Emergence of Time and Dimensionality from Minimal Interacting Entities: A Pregeometric Approach

We investigate the emergence of time and spacetime dimensionality from minimal interacting entities using Object-Relation-Object (O-R-O) structures. Our analysis suggests that three entities constitute a minimal system for establishing consistent temporal relations, and we examine how dimensionality may arise from O-R-O relations. The framework yields quantitative predictions regarding temporal structure at the Planck scale (Delta t ~ tau_P sqrt(E_P/E)) and offers a perspective on quantum entanglement through O-R-O relations, potentially contributing to discussions of the problem of time in quantum gravity. We derive several experimental predictions that could be tested through quantum optics (tau ~ 10^-25 s), particle physics (Delta E/E ~ 10^-15), and cosmological observations. The proposed approach appears compatible with holographic principles and background independence, while suggesting possible connections to quantum computation and error correction through O-R-O operations.