W. M. de Muynck

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.

Distinguishable- and indistinguishable-particle descriptions of systems of identical particles

The problem of distinguishability of identical particles is considered from both experimental and theoretical points of view. It is argued that distinguishability has to be defined relative to a definite set of experiments and that the criterion by which the particles are distinguished should be specified. Failure to do so may cause mismatching between theory and experiment. On the theoretical level a distinction is made between indexed- and unindexed-particle theories, indices being unobserved intrinsic properties of the particles. A field theory of indexed particles is constructed and shown to be equivalent to the second quantization formalism, which is an unindexed-particle theory.

Compatibility of observables represented by positive operator‐valued measures

The proof of a result analogous to that in Koelman and de Muynck [Phys. Lett. A 98, 1 (1983)] is given for the case of unbounded observables. If two, not necessarily bounded, observables are represented by a positive operator‐valued measure, then the measurement of any of them is undisturbed if and only if they commute. The Naimark theorem on dilations of spectral functions is exploited. A stronger version of Wigner’s theorem is given.

On the joint measurement of incompatible observables in quantum mechanics

Abstract Starting from a representation of a quantum-mechanical observable by a positive-operator-valued measure it is derived that if two incompatible observables A and B are measured jointly then both the A -and the B -measurements are disturbed. More specific: if the expectation values 〈 A 〉 and 〈 B 〉 are undisturbed then there is a broadening in the probability distributions of both the A - and the B -measurement results.

A derivation of local commutativity from macrocausality using a quantum mechanical theory of measurement

A theory of the joint measurement of quantum mechanical observables is generalized in order to make it applicable to the measurement of the local observables of field theory. Subsequently, the property of local commutativity, which is usually introduced as a postulate, is derived by means of the theory of measurement from a requirement of mutual nondisturbance, which, for local observables performed at a spacelike distance from each other, is interpreted as a requirement of macrocausality. Alternative attempts at establishing a deductive relationship between relativistic causality and local commutativity are reviewed, but found wanting, either because of the assumption of an unwarranted objectivity of the object system (algebraic approach) or because of the use of a projection postulate (operational approach). Finally, the quantum mechanical nonobjectivity is related to certain features of nonlocality which are present in the formalism of quantum mechanics.

Single and joint spin measurements with a Stern-Gerlach device

The measurement of spin-1/2 observables using a Stern-Gerlach type device is studied. A magnetic field with a dominant dipole component leads to a measurement of spin in one direction. The measurement is shown to be feasible (in principle) for electrons as well as for neutral particles. A quadrupole field leads to a joint measurement of two incompatible spin observables. Again, both the electron and the neutral case are presented. The accuracy of the joint measurement is compared to the limit imposed by the uncertainty principle.

Disturbance, conservation laws and the uncertainty principle

The interpretation of the uncertainty principle in terms of a measurement of a single observable disturbing other observables, originating in Heisenbergs 1927 paper, is shown to be derivable from an uncertainty principle for joint measurements of incompatible observables. The latter also limits measurements of a single observable in the presence of conservation laws.

Joint measurement of interference and path observables in optics and neutron interferometry

Abstract We discuss analogous measurement arrangements for the joint measurement of interference and path in both optical and neutron interferometry. Analogous to an optical experiment proposed by Busch we propose a neutron interferometric experiment that, contrary to the ones performed till now, is a nontrivial joint measurement of interference and path.

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.

Compensation of self-phase modulation in a QND measurement of photon number based on the optical Kerr effect

The authors study a quantum non-demolition (QND) set-up for the measurement of photon number, employing the optical Kerr effect. A method for the compensation of the negative effects of self-phase modulation is discussed. Losses are taken into account. It is seen that the performance of the device is limited in the first place by losses, rather than by self-phase modulation.