The law of nature is a core concept in the philosophy of science, but there are significant differences among science philosophers regarding the necessity and connotation of this concept. The current understanding of the law of nature can be roughly divided into two categories – the regularity approach and the necessity approach. How to understand the status of quantum states is a core issue in the philosophy of quantum mechanics. The following analysis focuses on the nomological interpretation of the wave function of quantum mechanics proposed by some scholars of the Bohmian school. To defend this interpretation, supporters have put forward various arguments and carefully distinguished different meanings of “nomology”. This is not only related to the several major approaches to understanding the law of nature that already exist in the philosophy of science but also shows a different perspective from the literature. In particular, these new arguments provide a reference for re-examining the formalism of the quantum histories interpretation.
The law of nature is a core concept in the philosophy of science, but there are significant differences among science philosophers regarding the necessity and connotation of this concept. The current understanding of the law of nature can be roughly divided into two categories – the regularity approach and the necessity approach. How to understand the status of quantum states is a core issue in the philosophy of quantum mechanics. The following analysis focuses on the nomological interpretation of the wave function of quantum mechanics proposed by some scholars of the Bohmian school. To defend this interpretation, supporters have put forward various arguments and carefully distinguished different meanings of “nomology”. This is not only related to the several major approaches to understanding the law of nature that already exist in the philosophy of science but also shows a different perspective from the literature. In particular, these new arguments provide a reference for re-examining the formalism of the quantum histories interpretation.
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.
We outline how Bohmian mechanics works: how it deals with various issues in the foundations of quantum mechanics and how it is related to the usual quantum formalism. We then turn to some objections to Bohmian mechanics, for example the fact that in Bohmian mechanics there is no back action of particle configurations upon wave functions. These lead us to our main concern: a more careful consideration of the meaning of the wave function in quantum mechanics, as suggested by a Bohmian perspective. We propose that the reason, on the universal level, that there is no action of configurations upon wave functions, as there seems to be between all other elements of physical reality, is that the wave function of the universe is not an element of physical reality. We propose that the wave function belongs to an altogether different category of existence than that of substantive physical entities, and that its existence is nomological rather than material. We propose, in other words, that the wave function is a component of physical law rather than of the reality described by the law.
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 thesis aims to contribute to the discussion of how to interpret the Bohmian ontology. Bohmian Mechanics is a quantum theory that describes the motion of particles, whose trajectories are determined by the quantum wave-function. This theory faces two key questions. The former concerns the metaphysical characterization of the particles; the latter relates to the ontological status of the wave-function. \nAfter briefly presenting two possible metaphysical characterizations of the particles, I dedicate the bulk of this work to investigating the status of the wave-function. In particular, I analyse the realist view (which regards the wave-function as a multi-dimensional field) and the nomological view (which considers the wave-function as a law-like entity). My investigation touches upon different levels of inquiry. First, I show that these two ontological interpretations depend on contrasting formulations of the law that dictates the particle motion. Second, I argue that both views defend very problematic ontologies that not only violate familiar metaphysical criteria but also fail to provide a satisfactory explanation of the relation between the particles and the wave-function. Third, I spell out the implicit methodologies that underlie the two views, arguing that they conflate three important categories that should rather be kept separate: the informationally-complete representation of the system, the ontologically-complete representation of the system, and the ontology itself. \nFinally, I present and advocate structural realism as the metaphysical framework for investigating and understanding the Bohmian ontology. According to the structuralist interpretation, the wave-function represents a network of modal relations whose relata are the particles. I argue that this third view provides the best account of the Bohmian system for three reasons. First of all, it offers a parsimonious ontology that does not create any issue of metaphysical underdetermination. Secondly, it supplies an explanatorily powerful ontology. Thirdly, it relies on a sound methodological program. I conclude with an interesting insight: this structuralist interpretation can be regarded as reconciling the realist view and the nomological view given that it takes on aspects of both views and is compatible with both formulations of the law of motion for the particles. \n
The aim of this book is to provide a comprehensive guide to the metaphysics of Bohmian mechanics. Bohmian mechanics is a quantum theory that describes the motion of particles following trajectories that are determined by the quantum wave-function. The key question that the theory has to face relates to the ontological interpretation of the quantum wave-function. The main debate has mostly centered around two opposing views, wave-function realism on the one hand, and the nomological view on the other hand. The supporters of the former believe that the wave-function is a physical field living in a high-dimensional space; the supporters of the latter regard the wave-function as just an entity that appears in the laws of nature and lacks physical status. This monograph discusses both views open-mindedly, illuminating their tacit problems and providing new insight into how they can be overcome. Moreover, it discusses the structuralist view, which is often neglected and which can be regarded as a reconciliation of the two main opposing camps.
A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review and compare several realist interpretations of the wave function. They fall into three categories: ontological interpretations, nomological interpretations, and the sui generis interpretation. For simplicity, I will focus on non-relativistic quantum mechanics.