Relative State Research Articles

The Many-Worlds Interpretation and Quantum Computation

David Deutsch and others have suggested that the Many-Worlds Interpretation of quantum mechanics is the only interpretation capable of explaining the special efficiency quantum computers seem to enjoy over classical ones. I argue that this view is not tenable. Using a toy algorithm I show that the Many-Worlds Interpretation must crucially use the ontological status of the universal state vector to explain quantum computational efficiency, as opposed to the particular ontology of the MWI, that is, the computational histories of worlds. As such, any other interpretation that treats the state vector as representing real ontological features of a system can explain quantum speedup too.

How Bohm's Theory Solves the Measurement Problem

I examine recent arguments based on functionalism that claim to show that Bohm's theory fails to solve the measurement problem, or if it does so, it is only because it reduces to a form of the many-worlds theory. While these arguments reveal some interesting features of Bohm's theory, I contend that they do not undermine the distinctive Bohmian solution to the measurement problem.

Quantum FRW cosmological solutions in the presence of Chaplygin gas and perfect fluid

We present a Friedmann–Robertson–Walker quantum cosmological model in the presence of Chaplygin gas and perfect fluid for early and late time epochs. In this work, we consider perfect fluid as an effective potential and apply Schutz's variational formalism to the Chaplygin gas which recovers the notion of time. These give rise to Schrödinger–Wheeler–DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets and study the time dependent behavior of the expectation value of the scale factor using the many-worlds interpretation of quantum mechanics. We show that contrary to the classical case, the expectation value of the scale factor avoids singularity at quantum level. Moreover, this model predicts that the expansion of Universe is accelerating for the late times.

Derivation of the Quantum Probability Rule without the Frequency Operator

We present an alternative frequencists' proof of the quantum probability rule which does not make use of the frequency operator, with expectation that this can circumvent the recent criticism against the previous proofs which use it. We also argue that avoiding the frequency operator is not only for technical merits for doing so but is closely related to what quantum mechanics is all about from the viewpoint of many-world interpretation.

Schrödinger–Wheeler–DeWitt Equation in Chaplygin Gas FRW Cosmological Model

We present a Chaplygin gas Friedmann–Robertson–Walker quantum cosmological model. In this work the Schutz’s variational formalism is applied with positive, negative, and zero constant spatial curvature. In this approach the notion of time can be recovered. These give rise to Schrödinger–Wheeler–DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets for each case. We study the time dependent behavior of the expectation value of the scale factor, using the many-worlds interpretations of quantum mechanics.

Quantum probability from subjective likelihood: Improving on Deutsch's proof of the probability rule

I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but the proof is simpler and proceeds from weaker decision-theoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.

Decision theory and information propagation in quantum physics

In recent papers, Zurek [(2005). Probabilities from entanglement, Born's rule p k =| ψ k | 2 from entanglement. Physical Review A, 71, 052105] has objected to the decision-theoretic approach of Deutsch [(1999) Quantum theory of probability and decisions. Proceedings of the Royal Society of London A, 455, 3129–3137] and Wallace [(2003). Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation. Studies in History and Philosophy of Modern Physics, 34, 415–438] to deriving the Born rule for quantum probabilities on the grounds that it courts circularity. Deutsch and Wallace assume that the many worlds theory is true and that decoherence gives rise to a preferred basis. However, decoherence arguments use the reduced density matrix, which relies upon the partial trace and hence upon the Born rule for its validity. Using the Heisenberg picture and quantum Darwinism—the notion that classical information is quantum information that can proliferate in the environment pioneered in Ollivier et al. [(2004). Objective properties from subjective quantum states: Environment as a witness. Physical Review Letters, 93, 220401 and (2005). Environment as a witness: Selective proliferation of information and emergence of objectivity in a quantum universe. Physical Review A, 72, 042113]—I show that measurement interactions between two systems only create correlations between a specific set of commuting observables of system 1 and a specific set of commuting observables of system 2. This argument picks out a unique basis in which information flows in the correlations between those sets of commuting observables. I then derive the Born rule for both pure and mixed states and answer some other criticisms of the decision theoretic approach to quantum probability.

Entanglement in the Schrödinger experiment

The mixed and entanglement states have been analyzed in the Schrodinger experiment. It is known that, in an open system, the “Schrodinger cat” paradox is explained by the decoherence phenomenon, but, in a closed system, it is explained by the Everett-Wheeler many-world interpretation of quantum mechanics. The quantum real world can be presented as a complex multispatial geometric figure and the classical world is one of the faces of this figure. In this paper it is shown that this figure is the simplex that is well known in the functional analysis. Such an interpretation of quantum mechanics enables one to obtain the nonuniform wave equation, and the Schrodinger equation is the uniform equation of this one. Perhaps this equation is the equation of the subquantum world about which Einstein has written.

On the Everettian Epistemic Problem

Recent work in the Everett interpretation has suggested that the problem of probability can be solved by understanding probability in terms of rationality. However, there are two problems relating to probability in Everett—one practical, the other epistemic—and the rationality-based program directly addresses only the practical problem. One might therefore worry that the problem of probability is only ‘half solved’ by this approach. This paper aims to dispel that worry: a solution to the epistemic problem follows from the rationality-based solution to the practical problem.

Quantum Sleeping Beauty

The Sleeping Beauty paradox in epistemology and the many-worlds interpretation of quantum mechanics both raise problems concerning subjective probability assignments. Furthermore, there are striking parallels between the two cases; in both cases personal experience has a branching structure, and in both cases the agent loses herself among the branches. However, the treatment of probability is very different in the two cases, for no good reason that I can see. Suppose, then, that we adopt the same treatment of probability in each case. Then the dominant ‘thirder’ solution to the Sleeping Beauty paradox becomes incompatible with the tenability of the many-worlds interpretation.

Kvantovye izmereniya, fenomen zhizni i strela vremeni: svyazi mezhdu «tremya velikimi problemami» (po terminologii Ginzburga)

Квантовые измерения, феномен жизни и стрела времени: связи между «тремя великими проблемами» (по терминологии Гинзбурга), Менский М.Б.

Probability in the Everett Interpretation

AbstractThe Everett (many‐worlds) interpretation of quantum mechanics faces a prima facie problem concerning quantum probabilities. Research in this area has been fast‐paced over the last few years, following a controversial suggestion by David Deutsch that decision theory can solve the problem. This article provides a non‐technical introduction to the decision‐theoretic program, and a sketch of the current state of the debate.

Epistemology Quantized: circumstances in which we should come to believe in the Everett interpretation

I consider exactly what is involved in a solution to the probability problem of the Everett interpretation, in the light of recent work on applying considerations from decision theory to that problem. I suggest an overall framework for understanding probability in a physical theory, and conclude that this framework, when applied to the Everett interpretation, yields the result that that interpretation satisfactorily solves the measurement problem. 1. Introduction 2. What is probability? 2.1Objective probability and the Principal Principle 2.2Three ways of satisfying the functional definition 2.3Cautious functionalism 2.4Is the functional definition complete? 3. The Everett interpretation and subjective uncertainty 3.1Interpreting quantum mechanics 3.2The need for subjective uncertainty 3.3Saunders' argument for subjective uncertainty 3.4Objections to Saunders' argument 3.5Subjective uncertainty again: arguments from interpretative charity 3.6Quantum weights and the functional definition of probability 4. Rejecting subjective uncertainty 4.1The fission program 4.2Against the fission program 5. Justifying the axioms of decision theory 5.1The primitive status of the decision-theoretic axioms 5.2Holistic scepticism 5.3The role of an explanation of decision theory 6. Conclusion

From Parallel Universes to Possible Worlds: Ontological Pluralism in Physics, Narratology, and Narrative

This essay explores how theoretical physics, narratology, and narrative itself deal with the idea that reality consists of a plurality of worlds. In physics, the existence of parallel universes has been postulated on the cosmic level to describe what lies on the other side of black holes and, on the level of subatomic particles, to avoid the paradoxes of quantum mechanics. In narratology, the philosophical idea of a plurality of possible worlds and the contrast between the actual and the possible provide a model of the cognitive pattern into which readers organize information in order to interpret it as a story. But the many-worlds interpretation of physics and the possible worlds (PW) model of narrative differ in their conception of the ontological status of the multiple worlds: in physics they are all actual, while narrative theory stresses the contrast between actuality and mere possibility. This does not mean that the PW model is incompatible with the many-worlds cosmology proposed by physics: faced with a narrative that presents multiple realities as existing objectively, the theory would simply claim that the actual domain is made up of a number of different worlds and that the distinction actual/nonactual repeats itself within each of these parts. The last section of the essay explores what it takes for a narrative to impose a many-worlds cosmology, distinguishing these narratives from other texts that present contradictory versions of facts and situating them with respect to three types of story common in fantasy and science fiction: the narrative of transworld exploration, the narrative of alternate history, and the time-travel narrative.

Measurement outcomes and probability in Everettian quantum mechanics

The decision-theoretic account of probability in the Everett or many-worlds interpretation, advanced by David Deutsch and David Wallace, is shown to be circular. Talk of probability in Everett presumes the existence of a preferred basis to identify measurement outcomes for the probabilities to range over. But the existence of a preferred basis can only be established by the process of decoherence, which is itself probabilistic.

Reality in quantum mechanics, Extended Everett Concept, and consciousness

Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer’s consciousness into the quantum theory of measurements. Most naturally, this is achieved in the framework of Everett’s “many-world interpretation” of quantum mechanics. According to this interpretation, various classical alternatives are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author, the separation of the alternatives is identified with the phenomenon of consciousness. This explains the classical character of the alternatives and unusual manifestations of consciousness arising “at the edge of consciousness” (i.e., in sleep or trance) when its access to “other alternative classical realities” (other Everett’s worlds) becomes feasible. Because of reversibility of quantum evolution in EEC, all time moments in the quantum world are equivalent, while the impression of flow of time appears only in consciousness. If it is assumed that consciousness may influence the probabilities of alternatives (which is consistent in case of infinitely many Everett’s worlds), EEC explains free will, “probabilistic miracles” (observing low-probability events), and decreasing entropy in the sphere of life.

Some introductory formalizations on the affine Hilbert spaces model of the origin of life: I. On quantum mechanical measurement and the origin of the genetic code: A general physical framework theory

A physical (affine Hilbert spaces) frame is developed for the discussion of the interdependence of the problem of the origin (symbolic assignment) of the genetic code and a possible endophysical (a kind of “internal”) quantum measurement in an explicite way, following the general considerations of Balázs (Balázs, A., 2003. BioSystems 70, 43–54; Balázs, A., 2004a. BioSystems 73, 1–11). Using the Everett (a dynamic) interpretation of quantum mechanics, both the individual code assignment and the concatenated linear symbolism is discussed. It is concluded that there arises a skewed quantal probability field, with a natural dynamic non-linearity in codon assignment within the physical model adopted (essentially corresponding to a much discussed biochemical frame of self-catalyzed binding (charging) of t RNA like proto RNAs (ribozymes) with amino acids). This dynamic specific molecular complex assumption of individual code assignment, and the divergence of the code in relation to symbol concatenation, are discussed: our frame supports the former and interpret the latter as single-type codon (triplet), also unambiguous and extended assignment, selection in molecular evolution, corresponding to converging towards the f i x e d p o i n t of the internal dynamics of measurement, either in a protein- or RNA-world. In this respect, the general physical consequence is the introduction of a fourth rank semidiagonal energy tensor (see also Part II) ruling the internal dynamics as a non-linear in principle second-order one. It is inferred, as a summary, that if the problem under discussion could be expressed by the concepts of the Copenhagen interpretation of quantum mechanics in some yet not quite specified way, the matter would be particularly interesting with respect to both the origin of life a n d quantum mechanics, as a dynamically supported natural measurement-theoretical split between matter (“hardware”) and (internal) symbolism (“software”) aspects of living matter.

Spatial Degrees of Freedom in Everett Quantum Mechanics

Stapp claims that, when spatial degrees of freedom are taken into account, Everett quantum mechanics is ambiguous due to a “core basis problem.” To examine an aspect of this claim I generalize the ideal measurement model to include translational degrees of freedom for both the measured system and the measuring apparatus. Analysis of this generalized model using the Everett interpretation in the Heisenberg picture shows that it makes unambiguous predictions for the possible results of measurements and their respective probabilities. The presence of translational degrees of freedom for the measuring apparatus affects the probabilities of measurement outcomes in the same way that a mixed state for the measured system would. Examination of a measurement scenario involving several observers illustrates the consistency of the model with perceived spatial localization of the measuring apparatus.

Drift–diffusion in mangled worlds quantum mechanics

In Everett's many-worlds interpretation, where quantum measurements are seen as decoherence events, inexact decoherence may let large worlds mangle the memories of observers in small worlds, creating a cutoff in observable world measure. I solve a growth–drift–diffusion–absorption model of such a mangled worlds scenario, and show that it reproduces the Born probability rule closely, though not exactly. Thus, inexact decoherence may allow the Born rule to be derived in a many-worlds approach via world counting, using a finite number of worlds and no new fundamental physics.

Reading the περιτρoπη: Theaetetus 170c-171c

AbstractTwo readings of the much-discussed περιτρoπη argument of Theaetetus 170c-171c have dominated the literature. One I call "the relativity reading". On this reading, the argument fails by ignoratio elenchi because it "carelessly" omits "the qualifications 'true for so-and-so' which [Protagoras'] theory insists on" (Bostock 1988: 90). The other reading I call "the many-worlds interpretation". On this view, Plato's argument succeeds in showing that "Protagoras' position becomes utterly self-contradictory" because "he claims that everyone lives in his own relativistic world, yet at the same time he is forced by that very claim to admit that no one does" (Burnyeat 1976b: 48). I discuss and criticise both readings, and present a third, according to which the point of the argument is, very roughly, that Protagoras is committed to equating truth and truth-for, and so, further, to their intersubstitutability. This further commitment proves fatal to his argument.