Quantizing the Geometry by Declaration: DeWitt's Two Choices and Their Effect at the Singularity
In 1967 Bryce DeWitt quantized general relativity by declaration: the metric became an operator, the Hamiltonian constraint became the Wheeler–DeWitt equation, and quantum geometrodynamics existed. This paper evaluates the founding declaration at its own address, converting census attack CC-165 whole. Two of the construction's load-bearing pieces are choices the founding paper flags and cannot remove — the operator ordering and the wave functional's inner product and measure. The bench evaluates them in a declared minisuperspace model (closed Friedmann, one scale factor) under the one-parameter ordering family \Psi'' + (p/a)\Psi' - (a^2 - a^4)\Psi = 0 with the paired measure a^p\,da: the near-singularity indicial branches are s = 0 and s = 1 - p, so the second branch's finiteness at a = 0 is ordering-chosen — finite exactly when p \leq 1, logarithmically divergent at p = 1's double root, divergent as a^{-1} and a^{-2} at p = 2 and p = 3 — and normalizability under the paired measure flips at p = -1 and p = 3. The wavefunctions themselves, computed by series and cross-checked by independent integration, differ at order unity between orderings. One declaration, two named choices, zero derivations of either in 1967 — and every quantum-cosmology number since uses both. Census headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.
Authors
- William Alexander Aldred
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-06
- DOI
- https://doi.org/10.5281/zenodo.24026878
- Primary Topic
- Noncommutative and Quantum Gravity Theories
- Type
- preprint