W. De Baere

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.

Locality and Bell's Theorem

It is shown that the violation of Bells inequality allowed by quantum mechanics and the related Bells theorem without inequalities is accounted for by local commutations of operators representing single-particle observables. It is argued that the idea of nonlocal influencing of one particle on another when they are in spacelike separated regions clearly has neither empirical nor theoretical support.

On the uniqueness of paths for spin-0 and spin-1 quantum mechanics

Abstract The uniqueness of the Bohmian particle interpretation of the Kemmer equation, which describes massive spin-0 and spin-1 particles, is discussed. Recently the same problem for spin-(1/2) was dealt with by Holland. It appears that the uniqueness of boson paths can be enforced under well determined conditions. This in turn fixes the nonrelativistic particle equations of the nonrelativistic Schrodinger equation, which appear to correspond with the original definitions given by de Broglie and Bohm only in the spin-0 case. Similar to the spin-(1/2) case, there appears an additional spin-dependent term in the guidance equation in the spin-1 case. We also discuss the ambiguity associated with the introduction of an electromagnetic coupling in the Kemmer theory. We argue that when the minimal coupling is correctly introduced, then the current constructed from the energy–momentum tensor is no longer conserved. Hence this current cannot serve as a particle probability four-vector.

Comment on ‘Bohmian prediction about a two double-slit experiment and its disagreement with standard quantum mechanics’

Recently Golshani and Akhavan 2001 J. Phys. A: Math. Gen. 34 5259 proposed an experiment that should be able to distinguish between standard quantum mechanics and Bohmian mechanics. It is our aim to show that the claims made by Golshani and Akhavan are unwarranted.

QUANTUM NONLOCALITY WITHOUT COUNTERFACTUAL DEFINITENESS

Stapps recent proof of the nonlocality of quantum mechanics is critically discussed. It is demonstrated that in his derivation of the Bell inequalities an extra requirement, over locality, is used, which is tantamount to counterfactual definiteness, and that is not a consequence of locality.

The Bell inequalities and the joint measurement of incompatible observables

A quantum-mechanical theory of joint nonideal measurement of incompatible polarization observables is applied to an EPR-like experiment. It is demonstrated that this experiment yields both information satisfying and information violating the Bell inequalities. The measurement is also discussed in the context of a local hidden-variables theory. It is argued that the violation of an additional assumption of reproducibility of the hidden variable rather than violation of locality may be responsible for the violation of the Bell inequalities.

On the Consequences of Retaining the General Validity of Locality in Physical Theory

The empirical validity of the locality (LOC) principle of relativity is used to argue in favour of a local hidden variable theory (HVT) for individual quantum processes. It is shown that such a HVT may reproduce the statistical predictions of quantum mechanics (QM), provided the reproducibility of initial hidden variable states is limited. This means that in a HVT limits should be set to the validity of the notion of counterfactual definiteness (CFD). This is supported by the empirical evidence that past, present, and future are basically distinct. Our argumentation is contrasted with a recent one by Stapp resulting in the opposite conclusion, i.e. nonlocality or the existence of faster-than-light influences. We argue that Stapp’s argumentation still depends in an implicit, but crucial, way on both the notions of hidden variables and of CFD. In addition, some implications of our results for the debate between Bohr and Einstein, Podolsky and Rosen are discussed.

Does the quantum formalism allow for the observability of empty quantum waves

The compatibility of the notion of empty wave with quantum mechanics is investigated. Invoking general physical requirements valid in quantum mechanics it is shown that a picture of a quantum system in terms of an empty wave and a non-empty wave containing a quantum particle is deficient.

Reality and Locality in Quantum Mechanics

It is argued in this work that in order to explain the conflict between Bells inequality (BI) and quantum mechanics (QM), it is neither necessary to give up the notion of Einstein locality (LOC), nor that of reality, as is done in some recent work. The definite existence of EPRs “elements of reality” is shown by using a result in a former thought experiment by M. Renninger. Einstein locality is saved by sticking to the failure of counterfactual definiteness (CFD) at the level of individual quantum processes.

Against Quantum Nonlocality

Abstract It is shown that all quantum “contradictions” disappear if one drops the assumption of unique initial conditions for a hidden variable theory for individual quantum processes. Our proposal corresponds with a deterministic world evolution such that local physical conditions are nonreproducible, in agreement with empirical observation