Since in GR and SR the basis vectors are generally orthogonal, how can we take derivatives of position with respect to time? For example, the current four-vector is $$J^{\alpha} = \sum_n e_{n} \frac{\partial x^{\alpha}}{\partial t} \delta^{3}(x - x_{n})$$ where n labels the n-th particle. In this case the derivative will generally not be zero, so how can time be orthogonal to ##x^{i}##?(adsbygoogle = window.adsbygoogle || []).push({});

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# B Time derivatives in GR and SR

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