Abstract This chapter investigates the formation and propagation of wave function “branches” through the process of entanglement with the environment. While this process is particularly important to some recent articulations of the Everett or “many-worlds” interpretation, it is a consequence of unitary dynamics, and hence significant to many if not all approaches to quantum theory. In this chapter we thus take a largely neutral stance on interpretation to investigate the shared consequences of unitary evolution. A highly idealized model of a locally interacting system and environment is described and investigated in several situations in which branching occurs, including those involving Bell inequality violating correlations; we illustrate how any nonlocality is compatible with the locality of the dynamics. Although branching is particularly important for many-worlds quantum theory, we take a neutral stance here, simply tracing out the consequences of a unitary dynamics. The overall goals are to provide a simple, concrete realization of the quantum physics of branch formation, and especially to emphasize the compatibility of branching with relativity; the chapter is intended to illuminate matters both for foundational work and for the application of quantum theory to non-isolated systems.
Abstract This chapter investigates the formation and propagation of wave function “branches” through the process of entanglement with the environment. While this process is particularly important to some recent articulations of the Everett or “many-worlds” interpretation, it is a consequence of unitary dynamics, and hence significant to many if not all approaches to quantum theory. In this chapter we thus take a largely neutral stance on interpretation to investigate the shared consequences of unitary evolution. A highly idealized model of a locally interacting system and environment is described and investigated in several situations in which branching occurs, including those involving Bell inequality violating correlations; we illustrate how any nonlocality is compatible with the locality of the dynamics. Although branching is particularly important for many-worlds quantum theory, we take a neutral stance here, simply tracing out the consequences of a unitary dynamics. The overall goals are to provide a simple, concrete realization of the quantum physics of branch formation, and especially to emphasize the compatibility of branching with relativity; the chapter is intended to illuminate matters both for foundational work and for the application of quantum theory to non-isolated systems.
This paper investigates the formation and propagation of wavefunction `branches' through the process of entanglement with the environment. While this process is a consequence of unitary dynamics, and hence significant to many if not all approaches to quantum theory, it plays a central role in many recent articulations of the Everett or `many worlds' interpretation. A highly idealized model of a locally interacting system and environment is described, and investigated in several situations in which branching occurs, including those involving Bell inequality violating correlations; we illustrate how any non-locality is compatible with the locality of the dynamics. Although branching is particularly important for many worlds quantum theory, we take a neutral stance here, simply tracing out the consequences of a unitary dynamics. The overall goals are to provide a simple concrete realization of the quantum physics of branch formation, and especially to emphasise the compatibility of branching with relativity; the paper is intended to illuminate matters both for foundational work, and for the application of quantum theory to non-isolated systems.
Abstract This introductory chapter summarizes the principal positive theses of the book (Section 1), namely, that the unitary evolution of the quantum state, for sufficiently large systems of particles in thermal environments, yields a multiplicity of branching structures (worlds) obeying approximately classical equations, a result that follows from decoherence theory with no special assumptions or additions to the quantum formalism; and that further, the branching of worlds has a natural interpretation in terms of probability, as quantified by the Born rule in terms of ratios of squared norms of branch amplitudes. In particular, an agent who knows the branching structures of the quantum state that will result from his actions is rationally compelled to order his preferences among actions by the expected utilities of those branching structures as defined by the Born rule. He is, moreover, entitled to view a branching process as involving uncertainty as to which branch he will find himself. But independent of the truth of these claims, the theory is still testable: an agent who does not know the branching structure of the state, and who is indeed undecided between a many-worlds and a one-world theory, is rationally bound to update her credences in such theories by conditionalisation on observed statistical evidence, just as she is bound to do in the case of conventional quantum mechanics. Section 2 summarizes some of the arguments and counter-arguments for these claims as developed in subsequent chapters. Section 3 provides some more mathematical and historical background to the Everett interpretation, including a brief introduction to the decoherent histories formalism.
Abstract This chapter argues for the view that the Everett (‘many worlds’) interpretation is nothing more or less than a literal reading of the formalism of unitary quantum mechanics. The central component of this story is decoherence: the process by which the evolution of the quantum state acquires a branching structure. The chapter gives a conceptual introduction to decoherence and its conceptual role, emphasizing the significance of its effects on the dynamics of degrees of freedom which are undergoing decoherence. It then argues that, although the branching structure generated by decoherence is ‘for all practical purposes’ in the sense that it is not part of the microscopic formalism of quantum theory, nonetheless it is a perfectly real, observer-independent feature of reality — it is emergent from that microscopic formalism in a way very familiar from many other parts of science.
This paper provides a self-contained mathematical derivation of the Many-Worlds Interpretation of quantum mechanics, relying exclusively on unitary Schrödinger evolution and quantum entanglement without a wave-function collapse postulate. The emergence of distinct physical branches is demonstrated through system, apparatus, and environment entanglement followed by decoherence. Using explicit matrix representations for spin-21 states, Pauli operators, and measurement interactions, we analyze a two-branch model where a quantum superposition produces world branches weighted by their corresponding squared amplitudes. This construction is extended to a sequence of N measurements, generating a branching tree of 2N worlds. We directly compare this unitary framework with the von Neumann–Lüders collapse mechanism of the Copenhagen interpretation and the epistemic probabilities of classical statistical mechanics. By evaluating these three approaches at the level of the same 2×2 density matrices, we show why they are locally equivalent while differing significantly regarding global state evolution, reversibility, and the status of the Born rule. We further use the Wigner’s-friend thought experiment and its modern generalization by Frauchiger and Renner to show how the question of what counts as an observer sharpens this comparison. Additionally, we address the preferred-basis problem and examine the decision-theoretic derivation of the Born rule by Deutsch and Wallace. Designed for graduate and advanced undergraduate courses in quantum foundations, this work bridges the gap between qualitative overviews and abstract Hilbert-space treatments by equipping students with concrete algebraic tools to evaluate measurement interpretations.
Abstract Initially proposed by Hugh Everett III as the “theory of the universal wave function,” the many worlds interpretation has since been developed and refined into one of the most influential ways of giving meaning to quantum mechanics. This volume explores the idea that if one adopts the many worlds interpretation, then one can avoid what Einstein called “spooky action at a distance,” the non-locality that is supposed to be a consequence of quantum entanglement according to other approaches. The essays in this volume articulate a clear and defensible formulation of the argument from locality for preferring the many worlds interpretation of quantum mechanics over its rivals and evaluate it. They question in what sense those in quantum foundations should care about locality, in particular, whether and how an interpretation of quantum mechanics must avoid action at a distance in order to maintain consistency with special relativity. Finally, these essays assess whether the many worlds theory needs a particular metaphysical or mathematical interpretation in order to achieve the aim of providing a local interpretation of quantum mechanics.
The Branched Hilbert Subspace Interpretation (BHSI) aims to provide a unitary account of quantum measurement while maintaining a single-world ontology. The framework reexamines scenarios such as Einstein 1927 electron-diffraction thought experiment by treating measurement as a finite dynamical process of information recording, comprising a sequence of unitary operations: branching, engaging, and disengaging. This perspective motivates a testable proposal: a dual-layer experiment in which the particle transit time between layers is shorter than the sensor response time, enabling a direct probe of measurement timing and potentially uncommitted outcomes. We introduce the Island of Coherence (IOC) as an operationally isolated quantum system, mathematically described by a Local Hilbert Subspace (LHS), which coexists with the background spacetime and within which unitary branching occurs. Historically, the first quantization already implies this dual structure. Applying the Gleason and Busch theorems to local unitary branching, the Born rule follows from the amplitudes given in the initial state. Moreover, quantum nonlocality (e.g., in Bell tests or tunneling) arises naturally from the inner-product structure of the LHS, which possesses no intrinsic spacetime metric. BHSI thus provides a coherent framework in which relativistic causality and quantum correlations remain structurally compatible.