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It is not the case that Julian Barbour and others argue that time is not extracted from GR but is rather eliminated entirely, making 'extraction' a category error.
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Reasons For
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1.
GR's spacetime metric still contains a time-like coordinate with causal properties distinct from space-like ones, suggesting time has real structure.
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2.
Elimination claims conflate mathematical formalism with physical reality; coordinate independence doesn't entail that temporal phenomena don't exist.
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3.
Emergent time theories still require time-like ordering relations at some level, so 'elimination' merely relocates rather than removes temporal structure.
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Reasons Against
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Reason against
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1.
GR's mathematical formalism treats time as a coordinate indistinguishable from spatial dimensions, suggesting time lacks fundamental ontological status.
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2.
The Wheeler-DeWitt equation describes quantum gravity without explicit time evolution, supporting the view that time emerges rather than being fundamental.
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3.
Calling time 'extracted' presupposes time exists prior to extraction, but if GR eliminates it, this language mistakes the map for the territory.
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