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arXiv:1205.1681

A Signal Processing Model of Quantum Mechanics

Christopher Thron, Johnny Watts

Published May 8, 2012• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1205.1681

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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.
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.
The basic idea of quantum mechanics is that the property of any system can be in a state of superposition of various possibilities (or eigen states).This state of superposition is also known as wave function and it evolves linearly with time in a deterministic way in accordance with the Schrodinger equation.However, when a measurement is carried out on the system to determine the value of that property (say position), the system instantaneously transforms to one of the eigen states and thus we get only a single value as an outcome of the measurement.Quantum measurement problem seeks to find the cause and exact mechanism governing this transformation.In an attempt to solve the above problem, in this paper, we will first define what the wave function represents in real-world and will identify the root cause behind the stochastic nature of events.Then, we will develop a model to explain the mechanism of collapse of the quantum mechanical wave function in response to a measurement.In the process of development of model, we will explain Schrodinger cat paradox and will show how Born's rule for probability becomes a natural consequence of the measurement 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.
I. The arena of quantum mechanics and quantum field theory is the abstract, unobserved and unobservable, M-dimensional formal Hilbert space ≠ spacetime. II. The arena of observations—and, more generally, of all events (i.e., everything) in the real physical world—is the classical four-dimensional physical spacetime. III. The “Born rule” is the random process “magically” transforming I into II. Wavefunctions are superposed and entangled only in the abstract space I, never in spacetime II. Attempted formulations of quantum theory directly in real physical spacetime actually constitute examples of “locally real” theories, as defined by Clauser and Horne, and are therefore already empirically refuted by the numerous tests of Bell’s theorem in real, controlled experiments in laboratories here on Earth. Observed quantum entities (i.e., events) are never superposed or entangled as they: (1) exclusively “live” (manifest) in real physical spacetime and (2) are not described by entangled wavefunctions after “measurement” effectuated by III. When separated and treated correctly in this way, a number of fundamental problems and “paradoxes” of quantum theory vs. relativity (i.e., spacetime) simply vanish, such as the black hole information paradox, the infinite zero-point energy of quantum field theory and the quantization of general relativity.
For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of the universe as a sample point of an accumulative stochastic process. The model give predictions that are nearly identical to the given quantum theory. The model is neither local nor causal in spacetime, but is both local and causal is in a non-observable path space. The probabilistic nature of the squared wavefunction is a natural consequence of the model. We verify the model with simulations, and we discuss possible discrepancies from conventional quantum theory that might be detectable via experiment. Finally, we briefly discuss the physical implications of the model.
A mathematical model for the slit experiments in the heart of quantum mechanics is developed to gain insight into quantum ‎theory. The proposed system-theoretical model is entirely based on commutative mathematics, i.e. convolution, and integral ‎transformations, and starts with spacetime functions with inherent energy-based cause and effect relations of the state-‎function Ѱ in the complex Hilbert space. The benefits of his approach are as 1-Invariance in time reversal. 2-Deterministic ‎result functions in the model in line with the outcome of slit experiments. 3- Separation of causality and cross-correlations of ‎attained states. 4- Disappearance of a posteriori probability of quantum states. 5- Quantum a priori fixed states after ‎causality interactions have ended, (even) when quanta are (light-years) separated. The model predicts the patterns in the ‎experiments with mathematical functions of the energy distributions. The quantum mechanical counterpart description of the ‎physical reality of slit experiments thus may be considered complete in A. Einstein’s definition. The patterns in double slit ‎experiments are found to be an effect of energy (amplitude-) modulation. An equivalent double-slit pattern can be retrieved ‎from an input modulated 1-slit experiment excluding interference interpretations. The system-theoretical model uses generic ‎properties of quanta and evolves into determinism in ‎quantum mechanics slit experiments. The mathematics in the model ‎handles beables by treatment ‎of momentum p in system theoretical I/O relations of the transformed functions and allows the ‎proposed description by the avoidance of a direct addressing of the individual quanta through variables. The following ‎method yields exact, non-probabilistic results.‎