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It is not the case that The theoretical status of the discreteness result in loop quantum gravity is questionable as a genuine physical prediction
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Reasons For
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Reason for
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1.
The discreteness result has been shown to hold only for operators on the kinematical Hilbert space
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2.
Operators on the kinematical Hilbert space are gauge-variant quantities
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3.
Genuine observables must be gauge-invariant (defined on the physical Hilbert space, satisfying all constraints)
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Reasons Against
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Reason against 1 of 2
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1.
Physical predictions require invariance under the full symmetry group of the theory, a criterion emphasized by Dirac's constrained Hamiltonian formalism.
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2.
The area and volume operators in LQG are constructed prior to solving the diffeomorphism and Hamiltonian constraints, making them kinematical artifacts.
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3.
A quantity that changes under gauge transformation cannot represent a measurable physical magnitude, regardless of its mathematical elegance or heuristic appeal.
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Reason against 2 of 2
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1.
The underdetermination problem identified by Belot and Earman shows that quantization ambiguities in background-independent theories systematically infect putative physical results.
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2.
LQG's discrete spectra depend on the choice of the Ashtekar-Barbero connection, which is not a spacetime covariant object but a gauge-dependent internal variable.
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