According to Carroll, [itex]\nabla \phi[/itex] is covariant under rotations. This really confuses me. For example, how could equations like [itex]\vec{F}=-\nabla V[/itex] be rotationally covariant if force is a contravariant vector?(adsbygoogle = window.adsbygoogle || []).push({});

I know this is strictly speaking more of a mathy question, but I still figured this was the best place to ask this question.

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# How can the gradient of a scalar field be covarient?

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