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.     

Cosmology and the pilot wave interpretation of quantum mechanics

Bell has recently revived the pilot wave interpretation of de Broglie and Bohm as a possible scheme for interpreting wave functions in quantum cosmology. I argue that the pilot wave interpretation cannot be applied consistently to systems whose wave functions split into macroscopically distinguishable states. At some stage the pilot wave interpretation must either tacitly invoke wave function reduction in the same manner as the Copenhagen interpretation, or else abandon locality by requiring physical particles to move faster than light. Consequently, the many-worlds interpretation is the only known realist interpretation of the quantum mechanical formalism which can be extended to quantum cosmology.     

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. The text was submitted by the author in English.     

Many worlds and the appearance of probability in quantum mechanics

The interpretation of the squared norm as probability and the apparent stochastic nature of observation in the quantum theory are derived from the law of large numbers and the algebraic properties of infinite sequences of simultaneous quantum observables. It is argued that this result validates the many-worlds view of quantum reality.     

Self-generating Universe and many worlds

A novel, compact conceptual framework for the origin of the Universe is proposed, whereby the Universe is identified with a baby universe born ofitself. This picture indicates an intimate meshing of gravitation, space-time, and the quantum and offers a framework for the many-worlds interpretation of quantum theory.On leave from School of Physics and Astronomy, Tel-Aviv University, 69978 Tel-Aviv, Israel.     

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

The classic “Bell’s Theorem” 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 allows two major variations—a many-worlds version and a neoclassical version based on Partial Differential Equations (PDE), in the spirit of Einstein. Section 2 of this paper discusses the origins of quantum measurement according to BTP, focusing on the issue of how we represent condensed matter objects like polarizers in a model “Bell’s Theorem” experiment. The backwards time telegraph (BTT) is not ruled out in BTP, but is highly speculative for now, as will be discussed. The views herein are not anyone’s official views, but this does constitute work produced on government time.     

Can Everett be Interpreted Without Extravaganza?

Everett’s relative states interpretation of quantum mechanics has met with problems related to probability, the preferred basis, and multiplicity. The third theme, I argue, is the most important one. It has led to developments of the original approach into many-worlds, many-minds, and decoherence-based approaches. The latter especially have been advocated in recent years, in an effort to understand multiplicity without resorting to what is often perceived as extravagant constructions. Drawing from and adding to arguments of others, I show that proponents of decoherence-based approaches have not yet succeeded in making their ontology clear.     

Pure quantum states are fundamental, mixtures (composite states) are mathematical constructions: An argument using algorithmic information theory

From the philosophical viewpoint, two interpretations of the quantum measurement process are possible: According to the first interpretation, when we measure an observable, the measured system moves into one of the eigenstates of this observable (“the wave function collapses”); in other words, the universe “branches” by itself, due to the very measurement procedure, even if we do not use the result of the measurement. According to the second interpretation, the system simply moves into amixture of eigenstates, and the actual “branching” occurs only when anobserver reads the measurement results. According to the first interpretation, a mixture is a purely mathematical construction, and in the real physical world, a mixture actually means that the system is in one of the “component” states. In this paper, we analyze this difference from the viewpoint ofalgorithmic information theory; as a result of this analysis, we argue that onlypure quantum states are fundamental, while mixtures are simply useful mathematical constructions.     

Quantum mechanics without the projection postulate and its realistic interpretation

It is widely held that quantum mechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory doesnot present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantum mechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given tomeasurement by the projection postulate. But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantum mechanics. A realistic interpretation is possible in which only the reality ofone (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory.     

On the probabilistic postulate of quantum mechanics

We study whether the probabilistic postulate could be derived from basic principles. Through the analysis of the Strong Law of Large Numbers and its formulation in quantum mechanics, we show, contrary to the claim of the many-worlds interpretation defenders and the arguments of some other authors, the impossibility of obtaining the probabilistic postulate by means of the frequency analysis of an ensemble of infinite copies of a single system. It is shown, though, how the standard form of the probability as the square of the scalar product follows from Gleason's theorem.     

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.     

Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the so-called “quantum liar paradox,” an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s implications for quantum gravity.     

A mathematical characterization of the physical structure of observers

It is proposed that the physical structure of an observer in quantum mechanics is constituted by a pattern of elementary localized switching events. A key preliminary step in giving mathematical expression to this proposal is the introduction of an equivalence relation on sequences of spacetime sets which relates a sequence to any other sequence to which it can be deformed without change of causal arrangement. This allows an individual observer to be associated with a finite structure. The identification of suitable switching events in the human brain is discussed. A definition is given for the sets of sequences of quantum states which such an observer could occupy. Finally, by providing an a priori probability for such sets, the definitions are incorporated into a complete mathematical framework for a many-worlds interpretation. At a less ambitious level, the paper can be read as an exploration of some of the technical and conceptual difficulties involved in constructing such a framework.     

Undecidability and the Problem of Outcomes in Quantum Measurements

We argue that it is fundamentally impossible to recover information about quantum superpositions when a quantum system has interacted with a sufficiently large number of degrees of freedom of the environment. This is due to the fact that gravity imposes fundamental limitations on how accurate measurements can be. This leads to the notion of undecidability: there is no way to tell, due to fundamental limitations, if a quantum system evolved unitarily or suffered wavefunction collapse. This in turn provides a solution to the problem of outcomes in quantum measurement by providing a sharp criterion for defining when an event has taken place. We analyze in detail in examples two situations in which in principle one could recover information about quantum coherence: (a) “revivals” of coherence in the interaction of a system with the measurement apparatus and the environment and (b) the measurement of global observables of the system plus apparatus plus environment. We show in the examples that the fundamental limitations due to gravity and quantum mechanics in measurement prevent both revivals from occurring and the measurement of global observables. It can therefore be argued that the emerging picture provides a complete resolution to the measurement problem in quantum mechanics.     

An analysis of the Einstein-Podolsky-Rosen correlations in terms of events

It is shown that Bell's inequalities can be derived from two general assumptions bearing on events, namely the possibility of their retrodiction and their locality. The meaning of a possible violation of the retrodiction principle is interpreted by making use of the many-worlds formulation of quantum mechanics.     

Some Remarks on the Notion of Separability Within the Creation Discovery View

In this paper we present Aerts’ vessels of water model which violates Bell inequalities, and discuss how this fits in the Creation Discovery View in the context of the Operational Quantum Logic approach. We analyze the 2 different ways in which correlation is classically observed, either as pre-existing ‘independent of measurement’ or established by sending a signal, hence limited by the speed of light. As the Aerts’ model shows, there is yet a third possibility, namely a situation in which correlation is potentially present, but only actualized to its full extent by the act of measurement. This creation-discovery view can be applied to the quantum mechanical situation of two entangled photons, and shows that in the debate of understanding ‘what is really going on in Aspects experiments’ an alternative explanation can be found, in which potentiality, creation and discovery play a central role.     

Search for particle-antiparticle back-to-back correlations in √sNN GeV Au + Au collisions

A novel type of quantum mechanical correlations, hypothesized in the 1990’s, the (squeezed) back-to-back correlations, was predicted to appear in heavy ion collisions among particle-antiparticle (eg. π⁺π⁻, K ⁺ K ⁻, p[`(p)]p\bar p) pairs, if their in-medium masses are different from the vacuum values. Observation of this correlation would provide new insight in the freeze-out dynamics of the created matter. The latest status of the PHENIX measurement, comprising the first measurement of this new effect, is presented.