Objective Phase-Space Quantum Information-Capacity Mechanics--An Information Ontology and Mathematical Framework for Quantum Mechanics
Objective Phase-Space Quantum Information-Capacity Mechanics--An Information Ontology and Mathematical Framework for Quantum Mechanics
Fangzhou Jin1
作者信息
- 1. Basic Science Department, Wuchang Shouyi College, Wuhan 430064, China
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摘要
Standard quantum interpretations-based on point trajectories, branching wave functions, or instantaneous projection-rely on two continuum idealizations: infinite spatial information density and infinite measurement bandwidth. A central foundational question is whether complex Hilbert-space kinematics, noncommuting observables, and single-outcome collapse follow from real physical fields under finite information capacity and bandwidth. We formulate Objective Phase-Space Quantum Information-Capacity Mechanics (QICM), specifying the state on a configuration manifold by a real probability density and a compact flow potential. Three axioms govern the theory: the first requires finite Fisher information and defines the potential on a flat circle bundle with quantized holonomy and half-period nodal jumps, resolving Wallstrom's objection; the second sets an elementary resolution quantum from the Bloch-sphere Fisher solid angle; and the third pairs Fisher localization energy with a Nyquist-Planck capacity bound in stochastic equations for closed flow and continuous measurement. On the reduced tangent space, the symplectic form, Fisher-Rao metric, and complex structure form a Kahler geometry inducing the Hermitian inner product, self-adjoint operators, and Heisenberg commutators. The axioms yield uncertainty bounds, the minimum resolution time, oscillator and hydrogen spectra, martingale Born-rule collapse, and the Lindblad equation, and extend to relativistic fields, half-integer spin, Pauli pressure, Compton-scale ultraviolet regularization, and ensemble no-signaling. QICM thus unifies unitary evolution and collapse in a single-world field dynamics without superluminal signaling, yielding testable bounds on compression times, readout horizons, and short-pulse thresholds in circuit-QED, optomechanics, and trapped ions.
Abstract
Quantum mechanics predicts experimental measurement statistics with high precision, yet the ontological status of the wave function and the dynamical mechanism of single-outcome state reduction remain unresolved. Prevailing quantum interpretations inherit two classical continuum idealizations: pointlike particle coordinates requiring unbounded localization precision and instantaneous state projections requiring infinite information-transfer bandwidth. Here we formulate Objective Phase-Space Quantum Information-Capacity Mechanics (QICM), representing a microscopic state on a configuration manifold by an objective probability density and a compact flow potential, extended across nodes as complex bundle sections in the Hamiltonian form domain. Calibrated by the Bloch-sphere quantum-Fisher solid angle, QICM rests on two axioms and explicit domain conditions. Axiom I requires finite Fisher information, quantized vortex holonomy, and half-period jumps across first-order real-phase nodal surfaces, addressing Wallstrom's objection. Axiom II pairs Fisher localization kinetic energy with a conditional Nyquist-Planck capacity bound for predeclared diffusive measurement ports and bath correlation scales in coupled Ito equations unifying closed transport and record-conditioned state reduction. On positive-density Sobolev charts (equipped with the regular L2-paired cotangent subbundle) and a noncompact relative-Gaussian Banach chart, the symplectic form, Fisher-Rao metric, and tangent rotation form a weak Kahler structure; given a projective Hilbert completion and unitary lift, this reconstructs self-adjoint generators, common-domain commutators, uncertainty bounds, resolution-time benchmarks, Schrodinger dynamics, and bound-state spectra. For open monitoring, we prove finite-exposure H1 regularity, global form- and operator-domain evolutions for bounded smooth monitors, asymptotic martingale Born-weight consistency, and linear Lindblad dynamics. Extensions establish a normal-ordered Gaussian Dirichlet form for free fields, Hopf spin geometry, variational Pauli gaps, and hydrogen fine structure; prove subluminal transport and 2mc^2 nodal saturation for a Compton-scale Dirac-Born-Infeld functional alongside its high-gradient negative curvature, loss of L2 lower semicontinuity, and convex comparison; and prove linear CPTP no-signaling and boundary capacity bounds. Finally, reachable-gain, Gaussian-compression, and coherent-pointer Holevo budgets yield falsifiable tests in circuit QED and optomechanics alongside a Poisson reference benchmark for trapped-ion readout.关键词
quantum foundations/information geometry/continuous quantum measurement/wave-function collapse/finite channel capacity.Key words
quantum foundations/information geometry/continuous quantum measurement/wave-function collapse/finite channel capacity.引用本文复制引用
Fangzhou Jin.Objective Phase-Space Quantum Information-Capacity Mechanics--An Information Ontology and Mathematical Framework for Quantum Mechanics[EB/OL].(2026-11-12)[2026-11-15].https://chinaxiv.org/abs/202610.00243.学科分类
物理学
