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A PROCESS MODEL OF QUANTUM FIELD THEORY

Hans H. Diel

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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
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.
Quantum field theory (QFT) can be analyzed in terms of its mathematical structure, its conceptual system for physical descriptions, or its basic ontology. The analysis can be done logically or historically. In this chapter, only the genesis of the conceptual foundations of QFT relevant to its basic ontology will be treated; no discussion of its mathematical structures or its epistemological underpinnings will be given. Some conceptual problems, such as those related to probability and measurement, will be discussed, but only because of their relevance to the basic ontology of QFT, rather than their intrinsic philosophical interest. Here, by basic ontology I mean the irreducible entities that QFT is invented to describe. The often mentioned candidates for the basic ontology of QFT, in fact of the physical world, are the discrete particle and the continuous field. Another possible candidate (the spacetime point) has also been suggested recently (Redhead, 1983). Since the aim of this chapter is to analyze the historical process in which the conceptual foundations of QFT were laid down, rather than the logical structure of QFT which philosophers of the present day treat, no discussion of the last possibility will be given. The content of this chapter involves the formation and interpretation, in a roughly chronological order, of the concepts of the wave function, quantization, quantization of the field, the vacuum, interactions between fields, and renormalization. The first two topics will be discussed in relation to the quantization of the field, with their role being taken as the starting point of the conceptual development of QFT.
A computer model of Quantum Theory (QT) has been developed by the author. Major goal of the computer model was support and demonstration of an as large as possible scope of QT. This includes simulations for the major QT (Gedanken-) experiments such as, for example, the famous double-slit experiment. Besides the anticipated difficulties with (1) transforming exacting mathematics into a computer program, two further types of problems showed up, namely (2) areas where QT provides a complete mathematical formalism, but when it comes to concrete applications the equations are not solvable at all, or only with extremely high effort; (3) QT rules which are formulated in natural language and which do not seem to be translatable to precise mathematical expressions, nor to a computer program. The paper lists problems in all three categories and describes also the possible solutions or circumventions developed for the computer model.