A Constructive Definition of Space via Dynamical Evolution and Observational Acts
Abstract
We propose a constructive and dynamical redefinition of spatial structure, grounded in the interplay between mechanical evolution and observational acts. Rather than presupposing space as a static background, we interpret space as an emergent entity that arises through observational acts. Using the framework of pre-topologies, measurable structures, and the GNS construction, we analyze how the choice of observables and the system's time evolution dynamically determine the topological and measure-theoretic features of space. This approach highlights the observer-dependent and context-sensitive nature of spatial concepts in both classical and quantum domains.
Cite
@article{arxiv.2505.09838,
title = {A Constructive Definition of Space via Dynamical Evolution and Observational Acts},
author = {So Katagiri},
journal= {arXiv preprint arXiv:2505.09838},
year = {2025}
}
Comments
26 pages, Clarified notation in Sec. 2.1, added discussion on point-less geometry in noncommutative geometry, and included remarks on phase-space-first perspectives in quantum gravity