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Jul 26 at 1:32 comment added Ján Lalinský Think about what $\frac{\partial L}{\partial g_{\mu\nu}}$ means. It does not mean a derivative of 0; $L$ here is meant to be a function of $g$, so it can change, when $g$ changes.
Jul 25 at 22:25 answer added Andrew timeline score: 0
Jul 25 at 22:02 answer added Lenard Kasselmann timeline score: 1
Jul 25 at 17:32 comment added Lenard Kasselmann The Lagrangian itself might be zero for a free field, but that doesn't imply that its derivative with respect to the metric tensor is also zero.
Jul 25 at 17:25 history asked Khun Chang CC BY-SA 4.0