I'd really never studied tensors until I started studying the Einstein Field Equations. Since then, I have realized they are fairly common tool in physics and pretty basic to understanding many areas. But for the majority of my initial introduction to special relativity, I never needed tensors. They never really came up. As I try to think about how Einstein moved from creating special relativity to general relativity, I wonder how he knew that tensors would be useful for general relativity.

What led him to think tensors would be needed to formulate the EFEs?

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    $\begingroup$ Riemannian geometry and tensor calculus predate GR; Einstein had the idea that gravity is a geometrical effect, and if I remember my history correctly, had a lecture set up for himself with the explicit purpose of familiarizing himself with the subject $\endgroup$ – Christoph Jan 26 '15 at 0:31
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    $\begingroup$ So, because ideas about curvature existed, he reasoned tensors like the Riemann tensor, Ricci, etc would be needed? Therefore, the equations should be tensor equations? $\endgroup$ – Stan Shunpike Jan 26 '15 at 0:33
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    $\begingroup$ Yes. He also put emphasis on form-invariance of physical laws and lack of prior geometry ('general covariance'). $\endgroup$ – Christoph Jan 26 '15 at 0:39
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    $\begingroup$ It's more a case of "I need some compact formalism to handle this set of equations..." . Similar thing happend when Lie Groups turned out to be handy for particle physics. $\endgroup$ – Carl Witthoft Jan 26 '15 at 1:21
  • $\begingroup$ It's not really true that tensors are only needed for GR, not just SR. There are some problems with the foundational aspects of SR that you really can't solve correctly unless you introduce the stress-energy tensor. See Ohanian, "Einstein's E = mc^2 mistakes," 2008, arxiv.org/abs/0805.1400 . Although IMO Ohanian gets the emphasis wrong, he is technically right. $\endgroup$ – Ben Crowell Feb 1 '15 at 23:54

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