Previous work has shown that the problem of measurement in quantum mechanics is not correctly seen as one of understanding some allegedly univocal process of measurement in nature which corresponds to the projection postulate. The present paper introduces a new perspective by showing that how we are to understand the nature of the change of quantum mechanical state on measurement depends very sensitively on the interpretation of the state function, and by showing how attention to this dependence can greatly sharpen (...) the problems and relations between them. In particular, the problems take a form resembling their traditional formulation only on an inexact value interpretation, according to which the state function attributes inexact values of quantities to systems. On other interpretations we can apply (with various drawbacks) the subensemble idea, according to which a discontinuous change of quantum mechanical description results on measurement simply because we need a new state function to describe a new object. (shrink)

Under the influence of Quine’s famous manifesto, many philosophers have thought that logical theories are scientific theories that can be ‘adopted’ and tested as scientific theories. Here we argue that this idea is untenable. We discuss it with special reference to Putnam’s proposal to ‘adopt’ a particular non-classical logic to solve the foundational problems of quantum mechanics in his famous paper ‘Is Logic Empirical?’ (1968), which we argue was not really coherent.

In a recent paper, Michael Friedman and Hilary Putnam argued that the Luders rule is ad hoc from the point of view of the Copenhagen interpretation but that it receives a natural explanation within realist quantum logic as a probability conditionalization rule. Geoffrey Hellman maintains that quantum logic cannot give a non-circular explanation of the rule, while Jeffrey Bub argues that the rule is not ad hoc within the Copenhagen interpretation. As I see it, all four are wrong. Given that (...) there is to be a projection postulate, there are at least two natural arguments which the Copenhagen advocate can offer on behalf of the Luders rule, contrary to Friedman and Putnam. However, the argument which Bub offers is not a good one. At the same time, contrary to Hellman, quantum logic really does provide an explanation of the Luders rule, and one which is superior to that of the Copenhagen account, since it provides an understanding of why there should be a projection postulate at all. (shrink)

A new proof of the impossibility of reconciling realism and locality in quantum mechanics is given. Unlike proofs based on Bell's inequality, the present work makes minimal and transparent use of probability theory and proceeds by demonstrating a Kochen-Specker type of paradox based on the value assignments to the spin components of two spatially separated spin-1 systems in the singlet state of their total spin. An essential part of the argument is to distinguish carefully two commonly confused types of contextuality; (...) we call them ontological and environmental contextuality. These in turn are associated with two quite distinct senses of nonlocality. We indicate the relevance of our treatment to other related discussions in recent literature on the philosophy of quantum mechanics. (shrink)

Standard proofs of generalized Bell theorems, aiming to restrict stochastic, local hidden-variable theories for quantum correlation phenomena, employ as a locality condition the requirement of conditional stochastic independence. The connection between this and the no-superluminary-action requirement of the special theory of relativity has been a topic of controversy. In this paper, we introduce an alternative locality condition for stochastic theories, framed in terms of the models of such a theory (§2). It is a natural generalization of a light-cone determination condition (...) that is essentially equivalent to mathematical conditions that have been used to derive Bell inequalities in the deterministic case. Further, it is roughly equivalent to a condition proposed by Bell that, in one investigation, needed to be supplemented with a much stronger assumption in order to yield an inequality violated by some quantum mechanical predictions. It is shown here that this reflects a very general situation: from the proposed locality condition, even adding the strict anticorrelation condition and the auxiliary hypotheses needed to derive experimentally useful (and theoretically telling) inequalities, no Bell-type inequality is derivable. (These independence claims are the burden of §4.) A certain limitation on the scope of the proposed stochastic locality condition is exposed (§5), but it is found to be rather minor. The conclusion is thus supported that conditional stochastic independence, however reasonable on other grounds, is essentially stronger than what is required by the special theory.Our results stand in apparent contradiction with a class of derivations purporting to obtain generalized Bell inequalities from locality alone. It is shown in Appendix (B) that such proofs do not achieve their goal. This fits with our conclusion that generalized Bell theorems are not straightforward generalizations of theorems restricting deterministic hidden-variable theories, and that, in fact, such generalizations do not exist. This leaves open the possibility that a satisfactory, non-deterministic account of the quantum correlation phenomena can be given within the framework of the special theory. (shrink)

If we take the state function of quantum mechanics to describe belief states, arguments by Stairs and Friedman-Putnam show that the projection postulate may be justified as a kind of minimal change. But if the state function takes on a physical interpretation, it provides no more than what I call a fortuitous approximation of physical measurement processes, that is, an unsystematic form of approximation which should not be taken to correspond to some one univocal "measurement process" in nature. This fact (...) suggests that the projection postulate does not provide a proper locus for interpretive investigation. Readers will also find section 3's analysis of fortuitous approximations of independent interest and presented without the perils of quantum mechanics. (shrink)