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The African review of physics

A SIGNAL-PROCESSING INTERPRETATION OF QUANTUM MECHANICS

Christopher Thron, Johnny Watts

Published Oct 25, 2013• 5 citations
OpenAlex

Abstract

We present a new model to explain the behavior of transmitted quantum particles, by analogy with a wireless communication system. The particle’s complex wavefunction is interpreted as the amplitude and phase of a modulated carrier wave. Particle transmission events are modeled as the outcome of a process of signal accumulation that occurs in an extra (non-spacetime) dimension. The standard probability density interpretation of the squared amplitude of the wavefunction is a derivable consequence of the model. The so-called “collapse of the wave packet” also has a simple interpretation within the model’s framework. We simulate the model for a 2-slit diffraction experiment, and indicate possible deviations of the model’s predictions from conventional quantum mechanics.

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We present a new model to explain the behavior of transmitted quantum particles, by analogy with a wireless communication system. The particle’s complex wavefunction is interpreted as the amplitude and phase of a modulated carrier wave. Particle transmission events are modeled as the outcome of a process of signal accumulation that occurs in an extra (non-spacetime) dimension. The standard probability density interpretation of the squared amplitude of the wavefunction is a derivable consequence of the model. The so-called “collapse of the wave packet” also has a simple interpretation within the model’s framework. We simulate the model for a 2-slit diffraction experiment, and indicate possible deviations of the model’s predictions from conventional quantum mechanics.
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing the amplitude and phase information of a modulated carrier wave. Particle transmission events are modeled as the outcome of a process of signal accumulation that occurs in an extra (non-spacetime) dimension. Besides giving a natural interpretation of the wavefunction and the Born rule, the model accommodates the collapse of the wave packet and other quantum paradoxes such as EPR and the Ahanorov-Bohm effect. The model also gives a new perspective on the 'relational' nature of quantum mechanics: that is, whether the wave function of a physical system is "real" or simply reflects the observer's partial knowledge of the system. We simulate the model for a 2-slit experiment, and indicate possible deviations of the model's predictions from conventional quantum mechanics. We also indicate how the theory may be extended to a field theory.
This paper proposes a spectral reinterpretation of wavefunction collapse based on the electromagnetic nature of the electron. In this framework, the electron is not a point particle but a confined electromagnetic wave. The so-called “collapse of the wavefunction” is not a mysterious or observer-induced process, but a real physical phenomenon — a destructive spectral interaction between the electron’s wave field and the electromagnetic field of the measuring device. This interaction destroys the spectral coherence of the electron wave, transforming it from a complex interference-capable field into a linear mode that manifests as a localized detection event. The model provides a tangible physical mechanism for the disappearance of interference in the double-slit experiment when measurement occurs.
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.
This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown to be consistent with existing experiments and our macroscopic experience. In addition, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and dynamical collapse theories, and briefly analyze the problem of the incompatibility between quantum mechanics and special relativity.
This article presents a conceptual interpretation of the double-slit experiment using Feynman's path integral formulation. Rather than treating a quantum particle as a point-like object following a single trajectory, the particle's propagation is viewed as a distributed structure in 4D spacetime. In the path-integral picture, this structure is represented by a coherent sum over possible paths between emission and detection. From this perspective, the observed interference pattern emerges from the phase relationships between these possible spacetime paths. The article distinguishes between propagation and interaction. Propagation is described as an extended 4D process, while measurement appears as a localized spacetime event within a 3D spatial slice, producing the point-like detections observed in the double-slit experiment. The aim is not to propose a new physical theory or to explain the mechanism of collapse, but to provide an intuitive geometric interpretation of the standard quantum formalism and its relationship between quantum propagation, interference, and localized measurement outcomes. This is a conceptual essay and interpretive synthesis, not a proposal of a new physical theory.
The meaning of the wave function and its evolution are investi-gated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A dis-crete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic expe-rience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity.