Discrete-Continuum Coupling Axiomatic System for a Unified Solution to the Quantum Measurement Problem: First-Principles Derivation of Dynamical Collapse and Experimental Predictions
We present a complete, mathematically rigorous, and observer-free resolution of the quantum measurement problem. Building entirely on the axiomatic framework established in the preceding work, which derives the Born rule exclusively from unitary dynamics, uniqueness of classical records, unitary invariance, and ergodic stability, we show that the entire measurement process is governed by a single deterministic law: unitary evolution. The apparent wavefunction collapse is not a physical process but an effective description of the emergence of a unique dynamically stable classical record under decoherence and unique ergodicity. No auxiliary postulates, collapse mechanisms, or observer-dependent inputs are required. We explain the origin of definite measurement outcomes, the emergence of objective probability, the elimination of quantum-classical duality, and provide a fully consistent resolution of the Wigner’s friend paradox. The framework reproduces all experimental predictions of quantum mechanics without contradictions and establishes a unified, self-contained foundation for quantum measurement theory. This work constitutes the first complete, minimal, and mathematically closed solution to the quantum measurement problem.
Abstract The quantum measurement problem remains one of the most profound challenges in physics. Standard quantum mechanics lacks a dynamical mechanism for observation, treating wavefunction collapse as either postulated, stochastic, or external to the formalism. We introduce the MultiElectron Unified Wave Equation (MEUWE), a new quantum framework that derives collapse, the Born rule, and the arrow of time from first principles. MEUWE extends the multi-electron Schrödinger equation with nonlocal, fractional memory kernels that couple the system to observer fields, modeling collapse as an emergent, entropy-driven transfer of memory norm. This formulation yields a natural derivation of the Born rule from entropic maximization, predicts irreversible decoherence from fractional time dynamics, and recovers unitary evolution in the absence of observation. We show that MEUWE explains temporal asymmetry as a flow of coherence from system to observer, offering a physical origin for measurement irreversibility without postulates, hidden variables, or branching universes. Beyond interpretation, MEUWE is validated against full Configuration Interaction (CI) and Variational Monte Carlo (VMC) benchmarks, and embedded within quantum field theory, renormalization group flows, and curved spacetime. We conclude with experimental predictions—including curvature-dependent decoherence, fractional signal decay, and observer-field entanglement—that distinguish MEUWE from all existing quantum collapse models. Our results suggest that collapse is not an axiom of nature, but a dynamical consequence of memory.
This work presents a unified axiomatic framework that resolves Hilbert’s Sixth Problem by integrating two complementary foundations: Unified Relational Projection Dynamics (URPD), which defines probability, time, and measurement as geometric relations on CP^{N−1}, and Reflexive Micro-Granular Dynamics (RMG), which models fields not as continuous backgrounds but as finite, self-differential information structures. By combining these principles, the framework reproduces quantum mechanics, classical mechanics, gauge interactions, Navier–Stokes continuum physics, thermodynamic irreversibility, and emergent spacetime geometry without divergences, renormalization procedures, or additional postulates. The result is a coherent and complete axiomatization of physical law that satisfies Hilbert’s original requirement for a mathematically rigorous physics.