Fine has recently proved the surprising result that satisfaction of the Bell inequality in a Clauser-Horne experiment implies the existence of joint probabilities for pairs of noncommuting observables in the experiment. In this paper we show that if probabilities are interpreted in the von Mises-Church sense of relative frequencies on random sequences, a proof of the Bell inequality is nonetheless possible in which such joint probabilities are assumed not to exist. We also argue that Fine's theorem and related results do (...) not impugn the common view that local realists are committed to the Bell inequality. (shrink)

A physical theory of experiments carried out in a space-time region can accommodate a detector localized in another space-like separated region, in three, not necessarily exclusive, ways: (1) the detector formally collapses physical states across space-like separations, (2) the detector enables superluminal signals, and (3) the theory becomes logically inconsistent. If such a theory admits autonomous evolving states, the space-like collapse must be instantaneous. Time-like separation does not allow such conclusions. We also prove some simple results on structural stability: within (...) the set of all possible theories, under a weak empirical topology, the set of all theories with superluminal signals and the set of all theories with retrograde signals are both open and dense. (shrink)

LetA be a quasi-manual with finite operations. Associate to each E = {e 1 ,..., en} εA the set ΓE of modal formulas: □(e 1 ⋁ ··· ⋁ en), ◊ei → ∼□(e 1 ⋁ ··· ⋁ ei−1 ⋁ ei+1 ⋁ ··· ⋁ en), i=1,..., n. Set Γ A = ώ{ΓE|E εA}. We show that supports ofA are in one-to-one correspondence with certain Kripke models of Γ A where the supports are given by {x ε |A ‖ ◊ x is true}.

We axiomatize the foundations of experimental statistical sciences by introducing a logico-algebro-geometric formalism related to the notions of state preparation and test procedures, that is well defined acts performed on states that lead to one of a possible finite number of results. We relate the formalism to existing partial structures and construct explict examples. A few general results about the formalism are demonstrated.

Given the collapse hypothesis (CH) of quantum measurement, EPR-type correlations along with the hypothesis of the impossibility of superluminal communication (ISC) have the effect of globalizing gross features of the quantum formalism making them universally true. In particular, these hypotheses imply that state transformations of density matrices must be linear and that evolution which preserves purity of states must also be linear. A gedanken experiment shows that Lorentz covariance along with the second law of thermodynamics imply a nonentropic version of (...) ISC. Partial results using quantum logic suggest, given ISC and a version of CH, a connection between Lorentz covariance and the covering law. These results show that standard quantum mechanics is structurally unstable, and suggest that viable relativistic alternatives must question CH. One may also speculate that some features of the Hilbert-space model of quantum mechanics have their origin in space time structure. (shrink)

We apply a formalism developed previously to study the notion of the complexity of states in a general statistical theory. We identify the extreme points of the instrument sets as those instruments that view an intrinsic complexity of states and are uncontaminated by stochastic contributions of the experimenter. Various notions of entropy of a state are investigated.

A Hilbert-space model for quantum logic follows from space-time structure in theories with consistent state collapse descriptions. Lorentz covariance implies a condition on space-like separated propositions that if imposed on generally commuting ones would lead to the covering law, and such a generalization can be argued if state preparation can be conditioned to space-like separated events using EPR-type correlations. The covering law is thus related to space-time structure, though a final understanding of it, through a self-consistency requirement, will probably require (...) quantum space-time. (shrink)

The notion of quantum supports introduced by Foulis, Piron, and Randall can be used to construct combinatorial versions of contextualist hidden-variable models for finite quantum logics. The original logic can be uniquely recovered from appropriate such models as a solution of a combinatorial inverse problem. One can thus set up a classical ontology for a finite quantum logics that completely specifies it. Computer studies are used to explore the ideas.