This short paper proposes the project of a modal logical semantics that will represent not the classical modalities but the many-worlds interpretation for the physical theory of quantum mechanics. It also views some problematic methodological questions of the doctrine such as measurement and a role of an interpreter. Special attention is given to the famous paradoxes of the QM such as EPR Paradox and Schrodinger’s Cat. The paper will be interesting for logicians, physicists and philosophers of science.
This short paper proposes the project of a modal logical semantics that will represent not the classical modalities but the many-worlds interpretation for the physical theory of quantum mechanics. It also views some problematic methodological questions of the doctrine such as measurement and a role of an interpreter. Special attention is given to the famous paradoxes of the QM such as EPR Paradox and Schrodinger’s Cat. The paper will be interesting for logicians, physicists and philosophers of science.
Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.
The Everett interpretation of quantum mechanics - better known as the Many-Worlds Theory - has had a rather uneven reception. Mainstream philosophers have scarcely heard of it, save as science fiction. In philosophy of physics it is well known but has historically been fairly widely rejected. Among physicists (at least, among those concerned with the interpretation of quantum mechanics in the first place), it is taken very seriously indeed, arguably tied for first place in popularity with more traditional operationalist views of quantum mechanics. In this article, I provide a fairly short (15,000 words) and self-contained introduction to the Everett interpretation as it is currently understood. I use little technical machinery, although I do assume the reader has encountered the measurement problem already (at about the level of the well-known discussions by Penrose or Albert).
This book is about how to understand quantum mechanics by means of a modal interpretation. Modal interpretations provide a general framework within which quantum mechanics can be considered as a theory that describes reality in terms of physical systems possessing definite properties. Quantum mechanics is standardly understood to be a theory about probabilities with which measurements have outcomes. Modal interpretations are relatively new attempts to present quantum mechanics as a theory which, like other physical theories, describes an observer-independent reality. In this book, Pieter Vermaas summarises the results of this work. The book will be of great value to undergraduates, graduate students and researchers in philosophy of science, and physics departments with an interest in learning about modal interpretations of quantum mechanics.
The interplay between non-relativistic quantum theory and metaphysics has generated radically opposed interpretations for quantum theory: Niels Bohr's 'orthodox' interpretation, and Einstein's 'realist' one. Out of this debate emerged the classical first-generation paradoxes of quantum theory: Schrodinger's Cat and the Einstein-Podolsky-Rosen paradoxes. And more recently a range of new paradoxes has emerged from the work of J.S. Bell which questions the `local' nature of quantum theory, prefiguring a return either to an action-at-a-distance metaphysics or to a radically holistic conception of matter. This book outlines the contours of these debates, and presents an interpretation of quantum theory which, while metaphysically realist, resolves most of the paradoxes. This interpretation takes quantum systems to be fuzzy particles, piloted by fields of propensities which are represented by density operators on Hilbert space; and constitutes, in part, a return to an earlier view of quantum systems advanced by De Broglie, Schrodinger, Born, and Einstein. A book for philosophers and physicists who are interested in the philo sophy o f science.
Abstract Quantum physics is changed in an unexpected way. Scientists believe that the study of quantum physics will play an important role in future technology. Therefore, it is meaningful to study quantum physics. The aim of this paper is to provide an initial explanation of the quantum world through the classical single particle double-slit interpretation experiment, and to answer a few questions about the experiment using mainstream quantum mechanical interpretations, such as the Copenhagen interpretation and the Many-Worlds interpretation. The superposition state, which is the core of the Copenhagen interpretation, is then introduced. The Einstein-Podolsky-Rosen paradox and locality are also introduced, and the relationship between the latter and special relativity is analyzed. The author also discusses whether non-locality leads to retrocausality. Finally, the author discusses the relationship between multi-world interpretation and Schrodinger’s cat, but this may raise some philosophical questions. However, realist and hidden variable interpretation are also consistent as long as locality is abandoned.
The resolutions to the paradox of Schrödinger’s cat engendered by three major perspectives on quantum mechanics—quantum logic, the many worlds interpretation, and the Copenhagen interpretation—are discussed. The core of each perspective is revealed in the process. Each resolution to Schrödinger’s cat has a counterpart which solves the logical paradox known as the unexpected hanging. The rather striking parallels serve to emphasize several points. First, the quantum paradox is an epistemological and not a physical one. Second, the three interpretations mentioned, unlike some others, are faithful to this understanding. And third, the pitfalls in these two paradoxes have a somewhat universal character.