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 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 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. 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 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.
This paper presents the measurement problem from the point of view of the thermal interpretation of quantum physics introduced in Part II. The measurement of a Hermitian quantity A is regarded as giving an uncertain value approximating the q-expectation ⟨A⟩ rather than (as tradition wanted to have it) as an exact revelation of an eigenvalue of A. Single observations of microscopic systems are (except under special circumstances) very uncertain measurements only. The thermal interpretation * treats detection events as a statistical measurement of particle beam intensity. * claims that the particle concept is only asymptotically valid, under conditions where particles are essentially free. * claims that the unmodeled environment influences the results enough to cause all randomness in quantum physics. * allows one to derive Born's rule for scattering and in the limit of ideal measurements; but in general, only part of Born's rule holds exactly: Whenever a quantity A with zero uncertainty is measured exactly, its value is an eigenvalue of A. * has no explicit collapse -- the latter emerges approximately in non-isolated subsystems. * gives a valid interpretation of systems modeled by a quantum-classical dynamics. * explains the peculiar features of the Copenhagen interpretation (lacking realism between measurements) and the minimal statistical interpretation (lacking realism for the single case) where these interpretations apply -- in the microscopic domain. The thermal interpretation is an interpretation of quantum physics that is in principle refutable by theoretical arguments leading to a negative answer to a number of open issues collected at the end of the paper, since there is plenty of experimental evidence for each of the points mentioned there.
Starting with a more philosophical review, I discuss how modal interpretations describe reality. Firstly, it is shown that they describe states of affairs which need not be observable. Secondly, I underpin my position that in order to be metaphysically tenable, interpretations need only to satisfy the criteria of Consistency and Internal Completeness. Thirdly, I analyse how properties, states and measurement outcomes are related to one another within the modal descriptions of reality. Finally, I show how modal interpretations recover the standard formulation of quantum mechanics if one defines, in addition to the true states, so-called effective states of systems. Noumenal states of affairs The aim of an interpretation of quantum mechanics is, as I said in the introduction, to provide a description of what reality would be like if quantum mechanics were true. This formulation underlines two aspects of interpretations. Firstly, interpretations intend to construe quantum mechanics in terms of a description of reality and not merely in terms of the outcomes of measurements. Secondly, this description need not be correct. The objective is only to prove that there exists a construal of quantum mechanics which yields an acceptable description of reality. And because it is already difficult enough to give such a proof of existence, it is not (yet) the aim of interpretations to provide the one and only correct description of reality. The above formulation, however, disregards another aspect of interpretations of quantum mechanics, namely that they describe states of affairs which need not always be observable.
During many years since the birth of quantum mechanics, instrumentalist interpretations prevailed: the meaning of the theory was expressed in terms of measurements results. However, in the last decades, several attempts to interpret it from a realist viewpoint have been proposed. Among them, modal interpretations supply a realist non-collapse account, according to which the system always has definite properties and the quantum state represents possibilities, not actualities. But the traditional modal interpretations faced some conceptual problems when addressing imperfect measurements. The modal-Hamiltonian interpretation, on the contrary, proved to be able to supply an adequate account of the measurement problem, both in its ideal and its non-ideal versions. Moreover, in the non-ideal case, it gives a precise criterion to distinguish between reliable and non-reliable measurements. Nevertheless, that criterion depends on the particular state of the measured system, and this might be considered as a shortcoming of the proposal. In fact, one could ask for a criterion of reliability that does not depend on the features of what is measured but only on the properties of the measurement device. The aim of this article is precisely to supply such a criterion: we will adopt an informational perspective for this purpose.During many years since the birth of quantum mechanics, instrumentalistinterpretations prevailed: the meaning of the theory was expressed in terms of measurementsresults. However, in the last decades, several attempts to interpret it from a realist viewpointhave been proposed. Among them, modal interpretations supply a realist non-collapseaccount, according to which the system always has definite properties and the quantum staterepresents possibilities, not actualities. But the traditional modal interpretations faced someconceptual problems when addressing imperfect measurements. The modal-Hamiltonianinterpretation, on the contrary, proved to be able to supply an adequate account of themeasurement problem, both in its ideal and its non-ideal versions. Moreover, in the non-idealcase, it gives a precise criterion to distinguish between reliable and non-reliable measurements.Nevertheless, that criterion depends on the particular state of the measured system, and thismight be considered as a shortcoming of the proposal. In fact, one could ask for a criterionof reliability that does not depend on the features of what is measured but only on theproperties of the measurement device. The aim of this article is precisely to supply such acriterion: we will adopt an informational perspective for this purpose.