Conditional State Distances in Page-Wootters Quantum Clocks: When Does Ultrametricity Emerge?
The Page-Wootters formalism resolves the problem of time in quantum gravity by conditioning a globally static Wheeler-DeWitt state on clock readings, producing an emergent notion of evolution. We investigate the mathematical structure of distances between these conditional states and ask: under what conditions do they organize into an ultrametric hierarchy. --- *Published under QNFO-ULA. [legal.qnfo.org](https://legal.qnfo.org/)*
Conditional State Distances in Page-Wootters Quantum Clocks: When Does Ultrametricity Emerge?
Authors: Rowan Brad Quni-Gudzinas
Published: 2026-07-04
DOI: [https://doi.org/10.5281/zenodo.21120286](https://doi.org/https%3A%2F%2Fdoi.org%2F10.5281%2Fzenodo.21120286)
Abstract
The Page-Wootters formalism resolves the problem of time in quantum gravity by conditioning a globally static Wheeler-DeWitt state on clock readings, producing an emergent notion of evolution. We investigate the mathematical structure of distances between these conditional states and ask: under what conditions do they organize into an ultrametric hierarchy. --- Published under QNFO-ULA. [legal.qnfo.org](https://legal.qnfo.org/)
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This paper is part of the QNFO research corpus.