Abstract To reach the point I want to discuss, I must begin with a sketchy review of quantum mechanics. I apologise to those of you who know this material already, perhaps better than I do. But it will be an opinionated review: some of my opinions are eccentric. So there may be something in it even for those who are already expert. Quantum mechanics is, in a nutshell, the theory of suprpostons. To introduce this concept, I begin with the standard account of the benzene ring-an account so well entrenched in organic chemistry that it would probably survive even if its quantum-mechanical foundation crumbled away beneath it. The benzene ring is a hexagon of carbon atoms, each with a hydrogen atom attached. Replace two adjacent hydrogens with two different substituents, so that we can unambiguously number the sides of the hexagon. Two structures conform to the rules of valence: one with double bonds on the odd-numbered sides, another with double bonds on the even-numbered sides (see Figure 1).The molecule reacts sometimes as if it had one structure, sometimes as if it had the other. Yet we do not think that a population of molecules is a mixture of the two structures. Neither do we think that each molecule oscillates rapidly between one structure and the other. Neither do we think that the molecule has a betwixt-and-between structure- there is no such thing as a bond midway between double and single. Rather, we think that each molecule is in a superposition: a state objectively indeterminate between the two structures. Objective indeterminacy is multiplicity: a cloud of indeterminate extent, for instance, is really many clouds, almost but not quite identical to one another [Unger 1980; Lewis 1999b]. Likewise a molecule with an objectively indeterminate structure is really two coexisting molecules, one with one structure and one with the other. (Or at any rate, two things that are molecule-like except for from their coexistence with one another.)

Sep 2, 20040 citations

Branching Space-Times : Theory and Applications

Nuel Belnap, Thomas Müller, Tomasz Placek

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.

Jan 1, 202117 citations