A Constructive Definition of Space via Dynamical Evolution and Observational Acts

TL;DR

This paper introduces a dynamic, observer-dependent framework for defining space as an emergent property resulting from observational acts and system evolution, challenging traditional static notions of space.

Contribution

It presents a novel constructive approach to space based on dynamical evolution and observational acts, integrating pre-topologies, measurable structures, and the GNS construction.

Findings

Space emerges from observational acts and system dynamics.

The framework applies to both classical and quantum systems.

Observer-dependent nature of spatial concepts is highlighted.

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.