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 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 dispositions.
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 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 dispositions.
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.
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. The nature of selective interactions, and more generally selections, is then clarified, and three arguments in their favour are offered. 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. 1. Introduction 2. The problem of quantum measurement 2.1 The ignorance interpretation of mixtures 2.2 The eigenstate–eigenvalue link 2.3 The quantum theory of measurement 3. The insolubility proof of the quantum measurement 3.1 Some notation 3.2 The transfer of probability condition (TPC) 3.3 The occurrence of outcomes condition (OOC) 4. A defence of the insolubility proof 4.1 Stein's critique 4.2 Ignorance is not required 4.3 The problem of quantum measurement is an idealisation 5. Selections 5.1 Representing dispositional properties 5.2 Selections solve the measurement problem 5.3 Selections and ignorance 6. Non-ideal selections 6.1 No-collapse interpretations and non-ideal measurements 6.2 Exact and approximate measurements 6.3 Selections for non-ideal interactions 6.4 Approximate selections 6.5 Implications for ignorance 7. Selective interactions test quantum propensities 7.1 Equivalence classes as physical ‘aspects’: a critique 7.2 Quantum dispositions 7.3 Selections as a propensity modal interpretation 7.4 A comparison with Popper's propensity interpretation
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.
ABSTRACT This essay aims at reviewing one of the major difficulties affecting the standard formulation of quantum mechanics, that is, the well‐known measurement problem. As it will be explained, the latter originates as a consequence of the quantum theory's postulates. Referring to this, we analyze in particular the conceptual issues implied by the projection (or collapse) rule. After having presented the measurement problem, we then illustrate three possible solutions offered by major interpretations of/alternatives to quantum theory: Bohmian mechanics, Ghirardi–Rimini–Weber theories, and the many‐worlds interpretation. As the reader will see, these theoretical frameworks solve this issue by virtue of their unambiguous ontologies and consistent dynamical laws. Finally, a synopsis of the open debates and future perspectives concerning the measurement problem in relativistic contexts concludes the paper.
The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this problem by eliminating idealizations from the characterization of measurement. We state and prove two ‘insolubility theorems’ that disappoint this hope. In both the initial state of the apparatus is taken to be mixed rather than pure, and the correlation of the object observable and the pointer observable is allowed to be imperfect. In the insolubility theorem for sharp observables, which is only a modest extension of previous results, the object observable is taken to be an arbitrary projection valued measure. In the insolubility theorem for unsharp observables, which is essentially new, the object observable is taken to be a positive operator valued measure. Both theorems show that the measurement problem is not the consequence of neglecting the ever-present imperfections of actual measurements.
We demonstrate that the measurement problem is resolved by providing the right mechanism of how a measurement basis is selected. The measurement basis of a subsystem is what diagonalizes subsystem's reduced density matrix. As expected empirically, the measurement problem ceases to be relevant for actual measurements, due to semi-classical nature of measurement apparatuses. The collapse interpretation is consistent with continuous evolution of the pure state vector of the universe. Quantum mechanics thus is safe, both in practice and in theory.