mentioned, yes that is the main one to which I was referring. And if you check the revision history, you will see that you did indeed add it (without 1/4 on the second term). I did not add or change that formula, yet. JRSpriggs 07:17, 25 April 2007 (UTC)

I tried to fix the problems that were apparent to me, but they may still have errors. JRSpriggs 04:09, 1 May 2007 (UTC)

• For the information about geometric units (including c=1), see the article Geometrized unit system. As for what you mentioned about the revision history, I'll check it later. :) --KasugaHuang 09:30, 1 May 2007 (UTC)

Sign conventions and sign problems

I think there is not only a problem with the common prefactor (which may be different in different unit systems), but there is also a problem about the definition of the common sign for the stress-energy tensor.

Apart from the sign and prefactor convention problems, there might be a sign confusion: the first and second summand in the em. stress-energy tensor might have same or opposite sign depending on how the contractions are performed. Since F is antisymmetric, one has to specify for the form with upper and lower indices, which one is first and which is second. -- 17:16, 24 March 2008 83.243.113.85 (talk · contribs)

I calculated the whole thing. I do think there should be a minus sign before everything. This formula is for (-1, 1, 1, 1) metric tensor but not for (1, -1, -1, -1) one. --128.122.52.204 (talk) 21:42, 22 September 2008 (UTC)

The sign convenion for the metric is opposite to the one used in the definition of the E-M field-tensor electromagnetic tensor Nielswalet (talk) 11:28, 13 December 2012 (UTC)

Also disagrees with Stress–energy tensor Nielswalet (talk) 15:29, 13 December 2012 (UTC)

Units of the components in the explicit matrix form

I believe in this article there is a problem in the explicit matrix form of the electromagnetic stress-energy tensor. The Pointing vectors S_x, S_y, S_z in the matrix should be divided by the speed of light, c[m/s]. This is because all elements of the matrix should have the same dimension of [J/m³]. Bspasov (talk) 19:27, 10 April 2008 (UTC)

Actually, the components of a tensor should not all have the same units. In SI units, time is measured in seconds and distance is measured in meters. Thus the position 4-vector has units of [seconds, meters, meters, meters]. More generally, a factor of (seconds/meter)^(# of contravariant time indices − # of covariant time indices) must be multiplied by the units of the purely spatial components to get the units of components involving time. JRSpriggs (talk) 06:00, 11 April 2008 (UTC)

This is an old conversation, but for the record, I disagree with JRSpriggs here. In the textbooks I've seen, all four components of a four-vector always have the same units. For example, the "position 4-vector" is defined as (ct,x,y,z). --Steve (talk) 00:15, 18 January 2011 (UTC)

Source please.

Who derived this tensor equation? Maxwell was of course a while ago. But who came up with this portrayal? Oh, just found it in The Foundations of the Genreal Theory of Relativity by Einstein.

Bruce rout (talk) 22:45, 17 September 2008 (UTC)

The tensor is wrong

The two terms of the tensor should have opposite sign. Look at Wald's book, equation 4.3.14 —Preceding unsigned comment added by 147.52.186.56 (talk) 14:31, 17 January 2011 (UTC)

Definition of sigma must be wrong.

The definition of σ[sub i j] must be wrong. There is a kronecker delta indexed by i and j, but it multiplies a term that has no subscripts at all. — Preceding unsigned comment added by Zfiddler (talk • contribs) 08:58, 14 November 2016 (UTC)

The term without index is the absolute value of the electric/ magnetic field field. Biggerj1 (talk) 12:27, 4 September 2018 (UTC)