Abstract Until recently Jeffrey Bub and Itamar Pitowsky, in the framework of an information-theoretic view of quantum mechanics, claimed first that to the measurement problem in its ordinary formulation there correspond in effect two measurement problems (simply called the big and the small measurement problems), with a different degree of relevance and, second, that the analysis of a quantum measurement is a problem only if other assumptions – taken by Pitowsky and Bub to be unnecessary ‘dogmas’ – are assumed. Here I critically discuss this unconventional stance on the measurement problem and argue that the Bub-Pitowsky arguments are inconclusive, mainly because they rely on an unwarranted extension to the quantum realm of a distinction concerning the foundations of special relativity which is in itself rather controversial.
Abstract Until recently Jeffrey Bub and Itamar Pitowsky, in the framework of an information-theoretic view of quantum mechanics, claimed first that to the measurement problem in its ordinary formulation there correspond in effect two measurement problems (simply called the big and the small measurement problems), with a different degree of relevance and, second, that the analysis of a quantum measurement is a problem only if other assumptions – taken by Pitowsky and Bub to be unnecessary ‘dogmas’ – are assumed. Here I critically discuss this unconventional stance on the measurement problem and argue that the Bub-Pitowsky arguments are inconclusive, mainly because they rely on an unwarranted extension to the quantum realm of a distinction concerning the foundations of special relativity which is in itself rather controversial.
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 chapter argues that the intractable part of the measurement problem — the ‘big’ measurement problem — is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell's assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the ‘truthmaker’ for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. The chapter shows how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the ‘big’ measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, the chapter accepts that measurements have definite outcomes. By contrast with the Bohmians and the GRW ‘collapse’ theorists who add structure to the theory and propose dynamical solutions to the ‘big’ measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic (i.e., pre-dynamic) objective probabilistic constraints on correlations between events.
Some approaches which seek to make progress with the conceptual troubles of quantum theory using information-theoretic ideas are investigated. These include Zeilinger’s Foundational Principle and the information-theoretic characterization theorem of Clifton, Bub and Halvorson. It is shown that Zeilinger’s Foundational Principle does not provide a foundational principle for quantum mechanics and fails to underwrite explanations of the randomness of quantum measurement and the existence of entanglement. The Clifton- Bub-Halvorson theorem is more positively assessed: here an axiomatisation of quantum mechanics has been achieved. However some questions are raised concerning the C ∗-algebraic starting point of the theorem, which seems not a sufficiently neutral theoretical framework for the axiomatic project. Moreover, it is argued that rather than the Clifton-Bub-Halvorson result motivating an information-theoretic approach (principle theory approach) to understanding the quantum world which obviates our traditional concerns, such an approach simply fails to engage with the crucial interpretational issues.
About ten years ago, Itamar Pitowsky and I wrote a paper, 'Two dogmas about quantum mechanics,' in which we outlined an information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. Here I revisit the paper and, following Frauchiger and Renner, I show that the Everett interpretation leads to modal contradictions in 'Wigner's-Friend'-type scenarios that involve 'encapsulated' measurements, where a super-observer (which could be a quantum automaton), with unrestricted ability to measure any arbitrary observable of a complex quantum system, measures the memory of an observer system (also possibly a quantum automaton) after that system measures the spin of a qubit. In this sense, the Everett interpretation is inconsistent.
Abstract The proposed interpretation, if it is to count as realism, must say more about the evolution of the state while the argument that more about its dynamics oughtn't to be said (given the no-broadcasting principle) is suggested to be unsound. Nor are the alleged dogmas of quantum mechanics dogmas — on the contrary, the fact that measurements cannot count as primitives is a consequence of realism, not a presupposition of it. And the parallel with special relativity cuts both ways: the dynamical explanations for the length contractions and time dilations demanded by Lorentz in special relativity must indeed be forthcoming, as Einstein later acknowledged. Finally, there is little in the proposed interpretation that is specifically information-theoretic.
The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics. It will be argued that some of the more obvious approaches - that quantum information theory shows us that ultimately the world is made of information, and quantum Bayesianism - fail as philosophical interpretations of quantum mechanics. However, the information-theoretic approach of Clifton, Bub, and Halvorson introduces Einstein's distinction between principle theories and constructive theories, arguing that quantum mechanics is best understood as an information-theoretic principle theory. While I argue that this particular approach fails, it does offer a viable new philosophical role for information theory. Specifically, an investigation of interpretationally successful principle theories such as Newtonian mechanics, special relativity, and general relativity, shows that the particular principles employed are necessary as constitutive elements of a framework which partially defines the basic explanatory concepts of space, time, and motion. Without such constitutive principles as preconditions for empirical meaning, scientific progress is hampered. It is argued that the philosophical issues in quantum mechanics stem from an analogous conceptual crisis. On the basis of this comparison, the best strategy for resolving these problems is to apply a similar sort of conceptual analysis to quantum mechanics so as to provide an appropriate set of constitutive principles clarifying the conceptual issues at stake. It is further argued that quantum information theory is ideally placed as a novel conceptual framework from which to conduct this analysis.