page 71 he appears to define the affine connection in terms of derivatives on the locally inertial coordinates with respect to the laboratory coordinates(adsbygoogle = window.adsbygoogle || []).push({});

and then the very next page claims that all you need is the affine connection and metric tensor to determine the locally inertial coordinate system

he says you get a differential equation for the locally inertial coordinate system in terms of laboratory coordinates, but this differential equation comes from the definition on the previous page

I guess my question is what is the logic here? This seems circular, no wait... it IS circular. We need something else for this "differential equation" to be useful.

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# Question about affine connection definition, Weinberg's Gravitation

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