A Constructive Definition of Space via Dynamical Evolution and Observational Acts

• URL: http://arxiv.org/abs/2505.09838v1
• Date: Wed, 14 May 2025 22:39:43 GMT
• Title: A Constructive Definition of Space via Dynamical Evolution and Observational Acts
• Authors: So Katagiri,
• Abstract summary: Rather than presupposing space as a static background, we interpret space as an emergent entity that arises through observational acts.<n>This approach highlights the observer-dependent and context-sensitive nature of spatial concepts in both classical and quantum domains.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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