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I stumbled upon the following article: https://www.livescience.com/einstein-biggest-failure-teleparallel-gravity.html . The following quote is taken from the mentioned article.

In his attempts to make a super-theory of everything, Einstein introduced General Relativity 2.0. The basic version of relativity only cares about space-time's curvature. But Einstein's reboot also paid attention to space-time's twistiness, or torsion. There was no need to include torsion in his original theory, because it turned out that all you needed was curvature to explain gravity. But now that Einstein was trying to explain more than gravity, he had to include additional effects.

When did Einstein come up with this second version, i.e 2.0, of the general theory of relativity?

Was NASA's Gravity Probe B experiment more about the General Relativity 2.0 than about General Relativity 1.0 since it was more about measuring the twistiness of space-time?

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    $\begingroup$ no, probe B explored frame dragging, not torsion. Also, torsion was first introduced by Cartan in 1922 en.wikipedia.org/wiki/Einstein%E2%80%93Cartan_theory $\endgroup$
    – Umaxo
    Dec 17, 2020 at 9:02
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    $\begingroup$ torsion is proper mathematical term, you do not need to put in quotes en.wikipedia.org/wiki/Torsion_tensor. It never became part of general relativity (GR), but there are generalizations of GR that also include it, like Einstein-Cartan theory I mentioned, but they do not seem to be superior to GR in their explanatory power. $\endgroup$
    – Umaxo
    Dec 19, 2020 at 22:00
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    $\begingroup$ GR addresses torsion - it says it is zero. $\endgroup$
    – Umaxo
    Dec 19, 2020 at 22:13
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    $\begingroup$ To clear some things, the GR explains gravitation as curvature of spacetime. The spacetime can twist, rotate and do a lot of dynamic things. The rotation of space for example is called frame dragging and this is what probe B explored. The GR then says, that freely falling test-body moves through this dynamic spacetime without twisting, i.e. it only "rolls along the curvature". In case of nonzero torsion the freely falling body could still rotate, even if spacetime would be completely flat. As far as I know, there is no proper and satisfactory justification to allow such behavior. $\endgroup$
    – Umaxo
    Dec 19, 2020 at 22:45
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    $\begingroup$ In summary, the torsion is less about "twistiness of space-time" and more about "twistiness of curves in space-time". The "twistiness of space-time" is well described by GR itself. This is at least the way I understand it, but I have only limited knowledge of torsion. $\endgroup$
    – Umaxo
    Dec 19, 2020 at 22:46

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From https://en.wikipedia.org/wiki/Teleparallelism

Teleparallelism (also called teleparallel gravity), was an attempt by Albert Einstein[1] to base a unified theory of electromagnetism and gravity on the mathematical structure of distant parallelism, also referred to as absolute or teleparallelism. In this theory, a spacetime is characterized by a curvature-free linear connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field.

[1] Einstein, Albert (1928). "Riemann-Geometrie mit Aufrechterhaltung des Begriffes des Fernparallelismus". Preussische Akademie der Wissenschaften, Phys.-math. Klasse, Sitzungsberichte. 1928: 217–221.

Here's an electronic version of Einstein's paper
https://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/echo/einstein/sitzungsberichte/B8AG2G5E/index.meta

which was translated in
https://arxiv.org/abs/physics/0503046v1
Translation of Einstein's Attempt of a Unified Field Theory with Teleparallelism
Alexander Unzicker, Timothy Case
(see the second paper, starting on pg.6)

Here's another article on it
https://arxiv.org/abs/physics/0405142v1
Field equations in teleparallel spacetime: Einstein's Fernparallelismus approach towards unified field theory
Tilman Sauer
Historia Math. 33 (2006) 399-439
10.1016/j.hm.2005.11.005

A historical account of Einstein's 'Fernparallelismus' approach towards a unified field theory of gravitation and electromagnetism is given. In this theory, a space-time characterized by a curvature-free connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field, is investigated. The approach was pursued by Einstein in a number of publications that appeared in the period from summer 1928 until spring 1931. In the historical analysis special attention is given to the question of how Einstein tried to find field equations for the tetrads. We claim that it was the failure to find and justify a uniquely determined set of acceptable field equations which eventually led to Einstein's abandoning of this approach. We comment on some historical and systematic similarities between the 'Fernparallelismus' episode and the 'Entwurf' theory, i.e. the precursor theory of general relativity pursued by Einstein in the years 1912-1915.

(I haven't read any of them.
I was just curious to see what this is about.
So, I did a Google search.)

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