Abstract This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory’s resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism.
This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory’s resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism.
This monograph presents the first detailed exposition of the formal theory of Branching Space-Times. The theory presented here by Nuel D. Belnap, Thomas Muller, and Tomasz Placek describes how real possibilities can play out in our spatio-temporal world. In our world, some things that are really possible in Cleveland are not really possible in San Francisco; other things were really possible in 1988 but are not really possible in 2021. The authors develop a rigorous, relativity-friendly theory of indeterminism as a local and modal concept, demonstrating that our world contains events with alternative possible outcomes. The book is divided into two parts. The first contains the exposition of the theory, including detailed proofs. The second contains three applications of Branching Space-Times in metaphysics and philosophy of science, focusing on the use of Branching Space-Times to represent pertinent forms of indeterminism in each area. Some specific applications include a formal analysis of modal correlations and of causation and a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. The authors link their theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, particularly in quantum non-locality and spatio-temporal relativity. They also relate the theory to philosophy of time, showing how it may be used to explicate the dynamic concept of the past, present, and future based on local indeterminism. The Branching Space-Times theory has been in development over the past 25 years. This volume provides a much needed first systematic and comprehensive book-length exposition of both the theory and its applications.
The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive QM from more basic principles, these principles should be of general, philosophical nature. Here, we derive the formalism of QM from well-motivated epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. First, an epistemic formalism is developed, using concepts like knowledge and potential knowledge, identifying a physical state
S with the potential knowledge of the physical world. It is demonstrated that QM emerges from this formalism. However, Hilbert spaces, wave functions and probabilities are defined in certain well-defined observational contexts only. This means that the epistemic formalism is broader than QM. In the fundamental layer of description, the physical state
S is a subset of a state space
S={Z}, such that
S always contains many elements
Z. These elements correspond to unattainable states of complete knowledge of the world. The evolution of
S cannot be determined in terms of the individual evolution of the elements
Z, unlike the evolution of an ensemble in classical phase space. The evolution of
S is described in terms of sequential time
n∈N, which is updated according to
n→n+1 each time an event occurs, each time potential knowledge changes. Sequential time
n can be separated from relational time
t, which describes distances between events in space-time. There is an entire space-time associated with each
n, in which
t represents the knowledge at sequential time
n about the temporal relations between present and past events.
This book examines in detail two of the fundamental questions raised by quantum mechanics. Is the world indeterministic? Are there connections between spatially separated objects? In the first part of the book after outlining the formalism of quantum mechanics and introducing the measurement problem, the author examines several interpretations, focusing on how each proposes to solve the measurement problem and on how each treats probability. In the second part, the author argues that there can be non-trivial relationships between probability (specifically, determinism and indeterminism) and non-locality in an interpretation of quantum mechanics. The author then re-examines some of the interpretations of part one of the book in the light of this argument, and considers how they are with regard to locality and Lorentz invariance. One of the important lessons that comes out of this discussion is that any examination of locality, and of the relationship between quantum mechanics and the theory of relativity, should be undertaken in the context of a detailed interpretation of quantum mechanics. The book will appeal to anyone with an interest in the interpretation of quantum mechanics, including researchers in the philosophy of physics and theoretical physics, as well as graduate students in those fields.
This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals (subjunctive conditionals) enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world semantics of quantum counterfactuals using David Lewis’s famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactual semantics to strengthen Bell’s theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell’s theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation.
Abstract Contingency is everywhere, but what is it? This book defends a radical new theory of contingency as a physical phenomenon. Drawing on the many-worlds approach to quantum theory and on cutting-edge metaphysics and philosophy of science, it argues that quantum theories are best understood as telling us about the space of genuine possibilities rather than as telling us solely about actuality. When quantum physics is taken seriously in the way first proposed by Hugh Everett III, it provides the resources for a new systematic metaphysical framework encompassing possibility, necessity, actuality, chance, counterfactuals, and a host of related modal notions. The framework is a modal realist one, in the tradition of David Lewis: all genuine possibilities are on a par, and the actual world is simply the one that we ourselves inhabit. It departs from Lewisian modal realism in that quantum possible worlds are not philosophical posits but scientific discoveries. Contingency and other modal notions have often been seen as beyond the limits of science. Rationalist metaphysicians argue that the metaphysics of modality is strictly prior to any scientific investigation: metaphysics establishes which worlds are possible, and physics merely checks which of these worlds is actual. Naturalistic metaphysicians respond that science may discover new possibilities and new impossibilities. This book’s quantum theory of contingency takes naturalistic metaphysics one step further, allowing that science may discover what it is to be possible. As electromagnetism revealed the nature of light, as acoustics revealed the nature of sound, as statistical mechanics revealed the nature of heat, so quantum physics reveals the nature of contingency.