Nonlocality in Relativistic Dynamics

Recent experiments have renewed interest in nonlocal interpretations of quantum mechanics. The experimental observation of the violation of Bell's inequalities implies the existence of nonlocality. Bohm expressed the nonlocal connection between quantum particles through the wave function and the quantum potential. This paper shows that a similar connection exists in a relativistic dynamical theory known as parametrized relativistic quantum theory (PRQT). We present an introduction to PRQT, derive the quantum potential for a system of relativistic scalar particles, and discuss alternative interpretations of nonlocality.     

Comments on Shimony’s “An Analysis of Stapp’s ‘A Bell-Type Theorem without Hidden Variables’ ”

The hidden-variable theorems of Bell and followers depend upon an assumption, namely the hidden-variable assumption, that conflicts with the precepts of quantum philosophy. Hence from an orthodox quantum perspective those theorems entail no faster-than-light transfer of information. They merely reinforce the ban on hidden variables. The need for some sort of faster-than-light information transfer can be shown by using counterfactuals instead of hidden variables. Shimony’s criticism of that argument fails to take into account the distinction between no-faster-than-light connection in one direction and that same condition in both directions. The argument can be cleanly formulated within the framework of a fixed past, open future interpretation of quantum theory, which neatly accommodates the critical assumptions that the experimenters are free to choose which experiments they will perform. The assumptions are compatible with the Tomonaga–Schwinger formulation of quantum field theory, and hence with orthodox quantum precepts, and with the relativistic requirement that no prediction pertaining to an outcome in one region can depend upon a free choice made in a region spacelike-separated from the first.     

Intrinsic Properties of Quantum Systems

A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be attributed to individual quantum systems without violating standard quantum mechanics, which are called intrinsic. The intrinsic properties are classified into structural and conditional. A systematic and self-consistent account is given. Much more statements become meaningful than any version of Copenhagen interpretation would allow. A new approach to classical properties and measurement problem is suggested. A quantum definition of classical states is proposed.     

A Modal Interpretation of Quantum Mechanics Based on a Principle of Entropy Minimization

Within many approaches to the interpretation of quantum mechanics, especially modal interpretations, one singles out a particular decomposition of the state vector in order to fix the properties that are well-defined for the system. We present a novel proposal for this preferred decomposition. Given a distinguished factorization of the Hilbert space, it is the decomposition that minimizes the Ingarden–Urbanik entropy from among all product decompositions with respect to the distinguished factorization. We incorporate this choice of preferred decomposition into a framework for modal interpretations and investigate in detail the extent to which it provides a solution to the measurement problem and the extent to which it ensures that measurements whose outcomes are predictable with probability 1 reveal pre-existing properties of the system under investigation.     

A Unified Algebraic Approach to Quantum Theory

Conventional approaches to quantum mechanics are essentially dualistic. This is reflected in the fact that their mathematical formulation is based on two distinct mathematical structures: the algebra of dynamical variables (observables) and the vector space of state vectors. In contrast, coherent interpretations of quantum mechanics highlight the fact that quantum phenomena must be considered as undivided wholes. Here, we discuss a purely algebraic formulation of quantum mechanics. This formulation does not require the specification of a space of state vectors; rather, the required vector spaces can be identified as substructures in the algebra of dynamical variables (suitably extended for bosonic systems). This formulation of quantum mechanics captures the undivided wholeness characteristic of quantum phenomena, and provides insight into their characteristic nonseparability and nonlocality. The interpretation of the algebraic formulation in terms of quantum process is discussed.     

Violation of Locality Beyond Bell's Theorem for Multiparticle Perfect Correlations

We present the analogous inequalities of Bell's inequality for N-qubit system predicted respectively by realistic theory, quantum mechanics, local theory, local realistic theory, and local quantum theory on the same Bell-type joint experiment. It is shown that quantum mechanics can be interpreted by hidden-variable theories while being incompatible to any local theory. A necessary condition for the separability of N-qubit system is derived.     

Interpretations of quantum mechanics,joint measurement of incompatible observables,and counterfactual definiteness

The validity of the conclusion to the nonlocality of quantum mechanics, accepted widely today as the only reasonable solution to the EPR and Bell issues, is questioned and criticized. Arguments are presented which remove the compelling character of this conclusion and make clear that it is not the most obvious solution. Alternative solutions are developed which are free of the contradictions related with the nonlocality conclusion. Firstly, the dependence on the adopted interpretation is shown, with the conclusion that the alleged nonlocality property of the quantum formalism may have been reached on the basis of an interpretation that is unnecessarily restrictive. Secondly, by extending the conventional quantum formalism along the lines of Ludwig and Davies it is shown that the Bell problem may be related to complementarity rather than to nonlocality. Finally, the dependence on counterfactual reasoning is critically examined. It appears that locality on the quantum level may still be retained provided one accepts a newly proposed principle of nonreproducibility at the individual quantum level as an alternative of quantum nonlocality. It is concluded that the locality principle can retain its general validity, in full conformity with all experimental data.     

Properties and operational propositions in quantum mechanics

In orthodox quantum mechanics, it has virtually become the custom to identify properties of a physical system with operationally testable propositions about the system. The causes and consequences of this practice are explored mathematically in this paper. Among other things, it is found that such an identification imposes severe constraints on the admissible states of the physical system.     

Time and Causality: A Thermocontextual Perspective

The thermocontextual interpretation (TCI) is an alternative to the existing interpretations of physical states and time. The prevailing interpretations are based on assumptions rooted in classical mechanics, the logical implications of which include determinism, time symmetry, and a paradox: determinism implies that effects follow causes and an arrow of causality, and this conflicts with time symmetry. The prevailing interpretations also fail to explain the empirical irreversibility of wavefunction collapse without invoking untestable and untenable metaphysical implications. They fail to reconcile nonlocality and relativistic causality without invoking superdeterminism or unexplained superluminal correlations. The TCI defines a system’s state with respect to its actual surroundings at a positive ambient temperature. It recognizes the existing physical interpretations as special cases which either define a state with respect to an absolute zero reference (classical and relativistic states) or with respect to an equilibrium reference (quantum states). Between these special case extremes is where thermodynamic irreversibility and randomness exist. The TCI distinguishes between a system’s internal time and the reference time of relativity and causality as measured by an external observer’s clock. It defines system time as a complex property of state spanning both reversible mechanical time and irreversible thermodynamic time. Additionally, it provides a physical explanation for nonlocality that is consistent with relativistic causality without hidden variables, superdeterminism, or “spooky action”.     

On the relation between the Einstein-Podolsky-Rosen paradox and the problem of nonlocality in quantum mechanics

The EPR problem is studied both from an instrumentalistic and from a realistic point of view. Bohr's reply to the EPR paper is analyzed and demonstrated to be not completely representative of Bohr's general views on the possibility of defining properties of a microscopic object. A more faithful Bohrian answer would not have led Einstein to the conclusion that Bohr's completeness claim of quantum mechanics implies nonlocality. The projection postulate, already denounced in 1936 by Margenau as the source of the EPR paradox, is found to be also at the origin of the nonlocality conundrum. Its unobservability in EPR-like experiments is demonstrated, thus showing the redundancy of the idea of nonlocality in the instrumentalist interpretation of quantum mechanics. It is argued that also from a realist point of view there is no reason to assume nonlocality. The relevance of Bohm's quantum potential and of Bell's inequalities with respect to the (non)locality problem is discussed.     

Geometro-stochastic locality in quantum spacetime and quantum diffusions

The issue of the intrinsic nonlocality of quantum mechanics raised by J. S. Bell is examined from the point of view of the recently developed method of geometro-stochastic quantization and its applications to general relativistic quantum theory. This analysis reveals that a distinction should be made between the topological concept of locality used in formulating relativistic causality and a type of geometric locality based on the concept of fiber bundle, which can be used in extending the strong equivalence principle to the quantum domain. Both play an essential role in formulating a notion of geometro-stochastic propagation based on quantum diffusions, which throws new light on the EPR paradox, on the origin of the arrow of time, and on other fundamental issues in quantum cosmology and the theory of measurement.     

Quantum Logics and Relative Lindenbaum Property

The relative Lindenbaum property is considered in orthomodular quantum logic and in partial class ical logic. The properties of these models are connected with the possibility of hidden-variable reconstruction of particular (1/2-spin particle e.g.) quantum physical systems.     

Dynamics for Modal Interpretations

An outstanding problem in so-called modal interpretations of quantum mechanics has been the specification of a dynamics for the properties introduced in such interpretations. We develop a general framework (in the context of the theory of stochastic processes) for specifying a dynamics for interpretations in this class, focusing on the modal interpretation by Vermaas and Dieks. This framework admits many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of them. This approach is applicable to a wider class of theories, in particular, those using (discrete) strict effective—as in decoherence theory—superselection rules.     

Extending Newton's law from nonlocal-in-time kinetic energy

We study a new equation of motion derived from a context of classical Newtonian mechanics by replacing the kinetic energy with a form of nonlocal-in-time kinetic energy. It leads to a hypothetical extension of Newton's second law of motion. In a first stage the obtainable solution form is studied by considering an unknown value for the nonlocality time extent. This is done in relation to higher-order Euler-Lagrange equations and a Hamiltonian framework. In a second stage the free particle case and harmonic oscillator case are studied and compared with quantum mechanical results. For a free particle it is shown that the solution form is a superposition of the classical straight line motion and a Fourier series. We discuss the link with quanta interpretations made in Pais-Uhlenbeck oscillators. The discrete nature emerges from the continuous time setting through application of the least action principle. The harmonic oscillator case leads to energy levels that approximately correspond to the quantum harmonic oscillator levels. The solution to the extended Newton equation also admits a quantization of the nonlocality time extent, which is determined by the classical oscillator frequency. The extended equation suggests a new possible way for understanding the relationship between classical and quantum mechanics.     

Speakable and Unspeakable in Quantum Measurements

Quantum mechanics, in its orthodox version, imposes severe limits on what can be known, or even said, about the condition of a quantum system between two observations. A relatively new approach, based on so-called “weak measurements”, suggests that such forbidden knowledge can be gained by studying the system's response to an inaccurate weakly perturbing measuring device. It goes further to propose revising the whole concept of physics variables, and offers various examples of counterintuitive quantum behavior. Both views go to the very heart of quantum theory, and yet are rarely compared directly. A new technique must either transcend the orthodox limits, or just prove that these limits are indeed necessary. Both possibilities are studied and orthodoxy is vindicated.     

Optical Test of Local Hidden—Variable Model

An inequality is deduced from local realism and a supplementary assumption.This inequality defines an experiment that can be actually performed with the present technology to test local hidden-variable models,and it is violated by quantum mechanics with a factor 1.92,while it can be simplified into a form where just two measurements are required.     

Proposal for a quantum delayed-choice experiment

Gedanken experiments help to reconcile our classical intuition with quantum mechanics and nowadays are routinely performed in the laboratory. An important open question is the quantum behavior of the controlling devices in such experiments. We propose a framework to analyze quantum-controlled experiments and illustrate it by discussing a quantum version of Wheeler's delayed-choice experiment. Using a quantum control has several consequences. First, it enables us to measure complementary phenomena with a single experimental setup, pointing to a redefinition of complementarity principle. Second, it allows us to prove there are no consistent hidden-variable theories having "particle" and "wave" as realistic properties. Finally, it shows that a photon can have a morphing behavior between particle and wave. The framework can be extended to other experiments (e.g., Bell inequality).