A Constructive Definition of Space via Dynamical Evolution and Observational Acts

So Katagiri

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arXiv · 2505.09838

A Constructive Definition of Space via Dynamical Evolution and Observational Acts

So Katagiri

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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.

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So Katagiri. 2025-05-14. A Constructive Definition of Space via Dynamical Evolution and Observational Acts. https://arxiv.org/abs/2505.09838

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