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arXiv:2512.15932

A Dough-Like Model for Understanding Double-Slit Phenomena

Ping-Rui Tsai, Tzay-Ming Hong

quant-phSubmitted Dec 17, 2025• Announced Dec 19, 2025• 0 citations• Revised Dec 25, 2025 (v2)
v1 · Dec 17, 2025v2 · Dec 25, 2025
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Abstract

The probabilistic interference fringes observed in the double slit experiment vividly demonstrate the quantum superposition principle, yet they also highlight a fundamental conceptual challenge: the relationship between a system before and after the measurement. According to Copenhagen interpretation, an unobserved quantum system evolves continuously based on the Schrodinger equation, whereas observation induces an instantaneous collapse of the wave function to an eigenstate. This contrast between continuous evolution and sudden collapse renders the single particle behavior particularly enigmatic, especially given that quantum mechanics itself is constructed upon the statistical behavior of ensembles rather than individual entities. In this study, we introduce a Double Slit Diffraction Surrogate Model DSM based on deep learning, designed to capture the mapping between wave functions and probability distributions. The DSM explores multiple potential propagation paths and adaptively selects optimal transmission channels using gradient descent, forming a backbone for the information through the network. By comparing the interpretability of paths and interference, we propose an intuitive physical analogy: the particle behaves like a stretchable dough, extending across both slits, reconnecting after transmission, allowing detachment before the barrier. Monte Carlo simulations confirm that this framework can naturally reproduce the characteristic interference and diffraction probability patterns. Our approach offers a novel, physically interpretable perspective on quantum superposition and measurement induced collapse. The dough analogy is expected to extend to other quantum phenomena. Finally, we provide a dough based picture, attempting to unify interference, entanglement, and tunneling as manifestations of the same underlying phenomenon.

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The probabilistic interference fringes observed in the double slit experiment vividly demonstrate the quantum superposition principle, yet they also highlight a fundamental conceptual challenge: the relationship between a system before and after the measurement. According to Copenhagen interpretation, an unobserved quantum system evolves continuously based on the Schrodinger equation, whereas observation induces an instantaneous collapse of the wave function to an eigenstate. This contrast between continuous evolution and sudden collapse renders the single particle behavior particularly enigmatic, especially given that quantum mechanics itself is constructed upon the statistical behavior of ensembles rather than individual entities. In this study, we introduce a Double Slit Diffraction Surrogate Model DSM based on deep learning, designed to capture the mapping between wave functions and probability distributions. The DSM explores multiple potential propagation paths and adaptively selects optimal transmission channels using gradient descent, forming a backbone for the information through the network. By comparing the interpretability of paths and interference, we propose an intuitive physical analogy: the particle behaves like a stretchable dough, extending across both slits, reconnecting after transmission, allowing detachment before the barrier. Monte Carlo simulations confirm that this framework can naturally reproduce the characteristic interference and diffraction probability patterns. Our approach offers a novel, physically interpretable perspective on quantum superposition and measurement induced collapse. The dough analogy is expected to extend to other quantum phenomena. Finally, we provide a dough based picture, attempting to unify interference, entanglement, and tunneling as manifestations of the same underlying phenomenon.
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The double-slit interference experiment serves as a fundamental experiment in quantum mechanics. Core theories including wave-particle duality, quantum superposition and measurement collapse are established on the basis of this phenomenon. The mainstream Copenhagen interpretation and Bohmian pilot-wave theory rely heavily on mathematical statistical fitting to interpret experimental outcomes, yet they fail to reveal the real physical evolution mechanism of photons at the microscale. Moreover, they inherently suffer from symmetry breaking, causal discontinuity and logical inconsistency. The symmetry-breaking analogy widely adopted in academic circles contains dimensional mismatch and conceptual substitution, representing a cognitive bias that places mathematical tools above physical mechanisms. Based on the symmetry principle of classical physics and the rule of continuous causal evolution, this paper systematically identifies the core defects of mainstream quantum interpretations and points out the paradigm limitation of quantum mechanics that prioritizes mathematical fitting over physical ontology. A spatial particle resonance propagation model is proposed. This model explains that photons are essentially the resonance manifestation of space particles. When resonance passes through double slits, the resonance body splits symmetrically, and then recombines after passing through the slits to form interference. Measurement will break the symmetry of resonance, resulting in the disappearance of interference fringes. This model maintains continuous causality and geometric symmetry, and provides a new physical mechanism explanation for quantum uncertainty and measurement effects in double-slit experiments.
The standard Copenhagen interpretation of quantum mechanics relies on a set of historically established, ad hoc postulates to describe particle-wave duality, measurement, and non-locality. In this paper, we propose a single foundational axiom that fully reproduces the standard mathematical formalism of quantum mechanics while eliminating the need for supplementary assumptions. From this singular postulate, we rigorously derive the fundamental origin of the wave function and the mathematical generator of the Schrödinger equation. Furthermore, we demonstrate via isomorfism that all seemingly inexplicable quantum phenomena—including wave-function collapse and quantum entanglement—are mathematically and conceptually reducible to the underlying dynamics of the double-slit experiment. By establishing a direct fundamental correlation between the double-slit interference mechanism and the Monty Hall phenomenon, we prove that these effects are distinct manifestations of the exact same principle. We framed the double-slit experiment as an interference of the space of possibilities affected by information and simetrys. Ultimately, by anchoring the existing quantum mathematical framework to this unique axiom, this work provides a coherent, paradox-free ontological foundation that resolves the interpretational crisis of quantum mechanics without altering its empirical predictive power.
Standard quantum mechanics interprets the double-slit experiment through the lens of wave-particle duality, asserting that entities propagate as probability waves and collapse into discrete particles solely upon observation. However, this interpretation evades direct physical and mechanical causality by relying on abstract mathematics and assumed vacuums. This paper introduces a rigorous fluid-dynamic framework, grounded in the principles of **Dark Primordialism**, which posits that the universe operates exclusively through concrete hydraulic interactions. By replacing the probabilistic wave function with a continuous, incompressible cosmic fluid medium, we demonstrate that interference patterns are not emergent from abstract "wave collapse," but are the mechanical result of pressure-field superposition. The core overlapping pressure mechanics driving this phenomenon is formulated as: P_overlap = Sf ⊕ Mr = Φ + ((∇ρ_solar * ∇ρ_lunar) / R_medium) This paper provides: 1. A mechanical explanation for the interference pattern based on pressure streamlines. 2. A deterministic resolution to the "observer effect" through physical measurement perturbation. 3. Clear, testable experimental predictions regarding medium density modification and resistance gradients.
This work extends the previous one-dimensional formulation of the double-slit problem to a two-dimensional framework within the Schrödinger equation, providing a more realistic representation of the physical configuration. The wavefunction is constructed through a spectral decomposition in terms of eigenstates, with a Gaussian distribution of initial energies. The temporal evolution of the system is explicitly analyzed, showing how interference patterns develop as a function of propagation time. In particular, the passage of electrons at different times is simulated, highlighting the progressive formation of fringes. A stochastic reconstruction of detection events is then introduced for the case of neutron beams, using physically realistic parameters, reproducing the emergence of the interference pattern from discrete particle-like impacts. The results show that both interference and particle-like behavior arise directly from the intrinsic mathematical structure of quantum mechanics, with no need for additional interpretative assumptions.
In this work the author presents a fully explicit mathematical derivation of interference-like structures in a simulated double-slit configuration within the framework of the Schrödinger equation. The mathematical structure of the slits is directly incorporated into the initial wavefunction, avoiding simplified assumptions such as plane waves. The slit is modeled as a spatial constraint, and the resulting state is expanded over the eigenbasis of the system. The time evolution of the wavefunction naturally leads to the formation of structured spatial patterns. A multiscale potential based on the Livio function is introduced and treated through an explicit matrix formulation, allowing a direct comparison between the free case and a system with structured perturbations. In addition, a stochastic reconstruction of the probability density is performed by sampling individual detection events according to the Born rule, simulating the arrival of particles at a finite rate and showing the progressive emergence of the pattern over time. The results indicate that the interference fringes emerge as an intrinsic consequence of the spectral decomposition of a spatially structured quantum state. The close qualitative agreement between the simulated patterns and those observed in physical experiments therefore suggests that wave–particle-like behavior is intrinsically contained in the mathematical framework of quantum mechanics.