Everett's Theory Research Articles

Everettian quantum mechanics and the ghost of fission

Abstract Arguments from fission cases, most notably made by Parfit, have historically been utilized in discussions of Everettian quantum mechanics (EQM) in an attempt to illuminate details of familiar accounts in which an agent ‘splits’. Whilst such imagery is often seen as an innocuous depiction of Everett's theory, it is in fact a poisoned chalice. I argue firstly that the fission case analogy is responsible for the conceptual foundations of probability arguments in EQM and secondly, following a number of disanalogies between fission cases and Everettian branching, I argue that the analogy is unfounded. I conclude that much of the discussion of the probability problem over the past 20 years has been predicated on a problematic analogy and its effects are still apparent today.

WHAT MAKES A QUANTUM PHYSICS BELIEF BELIEVABLE? MANY‐WORLDS AMONG SIX IMPOSSIBLE THINGS BEFORE BREAKFAST

AbstractAn extraordinary, if circumscribed, positive shift has occurred since the mid‐twentieth century in the perceived status of Hugh Everett III's 1956 theory of the universal wave function of quantum mechanics, now widely called the Many‐Worlds Interpretation (MWI). Everett's starkly new interpretation denied the existence of a separate classical realm, contending that the experimental data can be seen as presenting a state vector for the whole universe. Since there is no state vector collapse, reality as a whole is strictly deterministic. Explained jointly by the dynamical variables and the state vector, “this reality is not the reality we customarily think of, but is a reality composed of many worlds,” wrote Everett's colleague Bryce DeWitt. In this essay, I account briefly for the change of status in conventional scientific terms, yet chiefly in extended terms of three sets of ideas that I argue can be understood to affect believability in both scientific and religious contexts, illuminating helpfully the MWI phenomenon, and its engagement with theology: orthodoxy and heresy, language and reference, and faith and agnosticism. One's orientation relative to the variable content of these dynamic, socially oriented categories helps to make belief in ideas as metaphysically challenging as Everettian Quantum Mechanics, or particular ideas about God, either more or less believable. The categories will have the same function in a theology engaging Everett's theory, and in any theology at all written in a society deeply marked by what I further argue is a subtle, powerful, and pervasive mode of quasi‐scientific thinking we can call societal constructive agnosticism, of which anyone doing theology today must be aware.

Quantum mechanics: how to use Everett theory practically

Among theories of the physical world, quantum mechanics remains a topic of lively discussions on its so-called interpretation. For some it remains an open question to understand how deterministic equations of this theory, as established long ago, may combine with a fundamental uncertainty. We consider the process of spontaneous emission by an atom interacting with infinite number of degrees of freedom of the electromagnetic field. There is uncertainty in the evolution of the photo-emission process which was characterized as Markovian by using the equations of quantum mechanics when the decay of the atom is due to the coupling with the vacuum field. The Markovian property leads us naturally to describe spontaneous emission by using the classical Kolmogorov equation for the probability evolution of a parameter defining the state of the atom. We explain that Everett’s many-worlds interpretation weld together our description, and appears therefore as a consequence of the equations of quantum mechanics, that solves in this case the riddle of deterministic equations describing random events.

Quantum fractionalism: The Born rule as a consequence of the complex Pythagorean theorem

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in orthogonal projections from the complex line of a quantum state to eigenspaces of an observable. Unit total probability corresponds to a complex Pythagorean theorem: the measure of a subset of the complex line is the sum of the measures of its projections on all eigenspaces.Postulating the existence of a continuum infinity of identical quantum universes, all with the same quasi-classical worlds, we show that projection factors give relative amounts of worlds. These appear as relative frequencies of results in quantum experiments, and play the role of probabilities in decisions and inference. This solves the probability problem of Everett's theory, allowing its preferred basis problem to be solved as well, and may help settle questions about the nature of probability.

The measurement problem revisited

It has been realized that the measurement problem of quantum mechanics is essentially the determinate-experience problem, and in order to solve the problem, the physical state representing the measurement result is required to be also the physical state on which the mental state of an observer supervenes. This necessitates a systematic analysis of the forms of psychophysical connection in the solutions to the measurement problem. In this paper, I propose a new, mentalistic formulation of the measurement problem which lays more stress on psychophysical connection. By this new formulation, it can be seen more clearly that the three main solutions to the measurement problem, namely Everett's theory, Bohm's theory and collapse theories, correspond to three different forms of psychophysical connection. I then analyze these forms of psychophysical connection. It is argued that the forms of psychophysical connection required by Everett's and Bohm's theories have potential problems, while an analysis of how the mental state of an observer supervenes on her wave function may help solve the structured tails problem of collapse theories.

The many facets of Everett’s many worlds

The 50th anniversary of Everett’s 1957 paper has brought in its wake the publication of a number of important books on Everett’s life, work and theory. This book provides arguably the most vivid and comprehensive treatment of both state-of-theart developments within and criticism of the Everett interpretation (hence the question mark in the title!). By ‘vivid’ I mean a display of argument and eloquence in papers and discussions that at times makes the book literally difficult to put down. The papers were originally given at the two main conferences that marked the Everett anniversary, at the University of Oxford and at the Perimeter Institute for Theoretical Physics (Waterloo, Ontario). The end result, published in 2010, is a wonderful achievement by the four editors, Simon Saunders, Jonathan Barrett, Adrian Kent and David Wallace, who have managed to combine a vast breadth of diverging views (including their own) into a volume that is a must for anyone interested in the Everett theory. Chapter 1 is a masterly introduction by Simon Saunders, almost 50 pages long, in which he explains and comments on the material in the book. This introduction is both detailed enough to be a really useful guide to the rest of the book and very even-handed in its treatment of contrasting positions. Part I (Chapters 2–4, by David Wallace, Jim Hartle and Jonathan Halliwell) is devoted to discussing the theory of decoherence and its role in modern-day Everett theory. Indeed, it is only with the advent of decoherence—specifically in its ability to create temporally stable structures at the level of components of the wavefunction—that the problem of the ‘preferred basis’ in Everett has achieved a solution commanding a broad consensus. Wallace’s chapter is already a classic, and arguably the place to look if one wants to understand the modern-day approach to the ontology of the Everett theory, which

Everett's “Many-Worlds” proposal

Hugh Everett III proposed that a quantum measurement can be treated as an interaction that correlates microscopic and macroscopic systems—particularly when the experimenter herself is included among those macroscopic systems. It has been difficult, however, to determine precisely what this proposal amounts to. Almost without exception, commentators have held that there are ambiguities in Everett's theory of measurement that result from significant—even embarrassing—omissions. In the present paper, we resist the conclusion that Everett's proposal is incomplete, and we develop a close reading that accounts for apparent oversights. We begin by taking a look at how Everett set up his project—his method and his criterion of success. Illuminating parallels are found between Everett's method and then-contemporary thought regarding inter-theoretic reduction. Also, from unpublished papers and correspondence, we are able to piece together how Everett judged the success of his theory of measurement, which completes our account of his intended contribution to the resolution of the quantum measurement problem.

Time, Quantum Mechanics, and Probability

A variety of ideas arising in decoherence theory, and in the ongoing debate over Everett's relative-state theory, can be linked to issues in relativity theory and the philosophy of time, specifically the relational theory of tense and of identity over time. These have been systematically presented in companion papers (Saunders 1995; 1996a); in what follows we shall consider the same circle of ideas, but specifically in relation to the interpretation of probability, and its identification with relations in the Hilbert Space norm. The familiar objection that Everett's approach yields probabilities different from quantum mechanics is easily dealt with. The more fundamental question is how to interpret these probabilities consistent with the relational theory of change, and the relational theory of identity over time. I shall show that the relational theory needs nothing more than the physical, minimal criterion of identity as defined by Everett's theory, and that this can be transparently interpreted in terms of the ordinary notion of the chance occurrence of an event, as witnessed in the present. It is in this sense that the theory has empirical content.

Modelling and identification of iron losses in nonoriented steel laminations using Preisach theory

A numerical method for the evaluation of magnetic iron losses in steel laminations used in electrical machines is described. The magnetodynamic model for the magnetic field strength H, derived from the Maxwell equations, is coupled with the Preisach theory, describing the hysteresis behaviour. The resulting highly nonlinear and transient boundary value problem for H is solved numerically by a modified finite-element, finite-difference method. The direct identification of the material parameters, for which the authors invoke the Everett theory, is discussed in detail. The model is validated by the comparison of numerical experiments and measurements for the B-H loops. For the material considered the rate-dependent Preisach model is found to be more reliable than the classical Preisach model.

Relative-state theory: Four new aspects

It is shown that Everett's relative-state theory is distinguished from other versions of quantum mechanics in 4 novel respects: (1) It is exempt from Bell's theorem. (2) It does without amplitudes. (3) It is immune to Einstein completion. (4) It is rotational-frame covariant. The last point is (a) shared with micro relativity and (b) falsifiable. Everett's theory therefore is an alternative theory of physical reality.

An ?observer decomposition? for Everett's theory

Several authors have noted that Everett's theory needs a specification of a “special decomposition” in order to account for our perceived experience, including quantum measurement results. It is suggested here that a possible way to arrive at such a specification is to relate it to the internal structure of the observer himself.

Effects of surface heterogeneity in adsorption from binary liquid mixtures: II. Adsorption from nonideal bulk solutions

A theoretical description of adsorption from nonideal binary liquid mixtures on heterogeneous solid surfaces has been proposed. All the theoretical considerations presented here are based on IAP model (ideal adsorbed phase/nonideal bulk phase), which was used previously by Everett, Sircar and Myers, Kiselev and others. Using Everett's theory of adsorption from regular and non-athermal solutions, a method for calculating differential distribution function of equilibrium constant of the phase-exchange reaction has been proposed in terms of the condensation approximation method appropriately modified. Applying this method, the influence of the surface phase thickness and the type of the lattice model of a liquid solution on distribution function has been investigated. Furthermore, using the method of Stieltjes transforms, a new equation has been derived, which describes adsorption from binary solutions on the heterogeneous solid surfaces. On the basis of this equation a number of various model studies were carried out, the results of which confirmed the suggestions put forward by Zettlemoyer, Everett, Hansen and other authors that heterogeneity of solids is the major factor which can control the type, magnitude, and the range of the preferential adsorption from solutions. It was simultaneously shown that energetic heterogeneity of the solid surface play a greater role in adsorption from solutions than the nonideality of the bulk phase.

Structural information theory

A method of defining structural information in Hilbert space is described. Instead of commencing an information theory analysis with a simple signal and progressing to an n-dimensional information space, the reverse procedure can be followed: the signal is defined completely in both real and imaginary spaces, and is then represented as a dimensionless number in Hilbert space. Thus, a signal can be analyzed into a Hilbert space measure of information. This measure has similarities to the relativity of states of Everett's (1957) reformulation of quantum mechanics involving observer-observed interaction. Whereas Everett's theory deals with the totality of all possible ways in which a state function can be decomposed into the sum of products of state functions for subsystems of the overall system, the theory presented here deals with the totality of possible ways in which a Hilbert space measure of signal state can be decomposed by signal definition into reciprocally related measures of the state for subsystems of the overall system. In the overall system presented here, a signal is given a concise representation either as a quadratic form on a Hilbert space, or as a Fourier coefficients in isomorphic function space. The total information content of a signal qualified as a dimensionless number in Hilbert space may be given a representation in familiar units by the use of such methods. A primary postulate of quantum mechanics is obeyed in that all physically relevant information about a system is derivable from the knowledge of the state function of the system. Thus, a signal is defined firstly as an information measure, and secondly in the familiar units of frequency, bandwidth, midperiod, and duration.

Low-frequency photon-assisted tunneling in superconducting tunnel junctions

The photon-assisted tunneling response of Sn-SnO-Pb and Sn-SnO-Sn superconducting junctions to a 3.9 GHz microwave field has been measured. The experimental response of the tunneling current to the rf field agrees very closely with the response predicted by the theory of Tien and Gordon. The predictions of the Cook and Everett theory do not fit the data well.

RARE EARTH OXIDE SYSTEMS. THE HYSTERESIS EFFECTS IN PRASEODYMIUM OXIDE

The composition-- pressure diagram of the Pr- O system was studied between 10/sup -6/ and 150 mm oxygen pressure using a quartz beam microbalance. The isotherms between 400 and 500 deg show hysteresis between PrO/sub 1.80/ and PrO/sub 1.89/ as the pressure varies. At 465 deg a hysteresis loop extends over the entire pressure range. Everett's theory of hysteresis is compared to the Pr-- O isotherms at 465 deg . The seven theorems proposed by Everett are cited and discussed with reference to the Pr--O data. In general, the agreement between the properties of Everett's theoretical model of a domain system and the properties of the Pr-O system is good. Results of a preliminary study of the region between loop boundaries indicate that more than two domain states are present. The behavior of the praseodymium oxide system is thought to be a result of its being composed of domains of various stable compositions, such as PrO/sub 1.89/ and PrO/sub 1.80/. The domains change composition as a function of the oxygen pressure. (auth)