Relative State Research Articles

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

Contiguity of Parallel Worlds: Buddhist and Everett's

Niels Bohr himself pointed out to similarity of some philosophic approaches in quantum mechanics and in Buddhism. Some modern interpretations of quantum mechanics go even closer to the Buddhist approach, such as Everett interpretation and, specifically, the recent 'Extended Everett Concept' developed by M.B. Mensky. The present paper shows that both Buddhist thinkers and modern physicists, using very different methods, arrived basically at the same description of reality we live in. This is the point where the parallel worlds of Buddhism and Physics unexpectedly touched each other, and the deeper meaning of this contact is yet to be appreciated by both parties. NeuroQuantology | March 2013 | Volume 11 | Issue 1| Suppl 1 | Page 123-128

Everett Interpretation and Quantum Concept of Consciousness

Subjective aspects of quantum mechanics (QM) are most radically expressed in the (EI) of QM which suggests coexisting macroscopically distinct configurations of the world in the form of a superposition of the (quasi-)classical state vectors. The components of such a superposition are often verbally denoted as Everett's worlds, hence the name Many-Worlds Interpretation (MWI) for EI. Explicit accounting the correlation of each classical configuration of the world with the corresponding state of an observer's mind yields the so-called Many-Minds interpretation (MMI). This is maximum that may be done in the context of EI if the restriction by pure physics is implied. In the author's Extended Everett Concept (EEC) the observer's consciousness is defined in the spirit of psycho-physical parallelism, i.e. as going beyond pure physics. As a consequence, according to EEC, an observer, if he/she weakens or turns off his/her consciousness (perception), obtains the ability of super-intuition (obtaining seemingly unavailable information) and even of controlling the subjective reality (a picture of classical reality as it will be subjectively perceived). This may be interpreted as a realization of the Jung's collective unconscious as well as an explanation of the mystical elements in Oriental philosophies, world religions and deep psychological practices. NeuroQuantology | March 2013 | Vol 11 | Issue 1 | Suppl 1 | Page 85-96

Reasoning on Many-Worlds Interpretatıon of Quantum Theory

Some difficulties that arise, when we try to imagine how a packet is reduced in the many-worlds interpretation of quantum theory, are discussed in the work. It is shown that suggested by now explanations how the wave packet reduction happens cannot claim upon the role of the final answer to this question, even though they are not formally contradictory. NeuroQuantology | March 2013 | Volume 11 | Issue 1| Suppl 1 | Page 106-109

When an Atom Becomes a Message—Practicing Experiments on the Origins of Life

Practicing experiments on the origins of life within the framework of quantum mechanics comes to face a task of distinguishing the descriptive spaces of the object between a space of physical states and a space of probability distributions. One candidate for accommodating both the physical and the probabilistic description in a mutually tolerable manner is to apply first-second person descriptions to the space of physical states while letting the space of probability distributions addressable in third person descriptions be accessible via first-second person descriptions. The mediator or messenger for accommodating these two types of description is the process of probability flow equilibration. The relative state formulation of quantum mechanics opens a possibility for the likelihood that a simple atom such as a carbon atom may carry a message for holding the process of probability flow equilibration. An experimental example demonstrating a carbon atom serving as a messenger is found in the running of the citric acid cycle in the absence of biological enzymes.

Synchronicities of Carl Jung Interpreted in Quantum Concept of Consciousness

The phenomenon of synchronicities which has been first described by Carl Jung, is explained in the framework of Extended Everett Concept proposed by the author. EEC differs from the Everett's “many-worlds interpretation” of quantum mechanics in that it explicitly includes the phenomena of consciousness, super-intuition (direct vision of truth) and ability to choose the version of reality which is to be subjectively experienced. Extended Everett Concept can explain synchronicities since, according to this theory, the subjective perception of reality by humans is governed not only by material causes but also by goals that may be immaterial (words, images or ideas). NeuroQuantology | September 2012 | Volume 10 | Issue 3 | Page 468-481

Revisiting the Concepts of Subjectivity and Reality in Many-Worlds View of Consciousness and Super-Consciousness

We read with interest the theory of consciousness propounded by Mensky (2011), based on the many-worlds view by Everett. The work done by the author to mathematically frame the many-worlds theory in the field of consciousness is commendable. NeuroQuantology | June 2012 | Volume 10 | Issue 2 | Page 346-347

Chemical evolution as a concrete scheme for naturalizing the relative-state of quantum mechanics

The evolutionary onset of a reaction cycle such as an autocatalytic cycle requires a reliable framework for protecting the harbinger cycle, once it appears by any chance, against the hostile environments in the neighborhood. One natural candidate for protecting the fragile nascent cycle could be available from the operation of internal measurement envisioned in the relative-state formulation of quantum mechanics. Once every chemical reactant is taken to be relative to every other reactant in the act of measuring each other internally, the relative-state formulation provides the condition for favoring and protecting those events such that the reactions mediating between the reactants and the products may eventually form a reaction cycle.

Four Problems About Self-Locating Belief

This article defends the Doomsday Argument, the Halfer Position in Sleeping Beauty, the Fine-Tuning Argument, and the applicability of Bayesian confirmation theory to the Everett interpretation of quantum mechanics. It will argue that all four problems have the same structure, and it gives a unified treatment that uses simple models of the cases and no controversial assumptions about confirmation or self-locating evidence. The article will argue that the troublesome feature of all these cases is not self-location but selection effects.

Quantum discord and noncontextual hidden-variable models

It is shown that theoretically viable noncontextual hidden-variable models in $d=2$ lead to conflicting dispersion-free expressions in the analysis of the conditional measurement of two non-orthogonal projectors. No satisfactory criterion of the quantum discord, which relies on the analysis of conditional measurement, is formulated in the $d=2$ hidden-variable space due to a lack of uniqueness of the dispersion-free representation. We also make a speculative comment on a ``many-worlds interpretation'' of hidden-variable models to account for the conditional measurement.

Cosmological constant in the quantum multiverse

Recently, a new framework for describing the multiverse has been proposed which is based on the principles of quantum mechanics. The framework allows for well-defined predictions, both regarding global properties of the universe and outcomes of particular experiments, according to a single probability formula. This provides complete unification of the eternally inflating multiverse and many worlds in quantum mechanics. In this paper we elucidate how cosmological parameters can be calculated in this framework, and study the probability distribution for the value of the cosmological constant. We consider both positive and negative values, and find that the observed value is consistent with the calculated distribution at an order of magnitude level. In particular, in contrast to the case of earlier measure proposals, our framework prefers a positive cosmological constant over a negative one. These results depend only moderately on how we model galaxy formation and life evolution therein.

Curious and sublime: the connection between uncertainty and probability in physics

From its first significant appearance in physics, the notion of probability has been linked in the minds of physicists with the notion of uncertainty. But the link may prove to be tenuous, if quantum mechanics, construed in terms of the Everett interpretation, is anything to go by.

Mathematical Models of Subjective Preferences in Quantum Concept of Consciousness

We discuss mathematical models describing the action of consciousness and super-consciousness as these phenomena are defined in the Extended Everett's Concept (EEC) proposed by the author. According to the Everett's interpretation of quantum mechanics, the state of the quantum world is a superposition of various classical pictures of the world (classical realities, or alternatives). Humans, due to their ability called consciousness, perceive the alternatives separately: all alternatives are perceived, but subjectively perceiving one of them is accompanied by the sensation of the remaining alternatives as if being invisible. This causes the impression that only one of the alternatives really exists, but this is an illusion of consciousness. When consciousness (separating the alternatives) is turned off (in sleep, trance or meditation) or weakened, another ability arises called super-consciousness. Due to super-consciousness, the human gets access to the set of all alternative realities taken as a whole, selects those alternatives that are favorable, and ensures that just these selected alternatives are experienced after consciousness is turned on again. Thus, EEC explains, on the basis of quantum mechanics, those features of consciousness which are usually treated as mystical. It is shown in the paper how these features of consciousness and super-consciousness can be presented by simple mathematical models.

Born in an infinite universe: A cosmological interpretation of quantum mechanics

We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics. We also argue that after discarding a zero-norm part of the wavefunction, the remainder consists of a superposition of indistinguishable terms, so that arguably "collapse" of the wavefunction is irrelevant, and the "many worlds" of Everett's interpretation are unified into one. Finally, the analysis suggests a "cosmological interpretation" of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer's inability to self-locate in this collection.

On the Faithful Interpretation of Pure Wave Mechanics

Given Hugh Everett III’s understanding of the proper cognitive status of physical theories, his relative-state formulation of pure wave mechanics arguably qualifies as an empirically acceptable physical theory. The argument turns on the precise nature of the relationship that Everett requires between the empirical substructure of an empirically faithful physical theory and experience. On this view, Everett provides a weak resolution to both the determinate record and the probability problems encountered by pure wave mechanics, and does so in a way that avoids unnecessary metaphysical complications. Taking Everett’s goal to be showing the empirical faithfulness of the relative-state formulation agrees well with his characterization of his project as one of seeking a model for observation in the correlation structure described by pure wave mechanics and seeking a measure of typicality over this empirical substructure that covaries with our empirically warranted expectations.

Fungibility and the quantum multiverse

The idea of a “doppelganger” (a “double” of a person) is a frequent theme of science fiction.

Everett’s pure wave mechanics and the notion of worlds

Everett (1957a, b, 1973) relative-state formulation of quantum mechanics has often been taken to involve a metaphysical commitment to the existence of many splitting worlds each containing physical copies of observers and the objects they observe. While there was earlier talk of splitting worlds in connection with Everett, this is largely due to DeWitt’s (Phys Today 23:30–35, 1970) popular presentation of the theory. While the thought of splitting worlds or parallel universes has captured the popular imagination, Everett himself favored the language of elements, branches, or relative states in describing his theory. The result is that there is no mention of splitting worlds or parallel universes in any of Everett’s published work. Everett, however, did write of splitting observers and was willing to adopt the language of many worlds in conversation with people who were themselves using such language. While there is evidence that Everett was not entirely comfortable with talk of many worlds, it does not seem to have mattered much to him what language one used to describe pure wave mechanics. This was in part a result of Everett’s empirical understanding of the cognitive status of his theory.

Quantum scalar-metric cosmology with Chaplygin gas

A spatially flat Friedmann–Robertson–Walker (FRW) cosmological model with generalized Chaplygin gas is studied in the context of scalar-metric formulation of cosmology. Schutz's mechanism for the perfect fluid is applied with generalized Chaplygin gas and the classical and quantum dynamics for this model is studied. It is found that the only surviving matter degree of freedom played the role of cosmic time. For the quantum mechanical description it is possible to find the wave packet which resulted from the linear superposition of the wave functions of the Schrödinger–Wheeler–DeWitt (SWD) equation, which is a consequence of the above formalism. The wave packets show two distinct dominant peaks and propagate in the direction of increasing scale factor. It may happen that our present universe originated from one of those peaks. The many-world and ontological interpretation of quantum mechanics is applied to investigate about the behavior of the scale factor and the scalar field (considered for this model). In both the cases the scale factor avoids singularity and a bouncing non-singular universe is found.

Quantum singularities in the FRW universe revisited

The components of the Riemann tensor in the tetrad basis are quantized and, through the Einstein equation, we find the local expectation value in the ontological interpretation of quantum mechanics of the energy density and pressure of a perfect fluid with equation of state $p=\frac{1}{3}\ensuremath{\rho}$ in the flat Friedmann-Robertson-Walker quantum cosmological model. The quantum behavior of the equation of state and energy conditions are then studied, and it is shown that the energy conditions are violated since the singularity is removed with the introduction of quantum cosmology, but in the classical limit both the equation of state and the energy conditions behave as in the classical model. We also calculate the expectation value of the scale factor for several wave packets in the many-worlds interpretation in order to show the independence of the nonsingular character of the quantum cosmological model with respect to the wave packet representing the wave function of the Universe. It is also shown that, with the introduction of nonnormalizable wave packets, solutions of the Wheeler-DeWitt equation, the singular character of the scale factor, can be recovered in the ontological interpretation.

Many Worlds and Schrödinger’s First Quantum Theory

Schroedinger's first proposal for the interpretation of quantum mechanics was based on a postulate relating the wave function on configuration space to charge density in physical space. Schroedinger apparently later thought that his proposal was empirically wrong. We argue here that this is not the case, at least for a very similar proposal with charge density replaced by mass density. We argue that when analyzed carefully this theory is seen to be an empirically adequate many-worlds theory and not an empirically inadequate theory describing a single world. Moreover, this formulation--Schroedinger's first quantum theory--can be regarded as a formulation of the many-worlds view of quantum mechanics that is ontologically clearer than Everett's.