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arXiv:1405.5982 · Journal of Physics Conference Series

A model of the measurement process in quantum theory

Hans H. Diel

Published Jul 3, 2015• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1742-6596/626/1/012061

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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.
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.
The newly revised edition of this well-known book categorizes prevalent views on measurement as described by quantum mechanics, discusses basics agreed to by many who on other issues disagree, and describes some of the problems. Although many paragraphs rest unchanged from the first (1991) edition, results found since 1991 are used to reorganize and sharpen the focus of the book, so that even the old paragraphs are now understood differently and more clearly. One advance in the second edition is a new and more general no-go theorem; another is separation of formal derivations from interpretation. The dozen or so definitions essential to following the book even casually are stated clearly. By this means the authors succeed pretty well in achieving their stated desire to make the book comprehensible to those who do not share their philosophic predispositions. While I differ in philosophy from the authors, attending to their discussion uncovered weaknesses in my own thinking and improved it. The mathematical language of quantum mechanics expresses a system under measurement by states (as rays in a Hilbert space) and a hamiltonian operator, distinct from the apparatus that produces outcomes, which is expressed by a positive operator-valued (POV) measure. In this way quantum language separates state preparation from state measurement. Often the Hilbert space is viewed as a tensor product of subspaces, allowing further conceptual separations. The authors take the stance that quantum mechanics calls for splitting the empirical world into parts, the most essential being (1) objective systems S (to be observed) and (2) apparatus A (preparation and registration devices that produces outcomes (or, as the authors write, definite pointer values) of the observed system). In some interpretations, one or both of an observer and an environment appear as additional parts. What is to be included in the system S versus the apparatus A is not specified by the language, but is open to the theoretician; a probe, for example, can be analysed as either part of the apparatus or as part of the system, as was discussed by von Neumann in work cited by the authors. With what should a theory of measurement be concerned? A broad division of approaches is defined by how one answers the question: should one try to do away with the cut between measuring apparatus and system? The authors phrase this as a choice of REFERENT, a term which in my mind puts them on shaky semantic ground; anyway The Quantum Theory of Measurement is concerned with implications of the `yes'. The book unfolds with the power of a tragedy, in which the logical consequences lead, step-by-step, to the statement and proof of theorem 6.2.1, which, roughly speaking, asserts the non-existence of a solution to the problem of getting definite pointer values from measuring apparatus that exhibits the superposition demanded by its description as a quantum system. Possible responses to this theorem are discussed, among them the many-worlds interpretation and a modification of quantum mechanics that elevates decoherence to a principle. Citations of the literature are thorough, and many points of view are crisply summarized. The book is indispensable to both those who work in the broad direction chosen by the authors and to those who wish to set any other direction in context.
Abstract There is a consensus among physicists about the outcome of any experiment. However, there continues to be discussion about the interpretation of these results. At the heart of this discussion is the so-called measurement problem. The interaction of the particles with the measurement apparatus forms the measurement problem that has haunted physicists since the very early days of quantum mechanics. The problem is that quantum mechanics only describes the evolution of the wavefunction with time, but does not answer about the interaction with the measurement apparatus. These issues, related to the measurement problem, have led physicists to come up with different interpretations. Many possibilities are discussed. One of the most amazing resolutions of the measurement problem is via the possibility of the existence of multiple universes. This many-worlds approach is a desperate attempt to solve the measurement problem.
The measurement process of observables in a quantum system comes out to be an unsovable problem which started in the early times of the development of the theory. In the present note we consider the measured system part of an open system interacting with the measuring device and show under which ideal conditions the measure process may ideally work. Our procedure leads to the conclusion that there is no hope that any experimental procedure will be able to lead to a clean solution of the process, except maybe in very specific cases. The reasons for this situation are deeply rooted in the fundamental properties of quantum 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 term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing physics is regarded as a creative activity to develop a meaningful description of the world, then one has to carefully discriminate between the two notions: An observer's account of experience - consitutive to meaning - is hardly expressed exhaustively by the formal framework of an interaction within one particular theory. We develop a corresponding perspective onto central terms in quantum mechanics in general, and onto the measurement problem in particular.