Are conservation laws independent of field equations?

Changli Liu
Arxiv ID: 1002.0892Last updated: 5/23/2023
The charge conservation law (∂_α J^α =0) usually is considered as a corollary of Maxwell's equations and is not independent of Maxwell's field equations. A circular reasoning, however, is found in the derivation. A similar fallacy exists in the matter source's conservation law (∇^μT_μν=0) and Einstein's field equations. Therefore, the source's conservation laws are independent of Einstein's field equations.

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