ToCA Quantum Phase Regulation (QPR): A Parameter-Free Reinterpretation of Quantum Behaviour

This paper presents ToCA Quantum Phase Regulation (QPR), the quantum-mechanical application of the Theory of Cosmic Architecture (ToCA).

It demonstrates that fundamental quantum phenomena—such as superposition, entanglement, and wavefunction collapse—are not primitive features of nature, but emergent mechanical consequences of the universal tension minimization law:

∂ₜD(t) ≤ 0

where D(t) represents the deviation from local equilibrium in high-dimensional amplitude space.

Key Theoretical Advances:

• Emergent Quantum Mechanics: Shows that Schrödinger-type dynamics arise naturally as the most efficient path for reducing tension in a complex amplitude landscape. "Superposition" is reinterpreted as parallel tension minimization, and "Entanglement" as correlated geometric tension (D_corr > 0) across subsystems.

• Resolution of the Measurement Problem: The framework dissolves the measurement problem by defining "collapse" as a rapid tension lock-in event triggered by strong macroscopic gradients. This eliminates the need for observer-dependent postulates.

• The Universal Residual Floor: A central, falsifiable prediction is that no quantum system can reach zero tension (D(t) ≥ D_floor > 0). The paper identifies this predicted floor in data from seven independent high-precision experiments (2023–2025), including deviations in Bell tests, double-slit visibility, and superconducting qubit coherence.

• Physical Interpretation of Complex Action Theory (CAT): Aligning with the Nielsen-Ninomiya framework, QPR suggests that the "imaginary action" (S_I) corresponds to the integrated tension over a system's history: S_I ≡ ∫ D(t) dt This provides a tangible physical mechanism for the suppression of high-S_I histories.

Role in the ToCA Framework: This document focuses on the microscopic and quantum-information aspects of the theory. It is part of a series outlining the complete architecture:

• Main Theory: ToCA v2.4: The Theoretical Foundation for Tension Minimization (The axiomatic core).

• Gravity: ToCA Quantum Gravity Integration (QGI) (The application to spacetime and cosmology).