The traditional path integral formulation of quantum mechanics relies on complex probability amplitudes and the principle of least action, which has conceptual ambiguities in interpreting microphysical mechanisms — serving merely as effective mathematical statistical tools. Based on the Unified Cosmic Mechanics Evolution Theory — where the momentum unit (m₀·c) is the only physical reality, the field is an interaction protocol, and the particle is a momentum encapsulation structure — this paper reconstructs the mathematical description of multi-slit experiments. The new formulation replaces the complex path integral with a dual-integral system: the self-integral describes momentum unit self-evolution along their intrinsic direction, endowing linear motion; the interaction integral describes momentum flow interaction with the slit wall's electromagnetic field, realizing multi-path distribution and direction deflection. These two integrals together constitute the momentum flow distribution integral, interpreting "interference" as the superposition of real momentum flows dominated by the interaction integral. Key insight: Just as a stone falling from a height depends on the perceptual cross-section 1/(4πr²) for its integral result, all forces should be similarly understood — their underlying dynamics must be reduced to the perceptual cross-section mechanism. The interaction integral follows this logic: the relativistic mass-energy equation is a space-time state shaping equation, where the emergent space-time integral reflects Pythagorean conservation (Lorentz covariance); general relativistic integrals involve variable space-time redundancy under field strength; special relativistic integrals arise from perceptual space-time window compression during motion. For micro-particles in multi-slits, this paper primarily adopts the interaction integral mechanisms of special relativity, electromagnetism, and photoelectricity. This framework remains consistent with existing experimental phenomena and proposes testable predictions including slit thickness-dependent deflection and multi-slit interference fringe modulation.
The traditional path integral formulation of quantum mechanics relies on complex probability amplitudes and the principle of least action, which has conceptual ambiguities in interpreting microphysical mechanisms — serving merely as effective mathematical statistical tools. Based on the Unified Cosmic Mechanics Evolution Theory — where the momentum unit (m₀·c) is the only physical reality, the field is an interaction protocol, and the particle is a momentum encapsulation structure — this paper reconstructs the mathematical description of multi-slit experiments. The new formulation replaces the complex path integral with a dual-integral system: the self-integral describes momentum unit self-evolution along their intrinsic direction, endowing linear motion; the interaction integral describes momentum flow interaction with the slit wall's electromagnetic field, realizing multi-path distribution and direction deflection. These two integrals together constitute the momentum flow distribution integral, interpreting "interference" as the superposition of real momentum flows dominated by the interaction integral. Key insight: Just as a stone falling from a height depends on the perceptual cross-section 1/(4πr²) for its integral result, all forces should be similarly understood — their underlying dynamics must be reduced to the perceptual cross-section mechanism. The interaction integral follows this logic: the relativistic mass-energy equation is a space-time state shaping equation, where the emergent space-time integral reflects Pythagorean conservation (Lorentz covariance); general relativistic integrals involve variable space-time redundancy under field strength; special relativistic integrals arise from perceptual space-time window compression during motion. For micro-particles in multi-slits, this paper primarily adopts the interaction integral mechanisms of special relativity, electromagnetism, and photoelectricity. This framework remains consistent with existing experimental phenomena and proposes testable predictions including slit thickness-dependent deflection and multi-slit interference fringe modulation.
For a long time, classical mechanics, relativity, and quantum mechanics have been self-consistent within their respective fields, but their underlying logic remains ununified. This has led to the reality paradox of micro-particles "being in different spacetimes simultaneously" and unclear applicability boundaries among the three theories. Based on the Unified Cosmic Mechanics Evolution Theory, this paper concludes that the universe is a relational state evolution system, and the only physical reality is the momentum unit (m₀c), including the mass carrier m₀, the driving rate c, and vector superposition ability, with interaction strength determined by the perceptual cross-section. All particles are encapsulated by momentum units: fermions in a spherically symmetric vector superposition state, photons in a co-directional evolution state. Quantum entanglement is stable cooperative evolution between multi-layer encapsulations. The field is a set of rules constraining encapsulation, perception, and interaction. Particles can present three states: collapsed, diffused, and fluid. Thus, the probabilistic wave evolution of particles is not a mathematical fiction, but a deterministic dynamic process jointly determined by internal momentum flow and external causal interaction. The prediction of wave behavior is essentially the unified description of total momentum flow, internal self-constraint, and external causal interaction, consistent with the research direction of realist quantum mechanics.
Traditional quantum field theory, which regards fields as spacetime-pervading physical entities and particles as their excitations, faces three dilemmas: lower organizational efficiency than the "1/4πr² perceptual cross-section" collinear interaction, inability to explain force characteristics (e.g., vector superposition, action-at-a-distance) conflicting with quantum entanglement, and unclear field dynamic origin and coupling constant source. It also has redundant driving forces, using force, energy, momentum, etc., alternately, violating logical consistency and reflecting ununified underlying dynamic principles. Based on the information dynamics evolution theory framework, this paper holds that particles and their internal structures are the only physical entities, fields are evolution rule sets, and the universe is a relational state evolution system consisting of m₀, c, and R. Core conclusions: (1) Momentum units are the only underlying resources, c is the only dynamic driving force, with energy = momentum = force = m·c in eigenstate; (2)Particles form via multi-momentum unit cooperative encapsulation; (3) Fields are constraint rule sets, and the four fundamental forces are particle interaction protocols; (4) Quantum uncertainty is a macroscopic observation aliasing effect, with underlying strict causal determinism. This paper establishes core mechanisms such as momentum topological coding, reveals the underlying coding logic of basic physical quantities, and provides a complete framework for unifying quantum mechanics and relativity and reconstructing deterministic quantum theory.
Traditional quantum mechanics interprets quantum entanglement as non-local statistical correlation, but fails to answer the underlying physical mechanism of entanglement: what "maintains" the correlation between entangled particles? Why can this correlation transcend spatial distance? Based on the framework of the Unified Cosmic Mechanics Evolution Theory, this paper proposes that the essence of quantum entanglement is an inline perception protocol that maintains the coordinated evolution of multiple momentum units. The core conclusions include: (1) The core role of quantum entanglement is to support the conservation of carrier angular momentum, which is the fundamental premise for particles to realize spin and macroscopic rotation — a single momentum unit cannot rotate, and "rotatability" is an emergent property of the entanglement protocol. (2) A single elementary particle has three coordinated evolution forms (collapsed, diffused, fluid), and the state transition depends on the internal structure and coordinated evolution ability endowed by the quantum entanglement protocol. (3) The multi-particle entangled state can be regarded as "single-particle coordinated evolution" at the macroscopic level, which originates from the multi-layer encapsulation characteristics of momentum units m₀·c. (4) The core mechanism for quantum entanglement to realize superluminal action is perceptual angle interlocking — establishing a logical correlation independent of geometric distance through an inline protocol, rather than trans-spatial propagation. (5) Both instantaneous force interaction and quantum tunneling can be reconstructed as local potential space momentum borrowing and returning state transition processes, without relying on propagator flight. This paper further argues that quantum entanglement, elementary force interaction, and quantum tunneling are not isolated phenomena, but three manifestations of the same set of momentum topological coding and potential space borrowing and returning mechanisms under different boundary conditions — entanglement is a static protocol maintaining structural stability, force is a dynamic state update after protocol triggering, and tunneling is a potential space topological transition guided by the protocol. This framework reduces quantum mechanics to a deterministic information dynamics evolution process based on protocol rules, providing a new ontological support for understanding the causality of the microcosm.
Starting from three fundamental duality relations (time-energy, space-momentum, angle-angular momentum), we establish an integral equation of quantum action and its dual counterpart. This integral equation directly links the evolution of the wave function to the accumulated action of spacetime and rotational degrees of freedom, forming a unified framework for quantum theory. Through semiclassical expansion, local approximation, and relativistic covariance, we rigorously derive the Schr\"odinger equation, Klein-Gordon equation, Dirac equation, Heisenberg equation, Schwinger-Dyson equation, Feynman path integral, Yang-Mills equations, Einstein field equations, and the Friedmann and Schwarzschild solutions. The framework also yields the kinematic effects of special relativity (time dilation, length contraction, mass-energy equivalence) as consequences of the duality structure. Moreover, the nonlocal kernel in the integral equation gives an exponential damping factor in momentum space, providing an intrinsic regularization mechanism for ultraviolet divergences. We extend the framework to quantum electrodynamics (QED), quantum chromodynamics (QCD), the electroweak theory, the full Standard Model, and quantum gravity, obtaining dual formulations for each. From the integral equation and its dual, we automatically derive quantization conditions for energy, momentum, angular momentum, and their duals, and propose experimental schemes to observe these discrete effects. All derivations are complete and rigorous, based on the same integral equation, providing a possible answer to Dirac's criticism that "quantum electrodynamics lacks a fundamental equation" and opening a new path toward a unified theory.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.
A mathematical model for the slit experiments in the heart of quantum mechanics is developed to gain insight into quantum theory. The proposed system-theoretical model is entirely based on commutative mathematics, i.e. convolution, and integral transformations, and starts with spacetime functions with inherent energy-based cause and effect relations of the state-function Ѱ in the complex Hilbert space. The benefits of his approach are as 1-Invariance in time reversal. 2-Deterministic result functions in the model in line with the outcome of slit experiments. 3- Separation of causality and cross-correlations of attained states. 4- Disappearance of a posteriori probability of quantum states. 5- Quantum a priori fixed states after causality interactions have ended, (even) when quanta are (light-years) separated. The model predicts the patterns in the experiments with mathematical functions of the energy distributions. The quantum mechanical counterpart description of the physical reality of slit experiments thus may be considered complete in A. Einstein’s definition. The patterns in double slit experiments are found to be an effect of energy (amplitude-) modulation. An equivalent double-slit pattern can be retrieved from an input modulated 1-slit experiment excluding interference interpretations. The system-theoretical model uses generic properties of quanta and evolves into determinism in quantum mechanics slit experiments. The mathematics in the model handles beables by treatment of momentum p in system theoretical I/O relations of the transformed functions and allows the proposed description by the avoidance of a direct addressing of the individual quanta through variables. The following method yields exact, non-probabilistic results.