This chapter discusses the ontological and logical issues involved in criticisms. The ontology of quantum histories interpretation is based on two core contents. One is the stochastic evolution dynamics, which is similar to standard quantum mechanics; the other is the reasoning principles (especially the single-framework rule) that must be followed if the quantum process is expressed in the histories formalism, which makes the interpretation deviate from previous rules of classical propositional reasoning. Although in those cases where classical mechanics can be regarded as an approximation of quantum mechanics, the “quantum logic” proposed by histories interpretation is enough to reduce to the classical propositional logic, there are still unresolved challenges regarding the relationship between the new and old logics, the new and old ontologies. In particular, there is a certain anti-realism in the expressions of the founders of the quantum histories interpretation, which causes mutual influence between the characterization of the properties of quantum histories and the logical inference of quantum histories propositions.
This chapter discusses the ontological and logical issues involved in criticisms. The ontology of quantum histories interpretation is based on two core contents. One is the stochastic evolution dynamics, which is similar to standard quantum mechanics; the other is the reasoning principles (especially the single-framework rule) that must be followed if the quantum process is expressed in the histories formalism, which makes the interpretation deviate from previous rules of classical propositional reasoning. Although in those cases where classical mechanics can be regarded as an approximation of quantum mechanics, the “quantum logic” proposed by histories interpretation is enough to reduce to the classical propositional logic, there are still unresolved challenges regarding the relationship between the new and old logics, the new and old ontologies. In particular, there is a certain anti-realism in the expressions of the founders of the quantum histories interpretation, which causes mutual influence between the characterization of the properties of quantum histories and the logical inference of quantum histories propositions.
To revisit and analyze the histories formalism of quantum mechanics, this chapter will refer to the basic idea of the nomological interpretation of the quantum wave function as described in the previous chapter. The quantum wave functions can be interpreted as nomological and non-ontological elements of Bohmian mechanics. This inspires us that, in quantum histories formalism, the multiple conditions/criteria of determining the possible families of histories, whose validity can be examined by reasonable tests regarding the properties of subsystems, can be argued as lawful or nomological, while the quantum histories can be argued as the fundamental physical reality. We will specifically focus on this novel depiction of the formalism concerning quantum reality, which enables us to reconsider the numerous objections to the histories interpretation that were raised in previous chapters and re-examine/resolve from the nomological perspective the several aforementioned ontological and logical issues of quantum histories interpretation. However, there still remain challenging issues in the understanding of quantum histories.
The temporality and a certain degree of perspectivism of the quantum histories interpretation and its formalism seem to have similarities with relational ontology, process ontology, and Leibnizian monadology. This chapter specifically analyzes the relationship, similarities, and differences between these versions of ontologies and the historicized ontology. Then, some issues in the philosophy of history are discussed in the second section. In the philosophy of history, some scholars have borrowed concepts and the worldview of quantum mechanics to understand the ontology of history since the 20th century. However, due to an insufficient understanding of the specific controversies of different interpretations of quantum mechanics, the influence on the philosophy of history often has misunderstandings and biases. From the perspective of quantum histories interpretation and scientific metaphysics, some of these misunderstandings can be reasonably resolved.
The (consistent or decoherent) histories interpretation provides a consistent realistic ontology for quantum mechanics, based on two main ideas. First, a logic (system of reasoning) is employed which is compatible with the Hilbert-space structure of quantum mechanics as understood by von Neumann: quantum properties and their negations correspond to subspaces and their orthogonal complements. It employs a special (single framework) syntactical rule to construct meaningful quantum expressions, quite different from the quantum logic of Birkhoff and von Neumann. Second, quantum time development is treated as an inherently stochastic process under all circumstances, not just when measurements take place. The time-dependent Schrödinger equation provides probabilities, not a deterministic time development of the world. The resulting interpretive framework has no measurement problem and can be used to analyze in quantum terms what is going on before, after, and during physical preparation and measurement processes. In particular, appropriate measurements can reveal quantum properties possessed by the measured system before the measurement took place. There are no mysterious superluminal influences: quantum systems satisfy an appropriate form of Einstein locality. This ontology provides a satisfactory foundation for quantum information theory, since it supplies definite answers as to what the information is about. The formalism of classical (Shannon) information theory applies without change in suitable quantum contexts, and this suggests the way in which quantum information theory extends beyond its classical counterpart.
This book discusses the ontology in the quantum world and argues that it should be interpreted as a historicized ontology. This perspective is advocated by the quantum histories interpretation. Inspired by the nomological interpretation from Bohmian mechanics and the corresponding understanding of the law of nature and logic, the ontology will be useful to solve the difficulties of confusing ontology and perplexing logical inference. Furthermore, this book proposes that the historicized ontology can be generalized to more complicated structures and fit naturally into temporal correlation. Core philosophical issues such as the law of nature, the ontology of events, history, and processes, and the metaphysics of history are coherently discussed, revealing the profound meaning behind the formalism of quantum histories. By providing a new framework for a historicized picture of ontology, it will effectively promote the debates in the philosophy of physics and the fundamental research in quantum mechanics. This book will appeal to scholars and students of the philosophy of science, metaphysics, and quantum theory.
This chapter discusses the main points and thought sources of the quantum histories interpretation. Section 3.1 introduces its core concepts, theoretical assumptions, and basic formalism first, as well as how probability calculations and propositional reasoning are performed here, and shows how this interpretation depicts the process by which (quasi-)classicality is derived from quantum histories. Section 3.2 sorts out the five important thought sources from which it emerges: the Copenhagen interpretation, Feynman’s sum-over-histories formulation of quantum mechanics, Wigner’s measurement theory, Everett’s relative state interpretation or many-worlds interpretation, and the mechanism of decoherence. Their respective correlations, similarities, and differences with the quantum histories interpretation are briefly analyzed. In the appendix to this chapter, three notorious paradoxes showing intractable aspects of quantum mechanics, namely the Einstein-Podolsky-Rosen (EPR) paradox, Wheeler’s delayed choice gedankenexperiment, and Frauchiger–Renner paradox, are formulated via history chain operator analysis in the quantum histories formalism.
This chapter, based on the background information of the previous chapter, will review the formalism of quantum mechanics – its fundamental mathematical structure (the basic contents of Hilbert space representation and operator algebra representation) and physical assumptions (kinematics, dynamics, and measurement theory). These are the premise and foundation for discussing the quantum histories interpretation. Then, in combination with the viewpoints of some literature in recent years, we will explore what is the interpretation of quantum mechanics, analyze the relationship between the theory of quantum mechanics and its interpretation, and declare the author’s basic stance on these two issues. These two are the primary issues that all interpretive work in the philosophy of physics will face (not limited to the interpretation of quantum mechanics), and the necessary clarification here is also conducive to the subsequent discussion. Three common terms – theory, formalism, and interpretation – are explicated and differentiated by offering the necessary definitions of their meanings, based on the works of Acuña and Ruetsche. The clarification will help to make the subsequent related discussions more precise.