A Dough-Like Model for Understanding Double-Slit Phenomena

TL;DR

This work addresses the persistent puzzle of quantum superposition and measurement in the double-slit setup by introducing a Diffraction Surrogate Model (DSM) that learns to map wave packets to interference patterns. Through deep learning, interpretability analyses, and Monte Carlo simulations, the authors identify dominant latent transmission paths and formulate a dough-like physical analogy that envisions the quantum entity as an extended, deformable object traversing both slits and recombining. The approach yields interference and diffraction patterns consistent with TDSE simulations and offers a realist, nonlocal interpretation linking interference, entanglement, and tunneling under a single geometric/topological picture. While the dough model remains hypothetical, it provides a conceptual framework and a suite of computational tools for exploring intermediate quantum dynamics and potential experimental tests.

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.

Figures (9)

• Figure 1: Schematic layout of our approach to revisit the double-slit phenomenon via deep learning. (a) The interference framework is treated as an equivalent model, where input particles produce the output interference fringes. (b) The probability distribution results under the evolution of the input and output wavefunctions obtained via numerical simulation are presented in (c), with blue, purple, and red lines representing positions - just exiting, moderate and long distances from the slits. These results are then fed into the neural network depicted in (d). (e) By utilizing the latent path information within the DSM and applying gradient descent, the network selects the optimal paths for the interference probability distributions at different times, thereby providing possible insights for the theoretical representation.
• Figure 2: The color scheme follows that of Fig. 1(c). (a–c) correspond to the probability distributions of the three colored lines in Fig. 1(c), with each subplot containing three samples representing the interference when the wavefunction enters the slit slightly left, centered, or slightly right. The black line shows the predicted outcome by the DSM. (d) shows the similarity between the probability distributions from the numerical simulation and the DSM predictions. (e) compares the RMSE of the encoding models of three DSM models under different EL values. (f) ranks the models in (e) from smallest to largest RMSE. (g) illustrates the possible dynamic processes of particles passing through the double slits based on the ranking in (f), where the red and blue points represent NL1 and NL2.
• Figure 3: (a) The double-slit result was obtained from 3,200 simulation samples and with resolution of 165$\times$76. The answers (ANS) represents the ground truth under numerical simulation, also one of the sample input to the VAE. whiles, the reconstructed image (Res) denotes the reconstructed results after the decoder, and “Pipeline” refers to the images reconstructed by the VAE decoder after all EL values in the DSM are pipeline-transformed into the VAE latent space. (b$\sim$d) The clustering results of Res obtained by t-SNE with k $=$ 4. Note that (b) represents the two interference terms, while (c) and (d) correspond to non-interference information output from the two slits. (e) The representative information obtained by averaging (b) and (c, d) from left and right and taking the maximum value. (f) The DSM-based hypothesis of a slit convergence point for NL2. We expect this point to be a node with the highest closeness centrality and the fewest quantity. The blue line shows the maximum closeness centrality (MC), the orange line indicates the number of nodes with that MC, $r$ represents the minimum distance connecting different nodes, and the black line indicates the optimal $r$. (g) The network modeling results under the optimal $r$. The color bar is for different degrees of centrality, and the red-circle indicates the positions of MC.
• Figure 4: Learning curves for three DSMs and VAE where the blue/orange lines indicate the training/validarion curvse.
• Figure 5: (a) The spatial distribution of the arrival positions on the screen after 2000 inputs. (b) The probability distribution is obtained by drawing histogram with a bin size of 4 units, where the red curve is to highlight the interference pattern. (c) Trajectories from MP to the screen. (d, e) Bifurcation results near MP and along two selected stripes of trajectories.