Can the statistical postulate of quantum theory be derived?—A critique of the many-universes interpretation

The attempt to derive (rather than assume) the statistical postulate of quantum theory from the many-universes interpretation of Everett and De Witt is analyzed The many-universes interpretation is found to be neither necessary nor sufficient for the task.     

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.     

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.     

Quantum theory as a universal physical theory

The problem of setting up quantum theory as a universal physical theory is investigated. It is shown that the existing formalism, in either the conventional or the Everett interpretation, must be supplemented by an additional structure, the interpretation basis. This is a preferred ordered orthonormal basis in the space of states. Quantum measurement theory is developed as a tool for determining the interpretation basis. The augmented quantum theory is discussed.     

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.     

Physics and Causation

The paper makes a case for there being causation in the form of causal properties or causal structures in the domain of fundamental physics. That case is built in the first place on an interpretation of quantum theory in terms of state reductions so that there really are both entangled states and classical properties, GRW being the most elaborate physical proposal for such an interpretation. I then argue that the interpretation that goes back to Everett can also be read in a causal manner, the splitting of the world being conceivable as a causal process. Finally, I mention that the way in which general relativity theory conceives the metrical field opens up the way for a causal conception of the metrical properties as well.     

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.     

Identification of hidden variables through Everett’s formalism

It is well known that the conventional interpretation of quantum mechanics entails several paradoxes which have not been resolved in a complete and convincing way. To avoid these paradoxes other interpretations were suggested and advances, among which were the “hidden variables” theory (HV) of Bohm and Bub [1], and the “relative state” theory of Everett [2]. These HV have not, up to now, been identified, but if we compare these theories we can show an equivalence between them, and arrive at a possible definition of the HV.     

Everettian quantum mechanics

ABSTRACT

An interpretation of quantum mechanics dating back to mid-1950s, based on the ideas of Hugh Everett III, has found a new lease on life in recent decades. Significant efforts have been made by physicists and philosophers of physics to bring advances in physics and philosophy to bear on the interpretation, and to overcome some of the shortcomings in Everett's bold, but limited writings. This article presents an introduction to Everettian quantum mechanics.     

Decoherence,relative states,and evolutionary adaptation

We review the decoherent histories approach to the interpretation of quantum mechanics. The Everett relative-state theory is reformulated in terms of decoherent histories. A model of evolutionary adaptation is shown to imply decoherence. A general interpretative framework is proposed: probability and value-definiteness are to have a similar status to the attribution of tense in classical spacetime theory.Comments and suggestions by D. Albert, J. Butterfield, J. Halliwell, H. Putnam, A. Shimony, E. Squires, P. Tappenden, and R. Weingard are gratefully acknowledged. Versions of this material were presented at Rutgers, Budapest, Imperial College, London, Oxford, and Cambridge; I thank the organizers and participants for their hospitality and constructive criticisms.     

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.This work was sponsored by the Air Force under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the U.S. Government.     

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.     

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.     

回顾与展望——纪念量子论诞生100周年

回顾了量子论和量子力学产生的过程和围绕量子力学发生的争论 ,论述了量子力学对人类社会的科学、哲学、技术和经济带来的巨大影响 .对量子力学的进一步发展进行了讨论 .     

The physical meaning of quantization

After analyzing the difficulties for a local realistic interpretation of quantum theory, it is argued that such an interpretation might be possible if some new postulates are added to the standard ones. We propose a stochastic interpretation of quantum theory, which involves the need of joint probability distributions for all relevant observables. The well known problems for the existence of joint distributions are solved by assuming that neither all Hermitian operators correspond to observables nor all density matrices represent physical states. A research program along these lines is presented studying in particular the Maxwell quantum field and the Dirac field.