Beyond the Wave: Modeling Quantum Reality with ‘Dough’

Author: Denis Avetisyan

A new computational model reimagines quantum particles as deformable, extended entities, offering a physically intuitive explanation for phenomena like the double-slit experiment.

Through a deep learning framework modeled after the double-slit experiment, the research reconstructs interference patterns by training a neural network to identify optimal particle paths-determined via gradient descent on latent path information from a digital simulation-and thus offers a novel computational approach to understanding wave-particle duality and the evolution of probability distributions as particles traverse varying distances from the slits.

Monte Carlo simulations of a ‘dough-like’ particle reveal nonlocal correlations and challenge traditional interpretations of wave function collapse.

The enduring puzzle of quantum mechanics lies in reconciling the probabilistic nature of particle behavior with our intuitive expectation of objective reality. This challenge is addressed in ‘A Dough-Like Model for Understanding Double-Slit Phenomena’, which proposes a novel framework utilizing deep learning and Monte Carlo simulations to model quantum phenomena. By envisioning particles as extended, deformable entities-akin to a stretchable dough-this work demonstrates a physically interpretable path through both slits, offering an alternative to wavefunction collapse and suggesting nonlocal correlations as a fundamental aspect of quantum behavior. Could this “dough model” provide a unifying perspective on seemingly disparate quantum effects like entanglement and tunneling, ultimately bridging the gap between quantum theory and classical intuition?

The Crumbling Foundations of Classical Reality

The foundations of classical physics, built on deterministic principles, begin to crumble when applied to the realm of the incredibly small. Observations reveal that particles, such as electrons and photons, don’t always behave as discrete entities, but instead exhibit properties of both waves and particles – a phenomenon known as wave-particle duality. This isn’t merely a limitation of measurement; the very nature of quantum entities defies classical categorization. Experiments like the double-slit experiment demonstrably show particles interfering with themselves, creating wave-like patterns even when sent through the apparatus individually. This suggests that a particle’s location and momentum aren’t fixed properties until measured, but exist as probabilities described by the $WaveFunction$. Consequently, the predictable trajectories and well-defined characteristics central to classical mechanics give way to a probabilistic description of reality at the quantum level, challenging long-held assumptions about the fundamental building blocks of the universe.

The behavior of quantum entities is described by the WaveFunction, a mathematical object that doesn’t dictate a particle’s definite properties but rather outlines the probability of finding it in a specific state. Unlike classical physics, where a particle possesses defined characteristics like position and momentum, the WaveFunction suggests these properties are only determined upon measurement. This isn’t simply a matter of lacking precise information; the probabilistic nature is inherent to the quantum realm, meaning a particle exists as a superposition of possibilities until observed. The square of the WaveFunction, $| \Psi |^2$, provides the probability density, effectively predicting the likelihood of finding the particle at a given point. This fundamentally challenges classical intuition, as it suggests reality at the quantum level isn’t composed of definite states but a spectrum of potential outcomes, collapsing into a single observable value only through the act of measurement.

The Heisenberg Uncertainty Principle establishes a foundational limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, can be known. It isn’t a statement about the inadequacy of measuring instruments; rather, it’s an inherent property of the quantum world. Mathematically expressed as $ \Delta x \Delta p \geq \frac{\hbar}{2}$, where $\Delta x$ represents the uncertainty in position, $\Delta p$ the uncertainty in momentum, and $\hbar$ is the reduced Planck constant, the principle dictates that the more precisely one property is determined, the less precisely the other can be known. This isn’t due to limitations in observation, but a fundamental fuzziness built into the nature of reality at the quantum scale, suggesting that particles don’t possess definite properties until measured, and the act of measurement itself inevitably disturbs the system, introducing uncertainty.

A dough-based model explains quantum phenomena by representing interference and diffraction as stretching, entanglement as filling distribution, and tunneling as branching strands that maintain influence even after reaching an exit.

Demonstrating the Wave-Like Nature of Reality

The double-slit experiment consistently demonstrates that particles, such as electrons or photons, exhibit wave-like behavior. When these particles are fired at a barrier with two slits, they do not create two distinct bands on a detection screen, as would be expected from discrete particles. Instead, an interference pattern of alternating high and low intensity bands is observed. This pattern arises from the superposition of waves passing through both slits simultaneously, even when particles are sent through the apparatus individually and at low rates. The resulting interference pattern is mathematically described by the equation $I = I_1 + I_2 + 2\sqrt{I_1I_2}\cos(\Delta \phi)$, where $I$ is the resultant intensity, and $\Delta \phi$ represents the phase difference between the waves from each slit.

Double-slit diffraction, observed in the Double-Slit Experiment, demonstrates that particles – even when sent individually – create an interference pattern characteristic of waves. This pattern arises because each particle appears to pass through both slits simultaneously, interfering with itself. Classical physics dictates that particles follow definite trajectories; however, the interference pattern suggests a probabilistic distribution of possible paths. The resulting pattern is described by the equation $I = I_0 \frac{\sin^2(\beta)}{\beta^2}$, where $I$ is the intensity of the diffracted wave, $I_0$ is the initial intensity, and $\beta$ is the angle of diffraction.

The Which-Way Experiment demonstrates that any attempt to observe which slit a particle traverses in a double-slit setup results in the destruction of the interference pattern. Specifically, introducing a detector near either slit to register particle passage forces the particle to “choose” a single path, eliminating the superposition state necessary for interference. This isn’t limited to visual observation; any interaction that correlates the particle’s path with a measurable quantity – even theoretically – is sufficient to collapse the $ \Psi $ function and revert the observed pattern to two distinct bands corresponding to particles passing through each slit independently. The resulting loss of interference is not due to physical disturbance of the particles, but rather the fundamental principle that the act of measurement itself alters the system being measured, a phenomenon known as the observer effect.

Interference disruption causes particles passing through one slit to exhibit trajectories that appear to be pulled toward the detector, while the corresponding trajectory from the other slit retracts, suggesting a non-local influence on particle behavior.

A Novel Framework: Beyond Point-Like Particles

The DoughModel posits a departure from the standard model’s treatment of fundamental particles as dimensionless point-like entities. Instead, it proposes that particles possess an extended, deformable structure analogous to a three-dimensional “dough” – a continuous field rather than discrete points. This framework fundamentally alters how particle interactions are conceived; collisions are not simply interactions at a single point but involve deformation and energy transfer within these extended structures. Consequently, properties traditionally considered intrinsic to a particle, such as mass and charge, are emergent characteristics resulting from the specific configuration and deformation of the underlying field.

A Monte Carlo simulation, consisting of 2000 iterations, is utilized to model particle behavior within the DoughModel framework. This computational approach allows for the investigation of particle dynamics as extended, deformable structures, rather than point-like entities. Results demonstrate the successful reproduction of the double-slit interference pattern, validating the model’s ability to simulate wave-particle duality. The simulation tracks particle trajectories as they interact with the double-slit apparatus, generating an interference pattern consistent with experimental observations. Statistical analysis of the 2000 iterations confirms the robustness of the reproduced pattern and provides quantitative data on particle distribution probabilities.

The DoughModel’s capacity to reproduce quantum phenomena like the double-slit experiment lends support to interpretations based on Nonlocal Hidden Variable Theory. This theory posits the existence of underlying, presently unobserved variables that determine particle behavior, challenging the completeness of standard quantum mechanics. Specifically, the model suggests these variables are not limited by locality-meaning they can instantaneously influence particles regardless of distance-thereby providing a potential mechanism for Quantum Entanglement. This contrasts with interpretations requiring instantaneous communication exceeding the speed of light, as the hidden variables provide a pre-established correlation.

Analysis of wavefunction behavior through double slits reveals that the Dynamic State Model (DSM) accurately predicts interference patterns-as demonstrated by the similarity between numerical simulations and DSM predictions-and allows ranking of different DSM models based on encoding error, ultimately illustrating possible particle trajectories.

Quantum Connections: Implications for Reality

Quantum entanglement, a cornerstone of quantum mechanics, reveals a peculiar connection between particles that persists even when separated by vast distances. Experiments leveraging Beta Barium Borate (BBO) crystals have repeatedly demonstrated this phenomenon; these crystals are used to generate pairs of entangled photons, where measuring the properties of one instantaneously influences the state of the other, irrespective of the separation. This isn’t a result of information traveling between the particles – which would be limited by the speed of light – but rather a fundamental correlation embedded in their shared quantum state. The observed correlations violate classical physics predictions, as described by Bell’s theorem, and have been rigorously tested, confirming the non-local nature of entanglement.

The ER=EPR hypothesis, a provocative idea in theoretical physics, posits a fundamental connection between quantum entanglement and the geometric concept of wormholes – also known as Einstein-Rosen bridges. This intriguing proposal suggests that entangled particles aren’t merely correlated, but are instead linked via microscopic shortcuts through spacetime. While traditional general relativity describes wormholes as theoretical tunnels connecting distant points in the universe, ER=EPR proposes that these connections might arise naturally from the quantum entanglement of particles, even at incredibly small scales.

Emerging theories posit that the elusive nature of Dark Matter may be fundamentally linked to the phenomenon of quantum entanglement. These models suggest Dark Matter isn’t simply “missing mass,” but rather a manifestation of vast, interconnected networks of entangled particles extending beyond observable space. This entanglement could create a sort of “scaffolding” for the universe, influencing galactic rotation curves and large-scale structure formation without directly interacting with electromagnetic radiation – thus explaining its invisibility.

Reinterpreting Quantum Mechanics: A Deterministic View

Unlike standard quantum mechanics, which describes particles as existing in a probabilistic haze of potential locations, Bohmian mechanics proposes that particles possess definite positions and follow precise trajectories. These trajectories aren’t random; instead, each particle is guided by the quantum wave function, often visualized as a ‘pilot wave’ influencing its motion. This framework posits that the wave function isn’t merely a mathematical tool for calculating probabilities, but a real, physical entity determining particle behavior.

Bohmian mechanics presents a distinctly deterministic view of quantum reality, a characteristic that immediately sets it apart from the probabilistic nature of the Copenhagen interpretation and addresses several of its long-standing conceptual challenges. Unlike standard quantum mechanics, where particle positions are described by probability waves and remain fundamentally uncertain until measured, Bohmian mechanics posits that particles possess definite, albeit hidden, positions at all times. These particles are guided by the quantum wave function, acting much like surfers riding a wave, and their trajectories are fully determined by initial conditions.

Continued investigation into alternative quantum frameworks, such as Bohmian mechanics and models like the DoughModel, promises to refine the current understanding of quantum phenomena beyond the probabilistic interpretations of standard quantum mechanics. These deterministic approaches, while still under development, offer the potential for a more intuitive grasp of quantum reality, potentially resolving long-standing conceptual challenges. Such advancements aren’t merely theoretical; a deeper, more complete understanding of quantum processes could unlock innovations in diverse technological fields, from materials science and computing – envisioning, for instance, more efficient quantum algorithms or the design of novel materials with tailored properties – to potentially revolutionizing sensor technology and secure communication methods.

The pursuit of quantum realism, as demonstrated by this ‘dough model’ and Monte Carlo simulations, echoes a fundamental principle of scientific inquiry. It isn’t about finding the right answer, but rigorously testing the boundaries of what is known. As Richard Feynman observed, “The first principle is that you must not fool yourself – and you are the easiest person to fool.” This work, by embracing the complexities of nonlocal hidden variables and extended particle models, doesn’t offer a definitive resolution to the double-slit paradox. Instead, it presents a framework for continually refining understanding through iterative error analysis – a process where the value lies not in the initial result, but in the accumulated knowledge of what doesn’t work. The study highlights the wisdom in knowing one’s margin of error, rather than clinging to elegant, yet potentially flawed, interpretations.

Where Do We Go From Here?

The ‘dough model’, if it can be rigorously extended, proposes a shift in perspective rather than a resolution of quantum mechanics’ inherent challenges. The simulations offer a compelling visualization, but visualization is not verification. The crucial test lies in predicting outcomes beyond the scope of current Monte Carlo implementations – specifically, systems exhibiting more complex entanglement or interactions. Should discrepancies arise between prediction and experiment, the model, not reality, will require adjustment.

A significant limitation remains the computational cost of simulating even moderately complex systems. If the universe truly operates on principles of extended, deformable entities with nonlocal correlations, it does so with an efficiency far exceeding current algorithmic capabilities. Perhaps the true value of this approach isn’t in providing a complete description, but in highlighting the areas where current computational methods fall short, directing attention towards more efficient algorithms-or a deeper understanding of the universe’s inherent computational limits.

The pursuit of ‘quantum realism’ through physically intuitive models is not without its risks. A pleasing analogy is a poor substitute for predictive power. However, an error in this line of inquiry isn’t necessarily a failure. It’s a message, indicating a flaw in the assumptions-or, more interestingly, a genuine anomaly demanding a new interpretation. The next step isn’t to prove the dough model correct, but to devise experiments that might definitively prove it wrong.

Original article: https://arxiv.org/pdf/2512.15932.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/