There appear to be multiple mathematically and physically distinct theories that successfully reproduce the empirical predictions of quantum mechanics, so-called "interpretations" of quantum mechanics. This dissertation uses the tools of formal epistemology (prominently, the concept of self-locating uncertainty) to investigate which of the theories that have been put forward really are empirically adequate and what alternatives can be devised. The first chapter introduces a novel theory that incorporates aspects of two well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. The quantum wave function can be represented as a field on configuration space, the space of possible ways particles can be arranged. According to Bohmian mechanics a single point in this space is special; it represents the way all of the particles actually are arranged. The newly introduced theory holds that many of the points in configuration space are special; for each, there is a world in which particles are arranged that way. In general, there will be multiple worlds that are so similar that an agent cannot tell directly from experience which they are in; self-locating uncertainty is unavoidable. The next chapter argues for the empirical adequacy of the many-worlds interpretation. In this version of quantum mechanics, processes like quantum measurements cause agents to split into multiple copies and enter periods of self-locating uncertainty. An epistemic principle demarcating which facts about the world one's credences might reasonably depend on (only facts about what's happening around here) is used to derive probabilistic predictions from the many-worlds interpretation. In the third chapter self-locating uncertainty is employed in evaluating another version of quantum mechanics, Ghirardi-Rimini-Weber theory. In this theory, random collapse events prevent our world from splitting into many. If the collapse events are rare, this prevention fails. Other worlds have time to form but most are short-lived. Our survival provides evidence against that kind of theory. The final chapter is an original introduction to relativistic quantum field theory which lays groundwork for evaluating the prospects of extending various interpretations of quantum mechanics to this more sophisticated theory.
There appear to be multiple mathematically and physically distinct theories that successfully reproduce the empirical predictions of quantum mechanics, so-called "interpretations" of quantum mechanics. This dissertation uses the tools of formal epistemology (prominently, the concept of self-locating uncertainty) to investigate which of the theories that have been put forward really are empirically adequate and what alternatives can be devised. The first chapter introduces a novel theory that incorporates aspects of two well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. The quantum wave function can be represented as a field on configuration space, the space of possible ways particles can be arranged. According to Bohmian mechanics a single point in this space is special; it represents the way all of the particles actually are arranged. The newly introduced theory holds that many of the points in configuration space are special; for each, there is a world in which particles are arranged that way. In general, there will be multiple worlds that are so similar that an agent cannot tell directly from experience which they are in; self-locating uncertainty is unavoidable. The next chapter argues for the empirical adequacy of the many-worlds interpretation. In this version of quantum mechanics, processes like quantum measurements cause agents to split into multiple copies and enter periods of self-locating uncertainty. An epistemic principle demarcating which facts about the world one's credences might reasonably depend on (only facts about what's happening around here) is used to derive probabilistic predictions from the many-worlds interpretation. In the third chapter self-locating uncertainty is employed in evaluating another version of quantum mechanics, Ghirardi-Rimini-Weber theory. In this theory, random collapse events prevent our world from splitting into many. If the collapse events are rare, this prevention fails. Other worlds have time to form but most are short-lived. Our survival provides evidence against that kind of theory. The final chapter is an original introduction to relativistic quantum field theory which lays groundwork for evaluating the prospects of extending various interpretations of quantum mechanics to this more sophisticated theory.
An understanding of quantum theory is manifested by the ability successfully and unproblematically to use it to further the scientific goals of prediction, explanation, and control of natural phenomena. An Interpretation seeks further to formulate or reformulate it as a fundamental theory that provides a self-contained description of the world. I critically review three prominent but radically different Interpretations of quantum theory (Bohmian mechanics, non-linear theories, Everettian quantum mechanics) and give my reasons for rejecting each as a way of understanding quantum theory. These include problems associated with non-locality, failure of relativistic invariance, empirical inaccessibility, and decision-making. We can achieve a satisfactory understanding of quantum theory and how it successfully advances the goals of science without providing an Interpretation of the theory.
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.
It is well known that quantum physics deals with phenomena characterized by uncertainty. A typical expression of this uncertainty is the uncertainty principle, where, the more precisely we know the position of a particle, the more imprecisely we know its momentum (and vice versa).Opinions are divided as to whether this epistemological uncertainty is also an ontological uncertainty. Of some relevance here is the following observation by Quentin Smith: Heisenberg originally interpreted [the uncertainty] epistemically, but Bohr convinced him in private communications to accept a verificationist metaphysics, with its attendant ontological interpretation of the uncertainty relations (Smith 2002, 137) There are many competing interpretations of the quantum mechanical mathematical formalism. Of these interpretations, particularly well-known are the so-called Copenhagen interpretation of Bohr (where it is asserted that the position-view and the momentum-view of reality are complementary, and cannot be considered in the same context), and the many-universes interpretation of Hugh Everett. Roughly speaking, the latter asserts that whenever a measurement is made of a particle, the universe splits into copies, each one of which corresponds to the different possible outcomes of the measurement. Many scientists are happy to work with the many-universes interpretation-provided that their working with the theory has no ontological commitment. That is, they are not prepared to believe that the many universes actually exist. David Deutsch, who is one of the leading researchers in the field of quantum computation, is an exception. Indeed, he is the main advocate of the reality of the many universes; and he provides a number of important reasons why he is such an advocate. In the present essay, I intend to look at the arguments for and the arguments against the existence of the many universes, clarifying along the way what the meaning of exist in this regard should be considered to be. A first conclusion will be that while Deutsch's arguments are highly persuasive, there is one telling objection to the existence of the many universes-or multiverse, as the collection of them is becoming known-that must be addressed. My procedure then will be to show that the objection can in fact be met, using the so-called methodological solipsism approach introduced by Hans Driesch and employed subsequently by such theorists as Fodor and Putnam. The Many-Universes Interpretation of Quantum Physics It is not my intention in this essay to become bogged down in the minutiae of quantum physics, where the complexities of the mathematics are exacerbated by the lack of any single way of interpreting it. However, in order to provide a background for my subsequent arguments, I shall discuss briefly a typical and familiar quantum-mechanical scenario: the so-called experiment. My account is based on that of Penrose (1985). The results that may be expected in a performance of the two-slit experiment depend on the fact that sub-microscopic particles, such as electrons or photons, behave sometimes like particles and sometimes like waves. The experiment is simple to describe: typically, a beam of light is directed through a pair of closely-separated and parallel narrow slits to a screen located behind it. Penrose describes the scenario as follows (it is worth quoting him at length): The most evident manifestation of the light as particles . . occurs at the screen. The light arrives there in discrete localized units of energy.. .. Never is the energy of just half a photon... received. Light reception is an all-or-nothing phenomenon in photon units. Only whole numbers of photons are ever seen. However, a wavelike behaviour seems to arise as the photons pass through the slits. Suppose, first, that only one slit is open (the other being blocked off). After passing through, the light will spread out-by. …
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well as those of standard quantum mechanics. It has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Most importantly, the Born rule can be derived by straightforward application of the Laplacian rule, without reliance on a "quantum equilibrium hypothesis" that is crucial for Bohmian mechanics, and without reliance on a "branch weight" that is crucial for Everett-type theories. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett's approach, without being actually reducible to these. In particular, there is no "splitting of worlds", which is a typical feature of Everett-type theories. Altogether, the theory explains 1) the subjective occurrence of probabilities, 2) their quantitative value as given by the Born rule, 3) the identification of observables as self-adjoint operators on Hilbert space, and 4) the apparently random "collapse of the wavefunction" caused by the measurement, while still being an objectively deterministic theory.
Abstract Recent accounts of probability in the many worlds interpretation of quantum mechanics are vulnerable due to their dependence on probability theory per se. For this reason, the many worlds interpretation continues to suffer from the incoherence and quantitative problems. After discussing various theories of probability, I discuss the incoherence problem and argue that self-locating probabilities centered in time-extended worlds can solve it. I then discuss and refute various solutions to the quantitative problem. I argue that the only tenable way to ground these self-locating probabilities is to identify the mathematical form of the Born rule as a generic pattern in a time-extended wavefunction, and to distribute degrees of belief over the region of wavefunction occupied by this pattern. I then outline a time-symmetric version of quantum mechanics - the Fixed Point Formulation - which, interpreted within a time-symmetric Everettian framework, can provide the foundation for a theory of quantum probability.