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Ordered State Families and the Wheeler-DeWitt Constraint: An FLRW Mini-Superspace Construction

Year: 2026
Type: preprint
Abstract: The Wheeler-DeWitt equation occupies a central role in canonical quantum gravity and is frequently interpreted as implying a fundamentally timeless universe due to the absence of an explicit time derivative. This interpretation forms the basis of the long-standing Problem of Time. The present work examines a narrower question: whether the Wheeler-DeWitt constraint alone logically forbids an ordered family of physical quantum states. Using an FLRW mini-superspace cosmological model containing a homogeneous scale factor and scalar field, a continuous parameterized family of quantum states is constructed from solutions belonging to the kernel of the Wheeler-DeWitt operator. It is shown explicitly that every member of the family satisfies the Wheeler-DeWitt constraint while expectation values of physical observables evolve monotonically with respect to an invariant ordering parameter. The analysis demonstrates that the Wheeler-DeWitt equation may be interpreted as a state-admissibility constraint acting on individual spatial quantum states rather than as a prohibition on ordered physical evolution. In this framework, a single constraint-satisfying state corresponds to a static "frame," while a continuously ordered family of admissible states forms an evolving physical history. The present work does not derive a unique physical origin for the ordering parameter. Rather, it establishes that the Wheeler-DeWitt constraint alone does not logically exclude such ordering. The result provides an explicit FLRW realization of the Forward-QM interpretation and suggests that the standard inference from Wheeler-DeWitt timelessness to a frozen universe is not mathematically compelled by the constraint equation itself.
DOI: 10.5281/zenodo.24095409
Language: English
Open Access status: green
OpenAlex ID: W7225751706
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