Robert Griffiths has recently addressed, within the framework of a ‘consistent quantum theory’ that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-physics-type assumptions that are not entailed by the precepts of quantum mechanics. Thus whatever is proved is not a feature of quantum mechanics, but (...) is a property of a theory that tries to combine quantum theory with quasi-classical features that go beyond what is entailed by quantum theory itself. One cannot logically prove properties of a system by establishing, instead, properties of a system modified by adding properties alien to the original system. Hence Griffiths’ rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his ‘consistent quantum theory’ shows that the cited proof is valid within that restrictive version of quantum theory. An added section responds to Griffiths’ reply, which cites general possibilities of ambiguities that might make what is to be proved ill-defined, and hence render the pertinent ‘consistent framework’ ill defined. But the vagaries that he cites do not upset the proof in question, which, both by its physical formulation and by explicit identification, specify the framework to be used. Griffiths confirms the validity of the proof insofar as that pertinent framework is used. The section also shows, in response to Griffiths’ challenge, why a putative proof of locality that he has described is flawed. (shrink)

We propose an ideal experiment enabling the simultaneous assignment of the objective values, 0 or 1, of two incompatible properties of a system made up of two separated, non-interacting spin particles when a strict interpretation of the criterion of reality of Einstein, Podolsky and Rosen is adopted. We compare this experiment with the physical situation involving two-value observables of a system of two correlated spin-1/2 particles envisaged by Bohm; in particular, we show its inadequacy in the dual assignment at issue. (...) Finally, we discuss a number of questions of interpretation of the consistent quantum theory highlighted by our experiment. (shrink)

We critically evaluate the treatment of the notion of measurement in the Consistent Histories approach to quantum mechanics. We find such a treatment unsatisfactory because it relies, often implicitly, on elements external to those provided by the formalism. In particular, we note that, in order for the formalism to be informative when dealing with measurement scenarios, one needs to assume that the appropriate choice of framework is such that apparatuses are always in states of well defined pointer positions after measurements. (...) The problem is that there is nothing in the formalism to justify this assumption. We conclude that the Consistent Histories approach, contrary to what is claimed by its proponents, fails to provide a truly satisfactory resolution for the measurement problem in quantum theory. (shrink)

We present a quantum mechanical analysis of Bell’s approach to quantum foundations based on his hidden-variable model. We claim and try to justify that the Bell model contradicts to the Heinsenberg’s uncertainty and Bohr’s complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the Bohr’s quantum postulate: the existence of indivisible quantum of action given by the Planck constant h. By contradicting these basic principles of QM, Bell’s model implies (...) rejection of this postulate as well. Thus, this hidden-variable model contradicts not only the QM-formalism, but also the fundamental feature of the quantum world discovered by Planck. (shrink)

It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise to some conceptual difficulties, in particular the (...) correct choice of a framework (probabilistic sample space) or family of histories, and these are discussed. The central issue is that the principle of unicity, the idea that there is a unique single true description of the world, is incompatible with our current understanding of quantum mechanics. (shrink)

Stapp’s counterfactual argument for quantum nonlocality based upon a Hardy entangled state is shown to be flawed. While he has correctly analyzed a particular framework using the method of consistent histories, there are alternative frameworks which do not support his argument. The framework dependence of quantum counterfactual arguments, with analogs in classical counterfactuals, vitiates the claim that nonlocal (superluminal) influences exist in the quantum world. Instead it shows that counterfactual arguments are of limited use for analyzing these questions.

It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space rather than by hidden variables. In particular, a measurement using an appropriately constructed apparatus can be shown to reveal the value of an observable A possessed by the measured system before the measurement took place, whatever other compatible observable B may be measured at the same time.

The histories interpretation provides a consistent realistic ontology for quantum mechanics, based on two main ideas. First, a logic is employed which is compatible with the Hilbert-space structure of quantum mechanics as understood by von Neumann: quantum properties and their negations correspond to subspaces and their orthogonal complements. It employs a special syntactical rule to construct meaningful quantum expressions, quite different from the quantum logic of Birkhoff and von Neumann. Second, quantum time development is treated as an inherently stochastic process (...) under all circumstances, not just when measurements take place. The time-dependent Schr\"odinger equation provides probabilities, not a deterministic time development of the world. The resulting interpretive framework has no measurement problem and can be used to analyze in quantum terms what is going on before, after, and during physical preparation and measurement processes. In particular, appropriate measurements can reveal quantum properties possessed by the measured system before the measurement took place. There are no mysterious superluminal influences: quantum systems satisfy an appropriate form of Einstein locality. This ontology provides a satisfactory foundation for quantum information theory, since it supplies definite answers as to what the information is about. The formalism of classical information theory applies without change in suitable quantum contexts, and this suggests the way in which quantum information theory extends beyond its classical counterpart. (shrink)

The histories interpretation provides a consistent realistic ontology for quantum mechanics, based on two main ideas. First, a logic is employed which is compatible with the Hilbert-space structure of quantum mechanics as understood by von Neumann: quantum properties and their negations correspond to subspaces and their orthogonal complements. It employs a special syntactical rule to construct meaningful quantum expressions, quite different from the quantum logic of Birkhoff and von Neumann. Second, quantum time development is treated as an inherently stochastic process (...) under all circumstances, not just when measurements take place. The time-dependent Schrödinger equation provides probabilities, not a deterministic time development of the world.The resulting interpretive framework has no measurement problem and can be used to analyze in quantum terms what is going on before, after, and during physical preparation and measurement processes. In particular, appropriate measurements can reveal quantum properties possessed by the measured system before the measurement took place. There are no mysterious superluminal influences: quantum systems satisfy an appropriate form of Einstein locality.This ontology provides a satisfactory foundation for quantum information theory, since it supplies definite answers as to what the information is about. The formalism of classical information theory applies without change in suitable quantum contexts, and this suggests the way in which quantum information theory extends beyond its classical counterpart. (shrink)

Relying on some auxiliary assumptions, usually considered mild, Bell’s theorem proves that no local theory can reproduce all the predictions of quantum mechanics. In this work, we introduce a fully local, superdeterministic model that by explicitly violating ‘settings independence’—one of these auxiliary assumptions, requiring statistical independence between measurement settings and systems to be measured—is able to reproduce all the predictions of quantum mechanics. Moreover, we show that contrary to widespread expectations, our model can break settings independence without an initial state (...) that is too complex to handle, without visibly losing all explanatory power, and without outright nullifying all of experimental science. Still, we argue that our model is unnecessarily complicated and does not offer true advantages over its non-local competitors. We conclude that while our model does not appear to be a viable contender to its non-local counterparts, it provides the ideal framework to advance the debate over violations of statistical independence via the superdeterministic route. (shrink)

The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations 〈A i 〉, 〈B〉, 〈A i B〉, and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlation (...) 〈A 1 A 2〉 associated to different choices for B. The same analysis applies to the Hardy model and to the “perfect correlations” discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality. (shrink)