A Geometric Ontic Framework for Quantum States Based of SU(2) Symmetry and Non Factorizable Projections

We develop a geometric framework in which the operational structure of finite-dimensional quantum mechanics emerges from the dynamics of fields defined on an underlying ontic manifold. Two principles guide the construction. The Quantum Equivalence Principle (QEP) requires reversible dynamics to preserve local operational distinguishability in suitable “quantum inertial frames,” while the Quantum Mach Principle (QMP) assigns dynamical content to the ontic geometry by allowing the metric to depend on the global distribution of ontic configurations. For a single qubit, symmetry and minimality arguments identify \Omega = S^2 as the natural ontic manifold. In a symmetric regime—where the metric becomes homogeneous and backreaction is negligible—the induced operational state space inherits the round geometry of the Bloch sphere, and reversible flows act as its isometries. Standard unitary Schrödinger dynamics arise as an effective description without assuming Hilbert space structure at the fundamental level. For composite systems, non-factorizable components of the ontic metric generate intrinsic curvature on \Omega_A \times \Omega_B, which manifests operationally as entanglement. When symmetry is broken, the framework predicts deviations from standard quantum mechanics, including modified interference patterns, distortions of distinguishability, and effective non-unitarity. This work positions the familiar quantum formalism as a special high-symmetry phase of a broader geometric dynamical theory.