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Dynamic State-Space Theory for the Double-Slit Experiment: A Relational Account of Random Detection Events

Nicolas Antony Brown

Published Sep 27, 2026• 0 citations
Publisher

Abstract

We present a focused formulation of Dynamic State-Space Theory (DSST) applied exclusively to the double-slit experiment. The theory addresses a single question: why are individual detection events localized and unpredictable, while an ensemble of events yields a stable interference pattern? An energetic process (source, slits, propagation, environment and detector) is treated as generating and evolving a relational state-space S of dynamically accessible configurations. A measurement interaction is modelled as a physical sampling of S that produces one definite, localized outcome and a subsequent state. Individual outcomes remain intrinsically probabilistic; the Born distribution and the interference term are recovered exactly from the geometry of S. The framework is phenomenological: it does not modify the Schr¨odinger equation or the Born rule, and it makes no claim of experimental departure from standard quantum mechanics. Its contribution is a precise conceptual and mathematical language for the origin of randomness in the double-slit setting.

DOI
10.5281/zenodo.22984290

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We present a focused formulation of Dynamic State-Space Theory (DSST) applied exclusively to the double-slit experiment. The theory addresses a single question: why are individual detection events localized and unpredictable, while an ensemble of events yields a stable interference pattern? An energetic process (source, slits, propagation, environment and detector) is treated as generating and evolving a relational state-space S of dynamically accessible configurations. A measurement interaction is modelled as a physical sampling of S that produces one definite, localized outcome and a subsequent state. Individual outcomes remain intrinsically probabilistic; the Born distribution and the interference term are recovered exactly from the geometry of S. The framework is phenomenological: it does not modify the Schr¨odinger equation or the Born rule, and it makes no claim of experimental departure from standard quantum mechanics. Its contribution is a precise conceptual and mathematical language for the origin of randomness in the double-slit setting.
Abstract In this work, the double-slit experiment is analyzed within the framework of Medium Theory SMT, where space-time is described as a nonlinear physical medium Φ. Instead of treating interference as a purely probabilistic quantum phenomenon, SMT interprets the observed pattern as the result of coherent phase dynamics and elastic deformations of the underlying medium. It is shown that propagating δΦ-perturbations naturally produce interference structures through phase coherence and nonlinear medium response, while localized particle-like configurations correspond to stable topological excitations of Φ. The emergence of the standard interference law follows directly from the medium dynamics without invoking wavefunction collapse or intrinsic randomness. The SMT description provides a unified physical mechanism for wave–particle duality, coherence loss, and pattern formation in the double-slit experiment, linking quantum behavior to deterministic field dynamics of the physical medium.
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This article examines the double-slit experiment from a configurational perspective and compares it with the standard quantum-mechanical, Bohmian, and Many-Worlds interpretations. Rather than focusing on microscopic trajectories or wavefunction collapse, the work argues that the central question posed by the experiment is not “how” individual particles behave, but “why” a stable interference pattern emerges with overwhelming statistical certainty. By framing the experiment in terms of constrained configuration spaces and typicality, the article shows that interference can be understood as an inevitable macroscopic outcome, not a mysterious dynamical process.
Born's statistical interpretation of quantum mechanics transformed the wave function from a dynamical object into a quantity whose squared modulus determines the probability distribution of measurement outcomes. Since the formulation of the Born rule in 1926, the relation between a continuously evolving quantum state and discrete detection events has remained one of the central conceptual questions of quantum theory. This paper proposes a physical reconsideration of that relation. Rather than treating the appearance of a localized detection event as an immediate consequence of wave-function collapse, we distinguish two physically different stages: continuous wave-packet propagation and discrete detector readout. In the first stage, a localized wave packet evolves through an interaction potential and undergoes phase reconstruction, deflection, focusing, or redistribution. In the second stage, the continuously distributed wave amplitude interacts locally with microscopic detector degrees of freedom, producing discrete detection events. The central hypothesis explored here is that the experimentally observed distribution of individual events may arise from a local detector-response functional acting on the incident wave amplitude. In an appropriate regime, a detector response of the form R(x)∝∣ψ(x)∣2R(\mathbf{x}) \propto |\psi(\mathbf{x})|^2R(x)∝∣ψ(x)∣2could emerge from the microscopic interaction between the wave packet and the detector, rather than being imposed as a primitive probabilistic postulate. The paper does not claim a completed derivation of Born's rule. Instead, it identifies the physical assumptions that such a derivation would require, relates them to historical electron-scattering experiments, and formulates a concrete research program for deriving the observed quadratic detection law from wave amplitude, energy transfer, phase structure, and microscopic detector dynamics.
Abstract Spontaneous collapse models use non-linear stochastic modifications of the Schrödinger equation to suppress superpositions of eigenstates of the measured observable and drive the state to an eigenstate. It was recently demonstrated that the Born rule for transition probabilities can be modeled using the linear Schrödinger equation with a Hamiltonian represented by a random matrix from the Gaussian unitary ensemble. The matrices representing the Hamiltonian at different time points throughout the observation period are assumed to be independent. Instead of suppressing superpositions, such Schrödinger evolution makes the state perform an isotropic random walk on the projective space of states. The relative frequency of reaching different eigenstates of an arbitrary observable in the random walk is shown to satisfy the Born rule. Here, we apply this methodology to investigate the behavior of a particle in the context of the double-slit experiment with measurement. Our analysis shows that, in this basic case, the evolution of the particle’s state can be effectively captured through a random walk on a two-dimensional submanifold of the state space. This random walk reproduces the Born rule for the probability of finding the particle near the slits, conditioned on its arrival at one of them. To ensure that this condition is satisfied, we introduce a drift term representing a change in the variance of the position observable for the state. It is argued that the drift term accounts for the energy transfer and trapping incurred during the particle’s interaction with the detector. A drift-free model, based on equivalence classes of states indistinguishable by the detector, is also considered. The resulting random walk, with or without drift, serves as a suitable model for describing the transition from the initial state to an eigenstate of the measured observable in the experiment, offering new insights into its potential underlying mechanisms.
We present a first-principles, deterministic account of the quantum double-slit experiment with which-way detectors. Detectors are modeled as physical circuits possessing energetic barriers and therefore necessarily introduce localized interaction potentials. These interactions modify the action of electron paths and rotate the relative phase of each path. The continuous transition from interference to its suppression follows solely from unitary propagation. All probabilistic outcomes arise only from the quadratic mapping of the propagated state after propagation.