Hole argument

In general relativity, the hole argument is an apparent paradox that much troubled Albert Einstein while developing his famous field equations. Some philosophers of physics take the argument to raise a problem for manifold substantialism, a doctrine that the manifold of events in spacetime is a "substance" which exists independently of the metric field defined on it or the matter within it. Other philosophers and physicists disagree with this interpretation, and view the argument as a confusion about gauge invariance and gauge fixing instead.


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