Online research in philosophy

Call u the triplet of cone quantum catch for the light that is incident on a surface, and v the triplet of cone quantum catch for the light that is reflected off that surface. Philipona & O'Regan (2006) present results from numerical calculations showing that: 1. each surface can be associated with a 3 by 3 matrix A such that the relation v = A u to a very high degree of accuracy for any natural illuminant, 2. the vast majority of such matrices associated with Munsell chips have three real eigenvalues, 3. Munsell chips that are most often given a name in the World Color Survey are chips whose associated matrices have a singular configuration of eigenvalues, as measured by a "singularity index". The conclusion of the paper is that this striking coincidence lends credence to the idea that data about color naming derive from facts about natural lights, surface reflexion properties, and human photopigments, rather than from facts about neural pathways or cortical representations.

We recently showed that it is possible to deal withcollections of indistinguishable elementary particles (in thecontext of quantum mechanics) in a set-theoretical framework, byusing hidden variables. We propose in the presentpaper another axiomatics for collections of indiscernibleswithout hidden variables, where hidden predicates are implicitlyassumed. We also discuss the possibility of a quasi-settheoretical picture for quantum theory. Quasi-set theory, basedon Zermelo-Fraenkel set theory, was developed for dealing withcollections of indistinguishable, but, not identical objects.

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 (and hence violates Bell's inequality). 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.

A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger's 1926 proof, a myth. Schrödinger supposedly failed to prove isomorphism, or even a weaker equivalence (“Schrödinger-equivalence”) of the mathematical structures of the two theories; developments in the early 1930s, especially the work of mathematician von Neumann provided sound proof of mathematical equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large extent on this equivalence, was deemed a myth as well. In response, I argue that Schrödinger's proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism or a weaker mathematical equivalence. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr's Model that was discovered and published by Schrödinger in his first and second communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics are satisfied by assigning the auxiliary role to eigenfunctions in the derivation of matrices (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of both isomorphism and Schrödinger-equivalence of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr's atom. And although the mathematical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr's complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it.

Noncontextual hidden variables theories, assigning simultaneous values to all quantum mechanical observables, are inconsistent by theorems of Gleason and others. These theorems do not exclude contextual hidden variables theories, in which a complete state assigns values to physical quantities only relative to contexts. However, any contextual theory obeying a certain factorisability conditions implies one of Bell's Inequalities, thereby precluding complete agreement with quantum mechanical predictions. The present paper distinguishes two kinds of contextual theories, ‘algebraic’ and ‘environmental’, and investigates when factorisability is reasonable. Some statements by Fine about the philosophical significance of Bell's Inequalities are then assessed.

A recent analysis by de Barros and Suppes of experimentally realizable GHZ correlations supports the conclusion that these correlations cannot be explained by introducing local hidden variables. We show, nevertheless, that their analysis does not exclude local hidden variable models in which the inefficiency in the experiment is an effect not only of random errors in the detector equipment, but is also the manifestation of a pre-set, hidden property of the particles ("prism models"). Indeed, we present an explicit prism model for the GHZ scenario; that is, a local hidden variable model entirely compatible with recent GHZ experiments.

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.

It has long been recognized that a local hidden variable theory of quantum mechanics can in principle be constructed, provided one is willing to countenance pre-measurement correlations between the properties of measured systems and measuring devices. However, this ‘conspiratorial’ approach is typically dismissed out of hand. In this article I examine the justification for dismissing conspiracy theories of quantum mechanics. I consider the existing arguments against such theories, and find them to be less than conclusive. I suggest a more powerful argument against the leading strategy for constructing a conspiracy theory. Finally, I outline two alternative strategies for constructing conspiracy theories, both of which are immune to these arguments, but require one to either modify or reject the common cause principle. Introduction The incompleteness of quantum mechanics Hidden variables Hidden mechanism conspiracy theories Existing arguments against hidden mechanisms A new argument against hidden mechanisms Backwards-causal conspiracy theories Acausal conspiracy theories Conclusion.

This paper constructs two classes of models for the quantum correlation experiments used to test the Bell-type inequalities, synchronization models and prism models. Both classes employ deterministic hidden variables, satisfy the causal requirements of physical locality, and yield precisely the quantum mechanical statistics. In the synchronization models, the joint probabilities, for each emission, do not factor in the manner of stochastic independence, showing that such factorizability is not required for locality. In the prism models the observables are not random variables over a common space; hence these models throw into question the entire random variables idiom of the literature. Both classes of models appear to be testable.

Based partly on proving that algebraic relativistic quantum field theory (ARQFT) is a stochastic Einstein local (SEL) theory in the sense of SEL which was introduced by Hellman (1982b) and which is adapted in this paper to ARQFT, the recently proved maximal and typical violation of Bell's inequalities in ARQFT (Summers and Werner 1987a-c) is interpreted in this paper as showing that Bell's inequalities are, in a sense, irrelevant for the problem of Einstein local stochastic hidden variables, especially if this problem is raised in connection with ARQFT. This leads to the question of how to formulate the problem of local hidden variables in ARQFT. By giving a precise definition of hidden-variable theory within the operator algebraic framework of quantum mechanics, it will be argued that the aim of hidden-variable investigations is to determine those classes of quantum theories whose elements represent a statistical content that cannot be reduced in a given way. In some particular way to be stated, a proposition will be stated which distinguishes quantum field theories whose statistical content cannot be reduced without violating some relativistic locality principle.