This seems to be a more reasonable approach - derive a relation from a law of conservation. Starting from the differential form is fraught with indeterminism. A

This seems to be a more reasonable approach - derive a relation from a law of conservation. Starting from the differential form is fraught with indeterminism. Assuming this works, I wonder about maxwell’s equations. I assume they would have to be consistent with a conserved electromagnetic quantity added into this. Gravity?