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World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering

A Functional Interpretation Of Quantum Theory

Hans H. Diel

Published Feb 21, 2013• 5 citations
Publisher

Abstract

In this paper a functional interpretation of quantum theory (QT) with emphasis on quantum field theory (QFT) is proposed. Besides the usual statements on relations between a functions initial state and final state, a functional interpretation also contains a description of the dynamic evolution of the function. That is, it describes how things function. The proposed functional interpretation of QT/QFT has been developed in the context of the author-s work towards a computer model of QT with the goal of supporting the largest possible scope of QT concepts. In the course of this work, the author encountered a number of problems inherent in the translation of quantum physics into a computer program. He came to the conclusion that the goal of supporting the major QT concepts can only be satisfied, if the present model of QT is supplemented by a "functional interpretation" of QT/QFT. The paper describes a proposal for that

DOI
10.5281/zenodo.1084203

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In this paper a functional interpretation of quantum theory (QT) with emphasis on quantum field theory (QFT) is proposed. Besides the usual statements on relations between a functions initial state and final state, a functional interpretation also contains a description of the dynamic evolution of the function. That is, it describes how things function. The proposed functional interpretation of QT/QFT has been developed in the context of the author-s work towards a computer model of QT with the goal of supporting the largest possible scope of QT concepts. In the course of this work, the author encountered a number of problems inherent in the translation of quantum physics into a computer program. He came to the conclusion that the goal of supporting the major QT concepts can only be satisfied, if the present model of QT is supplemented by a "functional interpretation" of QT/QFT. The paper describes a proposal for that
In this paper, a functional model of interactions in quantum theory (QT) is proposed. A functional model describes the dynamic evolution of a physical system in terms of process steps and intermediate states. That is, it describes how things function. The proposed functional model of QT interactions was developed in the context of the author's work toward a computer model of QT with the goal of supporting the largest possible scope of QT concepts. In QT, the results of interactions are computed using quantum field theory (QFT). Therefore, the proposed functional model of interactions is based on QFT. There are a number of important QT concepts, such as measurement, entanglement, and decoherence, that are related to interactions. The functional model of interactions also addresses these phenomena.
The measurement problem of quantum theory (QT) is the unsolved problem of how the probabilistic predictions of QT are turned into definite measurement results. A related question is whether a measurement in QT implies a collapse of the wave function and what the collapse of the wave function exactly means. Theories proposed on these subjects have not found general agreements among physicists. This paper proposes a solution to the QT measurement problem in terms of a functional model of the measurement process. A functional model describes the process of the dynamic evolution of a physical system. The model assumes that the interactions between the measured QT object and the measurement apparatus are normal interactions which adhere to the laws of quantum field theory.
Theories on physics areas may be understood as models of real world phenomena. They explain a large part of the reality, but they usually do not achieve to explain all details and all aspects of the subject. The type of model chosen for the formulation of a theory determines largely the kind of questions which can be answered by the theory. As an example, the inability to provide a satisfactory answer to the Quantum Theory (QT) measurement problem (or the denial of the problem) is claimed to be largely a consequence of the fact that the present standard model of QT does not support the terms and concepts required for a proper formulation of the problem. This paper describes a process model for QT with emphasis on Quantum Field Theory (QFT). A process model describes how things work. Usually this implies the chronological order in which things happen. With quantum theory there are many questions which cannot be answered by the present theory or its model. It is claimed that a process model of QT is (a) not yet available, and (b) a prerequisite for solutions to certain open problems of QT, such as the measurement problem. The model is based on QFT with the perturbation (Feynman) approach. Key features of the proposed process model are (1) discrete representation of the QT observables (momentum, position, spin) and of the paths resulting from an interaction (2) particle/wave fluctuations taking the role of virtual particles (3) transition from probabilities to facts which is not tied to measurements (4) path collections in support of entanglement. In contrast to the standard theory of QT/QFT, process models are hard to describe in terms of the purely axiomatic mathematics and hard to evaluate by only derivations of mathematical formulas. In order to enable an evaluation of the proposed process model, including showing compatibility with the predictions of standard QFT, a computer program has been implemented which supports both, standard QFT and the proposed process model.
The so-called measurement problem of quantum theory (QT) is still lacking a satisfactory, or at least widely agreed upon, solution. A number of theories, known as interpretations of quantum theory, have been proposed and found differing acceptance among physicists. Most of the proposed theories try to explain what happens during a QT measurement using a modification of the declarative equations that define the possible results of a measurement of QT observables or by making assumptions outside the scope of falsifiable physics. This paper proposes a solution to the QT measurement problem in terms of a model of the process for the evolution of two QT systems that interact in a way that represents a measurement. The model assumes that the interactions between the measured QT object and the measurement apparatus are ''normal" interactions which adhere to the laws of quantum field theory.
This paper describes a computer model of Quantum Field Theory (QFT), referred to in this paper as QTModel. After specifying the initial configuration for a QFT process (e.g. scattering) the model generates the possible applicable processes in terms of Feynman diagrams, the equations for the scattering matrix, and evaluates probability amplitudes for the scattering matrix and cross sections. The computations of probability amplitudes are performed numerically. The equations generated by QTModel are provided for demonstration purposes only. They are not directly used as the base for the computations of probability amplitudes. The computer model supports two modes for the computation of the probability amplitudes: (1) computation according to standard QFT, and (2) computation according to a proposed functional interpretation of quantum theory.
We reconsider the problem of the interpretation of the Quantum Theory (QT) in the perspective of the entire universe and of Bphr idea that the classical language is the language of our experience and QT acquires a meaning only with a reference to it. We distinguish a classical or macroscopic level, and a quantum or microscopic one that is perceived only through the modifications that it induces in the first. The macroscopic state of the universe is assumed to be specified by a set of variables, a classical energy momentum tensor and some conserved currents, which are supposed to have a well defined value across the entire space-time. To the energy-momentum tensor a classical metric is related by the Einstein equation. The quantum state and dynamics are expressed by the usual QT formalism in terms of a density operator and the ordinary quantum operators in Heisenberg picture. For the macroscopic variables a basic distribution of probability is postulated in terms of a density and the corresponding quantum operators, so in some way their evolution is driven by the underlying QT. Such postulate essentially replaces the usual elfadjoint operators correspondence. For the Universe we adopt a variance of the ΛCDM model with Omega=1, one single inflaton with an Higgs type potential, the initial time at t=minus infinite. The expectation values of all fundamental fields are supposed to vanish for time going to minus infinite. In the framework the scalar fluctuation in the Cosmic Microwave Background are correctly explained giving appropriate calue to the parameters in the potential. As in more conventional models the absence of the tensor fluctuations remains not understood, if even a quantum metric is introduced. This seems to suggest that Gravity is a pure classical phenomenon, what could be consistently accommodated in our formalism by an appropriate even if somewhat ad hoc assumption