Abstract Two of the most deeply entrenched postulates of quantum mechanics—complementarity and wave function collapse—have been regarded as irreducible principles since their formulation in 1928 and 1932, respectively. This paper provides a first-principles resolution of both postulates through a single physical mechanism. A particle is a Q-ball—a stable localized non-topological soliton of a complex scalar field under a fixed U(1) conserved charge constraint, stabilized by the joint action of Derrick's theorem and Noether's theorem. A wave is the Yukawa tail of the Q-ball—the unique decaying solution of the massive scalar field radial equation under natural boundary conditions. Complementarity is replaced by the core-tail unified entity. Collapse is replaced by the physical process of conserved charge transfer: measurement is the gradient-flow-driven transfer of conserved charge from the Q-ball tail space to the detector local state, with the determinism of single detection events guaranteed by the exclusivity mechanism arising from the integer quantization of the conserved charge. Conserved charge transfer requires a finite time τ_c—a core prediction confirmed by recent data across five independent experimental domains: molecular charge transfer (CF₃I⁺, 1.46±0.41 fs), hydrated ion charge delocalization (20–hundreds of attoseconds), superconducting qubit quantum jumps (∼4 μs), entanglement formation (232 as), and solid-state interfacial charge transfer (300±200 as). Under the same postulate chain, the Q-ball is the unique stable field configuration capable of producing wave-particle duality. The two most fundamental puzzles of quantum mechanics since its inception—complementarity and collapse—are simultaneously resolved by a single physical process within this mechanism. ORCID: 0009-0007-1999-0293 Email: 1352533302@qq.com phone:+86 18278275520(china)
Abstract Two of the most deeply entrenched postulates of quantum mechanics—complementarity and wave function collapse—have been regarded as irreducible principles since their formulation in 1928 and 1932, respectively. This paper provides a first-principles resolution of both postulates through a single physical mechanism. A particle is a Q-ball—a stable localized non-topological soliton of a complex scalar field under a fixed U(1) conserved charge constraint, stabilized by the joint action of Derrick's theorem and Noether's theorem. A wave is the Yukawa tail of the Q-ball—the unique decaying solution of the massive scalar field radial equation under natural boundary conditions. Complementarity is replaced by the core-tail unified entity. Collapse is replaced by the physical process of conserved charge transfer: measurement is the gradient-flow-driven transfer of conserved charge from the Q-ball tail space to the detector local state, with the determinism of single detection events guaranteed by the exclusivity mechanism arising from the integer quantization of the conserved charge. Conserved charge transfer requires a finite time τ_c—a core prediction confirmed by recent data across five independent experimental domains: molecular charge transfer (CF₃I⁺, 1.46±0.41 fs), hydrated ion charge delocalization (20–hundreds of attoseconds), superconducting qubit quantum jumps (∼4 μs), entanglement formation (232 as), and solid-state interfacial charge transfer (300±200 as). Under the same postulate chain, the Q-ball is the unique stable field configuration capable of producing wave-particle duality. The two most fundamental puzzles of quantum mechanics since its inception—complementarity and collapse—are simultaneously resolved by a single physical process within this mechanism. ORCID: 0009-0007-1999-0293 Email: 1352533302@qq.com phone:+86 18278275520(china)
A deterministic quantum mechanics theory is presented. The proposed theory is shown to be consistent with the current mainstream statistical quantum theory as well as with classical physics. It produces solutions that demonstrate that causality, physical reality, and determinism are restored and can explain in simple form concerns raised by results from the current mainstream statistical quantum theory. The meaning of particle-wave duality and complementarity, the possibility of a particle, like an electron, crossing through the nucleus as it does when the angular momentum of the electron is zero at the ground state of the hydrogen atom, the possibility of a point-size particle to have an “intrinsic spin,” the possibility of “quantum jumps” as the electron transitions instantaneously from one stable orbital to another without passing through the space in between the orbitals and does that at irregular time intervals. The natural collapse of the wave function as part of the solution is a result that emerges from the proposed deterministic quantum mechanics theory. The phenomenon of entanglement is also discussed in the context that information transfer between entangled “particles” does not occur in a superluminal fashion and is not a “spooky action at a distance” but rather the local measurement of global property. A linear stability method presents actual analytical solutions consistent with current mainstream quantum theory and classical physics. The Bohr-Schrödinger energy levels leading to the experimentally confirmed spectral lines and the fine structure constant emerge from an approximate solution to these equations.
This paper derives measurement and identical principles, then makes the two principles into measurement and identical theorems of quantum mechanics, plus the three theorems derived earlier, we deduce the axiom system of current quantum mechanics, the general quantum theory no axiom presumptions not only solves the crisis to understand in current quantum mechanics, but also obtains new discoveries, e.g., discovers the velocities of quantum collapse and entanglement are instantaneously infinitely large. We deduce the general Schrȍdinger equation of any n particles from two aspects, and the wave function not only has particle properties of the complex square root state vector of the classical probability density of any n particles, but also has the plane wave properties of any n particles. Thus, the current crisis of the dispute about the origin of wave- particle duality of any n microscopic particles is solved. We display the classical locality and quantum non-locality for any n particle system, show entanglement origins, and discover not only any n-particle wave function system has the original, superposition and across entanglements, but also the entanglements are of interactions preserving conservation or correlation, three kinds of entanglements directly give lots of entanglement sources. This paper discovers, one of two pillars of modern physics, quantum mechanics of any n particle system is a generalization ( mechanics ) theory of the complex square root ( of real density function ) of classical statistical mechanics, any n particle system’s quantum mechanics of being just a generalization theory of the complex square root of classical statistical mechanics is both a revolutionary discovery and key new physics, which are influencing people’s philosophical thinking for modern physics, solve all the crisises in current quantum theories, quantum information and so on, and make quantum theory have scientific solid foundations checked, no basic axiom presumption and no all quantum strange incomprehensible properties, because classical statistical mechanics and its complex square root have scientific solid foundations checked. Thus, all current studies on various entanglements and their uses to quantum computer, quantum information and so on must be further updated and classified by the new entanglements. This and our early papers derive quantum physics, solve all crisises of basses of quantum mechanics, e.g., wave-particle duality & the first quantization origins, quantum nonlocality, entanglement origins & classifications, wave collapse and so on.Key words: quantum mechanics, operator, basic presumptions, wave-particle duality, principle of measurement, identical principle, superposition principle of states, entanglement origin, quantum communication, wave collapse, classical statistical mechanics, classical mechanics
This paper presents a finite, regulator-based resolution of wave–particle duality, showing that quantum duality is not a fundamental paradox but a natural consequence of domain separation. Within the Dual Regulator Framework, wave behavior is shown to arise exclusively in the virtual domain (momentum space, off-shell propagation), regulated by the finite invariant Λφ=ln(φ2),\Lambda_\varphi = \ln(\varphi^2),Λφ=ln(φ2), while particle behavior arises exclusively in the real domain (position space, on-shell detection), regulated by the Resolution Gap RG=ln(φ)/ln(π).\mathrm{RG} = \ln(\varphi)/\ln(\pi).RG=ln(φ)/ln(π). The double-slit experiment is reinterpreted as a virtual-domain interference process followed by a real-domain localization event. Which-path detection is shown to force a premature virtual-to-real transition, preventing interference from forming. Partial which-path information produces a quantitative reduction in visibility governed by a finite exponential law. The framework yields explicit, testable predictions with zero adjustable parameters, including: a φ-harmonic correction to interference fringe spacing, a sharp detector-coupling threshold for which-path information, an exact functional form for visibility–distinguishability relations, and scale-dependent corrections for matter-wave interferometry (electrons, neutrons, molecules). All results derive solely from the Trinity constants {π, φ, e}. Complementarity is shown to be a consequence of domain incompatibility, not a primitive principle. Wave–particle duality dissolves into a physically interpretable, observer-independent mechanism. This paper forms Paper II in a planned sequence addressing foundational inconsistencies in quantum field theory, following the finite resolution of the measurement problem.
Field-Theoretic Explanation of Wave-Particle Duality—Unification of Particle Locality and the Wave Nature of the Perturbation Field This paper provides a physical explanation of the most central puzzle in quantum mechanics—wave-particle duality—without relying on "probability-amplitude collapse" or "nonlocal entanglement." This theory divides all matter in the universe into Nie-matter entities (massive, Staticity) and Ji-matter entities (massless, Dynamicity), and maintains that quantum objects (electrons, neutrons, etc.) are always localized Nie-matter entity particles. Their "wave behavior" originates from the particle's local perturbation of the Ji-matter field that already fills space during motion—the perturbation propagates in the form of a wave, produces an interference field when passing through the double slits, and the interference field in turn guides the particle's landing position. The particle always passes through only one slit, while the field passes through both slits simultaneously; interference is the behavior of the field, not the behavior of the particle. This mechanism naturally explains double-slit interference, the coexistence of neutron collisions and wave behavior, the disturbance of interference fringes by observation devices, and the variation of interference contrast with source offset and slit spacing. This paper further gives three falsifiable predictions: P6-1 (a decisive distinction between device field-strength disturbance and which-path information disturbance), P6-2A (the disturbance effect varies continuously with field strength), and P6-2B (an argument for the explanatory power of double-slit interference contrast—naturally derived from one mechanism vs. jointly explained by four independent concepts). Compared with mainstream theory, this theory does not need "wavefunction collapse," does not need "nonlocality," and does not need "many worlds"—it only needs to acknowledge: particles are localized, the field fills space, and the motion of particles is guided by the local field gradient.
This work derives the fundamental framework of quantum mechanics intrinsically from the first-principle axioms of UD duality theory. Starting from the inherent binary expansive–condensative attributes of the UD ontology, four fundamental physical fields are naturally decomposed by spontaneous symmetry breaking across spatial and material existential domains. A two-component complex spinor structure is uniquely constructed, and the imaginary unit i is proven to be not merely a mathematical convention but a structurally necessary ingredient required by both the compact SU(2) symmetry and the orthogonal inter-containment of U and D attributes. Within the flat spacetime limit of the UD gravitational action, a system of coupled Klein–Gordon field equations is established, governed by a single self-consistent fundamental mass scale m₀=1/(2πe^π) with no adjustable free parameters. The coupling constant is determined analytically from the UD vacuum equilibrium background values and the U↔D duality symmetry. Through explicit construction of four-component Dirac spinors and auxiliary field decomposition, the on-shell equivalence between the UD coupled field equations and the free Dirac equation is rigorously demonstrated. The non-relativistic limit further recovers the Pauli equation and the Schrödinger equation sequentially, reconstructing the core dynamical equations of quantum mechanics from a unified foundational origin. Global U(1) phase invariance of the UD action is verified via total-derivative decomposition, yielding the standard Noether conserved current. The Born probability interpretation is deduced directly from the global normalization axiom by isolating localized laboratory-scale excitations from the cosmic background, eliminating the need for independent quantum postulates. Based on the intrinsic properties of the UD field components, a self-consistent ontological interpretation is provided for wave–particle duality, double-slit interference, and the quantum measurement problem. In this framework, the measurement problem is dissolved rather than solved: no collapse postulate is required, and determinism is restored at the ontological level. The theory naturally implies that the continuous D_U field permits quantum superposition, while condensed D_D intrinsic entities possess definite classicality without physical particle-state superposition. Three testable theoretical predictions are presented, establishing falsifiable physical consequences of the UD quantum formulation. This paper completes the intrinsic derivation of the foundational structure of quantum mechanics from UD theory. Together with the previously derived general relativity framework, it realizes the homologous unification of gravity and quantum mechanics within a single self-contained axiomatic system.