Relative State Research Articles

Science and exile: David Bohm, the cold war, and a new interpretation of quantum mechanics

ABSTRACT In the early 1950s the American physicist David Bohm (1917-1992) produced a new interpretation of quantum mechanics and had to flee from McCarthyism. Rejected at Princeton, he moved to São Paulo. This article focuses on the reception of his early papers on the causal interpretation, his Brazilian exile, and the culture of physics surrounding the foundations of quantum mechanics. It weighs the strength of the Copenhagen interpretation, discusses the presentation of the foundations of quantum mechanics in the training of physicists, describes the results Bohm and his collaborators achieved. It also compares the reception of Bohm's ideas with that of Hugh Everett's interpretation. The cultural context of physics had a more significant influence on the reception of Bohm's ideas than the McCarthyist climate.

Interpretações da mecânica quântica em um interferômetro virtual de Mach-Zehnder

Neste trabalho analisamos o fenômeno da interferência quântica no interferômetro de Mach Zehnder - um arranjo experimental análogo ao experimento das duas fendas, porém mais simples - sob a luz das principais escolas de interpretação da mecânica quântica. Embora fortemente inspirados pelo trabalho de Pessoa Jr. [1]-[3], damos especial ênfase à Interpretação dos Muitos Mundos ou Universos Paralelos, que experimenta um crescente interesse tanto por parte da comunidade científica quanto de leigos. A Interpretação dos Muitos Mundos é uma corrente da mecânica quântica para a qual, além do mundo do qual somos conscientes, há muitos outros mundos similares que existem em paralelo no espaço e ao mesmo tempo. A existência destes outros mundos torna possível a remoção da aleatoriedade e da ação à distância da teoria quântica. Uma introdução básica de uma interpretação que tem estado presente nos meios de comunicação é uma importante contribuição para a formação inicial e continuada de professores de Física, principalmente quando se busca uma discussão mais conceitual sobre o tema.

Physics versus Semantics: A Puzzling Case of the Missing Quantum Theory

A case for the project of excising of confusion and obfuscation in the contemporary quantum theory initiated and promoted by David Deutsch has been made. It has been argued that at least some theoretical entities which are conventionally labelled as “interpretations” of quantum mechanics are in fact full-blooded physical theories in their own right, and as such are falsifiable, at least in principle. The most pertinent case is the one of the so-called “Many-Worlds Interpretation” (MWI) of Everett and others. This set of idea differs from other “interpretations” since it does not accept reality of the collapse of Schrodinger’s wavefunction. A survey of several important proposals for discrimination between quantum theories with and without wavefunction collapse appearing from time to time in the literature has been made, and the possibilities discussed in the framework of a wider taxonomy.

Understanding Deutsch's probability in a deterministic multiverse

Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from ‘probability’ without recourse to indeterminism, ignorance, primitive identity over time or subjective uncertainty: all she needs is a particular rationality principle.The decision-theoretic approach recently developed by Deutsch and Wallace claims to provide just such a principle. But, according to Wallace, decision theory is itself applicable only if the correct attitude to a future Everettian measurement outcome is subjective uncertainty. I argue that subjective uncertainty is not available to the Everettian, but I offer an alternative: we can justify the Everettian application of decision theory on the basis that an Everettian should care about all her future branches. The probabilities appearing in the decision-theoretic representation theorem can then be interpreted as the degrees to which the rational agent cares about each future branch. This reinterpretation, however, reduces the intuitive plausibility of one of the Deutsch–Wallace axioms (measurement neutrality).

Two-component boson systems with hyperspherical coordinates

The effective potential is computed for two boson systems in one trap as a function of their two individual hyperadii and the distance between their centres. Zero-range interactions are used and only relative s-states are included. Existence and properties of minima are investigated as a function of these three collective coordinates. For sufficiently strong repulsion stable structures are found at a finite distance between the centres. The relative centre-of-mass motion corresponds to the lowest normal mode. The highest normal mode is essentially the breathing mode where the subsystems vibrate by scaling their radii in phase. The intermediate normal mode corresponds to isovector motion where the subsystems vibrate by scaling their radii in opposite phase. Stability conditions are established as substantially more restrictive than in mean-field computations.

Critical Stability in Nuclei ? An Old Problem Revisited

In this paper we will focus on the nucleon-nucleon interaction in relative S-states. The 1S0 interaction is known to be close to that for critical two-body binding. We will discuss two approaches to the NN interaction, which are equivalent on-shell but not off-shell. There is a well-defined transformation between these approaches [1]. One (my preferred approach) is to minimize the tensor forces far off-shell, which leads to more rapid convergence, but at the price of significant non-locality. This approach is used in a model of relativistic tensor quenching of OPEP [2]. With non-local NN interactions it is possible to fit not only NN observables, but also the NNN ground-state energies [3]. The other approach is to maximize the role of the π and keep the interaction as local as possible [4]. This approach is also internally consistent, but requires additional NNN interactions to fit nuclear data. Also, we discuss briefly a so-called low momentum interaction [5, 6], which fits S-wave phase shifts quite well. This interaction is strongly non-local, and it can be approximated by a schematic separable interaction. Finally, we mention the Nambu–Jona-Lasinio model [7] and a good approximation, the Hulthen potential, which provides some insight into the near critical two-body binding.

Solving the Measurement Problem: De Broglie--Bohm Loses Out to Everett

The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.

Three-body structure of the low-lying 17Ne-states

The Borromean nucleus 17Ne ( 15O+ p+ p) is investigated by using the hyperspheric adiabatic expansion for a three-body system. The measured size of 15O and the low-lying resonances of 16F ( 15O+ p) are first used as constraints to determine both central and spin-dependent two-body interactions. Then, the ground state structure of 17Ne is found to be an almost equal mixture of s 2 and d 2 proton- 15O relative states, the two lowest excited states have about 80% of sd-mixed components, and for the next two excited three-body states the proton- 15O relative s-states do not contribute. The spatial extension is as in ordinary nuclei. The widths of the resonances are estimated by the WKB transmission through the adiabatic potentials and found in agreement with the established experimental limits. We compare with experimental information and previous works.

An operator description of entanglement matching in quantum teleportation

The antilinear operator representation of bipartite pure states of the relative state formulation of quantum mechanics is applied to describe quantum teleportation schemes utilizing an arbitrary pure state as the entangled resource. Bennett type teleportation schemes with nonmaximally entangled pure states are characterized and the notion of 'entanglement matching' is introduced in general. Examples, including a scheme based on coherent-state superposition states of the electromagnetic field, are provided.

Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation

An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the Everett interpretation, and that in this context, it essentially succeeds. Some comments are made about the criticism of Deutsch's proof by Barnum, Caves, Finkelstein, Fuchs, and Schack; it is argued that the flaw which they point out in the proof does not apply if the Everett interpretation is assumed.

Everett and structure

I address the problem of indefiniteness in quantum mechanics: the problem that the theory, without changes to its formalism, seems to predict that macroscopic quantities have no definite values. The Everett interpretation is often criticised along these lines, and I shall argue that much of this criticism rests on a false dichotomy: that the macroworld must either be written directly into the formalism or be regarded as somehow illusory. By means of analogy with other areas of physics, I develop the view that the macroworld is instead to be understood in terms of certain structures and patterns which emerge from quantum theory (given appropriate dynamics, in particular decoherence). I extend this view to the observer, and in doing so make contact with functionalist theories of mind.

Relative Frequency and Probability in the Everett Interpretation of Heisenberg-Picture Quantum Mechanics

The existence of probability in the sense of the frequency interpretation, i.e., probability as “long term relative frequency,” is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the Heisenberg picture. This proof is free of the difficulties encountered in applying to the Everett interpretation previous results regarding relative frequency and probability in quantum mechanics. The ontology of the Everett interpretation in the Heisenberg picture is also discussed.

Worlds in the Everett interpretation

This is a discussion of how we can understand the world-view given to us by the Everett interpretation of quantum mechanics, and in particular the rôle played by the concept of ‘world’. The view presented is that we are entitled to use ‘many-worlds’ terminology even if the theory does not specify the worlds in the formalism; this is defended by means of an extensive analogy with the concept of an ‘instant’ or moment of time in relativity, with the lack of a preferred foliation of spacetime being compared with the lack of a preferred basis in quantum theory. Implications for identity of worlds over time, and for relativistic quantum mechanics, are discussed.

The basis problem in many-worlds theories

It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence effects are essentially Gaussian wave packets that form continua of non-orthogonal states. Hence they are not a discrete set of orthogonal basis states to which finite probabilities can be assigned by the usual rules. The natural way to get an orthogonal basis without going outside the Schrödinger dynamics is to use the eigenstates of the reduced density matrix, and this idea is the basis of some recent attempts by many-worlds proponents to solve the basis problem. But these eigenstates do not enjoy the locality and quasi-classicality properties of the states defined by environmental decoherence effects, and hence are not satisfactory preferred basis states. This core problem is obscured by approaches that treat the universe as a quantum computer, but it needs to be addressed and resolved before a many-worlds-type interpretation can be said to exist. PACS No.: 03.65Bz

Locality in the Everett Interpretation of Quantum Field Theory

Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation in which initial-condition information is transferred from the state vector to the field operators, making the locality of the theory manifest.

The Paradoxes of the Interaction-free Measurements

Abstract Interaction-free measurements introduced by Elitzur and Vaidman [Found. Phys. 23,987 (1993)] allow finding infinitely fragile objects without destroying them. Paradoxical features of these and related measurements are discussed. The resolution of the paradoxes in the framework of the Many-Worlds Interpretation is proposed.

Locality in the Everett Interpretation of Heisenberg-Picture Quantum Mechanics

Bell's theorem depends crucially on counterfactual reasoning, and is mistakenly interpreted as ruling out a local explanation for the correlations which can be observed between the results of measurements performed on spatially-separated quantum systems. But in fact the Everett interpretation of quantum mechanics, in the Heisenberg picture, provides an alternative local explanation for such correlations. Measurement-type interactions lead, not to many worlds but, rather, to many local copies of experimental systems and the observers who measure their properties. Transformations of the Heisenberg-picture operators corresponding to the properties of these systems and observers, induced by measurement interactions, “label” each copy and provide the mechanism which, e. g., ensures that each copy of one of the observers in an EPRB or GHZM experiment will only interact with the “correct” copy of the other observer(s). The conceptual problem of nonlocality is thus replaced with a conceptual problem of proliferating labels, as correlated systems and observers undergo measurement-type interactions with newly-encountered objects and instruments; it is suggested that this problem may be resolved by considering quantum field theory rather than the quantum mechanics of particles.

AN EXTENSION OF “POPPER'S EXPERIMENT” CAN TEST INTERPRETATIONS OF QUANTUM MECHANICS

Karl Popper proposed a way to test whether a proposed relation of a quantum-mechanical state to perceived reality in the Copenhagen interpretation (CI) of quantum mechanics—namely that the state of a particle is merely an expression of “what is known” about the system—is in agreement with all experimental facts. A conceptual flaw in Popper's proposal is identified and an improved version of his experiment (called “Extension step 1”)—which fully serves its original purpose—is suggested. The main purpose of this paper is to suggest to perform this experiment. The results of this experiment predicted under the alternative assumptions that the CI or the “many-worlds” interpretation (MWI) is correct are shown to be identical. Only after a further modification (called “Extension step 2”) (the use of an ion isolated from the macroscopic environment as particle detector) the predictions using the respective interpretations become qualitatively different. This is because “what is known” by a human observer H can fail as a basis for the prediction of the statistical distribution of measurement results within the MWI in special cases: The temporal evolution of a system un-entangled with H (like the isolated ion) can depend on another system's state components that are entangled with states ortogonal to H. Thus—within the CI—for H they are “known not to exist”. Yet H can infer their existence by studying the evolution of the ion.

On Time Asymmetry and History in an Everett Quantum World

It is usually held that the standard collapse model of a quantum measurement process grounds a kind of fundamental time asymmetry. The question whether and how it should be possible to reconstruct uniquely one's own history in an Everett no-collapse interpretation of quantum theory is investigated. A particular approach to the Everett interpretation, due to John S. Bell, is considered, according to which one of the chief claims of the Everett quantum theory is precisely that it allows us to do without the notion of history.

CONCEPTUAL FOUNDATIONS OF QUANTUM MECHANICS: THE ROLE OF EVIDENCE THEORY, QUANTUM SETS, AND MODAL LOGIC

Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.