Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann’s ‘no hidden variables’ proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense ‘like Bohm’s theory.’ His seminal result provides a positive answer to the question. I argue that Bell’s analysis misconstrues von Neumann’s argument. What von (...) Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the ‘beables’ of the theory, to use Bell’s term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm’s theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system. (shrink)

In this paper we first briefly review Bell's (1964, 1966) Theorem to see how it invalidates any deterministic "hidden variable" account of the apparent indeterminacy of quantum mechanics (QM). Then we show that quantum uncertainty, at the level of DNA mutations, can "percolate" up to have major populational effects. Interesting as this point may be it does not show any autonomous indeterminism of the evolutionary process. In the next two sections we investigate drift and natural selection as the (...) locus of autonomous biological indeterminacy. Here we conclude that the population-level indeterminacy of natural selection and drift are ultimately based on the assumption of a fundamental indeterminacy at the level of the lives and deaths of individual organisms. The following section examines this assumption and defends it from the determinists' attack. Then we show that, even if one rejects the assumption, there is still an important reason why one might think evolutionary theory (ET) is autonomously indeterministic. In the concluding section we contrast the arguments we have mounted against a deterministic hidden variable account of ET with the proof of the impossibility of such an account of QM. (shrink)

Although skeptical of the prohibitive power of no-hidden-variables theorems, John Bell was himself responsible for the two most important ones. I describe some recent versions of the lesser known of the two (familiar to experts as the "Kochen-Specker theorem") which have transparently simple proofs. One of the new versions can be converted without additional analysis into a powerful form of the very much better known "Bell's Theorem," thereby clarifying the conceptual link between these two results of Bell.

Existing "no hidden variable proofs" for quantum mechanics deal exclusively with observables with discrete spectra. This note shows that similar results hold for observables with continuous spectra.

Interpretations of the quantum mechanical formalism true to the spirit of scientific realism satisfy not only principles of scientific realism but also principles of causality that guide realist constructions. Formally, such interpretations are hidden variables theories and are commonly believed to be ruled out by the most recent no-hidden-variables argument expressed by Bell's theorem. This dissertation investigates the possibility of constructing indeterministic hidden variables theories in light of Bell's result. A pair of arguments in the literature lead (...) to the conclusion that there is no generality to be gained in moving to the stochastic case. The author uses limitations on measurements discovered by Wigner as the basis for a response to both. Proofs of the existence of the limitations are analyzed and it is shown that, contrary to claims in the literature, we cannot always assume that measurements subject to the limitations are perfectly revealing and, therefore, that the assumption of strict anti-correlations, an assumption crucial to one of those arguments, is unjustified in the Bell case. The author suggests how Bell's 1971 inequality must be modified to incorporate these limitations . This result is used against the second argument, due to Fine, which relies on Bell's 1971 inequality. A thought experiment due to Jarrett is reviewed and it is argued that the independence assumptions incorporated into hidden variables theories are not without additional and controversial assumptions about causality related to constraints imposed by the special theory of relativity. The author concludes that Bell's theorem tells us nothing about determinism or special relativity but does tell us that there can be no interpretation of quantum mechanics that does not violate either one of three principles of scientific realism or one of three traditional principles of causality. (shrink)

In the contemporary discussion of hidden variable interpretations of quantum mechanics, much attention has been paid to the “no hidden variable” proof contained in an important paper of Kochen and Specker. It is a little noticed fact that Bell published a proof of the same result the preceding year, in his well-known 1966 article, where it is modestly described as a corollary to Gleason's theorem. We want to bring out the great simplicity of Bell's formulation of (...) this result and to show how it can be extended in certain respects. (shrink)

We analyze the proof given by J. S. Bell of an inequality between mean values of measurement results which, according to him, would be characteristic of any local hidden-parameter theory. It is shown that Bell's proof is based upon a hypothesis already contained in von Neumann's famous theorem: It consists in the admission that hidden values of parameters must obey the same statistical laws as observed values. This hypothesis contradicts in advance well-known and certainly correct statistical relations in (...) measurement results: One must therefore reject the type of theory considered by Bell, and his inequality has no general meaning. (shrink)

Sept. 24, 1901 Chicago Ills. U.S.A.– 6026 Monroe Ave. Chicago University – William R. Harper, President Professor of Astronomy and Mathematics – School of Education Mr. H. Poincaré, Paris France My dear Sir: You have perhaps noticed in Professor André’s book entitled _“Traité d’astronomie stellaire”_ Vol II p. 303 that my discussions of β Lyrae and U Pegasi both seem to point to a concrete confirmation of your excellent work on rotating liquids. I am now curious to see if by (...) computing light curves based upon any of your other theoretical forms—perhaps the apiodal—I may be able to represent the light curves of any other variables. To this end I write to inquire whether you can put into my hands a copy of the paper containing your discussion, or discussions, of your various forms of rotating liquid masses in equilibrium. If you can do so, you will greatly oblige me and help me, perhaps, to accomplish something which may be of interest to you as furnishing tangible proof of the existence in th... (shrink)

The debate over the question whether quantum mechanics should be considered as a complete account of microphenomena has a long and deeply involved history, a turning point in which has been certainly the Einstein-Bohr debate, with the ensuing charge of incompleteness raised by the Einstein-Podolsky-Rosen argument. In quantum mechanics, physical systems can be prepared in pure states that nevertheless have in general positive dispersion for most physical quantities; hence in the EPR argument, the attention is focused on the question whether (...) the account of the microphysical phenomena provided by quantum mechanics is to be regarded as an exhaustive description of the physical reality to which those phenomena are supposed to refer, a question to which Einstein himself answered in the negative. However, there is a mathematical side of the completeness issue in quantum mechanics, namely the question whether the kind of states with positive dispersion can be represented as a different, dispersion-free kind of states in a way consistent with the mathematical constraints of the quantum mechanical formalism. From this point of view, the other source of the completeness issue in quantum mechanics is the no hidden variables theorem formulated by John von Neumann in his celebrated book on the mathematical foundations of quantum mechanics, the preface of which already anticipates the program and the conclusion concerning the possibility of ‘neutralizing’ the statistical character of quantum mechanics. (shrink)

We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.

It is a widespread belief that the Kochen-Specker theorem imposes a contextuality constraint on the ontology of beables in quantum hidden variables theories. On the other hand, after Bell’s influential critique, the importance of von Neumann’s wrongly called ‘impossibility proof’ has been severely questioned. However, Max Jammer, Jeffrey Bub and Dennis Dieks have proposed insightful reassessments of von Neumann’s theorem: what it really shows is that hidden variables theories cannot represent their beables by means of Hermitian operators in (...) Hilbert space. Hereby I show that i) the very same constraint can be derived from Gleason’s theorem, and that ii) if we consider the import of von Neumann’s and Gleason’s theorems, the relevance of the Kochen-Specker theorem for hidden variables theories gets substantially weakened: it does not force them to be contextual in any interesting sense of the term. (shrink)

I show that for any quantum dynamics and any choice of observables as hidden variables an adequate hidden variable theory always exists. I argue that hidden variable theories have no more problems in reconciling non-locality with relativity than no-hidden-variable theories.

This article takes up a suggestion that the reason we cannot find certain hidden variable theories for quantum mechanics, as in Bell’s theorem, is that we require them to assign joint probability distributions on incompatible observables. These joint distributions are problematic because they are empirically meaningless on one standard interpretation of quantum mechanics. Some have proposed getting around this problem by using generalized probability spaces. I present a theorem to show a sense in which generalized probability spaces can’t (...) serve as hidden variable theories for quantum mechanics, so the proposal for getting around Bell’s theorem fails. 1 Introduction2 Bell’s Theorem and Classical Probability Spaces2.1 Bell’s derivation of the Bell inequalities2.2 Pitowsky’s derivation of the Bell inequalities3 Incompatible Observables4 Generalized Probability Spaces5 A ‘No-Go’ Theorem6 Conclusions. (shrink)

Entangled states whose Wigner functions are non-negative may be viewed as being accounted for by local hidden variables (LHV). Recently, there were studies of Bell’s inequality violation (BIQV) for such states in conjunction with the well known theorem of Bell that precludes BIQV for theories that have LHV underpinning. We extend these studies to teleportation which is also based on entanglement. We investigate if, to what extent, and under what conditions may teleportation be accounted for via LHV theory. Our (...) study allows us to expose the role of various quantum requirements. These are, e.g., the uncertainty relation among non-commuting operators, and the no-cloning theorem which forces the complete elimination of the teleported state at its initial port. (shrink)

Bell's problem of the possibility of a local hidden variable theory of quantum phenomena is considered in the context of the general problem of representing the statistical states of a quantum mechanical system by measures on a classical probability space, and Bell's result is presented as a generalization of Maczynski's theorem for maximal magnitudes. The proof of this generalization is shown to depend on the impossibility of recovering the quantum statistics for sequential probabilities in a classical representation without (...) introducing a randomization process for the hidden variables. Hidden variable theories that exclude such a randomization process are termed “strict,” and it is shown that the class of local hidden variable theories is included in the class of strict theories. A counterargument by Freedman and Wigner is evaluated with reference to Clauser's extension of a hidden variable model proposed by Bell. (shrink)

According to what has become a standard history of quantum mechanics, von Neumann in 1932 succeeded in convincing the physics community that he had proved that hidden variables were impossible as a matter of principle. Subsequently, leading proponents of the Copenhagen interpretation emphatically confirmed that von Neumann's proof showed the completeness of quantum mechanics. Then, the story continues, Bell in 1966 finally exposed the proof as seriously and obviously wrong; this rehabilitated hidden variables and made serious foundational research (...) possible. It is often added in recent accounts that von Neumann's error had been spotted almost immediately by Grete Hermann, but that her discovery was of no effect due to the dominant Copenhagen Zeitgeist. We shall attempt to tell a more balanced story. Most importantly, von Neumann did not claim to have shown the impossibility of hidden variables tout court, but argued that hidden-variable theories must possess a structure that deviates fundamentally from that of quantum mechanics. Both Hermann and Bell appear to have missed this point; moreover, both raised unjustified technical objections to the proof. Von Neumann's conclusion was basically that hidden-variables schemes must violate the "quantum principle" that all physical quantities are to be represented by operators in a Hilbert space. According to this conclusion, hidden-variables schemes are possible in principle but necessarily exhibit a certain kind of contextuality. As we shall illustrate, early reactions to Bohm's theory are in agreement with this account. Leading physicists pointed out that Bohm's theory has the strange feature that particle properties do not generally reveal themselves in measurements, in accordance with von Neumann's result. They did not conclude that the "impossible was done" and that von Neumann had been shown wrong. (shrink)

It is argued that among possible nonlocal hidden-variable theories a particular class (called here “crypto-nonlocal” or CN) is relatively plausible on physical grounds. CN theories have the property that (for example) the two photons emitted in an atomic cascade process are indistinguishable in their individual statistical properties from photons emitted singly, and that in the latter case the effects of nonlocality are unobservable. It is demonstrated that all CN theories are constrained by inequalities which are violated by the (...) quantum-mechanical predictions; these inequalities bear no simple relation to Bell's inequalities, and an explicit example is constructed of a CN theory which violates the latter. It is also shown that while existing experiments cannot rule out general CN theories, they do rule out (subject to a few caveats such as the usual ones concerning the well-known “loopholes”) the subclass in which the photon polarizations are linear. (shrink)

A hidden-variables model is presented which, by using a hypothesis of “directionalization” of the photons at the deflectors, is able to reproduce all the quantum mechanical predictions for the Orsay realization of the Einstein-Podolsky-Rosen-Bohm experiment, even for ideal polarizers, detectors, time-coincidence windows, and “event-ready” setups. The model also holds for the no-enhancement assumption. The requirements for an experiment aimed to discriminate between quantum mechanics and the new model are discussed. Under some plausible assumptions, such experiment is achievable with the (...) current technology. It would be essentially a remake of the Orsay one with improved deflectors and a time-resolved measurement of the photon flows toward each detector. (shrink)

In the present paper we give a precise definition of a hidden-variable theory for quantum mechanics, whereby we adopt the weakest possible definition of a hidden-variable theory, which is compatible with the assumption that the bounded observables of a quantum mechanical system are represented by the elements of the real part Ar of a W*-algebra A (of the most general type) and the states are represented by the “normal states” (in the mathematical sense) of A. We (...) then go on to show that an example put forward by Bell in 1966 satisfies our definition (Sec. 2). Finally we make use of Bell's famous theorem to show that for a sufficiently non-commutative W*-algebra A no hidden-variable theory in our sense exists (Theorem 3.3 and its corollaries). (shrink)

Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no‐go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non‐contextual way. In contrast to (...) an earlier theorem (Breuer 2002) this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy. (shrink)

Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no-go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non-contextual way. In contrast to (...) an earlier theorem [Breuer, Phys. Rev. Lett. 88(2002), 240402] this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy. (shrink)

Bell's proof purports to show that any hidden variable theory satisfying a physically reasonable locality condition is characterized by an inequality which is inconsistent with the quantum statistics. It is shown that Bell's inequality actually characterizes a feature of hidden variable theories which is much weaker than locality in the sense considered physically motivated. We consider an example of non- local hidden variable theory which reproduces the quantum statistics. A simple extension of the theory, (...) which preserves the non- local character, alters the statistics in such a way that Bell's inequality is satisfied. (shrink)

J. Solomon [Journal de Physique 4, 34 (1933)] produced an argument of great generality claiming to demonstrate the impossibility of hidden variables in quantum theory, an argument which M. Jammer [The Philosophy of Quantum Mechanics(Wiley, New York, 1974)] said raised a number of questions. For the first time, this argument is discussed, a simple hidden variable model violating the argument is analysed in detail, and the error in the proof is located.

In this paper I discuss two objections raised against von Fintel’s (1994) and Stanley and Szabó’s (2000a) hidden variable approach to quantifier domain restriction (QDR). One of them concerns utterances of sentences involving quantifiers for which no contextual domain restriction is needed, and the other concerns multiple quantified contexts. I look at various ways in which the approaches could be amended to avoid these problems, and I argue that they fail. I conclude that we need a more flexible (...) account of QDR, one that allows for the hidden variables in the LF responsible for QDR to vary in number. Recanati’s (2002; 2004) approach to QDR, which makes use of the apparatus of “variadic functions”, is flexible enough to account successfully for the two phenomena discussed. I end with a few comments on what I take to be the most promising way to construe variadic functions. (shrink)

A hidden-variable model for quantum–mechanical spin, as represented by the Pauli spin operators, is proposed for systems illustrating the well-known no-hidden-variables arguments by Peres (Phys Lett A 151:107–108, 1990) and Mermin (Phys Rev Lett 65:3373–3376, 1990) and by Greenberger et al. (Bell’s theorem, quantum theory, and conceptions of the universe, Kluwer, Dordrecht, 1989). Both arguments rely on an assumption of non-contextuality; the latter argument can also be phrased as a non-locality argument, using a locality assumption. The model (...) suggested here is compatible with both assumptions. This is possible because the scalar values of spin observables are replaced by vectors that are components of orientations. (shrink)

In this paper, we discuss various aspects of Heisenberg’s thought on hidden variables in the period 1927–1935. We also compare Heisenberg’s approach to others current at the time, specifically that embodied by von Neumann’s impossibility proof, but also views expressed mainly in correspondence by Pauli and by Schroedinger. We shall base ourselves mostly on published and unpublished materials that are known but little-studied, among others Heisenberg’s own draft response to the EPR paper. Our aim will be not only to (...) clarify Heisenberg’s thought on the hidden-variables question, but in part also to clarify how this question was understood more generally at the time. (shrink)

We further develop a recent new proof (by Greenberger, Horne, and Zeilinger—GHZ) that local deterministic hidden-variable theories are inconsistent with certain strict correlations predicted by quantum mechanics. First, we generalize GHZ's proof so that it applies to factorable stochastic theories, theories in which apparatus hidden variables are causally relevant to measurement results, and theories in which the hidden variables evolve indeterministically prior to the particle-apparatus interactions. Then we adopt a more general measure-theoretic approach which requires that (...) GHZ's argument be modified in order to produce a valid proof. Finally, we motivate our more general proof's assumptions in a somewhat different way from previous authors in order to strengthen the implications of our proof as much as possible. After developing GHZ's proof along these lines, we then consider the analogue, for our proof, of Bohr's reply to the EPR argument, and conclude (pace GHZ) that in at least one respect (viz. that of most concern to Bohr) the proof is no more powerful than Bell's. Nevertheless, we point out some new advantages of our proof over Bell's, and over other algebraic proofs of nonlocality. And we conclude by giving a modified version of our proof that, like Bell's, does not rely on experimentally unrealizable strict correlations, but still leads to a testable “quasi-algebraic” locality inequality.“... to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics.”J. S. Bell. (shrink)

We show that a quantum system admits hidden variables if and only if there is a rich set of states which satisfy a Bayesian rule. The result is proved using a relationship between Bayesian type states and dispersion-free states. Various examples are presented. In particular, it is shown that for classical systems every state is Bayesian and for traditional Hilbert space quantum systems no state is Bayesian.

Given two unital C*-algebrasA, ℬ and their state spacesE A , Eℬ respectively, (A,E A ) is said to have (ℬ, Eℬ) as a hidden theory via a linear, positive, unit-preserving map L: ℬ →A if, for all ϕ εE A , L*ϕ can be decomposed in Eℬ into states with pointwise strictly less dispersion than that of ϕ. Conditions onA and L are found that exclude (A,E A ) from having a hidden theory via L. It is (...) shown in particular that, ifA is simple, then no (ℬ, Eℬ) can be a hidden theory of (A,E A ) via a Jordan homomorphism; it is proved furthermore that, ifA is a UHF algebra, it cannot be embedded into a larger C*-algebra ℬ such that (ℬ, Eℬ) is a hidden theory of (A,E A ) via a conditional expectation from ℬ ontoA. (shrink)

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. (shrink)

Laudisa (Found. Phys. 38:1110–1132, 2008) claims that experimental research on the class of non-local hidden-variable theories introduced by Leggett is misguided, because these theories are irrelevant for the foundations of quantum mechanics. I show that Laudisa’s arguments fail to establish the pessimistic conclusion he draws from them. In particular, it is not the case that Leggett-inspired research is based on a mistaken understanding of Bell’s theorem, nor that previous no-hidden-variable theorems already exclude Leggett’s models. Finally, I (...) argue that the framework of Bohmian mechanics brings out the importance of Leggett tests, rather than proving their irrelevance, as Laudisa supposes. (shrink)

ConclusionI think it is clear that Bqm and Oqm are quite different theories, even if they have the same empirical consequences. This is, of course, to adopt something like the realist perspective. Oqm is not normally interpreted realistically by physicists (the survey still has not been done!) but it can be, and what it says things are like is by no means the same as what Bqm says. One of the most puzzling features of Oqm is the status of the (...) particle when it is in an eigenstate of momentum: if it has no precise position how can it be anywhere at all, and if it isn’t anywhere how can it be said to exist? The great advantage of Bqm is that it restores definite trajectories.The books under review, on which I have based this exposition, are all to be recommended. I am particularly impressed with Peter Holland’s book and assure the reader that it will repay study. The collection by Cushinget al. is, on the whole, better than most in that it is consistently focused on the advertised theme, but it is mostly technical. Cushing’s book is the most accessible of the three volumes. (shrink)

In "The Indeterministic Character of Evolutionary Theory: No 'Hidden Variables Proof' But No Room for Determinism Either," Brandon and Carson (1996) argue that evolutionary theory is statistical because the processes it describes are fundamentally statistical. In "Is Indeterminism the Source of the Statistical Character of Evolutionary Theory?" Graves, Horan, and Rosenberg (1999) argue in reply that the processes of evolutionary biology are fundamentally deterministic and that the statistical character of evolutionary theory is explained by epistemological rather than ontological considerations. (...) In this paper I focus on the topic of mutation. By focusing on some of the theory and research on this topic from early to late, I show how quantum indeterminism hooks up to point mutations (via tautomeric shifts, proton tunneling, and aqueous thermal motion). I conclude with a few thoughts on some of the wider implications of this topic. (shrink)

The final portion of the thesis surveys proposals for the introduction of hidden variables into quantum mechanics, proofs of the impossibility of such hidden-variable proposals, and criticisms of these impossibility proofs. And arguments in favour of the partial-Boolean algebra, rather than the orthomodular lattice, formalization of the quantum propositional structures are reviewed. ;As for , each quantum state-induced expectation-function on a P truth-functionally assigns 1 and 0 values to the elements in a ultrafilter and dual (...) ultraideal of P, where in general the union of an ultrafilter and its dual ultraideal is smaller than the entire structure. Thus it is argued that each expectation-function is the quantum analog of a classical semantic mapping, even though the domain where each expectation-function is bivalent and truth-functional is usually a non-Boolean substructure of P. ;In classical propositional logic, propositions form a Boolean algebra, and each semantic mapping assigns the value 1 to the members of a certain subset of the algebra, namely, an ultrafilter, and assigns 0 to the members of the dual ultraideal, where the union of these two subsets is the entire algebra. The propositional structures of classical mechanics are likewise Boolean algebras, so one can straightforwardly provide a classical semantics, which also satisfies . However, quantum propositional structures are non-Boolean, so it is an open question whether a semantics satisfying , and can be provided. ;Von Neumann first proposed that the algebraic structures of the subspaces of Hilbert space be regarded as the propositional structures P of quantum mechanics. These structures have been formalized in two ways: as orthomodular lattices which have the binary operations "and", "or", defined among all elements, compatible and incompatible ; and as partial-Boolean algebras which have the binary operations defined among only compatible elements. In the thesis, two basic senses in which these structures are non-Boolean are discriminated. And two notions of truth-functionality are distinguished: truth-functionality ,) applicable to the Plattices; and truth-functionality ) applicable to both the Plattices and partial-Boolean algebras. Then it is shown how the lattice definitions of "and", "or", among incompatibles rule out a bivalent, truth-functional ,) semantics for any PQM lattice containing incompatible elements. In contrast, the Gleason and Kochen-Specker proofs of the impossibility of hidden-variables for quantum mechanics show the impossibility of a bivalent, truth-functional ) semantics for three-or-higher dimensional Hilbert space PQM structures; and the presence of incompatible elements is necessary but is not sufficient to rule out such a semantics. ;The thesis investigates the possibility of a classical semantics for quantum propositional structures. A classical semantics is defined as a set of mappings each of which is bivalent, i.e., the value 1 or 0 is assigned to each proposition, and truth-functional, i.e., the logical operations are preserved. In addition, this set must be "full", i.e., any pair of distinct propositions is assigned different values by some mapping in the set. When the propositions make assertions about the properties of classical or of quantum systems, the mappings should also be "state-induced", i.e., values assigned by the semantics should accord with values assigned by classical or by quantum mechanics. (shrink)

We review several no-go theorems attributed to Gisin and Hardy, Conway and Kochen purporting the impossibility of Lorentz-invariant deterministic hidden-variable model for explaining quantum nonlocality. Those theorems claim that the only known solution to escape the conclusions is either to accept a preferred reference frame or to abandon the hidden-variable program altogether. Here we present a different alternative based on a foliation dependent framework adapted to deterministic hidden variables. We analyse the impact of such an (...) approach on Bohmian mechanics and show that retrocausation necessarily comes out without time-loop paradox. (shrink)

John von Neumann was among the first to learn about Kurt Gödel’s results on the incompleteness of formal systems. Did this shape his views on the completeness of quantum mechanics? I will investigate this question from two viewpoints: von Neumann’s no-hidden-variables proof and his treatment of the quantum measurement problem.

We construct a local \-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state \\rangle \) as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state \\rangle \) which is different from the prepared quantum state \\rangle \) and has an ontic status. The ontic state of a single (...) particle consists of two parts. First, a single particle ontic quantum state \|i\rangle \), where \\) is a 3-space wavepacket and \ is a spin eigenstate of the future measurement setting. Second, a particle position in 3-space \\), which evolves via a de Broglie–Bohm type guidance equation with the 3-space wavepacket \\) acting as a local pilot wave. The joint ontic quantum state \\rangle \) fixes the measurement outcomes deterministically whereas the prepared quantum state \\rangle \) determines the distribution of the \\rangle \)’s over an ensemble. Both \\rangle \) and \\rangle \) evolve via the Schrodinger equation. Our model exactly reproduces the Bell correlations for any pair of measurement settings. We also consider ‘non-equilibrium’ extensions of the model with an arbitrary distribution of hidden variables. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. We argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics. (shrink)

The Bell 1964 theorem states that nonlocality is a necessary feature of hidden variable theories that reproduce the statistical predictions of quantum mechanics. In view of the no-go theorems for non-contextual hidden variable theories already existing up to 1964, and due to Gleason and Bell, one is forced to acknowledge the contextual character of the hidden variable theory which the Bell 1964 theorem refers to. Both the mathematical and the physical justifications of this contextualism (...) are reconsidered. Consequently, the role of contextualism in recent no-hidden-variables proofs and the import of these proofs are investigated. With reference to the physical intuition underlying contextualism, the possibility is considered whether a context-dependence of individual measurement results is compatible with context-independence of the statistics of measurement results. (shrink)

It is shown that the matrix models which give non-perturbative definitions of string and M theory may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their entries are the non-local hidden variables. This is shown by studying the bosonic matrix model at finite temperature, with T taken to scale as 1/N, with N the rank of the matrices. For large N the eigenvalues of the matrices undergo Brownian (...) motion due to the interaction of the diagonal elements with the off diagonal elements, giving rise to a diffusion constant that remains finite as N goes to infinity. The resulting probability density and current for the eigenvalues are then found to evolve in agreement with the Schroedinger equation, to leading order in 1/N, with hbar proportional to the thermal diffusion constant for the eigenvalues. The quantum uctuations and uncertainties in the eigenvalues are then consequences of ordinary statistical uctuations in the values of the off-diagonal matrix elements. Furthermore, this formulation of the quantum theory is background independent, as the definition of the thermal ensemble makes no use of a particular classical solution. The derivation relies on Nelson's stochastic formulation of quantum theory, which is expressed in terms of a variational principle. (shrink)

H.P. Stapp has proposed a number of demonstrations of a Bell-type theorem which dispensed with an assumption of hidden variables, but relied only upon locality together with an assumption that experimenters can choose freely which of several incompatible observables to measure. In recent papers his strategy has centered upon counterfactual conditionals. Stapp’s paper in American Journal of Physics, 2004, replies to objections raised against earlier expositions of this strategy and proposes a simplified demonstration. The new demonstration is criticized, several (...) subtleties in the logic of counterfactuals are pointed out, and the proofs of J.S. Bell and his followers are advocated. (shrink)

We claim that physics has been constructed because three “philosophical” principles have been respected, namely, realism, locality, and consistency. These principles lead to an interpretation of quantum mechanics (QM) in terms of local hidden-variables theories (LHV). In order to prove that LHV have not been refuted, we analyze the empirical proofs of Bell's inequalities and we argue that none is loophole-free. Then we propose a restricted QM that does not contain measurement postulates and that does not claim that (...) all state vectors (self-adjoint operators) are states (observables). The contradiction of such restricted QM with Bell's inequality cannot be shown as a theorem, but only by the design of a loophole-free experiment. Finally, we argue that noise has been underestimated in quantum theory. It does not appear in QM, but it is essential in quantum field theory. We conjecture that noise will prevent the violation of Bell's inequality. (shrink)

Einstein made several attempts to argue for the incompleteness of quantum mechanics, not all of them using a separation principle. One unpublished example, the box parable, has received increased attention in the recent literature. Though the example is tailor-made for applying a separation principle and Einstein indeed applies one, he begins his discussion without it. An analysis of this first part of the parable naturally leads to an argument for incompleteness not involving a separation principle. I discuss the argument and (...) its systematic import. Though it should be kept in mind that the argument is not the one Einstein intends, I show how it suggests itself and leads to a conflict between QM’s completeness and a physical principle more fundamental than the separation principle, i.e. a principle saying that QM should deliver probabilities for physical systems possessing properties at definite times. (shrink)

Symmetries are introduced into the convexity approach to physics. This allows one to make connections between classical and quantum theories by exploiting the properties of quantum mechanics on phase space. The measurement problem is discussed and many of the known no-go theorems are shown not to apply. Finally, hidden variable theories exhibiting these physical symmetries are shown to have a certain required group structure, if they exist at all.

In treatises or advanced textbooks on theoretical physics, it is apparent that the way mathematics is used is very different from what is to be found in books of mathematics. There is, for example, no close connection between books on analysis, on the one hand, and any classical textbook in quantum mechanics, for example, Schiff, [11], or quite recent books, for example Ryder, [10], on quantum field theory. The differences run a good deal deeper than the fact that the books (...) on theoretical physics are not written in the definition-theorem-proof style characteristic of pure mathematics. Although a good many propositions are proved in the books on physics, there are almost with exception no existential proofs, and consequently there is no really serious systematic use of quantifiers. Another important characteristic is the free use of infinitesimals. In fact, most results would not lose anything, from a physicist's point of view, by leaving them in approximate form, i.e., instead of strict equalities or inequalities, using equalities or inequalities only up to an infinitesimal.The discrepancy between the way mathematics is ordinarily done in theoretical physics and the way it is built up from a foundational standpoint in any of the standard modern views raises the question of whether it might be possible to construct quite directly a rigorous foundation that reflects a significant part of this standard practice in theoretical physics. Other parts of standard practice in physics, for example, the use of physically intuitive but nonrigorous arguments, are not present in our system. (shrink)

It is shown that completely entangled two-particle quantum states are simultaneous eigenstates of a large set of commuting, nonlocal observables, a characterization that generalizes to multiparticle systems. This leads to a nonstatistical proof of the Bell-EPR no-hidden-variable theorem for two-particle systems and to a family of multiparticle generalizations of the three-particle system of Greenberger, Horne, and Zeilinger.

In this paper we present a systematic formulation of some recent results concerning the algebraic demonstration of the two major no-hidden-variables theorems for N spin-1/2 particles. We derive explicitly the GHZ states involved and their associated eigenvalues. These eigenvalues turn out to be undefined for N=∞, this fact providing a new proof showing that the nonlocality argument breaks down in the limit of a truly infinite number of particles.