Arthur Fine's use of prism models to provide local and deterministic accounts of quantum correlation experiments is presented and analyzed in some detail. Fine's claim that “there is … no question of the consistency of prism models … with the quantum theory“ (forthcoming, p. 16) is disputed. Our criticisms are threefold: (1) consideration of the possibility of additional analyzer positions shows that prism models entail unacceptably high rejection rates in the relevant experiments; (2) similar considerations show that the models are at best only superficially local and deterministic; and (3) in any case, Fine extracts the quantum correlation statistics from prism models only by resurrecting conceptual problems similar to those that his models were to designed to solve.
Arthur Fine's use of prism models to provide local and deterministic accounts of quantum correlation experiments is presented and analyzed in some detail. Fine's claim that “there is … no question of the consistency of prism models … with the quantum theory“ (forthcoming, p. 16) is disputed. Our criticisms are threefold: (1) consideration of the possibility of additional analyzer positions shows that prism models entail unacceptably high rejection rates in the relevant experiments; (2) similar considerations show that the models are at best only superficially local and deterministic; and (3) in any case, Fine extracts the quantum correlation statistics from prism models only by resurrecting conceptual problems similar to those that his models were to designed to solve.
This thesis deals with the set of issues commonly known as the 'measurement problem' in quantum mechanics. The main thesis is that the problems are best understood as typically theoretical problems, in the sense that they are not problems directly concerned with the ability of the quantum theory to account for, or represent, actual measurements. This is contrary to the standard view that the quantum measurement problem is in fact about how to fit theory to experiment. I explain how I characterise a theoretical problem and argue against claims that quantum measurement theory is unrealistic or ineffective because it bears so little relation to actual measurement practice: I argue that the quantum theory's analysis of measurement need not be committed to doing for the experimenter what Henry Margenau and other critics think it should do. Its principal aim is to answer two questions. First, it tells us what properties are to be associated to quantum states; secondly, it tells us what, in the theory, a measurement must be if these properties are to emerge. I then discuss some of the specific aspects of the problem of measurement, in particular the results known as insolubility proofs of the quantum measurement problem and the characterisation of the quantum measurement interactions satisfying standard probabilistic constraints. I prove several results here, amongst them characterisations of all interactions jointly satisfying the conditions of unitarity and, first, objectification, then secondly, probability reproducibility conditions. These are the standard conditions which capture our intuitions about quantum measurement. I show how the results lead to negative consequences with respect to the interpretive questions in quantum mechanics. The discussion of these specific aspects of quantum measurements does, on the other hand, suggest a particular strategy for solving the problems. This is found in Arthur Fine's solution to the measurement problem, which is based on the idea of a selective interaction. The discussion of Fine's solution emphasises in general how simply implementing technical strategies is not sufficient to solve the measurement problem in quantum mechanics: further arguments must be given for why the strategy is appropriate, rather than just mathematically satisfactory. I claim that the arguments given by Fine are far from sufficient. The thesis concludes that, although the quantum theory of measurement is immune from Margenau's critique, and retains a theoretical autonomy, it is still plagued by numerous problems: the thesis identifies clearly what some of these problems are and considers some solutions, most of which, however, raise serious philosophical questions about the interpretation of quantum mechanics.
Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared with the probabilities provided by the algorithms of quantum theory (QT). In spite of statistical predictions of QT a claim was made that the theory provided the most complete description of the data and of the underlying physical phenomena. This claim could be easily rejected if some fine structures, averaged out in standard statistical descriptive analysis, were found in the time series of experimental data. To search for these structures one has to use more subtle statistical tools which were developed to study time series produced by various stochastic processes. In this talk we review some of these tools. As an example we show how the standard descriptive statistical analysis of the data is unable to reveal a fine structure in a simulated sample of AR(2) stochastic process. We emphasize once again that the violation of Bell inequalities gives no information on the completeness or the non locality of QT. The appropriate way to test the completeness of quantum theory is to search for fine structures in time series of experimental data by means of the purity tests or by studying the autocorrelation and partial autocorrelation functions.
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.
This paper expands on, and provides a qualified defence of, Arthur Fine’s selective interactions solution to the measurement problem. Fine’s approach must be understood against the background of the insolubility proof of the quantum measurement. I first defend the proof as an appropriate formal representation of the quantum measurement problem. Then I clarify the nature of selective interactions, and more generally selections, and I go on to offer three arguments in their favour. First, selections provide the only known solution to the measurement problem that does not relinquish any of the explicit premises of the insolubility proofs. Second, unlike some no-collapse interpretations of quantum mechanics selections suffer no difficulties with non-ideal measurements. Third, unlike most collapse-interpretations selections can be independently motivated by an appeal to quantum propensities.
The concept of a prism model was introduced by Arthur Fine to be used for local and realistic descriptions of quantum statistics. Recently Feintzeig and Fletcher have shown that a wide class of generalizations of the classical probability model are incapable of replicating the quantum statistics for certain experiments. We employ a modification of their strategy to see under what conditions prism models cannot replicate quantum statistics. In doing so we differentiate two interpretations: one which we can show to be inconsistent in replicating the statistics of certain experiments, and one which commits to unavoidable rejection rates for certain experiments.
Introduction We have now prepared the way for a quantum treatment of problems that are of interest in optics. We have examined some basic properties of the quantized field and have explored the coherent-state representation and some of its virtues. Until now our discussions have been essentially formal; we have not concerned ourselves with what is actually measured in the laboratory, nor with questions concerning the interactions of the quantized field with other systems. In the following sections we shall turn our attention to some of the quantum field theoretic quantities that are of particular interest in quantum optics and are of significance in the measurement of the field. Our discussions in this chapter will still be somewhat formal, in that we shall not yet come to grips with the problem of the interaction of the field with the apparatus. That problem will be tackled in Chapter 14. For the moment we shall continue to oversimplify and treat the field as a free field. However, within the idealized context of the free field we shall examine some of the questions encountered in measurements in quantum optics. We shall see that normally ordered correlations play a dominant role and examine some of their properties. Anti-normally ordered correlations will be seen to arise in much less common and less useful measurements of the field. We shall also examine the sense in which a photon may be said to be localized in a measurement in which a photoelectric emission is registered.