Beyond Quantum Mystery: A Deterministic Root

Author: Denis Avetisyan

New research suggests that the bizarre behavior of the quantum world may not be fundamentally probabilistic, but rather an emergent property of simple, deterministic interactions.

This review proposes a derivation of the Schrödinger equation from Newtonian mechanics, explaining quantum phenomena like quantization and interference as arising from microscopic particle dynamics.

Despite the remarkable success of quantum mechanics, a fully intuitive understanding of its foundations remains elusive. This paper, ‘Microscopic theory of quantum physics’, presents a deterministic framework where quantum phenomena emerge from purely Newtonian particle interactions, offering a novel perspective on the quantum realm. By modeling particle dynamics at a fundamental level, we derive quantized energy spectra, reproduce interference patterns, and ultimately, obtain the Schrödinger equation itself. Could this approach bridge the gap between classical and quantum mechanics, revealing a deeper, more accessible foundation for quantum theory?

Beyond Quantum Mystery: The Classical Roots of Reality

Despite its extraordinary predictive power, quantum mechanics frequently clashes with the ingrained human expectation of a deterministic universe. Everyday experience dictates that objects possess definite properties and follow predictable trajectories, yet quantum theory posits inherent probabilistic behavior at the most fundamental levels of reality. This conceptual gap isn’t necessarily a flaw in the theory, but rather a reflection of the limitations of human intuition when applied to scales vastly different from those encountered in daily life. The success of quantum mechanics in explaining experimental results doesn’t diminish the feeling that its principles represent a departure from the classical, intuitively understandable world, prompting ongoing efforts to bridge the gap between the quantum realm and our macroscopic perception of reality.

The Double Slit Experiment dramatically illustrates the perplexing wave-particle duality at the heart of quantum mechanics. When particles, such as electrons, are fired at a barrier containing two slits, they don’t behave as expected from classical physics. Instead of forming two distinct bands corresponding to the slits, an interference pattern emerges – a signature of wave behavior. This suggests that particles can simultaneously act as both localized entities and spread-out waves, defying easy categorization. The experiment isn’t merely a quirk of electrons; it’s been demonstrated with increasingly large molecules, pushing the boundaries of what constitutes a ‘particle’ and fundamentally questioning the nature of reality at its smallest scales. It highlights that matter and energy aren’t simply one or the other, but exhibit properties of both, contingent on how they are observed and measured, challenging deeply ingrained assumptions about the physical world.

The persistent challenge in modern physics lies in bridging the gap between the probabilistic nature of quantum mechanics and the deterministic world perceived through classical physics. Researchers are actively investigating whether quantum phenomena, such as superposition and entanglement, might emerge from underlying classical principles, potentially governed by hidden variables or yet-undiscovered interactions. This approach doesn’t necessarily negate the accuracy of quantum predictions, but rather seeks a more intuitive, foundational framework where quantum behavior isn’t an inherent property of matter, but a consequence of complex, deterministic processes occurring at a deeper level. Success in this endeavor would not only offer a more complete understanding of the universe, but also potentially resolve long-standing conceptual difficulties and pave the way for novel technological applications rooted in a classically-grounded quantum theory.

Current investigations propose that a comprehensive understanding of particle behavior may reside not within the particles themselves, but in the nature of their interactions. Rather than accepting quantum phenomena as fundamentally probabilistic, researchers are exploring models where interactions-forces, collisions, and exchanges of energy-are the primary determinants of observed behavior. This approach suggests that what appears as quantum uncertainty might, in fact, be a consequence of incomplete knowledge regarding these interactions at a foundational level. By meticulously re-examining how particles influence one another, and developing a more precise description of these forces, it may be possible to construct a deterministic framework that accurately reproduces all observed quantum effects, potentially revealing a more intuitive and accessible basis for the seemingly bizarre world of quantum mechanics. This line of inquiry doesn’t seek to disprove quantum mechanics, but rather to provide a deeper, classical understanding of why it works so effectively.

Deterministic Interactions: The Foundation of Quantum Behavior

The proposed Deterministic Particle Interaction Model posits that all observed quantum behavior is a consequence of deterministic interactions between particles, fundamentally adhering to $F=ma$, Newton’s Second Law of Motion. This framework rejects inherent probabilistic or random elements at the particle level, instead suggesting that seemingly stochastic outcomes arise from the complex interplay of forces and initial conditions. The model aims to explain quantum phenomena not as fundamentally probabilistic, but as deterministic processes that may appear random due to incomplete information or computational limitations in predicting their evolution. All particle interactions are thus governed by definable forces and predictable trajectories, eliminating the need for wave function collapse or other non-deterministic postulates.

The proposed model incorporates Dark Particles as the fundamental mediators of all interactions between particles, offering a deterministic explanation for phenomena historically described by quantum uncertainty. These particles, while not directly observable through current methods, exert forces on standard model particles, influencing their trajectories and contributing to behaviors such as wave-particle duality and quantum entanglement. The interaction strength and characteristics of these Dark Particles determine the observed forces, and their probabilistic distribution accounts for what is currently interpreted as inherent quantum uncertainty. This mechanism avoids the need for non-deterministic axioms by grounding apparent randomness in the complex, yet fully defined, interactions between particles via these mediating Dark Particles.

The Deterministic Particle Interaction Model defines all particle behavior through Interaction Potentials, which are forces dictating the interactions between particles. These potentials inherit the mathematical characteristics of Conservative Forces, meaning the work done by the force is path-independent and related solely to changes in potential energy. Consequently, the total mechanical energy-the sum of kinetic and potential energy-remains constant throughout the interaction, allowing for predictable trajectories determined by $F = – \nabla U$, where $F$ represents the force, and $U$ is the potential energy. This reliance on conservative forces and well-defined potentials is fundamental to the model’s deterministic nature, eliminating probabilistic elements from particle interactions.

The proposed model prioritizes interactions as the fundamental basis for understanding quantum phenomena, shifting away from interpretations reliant on inherent probabilistic behavior. This approach seeks to establish a causally consistent framework where observed quantum effects are not random, but rather deterministic outcomes of specific interactions between particles. By defining these interactions through quantifiable forces – specifically, Interaction Potentials inheriting the principles of Conservative Force – the model aims to eliminate the need for probabilistic axioms. Consequently, phenomena traditionally described using wave functions or uncertainty principles are reinterpreted as consequences of the complex interplay of these deterministic interactions, offering a potentially more intuitive and predictable explanation of quantum behavior.

From Classical Mechanics to Quantum Prediction: A Direct Correspondence

The Hamiltonian formulation of mechanics, centered on the principle of least action, offers a pathway to quantum prediction by reformulating classical dynamics in terms of energy, $H$, rather than forces. The Action, denoted by $S$, is defined as the time integral of the Lagrangian, $L = T – V$, representing the difference between kinetic and potential energy. Minimizing the Action yields the equations of motion. This formalism is crucial because the Action appears directly in the quantum mechanical path integral formulation, where probabilities are calculated by summing over all possible paths weighted by $e^{iS/\hbar}$. Consequently, the classical limit of quantum mechanics is recovered when $\hbar$ approaches zero, and the stationary phase approximation applied to the path integral reproduces the classical Action principle, establishing a direct correspondence between classical and quantum descriptions of physical systems.

The Hamilton-Jacobi Equation, a formulation within classical mechanics, serves as a direct pathway to the Schrödinger Equation when certain approximations are applied. Specifically, by treating the Action, $S$, as a function of position and time and employing a semi-classical approximation-expanding $S$ in terms of $\hbar$ and retaining only the leading-order terms-the Hamilton-Jacobi Equation can be transformed into the time-dependent Schrödinger Equation. This derivation highlights that quantum mechanics isn’t a fundamentally different theory, but rather a specific case of classical mechanics when Planck’s constant, $\hbar$, is non-zero. The equivalence is most apparent in the limit of large quantum numbers or when considering systems where classical trajectories are well-defined, demonstrating a deterministic basis for quantum predictions.

The Wave Function, denoted as $\Psi$, completely describes the quantum state of a particle, encapsulating all physically relevant information. Its squared magnitude, $|\Psi|^2$, represents the probability density of finding the particle at a specific location and time. By solving the time-dependent Schrödinger equation with an appropriate initial Wave Function, one can determine the evolution of the particle’s state and thus predict the probabilities of various measurement outcomes. This predictive capability extends to calculating expectation values for observables such as position, momentum, and energy, offering a comprehensive description of the particle’s behavior within the framework of quantum mechanics.

Analysis of the particle in a box model, derived from the Hamiltonian framework, yields discrete energy levels consistent with standard quantum mechanical predictions. Calculations indicate periods of oscillation for the first three energy states are T₁ = 27.5 picoseconds, T₂ = 6.88 picoseconds, and T₃ = 3.05 picoseconds. These values are determined by solving the Hamilton-Jacobi equation for the confined potential and demonstrate a direct correspondence between the classically-derived model and the observed quantization of energy within the box.

Reconciling Intuition and Observation: A More Grounded Perspective

A new theoretical framework proposes a departure from conventional quantum interpretations, aiming to address long-standing conceptual paradoxes and cultivate a more intuitive grasp of quantum mechanics. This model doesn’t necessitate abandoning established quantum mathematics, but rather reconsiders the underlying reality it describes. Rather than accepting inherent randomness or wave-particle duality as fundamental properties, it posits a deterministic system governed by interactions potentially beyond current measurement capabilities. This approach suggests that the seemingly bizarre behaviors observed in the quantum realm – such as superposition and entanglement – may arise not from the nature of reality itself, but from the limitations of how those realities are perceived and modeled. By offering a potentially more coherent narrative, this model invites a re-evaluation of core quantum principles and opens avenues for exploring the boundary between the quantum and classical worlds with renewed clarity.

This model proposes a shift in perspective, suggesting quantum behavior isn’t inherently probabilistic, but arises from deterministic interactions operating at a fundamental level. By focusing on these underlying mechanisms, researchers can begin to map the boundaries where classical mechanics breaks down and quantum phenomena emerge. The framework allows for a systematic exploration of how increasingly complex interactions give rise to wave-particle duality, superposition, and entanglement – phenomena traditionally considered counterintuitive. This approach doesn’t discard classical physics, but rather positions it as an approximation valid under specific conditions, offering a pathway to understand the transition from the predictable world of everyday experience to the probabilistic realm of quantum mechanics and potentially revealing the precise conditions required for the emergence of quantum behavior from classical foundations.

The perception of quantum mechanics as fundamentally bizarre may stem from an incomplete picture of the interactions governing reality. This model proposes that what appears as ‘quantum weirdness’ – such as superposition and entanglement – isn’t necessarily inherent to the universe itself, but a consequence of observing phenomena through the lens of classical approximations. By positing deterministic interactions at a more fundamental level, the approach suggests that seemingly probabilistic behaviors emerge not from randomness, but from the complexity of these underlying dynamics and the limitations of current measurement techniques. This perspective doesn’t dismiss quantum predictions, but rather reinterprets them as effective descriptions arising from a deeper, more ordered reality, implying that a complete understanding of these interactions could ultimately resolve long-standing conceptual paradoxes and reveal a universe less reliant on chance than previously thought.

The model successfully replicates the hallmark interference patterns observed in the Double Slit Experiment, specifically when employing a configuration of 100 nm slit separation and 10 nm slit width. This isn’t achieved through the introduction of probabilistic wave functions or the collapse of superposition, but rather through deterministic calculations of particle trajectories influenced by subtle, previously unmodeled interactions. The simulation demonstrates that the observed interference isn’t a consequence of particles existing in multiple states simultaneously, but emerges naturally from the precise geometry of the experiment and the underlying physics governing particle behavior. By accurately predicting the resulting pattern – the characteristic bright and dark fringes – the model offers a compelling alternative to standard quantum interpretations, suggesting that seemingly ‘quantum’ phenomena can be understood as a natural extension of classical physics operating at a refined level of detail.

The pursuit of a deterministic underpinning for quantum mechanics, as detailed in this paper, feels… familiar. The attempt to derive the Schrödinger equation from Newtonian interactions is a noble effort, yet one inevitably succumbs to the realities of implementation. As Paul Dirac once observed, “I have not the slightest idea how to apply this to anything.” This echoes the experience of building any complex system; elegant theoretical frameworks, like the derivation presented here, are quickly confronted by the messy details of production. The assertion that emergent phenomena, such as quantized energy levels, arise from simple interactions is predictable; it’s what happens after the derivation that proves interesting. If all simulations align with the theory, it simply means the test cases are insufficient to capture the inevitable edge cases.

The Road Ahead

The derivation of the Schrödinger equation from ostensibly classical interactions is, predictably, not a destination. It’s merely a shift in where the debugging begins. The model presented offers a new locus for approximations, a different set of parameters to misbehave when confronted with genuinely complex systems. Expect a flurry of activity attempting to reconcile this deterministic undercurrent with the observed peculiarities of quantum field theory – and, inevitably, the discovery of edge cases where the neatness collapses.

The true test won’t be reproducing established results – that’s merely demonstrating fluency in the existing language. The difficulty lies in prediction. Can this framework offer insight into phenomena not already accounted for, or will it simply re-describe the known universe with a more elaborate set of rules? The bug tracker, already filling with subtleties regarding many-body interactions, will be the judge of that.

Ultimately, this work doesn’t solve quantum mechanics; it relocates the problem. It replaces wave function collapse with a more granular, Newtonian chaos. The elegance is appealing, but remember: the universe doesn’t care about elegance. It cares about what breaks. The model does not deploy – it lets go.

Original article: https://arxiv.org/pdf/2511.13748.pdf

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

Beyond Quantum Mystery: The Classical Roots of Reality

Deterministic Interactions: The Foundation of Quantum Behavior

From Classical Mechanics to Quantum Prediction: A Direct Correspondence

Reconciling Intuition and Observation: A More Grounded Perspective

The Road Ahead

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