Hidden Variable Theory

 

Abstract

A Set-Theoretic Approach to Hidden Variable Theory and Universal Completeness

This conceptual framework explores the relationship between quantum states, hidden variables, and the totality of the Universe (   U   ). By formalizing the concept of a "complete state" through set theory, this study addresses the ontological gap between observed quantum phenomena and a deterministic underlying reality. The model defines the union of Quantum states (   Q   ) and Hidden Variables (   hv   ) as a subset of the Universe (   Q \cup hv \subseteq U   ), while positing that the Universe itself cannot be fully contained within this specific union, thereby suggesting that the Universe is not merely the sum of quantum mechanical descriptions.

The analysis proposes a recursive summation model,    U = \sum_{i=0}^{N} (Q \cup hv)_i   , suggesting that the totality of the Universe is reached as the number of states approaches infinity (   n \to N   ,    \pi \to \infty   ). By incorporating the concept of "Quantum Space" (   Q_s   ) as an encompassing container, the framework provides a structured, albeit speculative, methodology for visualizing the integration of hidden variables into a broader cosmological context. This approach invites further inquiry into whether a complete description of the Universe requires the summation of an infinite series of quantum-hidden variable complexes.

Session Tag: #OntologicalTemporalModeling