PreprintCC BY 4.0arXiv
Constraint Variance Identity and the Matter-Geometry Fluctuation Relation
Abstract
The quantum Hamiltonian constraint vanishes for physical states. For separable Hamiltonians in minisuperspace, its vanishing variance yields a fundamental identity. Under the Born-Oppenheimer approximation, we derive the Matter-Geometry Fluctuation Relation, dynamically linking spacetime clock fluctuations to matter fluctuations. This establishes a quantitative stability condition for the clock against total quantum noise. Finally, we obtain an uncertainty relation between matter energy and relational time. The stable existence of spacetime thus demands quantum fluctuations in matter.
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BibTeX
@misc{yokokura2026constraint,
title = {{Constraint Variance Identity and the Matter-Geometry Fluctuation Relation}},
author = {Yuki Yokokura},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07015},
eprint = {2611.07015},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07015},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constraint Variance Identity and the Matter-Geometry Fluctuation Relation
AU - Yuki Yokokura
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07015
UR - https://arxiv.org/abs/2611.07015
AB - The quantum Hamiltonian constraint vanishes for physical states. For separable Hamiltonians in minisuperspace, its vanishing variance yields a fundamental identity. Under the Born-Oppenheimer approximation, we derive the Matter-Geometry Fluctuation Relation, dynamically linking spacetime clock fluctuations to matter fluctuations. This establishes a quantitative stability condition for the clock against total quantum noise. Finally, we obtain an uncertainty relation between matter energy and relational time. The stable existence of spacetime thus demands quantum fluctuations in matter.
ER -