Philosophers of physics from Earman to Belot have argued that constraint-based reductions conflate mathematical redundancy with genuine physical degrees of freedom, making 'true' underdetermined without a fixed gauge.
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Mathematical redundancy(as what might be confused with physical degrees of freedom)
Extra mathematical descriptions that describe the same physical situation in multiple ways—like having two different equations that always give identical results.
gauge(Described as necessarily arbitrary in a pure infinitesimal geometry)
A locally chosen standard of length or scale used to assign magnitudes to vectors at a point on a manifold.
underdetermined(Used to contrast mathematical conjectures, whose correct answers are fixed by logical facts, with cases where no such determination exists.)
A decision or truth is underdetermined when logical facts alone do not fix a single correct answer.