Relative State Research Articles

Branching with Uncertain Semantics

Branching with Uncertain Semantics

Evidence and Uncertainty in Everett’s Multiverse

How does it come about then, that great scientists such as Einstein, Schrödinger and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. […] The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road. (Born [1954], pp. 8, 11)It is truly surprising how little difference all this makes. Most physicists use quantum mechanics every day in their working lives without needing to worry about the fundamental problem of its interpretation. (Weinberg [1992], p. 66)I endorse the view that it may be of no relevance to the acceptability of the Everett interpretation of quantum mechanics as a physical theory whether or not an informed observer can be uncertain about the outcome of a quantum measurement prior to its having occurred. However, I suggest that the very possibility of post-measurement, pre-observation uncertainty has an essential role to play in both confirmation theory and decision theory in a branching universe. This is supported by arguments which do not appeal to van Fraassen’s Reflection Principle. 1. Dendritic Unitary Evolution2. The Born–Vaidman Rule3. Greaves on Uncertainty4. Retroactive Counterfactual Uncertainty5. Odds and Ends

Qeauty and the books: a response to Lewis’s quantum sleeping beauty problem

In his 2007 paper “Quantum Sleeping Beauty”, Peter Lewis poses a problem for the supporters’ of the Everett interpretation of quantum mechanics appeal to subjective probability. Lewis’s argument hinges on parallels between the traditional “sleeping beauty” problem in epistemology and a quantum variant. These two cases, Lewis argues, advocate different treatments of credences even though they share important epistemic similarities, leading to a tension between the traditional solution to the sleeping beauty problem (typically called the “thirder” solution) and Everettian quantum mechanics. In this paper I examine the metaphysical and epistemological differences between Lewis’s two cases, and, in particular, I show how diachronic Dutch book arguments support both the thirder solution in the traditional case and the Everettian’s solution in the variant case. These Dutch books, I argue, reveal an important disanalogy between Lewis’s two cases such that Lewis’s argument does not reveal an inconsistency in either the Everettian’s or the thirder’s assignment of credences.

Formalism and Interpretation in Quantum Theory

Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation.

The EPR paradox, Bell’s inequality, and the question of locality

Most physicists agree that the Einstein–Podolsky–Rosen–Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell’s inequality are locality and counterfactual definiteness but not scientific realism, determinism, or hidden variables as are often suggested. We further examine the resulting constraints on physical theory with an illustration from the many-worlds interpretation of quantum mechanics—an interpretation that we argue is deterministic, local, and realist but that nonetheless violates the Bell inequality.

Probability, Self-Location, and Quantum Branching

The main problem with the many-worlds theory is that it is not clear how the notion of probability should be understood in a theory in which every possible outcome of a measurement actually occurs. In this paper, I argue for the following theses concerning the many-worlds theory: (1) If probability can be applied at all to measurement outcomes, it must function as a measure of an agent's self-location uncertainty. (2) Such probabilities typically violate reflection. (3) Many-worlds branching does not have sufficient structure to admit self-location probabilities. (4) Decision-theoretic arguments do not solve this problem.

Coherent states in the quantum multiverse

In this Letter, we study the role of coherent states in the realm of quantum cosmology, both in a second-quantized single universe and in a third-quantized quantum multiverse. In particular, most emphasis will be paid to the quantum description of multiverses made of accelerated universes. We have shown that the quantum states involved at a quantum mechanical multiverse whose single universes are accelerated are given by squeezed states having no classical analogs.

Informational Branching Universe

This paper suggests an epistemic interpretation of Belnap’s branching space-times theory based on Everett’s relative state formulation of the measurement operation in quantum mechanics. The informational branching models of the universe are evolving structures defined from a partial ordering relation on the set of memory states of the impersonal observer. The totally ordered set of their information contents defines a linear “time” scale to which the decoherent alternative histories of the informational universe can be referred—which is quite necessary for assigning them a probability distribution. The “historical” state of a physical system is represented in an appropriate extended Hilbert space and an algebra of multi-branch operators is developed. An age operator computes the informational depth of historical states and its standard deviation can be used to provide a universal information/energy uncertainty relation. An information operator computes the encoding complexity of historical states, the rate of change of its average value accounting for the process of correlation destruction inherent to the branching dynamics. In the informational branching models of the universe, the asymmetry of phenomena in nature appears as a mere consequence of the subject’s activity of measuring, which defines the flow of time-information.

A history of entanglement: Decoherence and the interpretation problem

This paper examines the interweaving of the history of quantum decoherence and the interpretation problem in quantum mechanics through the work of two physicists—H. Dieter Zeh and Wojciech Zurek. In the early 1970s Zeh anticipated many of the important concepts of decoherence, framing it within an Everett-type interpretation. Zeh has since remained committed to this view; however, Zurek, whose papers in the 1980s were crucial in the treatment of the preferred basis problem and the subsequent development of density matrix formalism, has argued that decoherence leads to what he terms the ‘existential interpretation’, compatible with certain aspects of both Everett's relative-state formulation and the Bohr's ‘Copenhagen interpretation’. I argue that these different interpretations can be traced back to the different early approaches to the study of environment-induced decoherence in quantum systems, evident in the early work of Zeh and Zurek. I also show how Zurek's work has contributed to the tendency to see decoherence as contributing to a ‘new orthodoxy’ or a reconstruction of the original Copenhagen interpretation.

Ghirardi-Rimini-Weber Collapse Theory and Whiteheadian Process Philosophy

Abstract There have been many attempts to undertand the connections between quantum theory and Whiteheadian process philosophy However, due to the ontological considerations, it is very important to specify which interpretation of quantum theory one embraces before inquiring into the details of Whitehead’s philosophy of organism. In this article, I argue that Ghirardi-Rimini-Weber (GRW) collapse interpretation of quantum theory serves as a suitable point of departure for future endeavors. Comparisons with manyworlds interpretation and decoherence approach have also been provided.

Everett and the Born rule

During the last 10 years or so, derivations of the Born rule based on decision theory have been proposed and developed, and it is claimed that these are valid in the context of the Everett interpretation. This claim is critically assessed and it is shown that one of its key assumptions is a natural consequence of the principles underlying the Copenhagen interpretation, but constitutes a major additional postulate in an Everettian context. It is further argued that the Born rule, in common with any interpretation that relates outcome likelihood to the expansion coefficients connecting the wavefunction with the eigenfunctions of the measurement operator, is incompatible with the purely unitary evolution assumed in the Everett interpretation.

Quantum measurement and quantum gravity: many-worlds or collapse of the wavefunction?

At present, there are two possible, and equally plausible, explanations for the physics of quantum measurement. The first explanation, known as the many-worlds interpretation, does not require any modification of quantum mechanics, and asserts that at the time of measurement the Universe splits into many branches, one branch for every possible alternative. The various branches do not interfere with each other because of decoherence, thus providing a picture broadly consistent with the observed Universe. The second explanation, which requires quantum mechanics to be modified from its presently known form, is that at the time of measurement the wavefunction collapses into one of the possible alternatives. The two explanations are mutually exclusive, and up until now, no theoretical reasoning has been put forward to choose one explanation over the other. In this article, we provide an argument which implies that the collapse interpretation is favored over the many-worlds interpretation. Our starting point is the assertion (which we justify) that there ought to exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. The need for such a reformulation implies that quantum theory becomes nonlinear on the Planck mass/energy scale. Standard linear quantum mechanics is an approximation to this nonlinear theory, valid at energy scales much smaller than the Planck scale. Using ideas based on noncommutative differential geometry, we develop such a reformulation and derive a nonlinear Schrödinger equation, which can explain collapse of the wavefunction. We also obtain an expression for the lifetime of a quantum superposition. We suggest ideas for an experimental test of this model.

An Introduction to Many Worlds in Quantum Computation

The interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest has come from those involved in quantum computing and information theory, as there has always been a strong foundational element in this field. This paper introduces one interpretation of quantum mechanics, a modern `many-worlds' theory, from the perspective of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific `neo-Everettian' theory is introduced and its claim as the best available interpretation defended. The main objections to the interpretation, including the so-called ``problem of probability'' are shown to fail. The local nature of the interpretation is demonstrated, and the implications of this both for the interpretation and for quantum mechanics more generally are discussed. Finally, the consequences of the theory for quantum computation are investigated, and common objections to using many worlds to describe quantum computing are answered. We find that using this particular many-worlds theory as a physical foundation for quantum computation gives several distinct advantages over other interpretations, and over not interpreting quantum theory at all.

Ghirardi-Rimini-Weber Collapse Theory and Whiteheadian Process Philosophy

There have been many attempts to undertand the connections between quantum theory and Whiteheadian process philosophy. However, due to the ontological considerations, it is very important to specify which interpretation of quantum theory one embraces before inquiring into the details of Whitehead`s philosophy of organism. In this article, I argue that Ghirardi-Rimini-Weber (GRW) collapse interpretation of quantum theory serves as a suitable point of departure for future endeavors. Comparisons with manyworlds interpretation and decoherence approach have also been provided.

Many-Worlds Interpretation of Quantum Theory and Mesoscopic Anthropic Principle

We suggest to combine the Anthropic Principle with Many-Worlds Interpretation of Quantum Theory. Realizing the multiplicity of worlds it provides an opportunity of explanation of some important events which are assumed to be extremely improbable. The Mesoscopic Anthropic Principle suggested here is aimed to explain appearance of such events which are necessary for emergence of Life and Mind. It is complementary to Cosmological Anthropic Principle explaining the fine tuning of fundamental constants. We briefly discuss various possible applications of Mesoscopic Anthropic Principle including the Solar Eclipses and assembling of complex molecules. Besides, we address the problem of Time's Arrow in the framework of Many-World Interpretation. We suggest the recipe for disentangling of quantities defined by fundamental physical laws and by an anthropic selection.

Branching and Uncertainty

Following Lewis, it is widely held that branching worlds differ in important ways from diverging worlds. There is, however, a simple and natural semantics under which ordinary sentences uttered in branching worlds have much the same truth values as they conventionally have in diverging worlds. Under this semantics, whether branching or diverging, speakers cannot say in advance which branch or world is theirs. They are uncertain as to the outcome. This same semantics ensures the truth of utterances typically made about quantum mechanical contingencies, including statements of uncertainty, if the Everett interpretation of quantum mechanics is true. The `incoherence problem' of the Everett interpretation, that it can give no meaning to the notion of uncertainty, is thereby solved.

Selection Postulates and Probability Rules in the Problem of Quantum Measurement

Various approaches to quantum measurement problem within the framework of usual unitary quantum dynamics are considered. It is argued that neither decoherence theory nor many-worlds interpretation of quantum mechanics do provide ultimate solution of the measurement problem: they cannot solve the problem of an alternative selection within the framework of unitary quantum dynamics. It is argued that the selection postulate in quantum theory is a very fundamental entity tightly connected with the nature of mathematics and with the nature of the mind, while the probability rules are more technical things admitting various approaches based on various sets of axioms.

Bell’s Theorem, Many Worlds and Backwards-Time Physics: Not Just a Matter of Interpretation

The classic of Clauser, Holt, Shimony and Horne tells us that we must give up at least one of: (1) objective reality (aka hidden variables); (2) locality; or (3) time-forwards macroscopic statistics (aka causality). The orthodox Copenhagen version of physics gives up the first. The many-worlds theory of Everett and Wheeler gives up the second. The backwards-time theory of physics (BTP) gives up the third. Contrary to conventional wisdom, empirical evidence strongly favors Everett-Wheeler over orthodox Copenhagen. BTP has two major variations -- a many-worlds version, and a neoclassical version of partial differential equations (PDE) in the spirit of Einstein. Section 2 discusses quantum measurement according to BTP, focusing on how we represent condensed matter objects like polarizers in a Bell's Theorem experiment or in tests of Hawking's cosmology. The Backwards Time Telegraph, though speculative, is discussed.

THE INEVITABLE NONLINEARITY OF QUANTUM GRAVITY FALSIFIES THE MANY-WORLDS INTERPRETATION OF QUANTUM MECHANICS

There are fundamental reasons why there should exist a reformulation of quantum mechanics which does not refer to a classical space–time manifold. It follows that quantum mechanics as we know it is a limiting case of a more general nonlinear quantum theory, with the nonlinearity becoming significant at the Planck mass/energy scale. This nonlinearity is responsible for a dynamically induced collapse of the wave function, during a quantum measurement, and it hence falsifies the many-worlds interpretation of quantum mechanics. We illustrate this conclusion using a mathematical model based on a generalized Doebner–Goldin equation. The non-Hermitian part of the Hamiltonian in this norm-preserving, nonlinear, Schrödinger equation dominates during a quantum measurement, and leads to a breakdown of linear superposition.

A formulação dos 'estados relativos' da teoria quântica

O objetivo desse artigo é uma apresentação didática, em português, da interpretação dos estados relativos, publicada por Hugh Everett em 1957. Nessa apresentação, reescrevemos os argumentos originais utilizando o formalismo de Dirac de modo a simplificar sua compreensão. A apresentação foi feita sem o uso de cargas ontológicas posteriores, seguindo principalmente os textos originais de Everett. Ao longo dos tópicos, evidenciaremos quais os principais problemas enfrentados por essa interpretação.