Quantum theory has played a significant role in modern philosophy both as a source of metaphysical ideas and as an important example of a 'scientific revolution'. In spite of the sixty or so years that have elapsed since its invention, a long lasting controversy concerning the interpretation and meaning of quantum theory prevails. Almost all authors, however, seem to agree on one major point, namely, that there could be no interpretation of this theory which is both realistic and local.;The purpose of this thesis is to demonstrate that this premiss is false and that a realistic, local and deterministic interpretation of quantum theory (at least of part of it) does exist, provided that we extend the classical concept of probability.;In order to establish this a 'quasi classical' probability theory is developed based on some non Lebesgue measurable 'events', which is then applied to account for spin-statistics. Finally I note how this model reflects on the problems of physical realism, locality, the status of probability theory and the philosophical foundations of mathematics.
Quantum theory has played a significant role in modern philosophy both as a source of metaphysical ideas and as an important example of a 'scientific revolution'. In spite of the sixty or so years that have elapsed since its invention, a long lasting controversy concerning the interpretation and meaning of quantum theory prevails. Almost all authors, however, seem to agree on one major point, namely, that there could be no interpretation of this theory which is both realistic and local.;The purpose of this thesis is to demonstrate that this premiss is false and that a realistic, local and deterministic interpretation of quantum theory (at least of part of it) does exist, provided that we extend the classical concept of probability.;In order to establish this a 'quasi classical' probability theory is developed based on some non Lebesgue measurable 'events', which is then applied to account for spin-statistics. Finally I note how this model reflects on the problems of physical realism, locality, the status of probability theory and the philosophical foundations of mathematics.
Quantum mechanics is basically a mathematical recipe on how to construct physical models. Historically its origin and main domain of application has been in the microscopic regime, although it strictly seen constitutes a general mathematical framework not limited to this regime. Since it is a statistical theory, the meaning and role of probabilities in it need to be defined and understood in order to gain an understanding of the predictions and validity of quantum mechanics. The interpretational problems of quantum mechanics are also connected with the interpretation of the concept of probability. In this thesis the use of probability theory as extended logic, in particular in the way it was presented by E. T. Jaynes, will be central. With this interpretation of probabilities they become a subjective notion, always dependent on one's state of knowledge or the context in which they are assigned, which has consequences on how things are to be viewed, understood and tackled in quantum mechanics. For instance, the statistical operator or density operator, is usually defined in terms of probabilities and therefore also needs to be updated when the probabilities are updated by acquisition of additional data. Furthermore, it is a context dependent notion, meaning, e.g., that two observers will in general assign different statistical operators to the same phenomenon, which is demonstrated in the papers of the thesis. It is also presented an alternative and conceptually clear approach to the problematic notion of "probabilities of probabilities", which is related to such things as probability distributions on statistical operators. In connection to this, we consider concrete numerical applications of Bayesian quantum state assignment methods to a three-level quantum system, where prior knowledge and various kinds of measurement data are encoded into a statistical operator, which can then be used for deriving probabilities of other measurements. The thesis also offers examples of an alternative quantum state assignment technique, using maximum entropy methods, which in some cases are compared with the Bayesian quantum state assignment methods. Finally, the interesting and important problem whether the statistical operator, or more generally quantum mechanics, gives a complete description of "objective physical reality" is considered. A related concern is here the possibility of finding a "local hidden-variable theory" underlying the quantum mechanical description. There have been attempts to prove that such a theory cannot be constructed, where the most well-known impossibility proof claiming to show this was given by J. S. Bell. In connection to this, the thesis presents an idea for an interpretation or alternative approach to quantum mechanics based on the concept of space-time.
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.
Quantum theory launched a revolution in twentieth-century physics. But we have yet to appreciate the revolution’s significance for philosophy. Most studies of the conceptual foundations of quantum theory first try to interpret the theory—to say how the world could possibly be the way the theory says it is. But, though fundamental, quantum theory is enormously successful without describing the world in its own terms. When properly applied, models of quantum theory offer good advice on the significance and credibility of claims about the world expressed in other terms. This first of several philosophical lessons of the quantum revolution dissolves the quantum measurement problem. Pragmatist treatments of probability and causation show how quantum theory may be used to explain the non-localized correlations that have been thought to involve ‘spooky’ instantaneous action at a distance. Given environmental decoherence, a pragmatist inferentialist approach to content shows when talk of quantum probabilities is licensed, resolves any residual worries about whether a quantum measurement has a determinate outcome, and solves a dilemma about the ontology of a quantum field theory. This approach to meaning and reference also reveals the nature and limits of objective description in the light of quantum theory. While these pragmatist approaches to probability, causation, explanation, and content may be independently motivated by philosophical argument, their successful application here illustrates their practical importance in helping philosophers come to terms with the quantum revolution.
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic framework for the formulation of mathematical models of physical systems that is general enough to encompass classical and quantum mechanical models. After a short discussion on the properties of classical systems (realism and determinism), we move on to the study of a general class of quantum-mechanical models of physical systems and explain what some of the key problems in a quantum theory of observations and measurements are. In the last part of our essay, we attempt to elucidate the roles played by entanglement between a system and its environment and of information loss in understanding "decoherence" and "dephasing", which are key mechanisms in a quantum theory of measurements and experiments. We also discuss the problem of "time in quantum mechanics" and sketch an answer to the question when an experiment can be considered to have been completed successfully.
My aim in this dissertation is to defend a realist interpretation of quantum mechanics.Firstly, I present considerations based on certain general features of theories in the natural sciences which indicate that realism affords a better account of those theories than instrumentalism.In particular, I consider certain issues surrounding the cognitive status of theories, including the role of models, the status of scientific explanation, and the referential character of theoretical terms.Secondly, I develop a detailed realist theory of measurement based on the notion of quantity terms as designators of objective properties of, and relations among, existing entities.I contrast this with the leading instrumentalist theories of measurement, and I argue that the realist theory is the better account of both the logic and practice of scientific measurement.Finally, I consider a number of objections to realism that arise because of certain theoretical features peculiar to quantum mechanics.In the course of this discussion, I consider crucial experimental evidence for the "dual" nature of microentities, various criteria of reality proposed by philosophers of science, the peculiar features of quantum mechanical measurement, and the status of causality in quantum mechanics.I argue that while certain realist viii ix interpretations of the quantum theory, namely the wave and wavicle interpretations, are unsatisfactory, an interpreta tion which construes micro-entities as existing particles is a tenable account.CHAPTER I ignored the considerations which arise at those more general levels of inquiry, but one can not adequately assess the status of quantum mechanics with respect to both realism and instrumentalism apart from those considerations.In the second two chapters of the dissertation, I shall argue that realist interpretations of quantitative theories in the natural sciences are preferable to instrumentalist interpretations.Then in the remainder of the dissertation, I shall go on to argue that realism is tenable at the quantum mechanical level despite the features peculiar to that theory.CHAPTER II THE COGNITIVE STATUS OF THEORIES transitions from one set of experiential statements to another.This view is in marked contrast to that of the realist who regards such terms as referential.This divergence in opinion between realists and instrumentalists about the referential character of theoretical terms leads to a related dispute over the role of models in the inter pretation of scientific theories.Before contrasting the various philosophical positions on this issue, it will be necessary to sort out different senses of the term "model."Upon inspecting the literature surrounding this dispute, it seems that much of the controversy about the role of models stems from a failure to make such distinctions.I will begin this task by distinguishing between 13 model-structures and model-objects.A model-structure is a definitely specifiable schema of mathematical-logical relationships which is exhibited by and can be abstracted from a set of objects.Any set of objects which exhibits a model-structure constitutes a set of model-objects.With respect to any particular scientific theory, there may be a variety of model-objects that scientists employ for various purposes.For example, in the kinetic theory of gases, one can distinguish the following.Firstly, there is the set of molecules themselves, the theoretical entities which we shall 13.For further detail in this regard, see Henry C. Byerly, "Model-Structures and Model-Objects," British Journal for the Philosophy of Science.Vol. 20, 1969, pp.135-144.i In fact, if one were to make that claim, I do not see how it could be supported without again falling prey to Maxwell's criticism cited above.And if one is simply troubled by the "ontological risk" involved in asserting the existence of theoretical entities because of the tentativeness of the corresponding theories, it should be noted that the risk of being wrong is a small price to pay for the potentially deeper understanding of nature that scientific theories afford us in the light of realist commitments.
The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum theory could be, if not resolved, at least mitigated by a proper interpretation of probability. We rather show, through a historical and analytical overview of probability and quantum theory, that if some interpretations of the one and the other go along particularly well, none follows in a unique way.