How to Avoid Peres' “incompatible results of quantum measurements”

It is demonstrated how, in terms of hidden variables, the claimed incompatibility of results of quantum measurements, obtained in a recent work by A. Peres, may be avoided. The new property which restores the compatibility of quantum measurement results is called the nonreproducibility of individual subquantum states.Research director N.F.W.O. (Belgium).     

Quantum nonlocality without counterfactual definiteness?

Stapp's 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.1. Research associate N.F.W.O. (Belgium).     

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.     

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.     

Locality and Measurements Within the SR Model for an Objective Interpretation of Quantum Mechanics

One of the authors has recently propounded an SR (semantic realism) model which shows, circumventing known no-go theorems, that an objective (noncontextual, hence local) interpretation of quantum mechanics (QM) is possible. We consider here compound physical systems and show why the proofs of nonlocality of QM do not hold within the SR model, which is slightly simplified in this paper. We also discuss quantum measurement theory within this model, note that the objectification problem disappears since the measurement of any property simply reveals its unknown value, and show that the projection postulate can be considered as an approximate law, valid FAPP (for all practical purposes). Finally, we provide an intuitive picture that justifies some unusual features of the SR model and proves its consistency.     

On the derivation of the Schrödinger equation from stochastic mechanics

It is shown that the existing formulations of stochastic mechanics are not equivalent to the Schrödinger equation, as had previously been believed. It is argued that this is a reflection of fundamental inadequacies in the physical foundations of stochastic mechanics.Some relatively minor difficulties with the demonstration of equivalence are already known for the special case in which the nodal surface separates the manifold of the diffusion into disjoint components.^(1,11) The problems described in this paper are much more general and quite unrelated.     

A second look at a recent algebraic proof of nonlocality

We reply to M. Jones' criticisms of our proof that factorable stochastic hidden-variable theories are inconsistent with GHZ-style strict correlations predicted by quantum mechanics. We endorse Jones' clarifications of our definitions of the setsM and _TF. And we reply to his main criticism by invoking one additional locality-motivated assumption. Further, we show how this additional assumption can be weakened while preserving our proof's validity.1. Ironically, a draft version of our paper (March, 1990) used this assumption, and discussed its motivation and weakening. But we were then misled into thinking it unnecessary: So all credit to Jones for seeing the wood for the trees!2. This new assumption, AI (see below), alsorestores the link between TF, the strict correlations, and Shimony'sTF, which is severed by Jones' criticism (as he notes—cf. Ref. 1, pp. 162, 165 for our original claim of a link). Thus the correct result is that if TF, the strict correlations,and AI hold in any state, then so doesTF.     

MGP Versus Kochen–Specker Condition in Hidden Variables Theories

Hidden variables theories} for quantum mechanics are usually assumed to satisfy the KS condition. The Bell–Kochen–Specker theorem then shows that these theories are necessarily contextual. But the KS condition can be criticized from an operational viewpoint, which suggests that a weaker condition (MGP) should be adopted in place of it. This leads one to introduce a class of hidden parameters theories in which contextuality can, in principle, be avoided, since the proofs of the Bell–Kochen–Specker theorem break down. A simple model recently provided by the author for an objective interpretation of quantum mechanics can be looked at as a noncontextual hidden parameters theory, which shows that such theories actually exist.     

Counterfactual Reasoning in Time-Symmetric Quantum Mechanics

A qualification is suggested for the counterfactual reasoning involved in some aspects of time-symmetric quantum theory (which involves ensembles selected by both the initial and final states). The qualification is that the counterfactual reasoning should only apply to times when the quantum system has been subjected to physical interactions which place it in a “measurement-ready condition” for the unperformed experiment on which the counterfactual reasoning is based. The defining characteristic of a “measurement-ready condition” is that a quantum system could be found to have the counterfactually ascribed property without direct physical interaction with the eigenstate corresponding to that property.     

Bell Locality and the Nonlocal Character of Nature

It is demonstrated that hidden variables of a certain type follow logically from a certain local causality requirement (“Bell Locality”) and the empirically well-supported predictions of quantum theory for the standard EPR-Bell set up. The demonstrated hidden variables are precisely those needed for the derivation of the Bell Inequalities. We thus refute the widespread view that empirical violations of Bell Inequalities leave open a choice of whether to reject (i) locality or (ii) hidden variables. Both principles are indeed assumed in the derivation of the inequalities, but since, as we demonstrate here, (ii) actually follows from (i), there is no choice but to blame the violation of Bell's Inequality on (i). Our main conclusion is thus no Bell Local theory can be consistent with what is known from experiment about the correlations exhibited by separated particles. Aside from our conclusion being based on a different sense of locality this conclusion resembles one that has been advocated recently by H.P. Stapp. We therefore also carefully contrast the argument presented here to that proposed by Stapp.     

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 classical models of Spin

We discuss two classical situations that lead to probabilities characteristic for systems with spin-1/2. (a) Pitowsky model: It is demonstrated that the definition of spin functions does not imply which circle (a parallel or a great circle) on the sphere should be taken as a probability space in calculation of conditional probabilities. Pitowsky's choice of parallels must be formulated as an assumption about the model. It is shown that the model explicitly avoiding this difficulty is possible and no contradiction with the Bell Theorem is found. The modification is based on a new pathological decomposition of the sphere and belongs to a class of hidden variable theories with undetected signals. (b) Aerts model: We show the importance of the polarization effect of the measurements for the sake of obtaining a non-Kolmogorovian probability model. It is also shown that the conditioning by a change of state leads in general to the non-Kolmogorovian probability calculus.2. For example, let _{Cw,z xCw,z}µ_c ({y C _w,z S ₊|(x,y) /2})=µ _c(C _w,z S ₊)= 1/2µ _c(C _w,z). Pitowsky spheres with white points distributed onC _w,z in this way exist. The proof is exactly analogous to this of Theorem 1 in [1]. Then (**) = 1 -/, if one takesC _w,z as the probability space. This example seems very instructive.3. If the chargeq falls down on some point then it clearly has not fallen down on another one. Having given a result of a measurement we cannot, within the model with polarization, talk in a sensible way about its alternative: We can think either aboutsuccessive measurements (then the Bell inequality is not derivable) or ask What would have happened if..., but then we deal with a different problem (in Aerts' terminology [2b] this is anobservation) and obtain again Eq. (8) (there is no complementarity but there is no model of spin either).     

Hidden Measurements,Hidden Variables and the Volume Representation of Transition Probabilities

We construct, for any finite dimension n, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For n=2 our model is equivalent to the Aerts sphere model and serves as a generalization of it for dimensions n . 3 We also show how to construct a hidden variables scheme based on hidden measurements and we discuss how joint distributions arise in our hidden variables scheme and their relationship with the results of Fine [J. Math. Phys. 23 1306 (1982)].     

A Local Realistic Theory for the Greenberger-Horne-Zeilinger Experiment

As a counterexample to conventional belief, a realistic theory, which is both local and reproduces all the probabilistic predictions of quantum theory, is constructed for the Greenberger-Horne-Zeilinger three-photon experiment.     

A Characterisation of Locality in Momentum Space

It is proved that a Poincaré invariant Wightman function which fulfils the spectral property and can be defined at sharp times, is local if and only if the integration over both the energy variables of a commutator in momentum space is a polynomial in the momentum conjugated to the spacial difference variable of the commutator with distributional coefficients depending on the remaining energy and momentum variables. Using this characterisation of locality in momentum space, the locality of a sequence of Wightman functions with nontrivial scattering behavior (associated to some quantum field in indefinite metric) can be proved by explicit calculations. We compare the above characterisation of locality with the classical integral representation method of Jost, Lehmann and Dyson.     

Modeling Modal Talk in Quantum Mechanics

In this paper, modal and counterfactual logical connectives are defined in an extended framework of branching space-time (Belnap, N. D. (1992). Branching space-time. Synthese 92, 385–434). It is shown that a variety of definitions of the counterfactual can be given. The validity of certain modal statements occurring in quantum mechanics depends on the choice of definition. These considerations can be applied to an analysis of Stapp’s premises LOC1 and LOC2 from his purported proof of non-locality (Stapp, H. P. (1997). Nonlocal character of quantum theory. American Journal of Physics 65, 300–304). It is shown that while the validity of LOC1 depends on the choice of the definition of the counterfactual, LOC2 is absolutely invalid.     

On the Dirac equation with anomalous magnetic moment term in a beam of electromagnetic wave

The object of the paper is to obtain the solution of the Dirac equation with the Pauli-term in an electromagnetic field depending on the single variable (ct -nr) along the directionn.