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It is not the case that In the Dirac quantization program, the Hamiltonian constraint annihilates physical states (HΨ=0), rendering 'pushing data forward' operationally meaningless.
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Reasons For
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Reason for
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1.
Gauge-invariant observables (those commuting with all constraints) have well-defined dynamics without invoking the Hamiltonian directly on physical states.
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2.
Reduced phase space quantization reconstructs evolution explicitly without relying on H|Ψ⟩=0, providing operational meaning to temporal propagation.
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3.
The problem of time has solutions beyond Dirac quantization (relational observables, deparameterization); dismissing all as 'operationally meaningless' overgeneralizes.
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Reasons Against
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Reason against
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1.
If H|Ψ⟩=0 for all physical states, then H generates no time evolution, making temporal propagation undefined in the constraint surface.
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2.
Observables that don't commute with H cannot have well-defined expectation values on the physical Hilbert space, breaking standard QM interpretation.
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3.
The constraint annihilation condition eliminates the standard Hamiltonian flow, so 'data forward' lacks a mathematical correspondence in phase space.
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