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It is not the case that Norton's hole argument analysis shows that general covariance in GR underdetermines the physical interpretation of spacetime-dependent transformations.
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Reasons For
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Reason for
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1.
Einstein's hole argument assumes substantivalism about spacetime points; relationalist interpretations dissolve the alleged indeterminacy entirely.
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2.
General covariance is a mathematical property ensuring consistency; physical interpretation requires additional dynamical content and boundary conditions.
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3.
Modern gauge-theoretic approaches show diffeomorphism freedom is a redundancy to eliminate, not an underdetermination of physical facts.
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Reasons Against
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Reason against
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1.
General covariance permits mathematically equivalent spacetime descriptions with different geometric interpretations of physical events.
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2.
Without additional constraints beyond field equations, observers cannot uniquely determine which coordinate-dependent structures represent real physical features.
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3.
The hole argument demonstrates that purely local diffeomorphisms preserve all physics yet alter spacetime point assignments, revealing interpretive indeterminacy.
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