Jeffrey Barrett

This chapter provides a detailed explanation of Everett's three works — his thesis “On the Foundations of Quantum Mechanics”, a short paper entitled “‘Relative State’ Formulation of Quantum Mechanics”, and a long paper “The Theory of the Universal Wave Function”. It also discusses what was wrong with von Neumann's theory. It evaluates five alternatives presented by Everett for developing a satisfactory formulation of quantum mechanics. It provides an explanation for Everett's interpretation of pure wave mechanics and his principle of the relativity of states. Lastly, it evaluates the classical appearance and behaviour of macroscopic systems.

This chapter begins by discussing the problems encountered in interpreting Everett's assumption of the same appearances in pure wave mechanics as predicted by the standard collapse theory. The significant gaps at critical points in his exposition and the contradicting evidence of what he wanted, explain the many mutually incompatible reconstructions of Everett that apologists and critics have devised. This chapter also provides the author's interpretation of the various theories discussed in this book.

This chapter begins by discussing a sense in which simple interference effects are destroyed when a system's environment becomes correlated with its state — a phenomenon called decoherence. It then considers three approaches in interpreting the said phenomenon. It then argues that environmental decoherence does not by itself explain determinate records. Next, it explains Murray Gell–Mann and James Hartle's (GH's) many-histories approach, which provides two rules — one rule that tells what sets of alternative histories of the universe can be assigned approximate probabilities, and another rule that tells what these probabilities are. The GH approach describes these rules in the context of the Heisenberg picture. This chapter also presents some problems in the many-histories approach.

This chapter evaluates another way of interpreting Everett's branches as describing the states of different minds in which an observer's determinate experiences and beliefs are explained by the fact that he always has a determinate mental state. In this sense, such theories might be said to predict appearances directly. It describes the efforts of Albert and Loewer in explaining how such a theory might work. This chapter also discusses Lockwood's many-minds theory and its relationship to Albert and Loewer's. Lastly, it explains the relative-fact theory and the correlations-without-correlata view.

This chapter begins by discussing the foundations of Hugh Everett III's relative state theory, which he regards as a new, more general, and complete theory than the standard von Neumann–Dirac theory. It then talks about why Albert Einstein rejected Max Born's formulation of quantum mechanics where he described his new statistical interpretation of the wave function. It also provides a discussion on von Neumann's formulation of quantum mechanics and the standard theory, as well as a summary of the said theory. The chapter goes on to detail several arguments presented by Einstein regarding von Neumann's interpretation of quantum mechanics. It then presents von Neumann's psychophysical parallelism and Wigner's friend experiment.

This chapter explains the many-worlds interpretations, particularly the DeWitt–Graham interpretation — the splitting-worlds interpretation. The splitting-worlds theory proposes that one must choose what physical quantities one wants to be determinate in a world, which amounts to choosing a physically preferred basis. It discusses several traditional and real problems encountered with the splitting-worlds theory. It also describes another theory, where one might stipulate that the global state always evolves in the usual linear way, selects a preferred basis that makes observers' records always determinate in each local state, and then chooses a connection rule that will link local states at different times into trajectories — the many threads theory.

This chapter begins by discussing several strategies for interpreting the global state. Next, it explains that the bare theory is simply the standard von Neumann–Dirac formulation of quantum mechanics with the standard interpretation of states (the eigenvalue-eigenstate link) without the collapse postulate — hence, bare. Subsequently, it examines several suggestive properties of the bare theory that tell what an observer would report concerning his experience in various measurement situations if the theory were true. It then explains that all measurement interactions induce an imperfect correlation between the state of an observer's most immediately accessible physical records and the observed quantity of the object system without disturbing the property being measured. This chapter also differentiates ordinary and disjunctive records, experiences, and beliefs. Lastly, it discusses several problems encountered with the bare theory.

This chapter discusses how one might add a physical quantity to the usual quantum-mechanical state description in order to account for the determinate measurement records. It explains that the value of this quantity in effect chooses exactly one Everett branch as actual, which is the branch describing an observer as recording the measurement results that he in fact records. In addition, it describes two essential ways of branch selection — stipulating a single preferred physical quantity as always determinate, something like particle configuration in Bohm's theory, or stipulating a rule, like the rules provided by different modal theories intended to select a determinate property for each physical system at each time given the quantum-mechanical state. This chapter also provides a description of the surreal trajectories and the persistence of memory. It discusses the incompatibility of Bohm's theory with relativity and other physical quantities, as well as the theory's limiting properties.

We introduce a framework uniting algorithmic randomness with exchangeable credences to address foundational questions in philosophy of probability and philosophy of science. To demonstrate its power, we show how one might use the framework to derive the Principal Principle---the norm that rational credence should match known objective chance---without circularity. The derivation brings together de Finetti's exchangeability, Martin-Löf randomness, Lewis's and Skyrms's chance-credence norms, and statistical constraining laws (arXiv:2303.01411). Laws that constrain histories to algorithmically random sequences naturally pair with exchangeable credences encoding inductive symmetries. Using the de Finetti representation theorem, we show that this pairing directly entails the Principal Principle of this framework. We extend the proof to partial exchangeability and provide finite-history bounds that vanish in the infinite limit. The Principal Principle thus emerges as a mathematical consequence of the alignment between nomological constraints and inductive learning. This reveals how algorithmic randomness and exchangeability can illuminate foundational questions about chance, frequency, and rational belief.

Skyrms–Lewis signaling games illustrate how meaningful language may evolve from initially meaningless random signals (Lewis, Convention1969; Skyrms 2008). Here we will consider how incommensurable languages might evolve in the context of signaling games. We will also consider the types of incommensurability exhibited between evolved languages in such games. We will find that sequentially evolved languages may be strongly incommensurable while still allowing for increasingly faithful descriptions of the world.

We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a nonstandard notion of chance. The second, a probabilistic* constraining law, impose relative frequency and randomness constraints that every physically possible world must satisfy. The constraining notion removes a major obstacle to a unified governing account of non-Humean laws, on which laws govern by constraining physical possibilities; it also provides independently motivated solutions to familiar problems for the Humean best-system account (the Big Bad Bug and the zero-fit problem). On either approach, probabilistic laws are tied more tightly to corresponding sets of possible worlds: some histories permitted by traditional probabilistic laws are now ruled out as physically impossible. Consequently, the framework avoids one variety of empirical underdetermination while bringing to light others that are typically overlooked.

This paper concerns how rule-following behavior might evolve in the context of a variety of Skyrms–Lewis signaling game (Lewis, Convention, 1969; Skyrms, Signals evolution, learning, & information 2010), how such rules might subsequently evolve to be used in new contexts, and how such appropriation allows for the composition of evolved rules. We will also consider how the composition of simpler rules to form more complex rules may be significantly more efficient than evolving the complex rules directly. And we will review an example of rule following by pinyon and scrub jays (Bond et al., Anim Behav 65:476–487, 2003) as an illustration of the appropriation of a rule to a new context (Barrett, Biol Theory 8(2):142–150, 2013a; Barrett, Philos Sci, 2014). The proposal here is that the composition of rules might occur in a way that is precisely analogous to such simple appropriation. Finally, we will briefly consider how any finite truth-functional operation might evolve by the sequential appropriation of simpler rules.

Hugh Everett III was an American physicist best known for his many-worlds interpretation of quantum mechanics, which formed the basis of his PhD thesis at Princeton University in 1957. Although counterintuitive, Everett's revolutionary formulation of quantum mechanics offers the most direct solution to the infamous quantum measurement problem--that is, how and why the singular world of our experience emerges from the multiplicities of alternatives available in the quantum world. The many-worlds interpretation postulates the existence of multiple universes. Whenever a measurement-like interaction occurs, the universe branches into relative states, one for each possible outcome of the measurement, and the world in which we find ourselves is but one of these many, but equally real, possibilities. Everett's challenge to the orthodox interpretation of quantum mechanics was met with scorn from Niels Bohr and other leading physicists, and Everett subsequently abandoned academia to conduct military operations research. Today, however, Everett's formulation of quantum mechanics is widely recognized as one of the most controversial but promising physical theories of the last century. In this book, Jeffrey Barrett and Peter Byrne present the long and short versions of Everett's thesis along with a collection of his explanatory writings and correspondence. These primary source documents, many of them newly discovered and most unpublished until now, reveal how Everett's thinking evolved from his days as a graduate student to his untimely death in 1982. This definitive volume also features Barrett and Byrne's introductory essays, notes, and commentary that put Everett's extraordinary theory into historical and scientific perspective and discuss the puzzles that still remain.

We consider the efficacy of various forms of reinforcement learning with punishment in evolving linguistic conventions in the context of Lewis-Skyrms signalling games. We show that the learning strategy of reinforcement with iterative punishment is highly effective at evolving optimal conventions in even complex signalling games. It is also robust and can be easily extended to a self-tuning variety of reinforcement learning. We briefly discuss some of the virtues of reinforcement with iterative punishment and how it may be related to learning in nature.

Humans and many animals are capable of learning and learning how to learn better. We are concerned here with one way that reinforcement learners might learn how to learn better. In an experiment described by Harlow in (Psychol Rev 56:51–65, 1949) a group of rhesus monkeys learn a new way of learning in the context of a specific type of problem. We will consider how such agents might coevolve a new learning dynamics and new attendant saliences. To this end, we propose a self-tuning dynamics that illustrates one way that a reinforcement learner might acquire forms of learning that are well-suited to context-specific problems.

The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.

A situated observer is an observer as modeled within the world characterized by one’s physical theory. A physical theory arguably only makes empirical predictions if it makes predictions for the records of a situated observer. In this spirit, one has a satisfactory solution to the measurement problem only if one has a formulation of quantum mechanics that makes the right empirical predictions for the records of a situated observer. Bohmian mechanics addresses the measurement problem by explaining what measurement records are, how a situated observer might produce them, and why a situated observer should expect the standard quantum predictions. The notion of an effective wave function is crucial in understanding how the theory makes empirical predictions.

David Hume’s skeptical solution to the problem of induction was grounded in his belief that we learn by means of custom. We consider here how a form of reinforcement learning like custom may allow an agent to learn how to learn in other ways as well. Specifically, an agent may learn by simple reinforcement to adopt new forms of learning that work better than simple reinforcement in the context of specific tasks. We will consider how such a bootstrapping process may lead to a system that includes trial-and-error forms of learning like win-stay/lose-shift, probe and adjust, and simple reinforcement itself together with higher-rationality inferential tools.

In order for Bayesian inquiry to count as objective, one might argue that it must lead to a consensus among those who use it and share evidence, but presumably this is not enough. It has been proposed that one should also require that the consensus be reached from very different initial opinions by conditioning only on basic experimental evidence, evidence free from subjective, social, or psychological influence. I will argue here, however, that this notion of objectivity in Bayesian inquiry is too narrow.