My question is simple: why do we use $T_{\mu\nu}$ to denote the stress energy momentum tensor, and when was the concept of the stress energy tensor first (or roughly the first) introduced (and by whom)?

Note: I'm well aware that such trivial notation differences make no difference to the actual underlying concepts. Rather I'm just wondering why the specific use of $T$? For instance, is it the case that the letter $T$ is the initial letter (in some other language) of the words stress or energy or momentum (for example, I know that we use $\Bbb{Z}$ for integers because it stems from the German word Zahl for number)? I'm just curious because if it were me back in the day, I might have used the notation $P_{\mu\nu}$, because lower case $p$ is already standard notation for momentum in classical mechanics, so if I were to create a tensor for stress-energy-momentum, I might consider $P_{\mu\nu}$ as a reasonable notation.


1 Answer 1


Because it is a $T$ensor. People do not deliberate much on choosing letters, as one can see from Gauss's $E,F,G$, among other examples. $T$ happened to be the first tensor that came up in Sommerfeld's On the Theory of Relativity I: Four-dimensional Vector Algebra, p. 767ff, after he dealt with $4$- and $6$-vectors and then scalar and vector products. It was the turn of $T$ensor product. Minkowski and Abraham before that used different letters. Von Laue after followed Sommerfeld in his 1911 textbook on relativity (the very first one), and so it stuck, see History of Topics in Special Relativity/Stress-energy tensor.

Btw, $T_{\mu\nu}$ is typically just "stress-energy tensor", despite the momentum components in it. The stress–energy–momentum pseudotensor is a modification by Landau and Lifshitz, typically denoted $t^{\mu\nu}_{LL}$.

  • $\begingroup$ I guess I'm just a little surprised that even something such as $S_{\mu\nu}$ (stress) or $E_{\mu\nu}$ (energy) was not adopted. But oh well, history is full of curiosities :) $\endgroup$ Jul 8, 2022 at 10:21

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