The insolubility proof of the quantum measurement problem

Časlav Brukner

Mauricio Suárez

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

R. W. Rendell, Michael Steiner

Mauricio Suárez

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.

Jeffrey Bub

Mauricio Suárez

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.