From Modal Coherence to Operator Dynamics: A Structural Resolution of the Quantum Measurement Problem

The interpretation of quantum measurement remains one of the most persistent conceptual challenges in theoretical physics. Standard quantum mechanics introduces a formal dichotomy between unitary evolution and wavefunction collapse, without an ontologically closed account of what constitutes an "observer" or a "measurement." This paper proposes a novel theoretical framework — based on modal differences and coherence structures — that unifies dynamics and measurement without invoking collapse. We introduce a structural ontology wherein the fundamental entities are not objects but context-dependent modal distinctions, linked through a symmetric coherence kernel. The evolution of these distinctions is governed by an integral operator that, in the continuous limit, converges to the Laplacian — establishing formal equivalence with the Schrödinger equation. Measurement is reconceptualized as a local stabilization of coherence, not a discontinuous collapse. We numerically verify the framework across key quantum phenomena, including double-slit interference, Bell inequality violations, quantum tunneling, the Zeno effect, and macroscopic decoherence. Additionally, we show the emergence of operator dynamics and Hilbert-space structure as limiting cases of the discrete modal network. Our results suggest that modal coherence theory provides a mathematically consistent, ontologically self-contained, and computationally verifiable foundation for quantum mechanics — potentially bridging the conceptual gap between quantum theory and gravity, and redefining the physical meaning of measurement.