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The British Journal for the Philosophy of Science

Is There Really No Projection Postulate in the Modal Interpretation?

W.Michael Dickson

Published Jun 1, 1995• 4 citations
Publisher

Abstract

Modal interpretations of quantum mechanics admit two kinds of state: physical states, which specify the values of observables on a system, and theoretical states, which specify a probability distribution over possible physical states. They appear to use this distinction to deny the projection postulate, claiming that collapse corresponds only to a change from discussing the theoretical state to discussing the physical state. I argue that modal interpretations should adopt a projection postulate at the level of the theoretical state. However, other features of modal interpretations might render the projection postulate immune from the usual objections.

DOI
10.1093/bjps/46.2.197

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Modal interpretations of quantum mechanics admit two kinds of state: physical states, which specify the values of observables on a system, and theoretical states, which specify a probability distribution over possible physical states. They appear to use this distinction to deny the projection postulate, claiming that collapse corresponds only to a change from discussing the theoretical state to discussing the physical state. I argue that modal interpretations should adopt a projection postulate at the level of the theoretical state. However, other features of modal interpretations might render the projection postulate immune from the usual objections.
The world of quantum theory is not deterministic; however, the quantum theory of an isolated system describes its state as evolving deterministically.How can these two points be reconciled? The modal interpretation (of which a number of variants have been developed) answers this as follows. An observable may have a value even if the system is not in the corresponding eigenstate of that observable. The state of the system only constrains the possible values the observable can have, and (at least under certain conditions) the probabilities that it has those values. Hence, the eigenvalue–eigenstate link is violated. There is no collapse; the state of an isolated system always evolves in accordance with the Schroedinger equation. Hence the values of observables can change indeterministically, though this stochastic process is constrained by the deterministically evolving quantum state. Terminology varies but in this book the quantum state is then called the dynamical state, and a summary of the values of the observables pertaining to the system is called the value state. Since not all observables are mutually compatible, they will not all have simultaneous sharp values, but for each there is a minimum Borel set of values as its current range. The specific modal interpretation developed here is the Copenhagen Variant of the Modal Interpretation, which places holistic constraints on values of observables pertaining to parts of composite systems.
Much of the recent discussion of problematic aspects of quantum-mechanical measurement centers around that feature of quantum theory which is called “the projection postulate.” This is roughly the claim that a change of a certain sort occurs in the state of a physical system when a measurement is made on the system. In this paper an argument for the projection postulate due to von Neumann is considered. Attention is focused on trying to provide an understanding of the notion of “the state of a physical system” which is compatible with the argument von Neumann offers. An attempt is made to formulate the argument in terms of an objectivistic interpretation of probability concepts. It is seen that such an interpretation does not provide a suitable way of understanding the argument. An attempt is made to illustrate the source of this failure in terms of a non-quantum-mechanical example.
In this work we attempt to confront the orthodox widespread claim present in the foundational literature of Quantum Mechanics (QM) according to which 'superpositions are never actually observed in the lab'. In order to do so, we begin by providing a critical analysis of the famous measurement problem which, we will argue, was originated by the strict application of the empirical-positivist requirements to subsume the quantum formalism under their specific understanding of 'theory'. In this context, the ad hoc introduction of the projection postulate (or measurement rule) can be understood as a necessary requirement coming from a naive empiricist standpoint which presupposes that observations are self evident givens of "common sense" experience --independent of metaphysical (categorical) presuppositions. We then turn our attention to two "non-collapse" interpretations of QM --namely, modal and many worlds-- which even though deny that the "collapse" is a real physical process anyhow retain the measurement rule as a necessary element of the theory. In contraposition, following Einstein's claim according to which "it is only the theory which decides what can be observed", we propose a return to the realist representational understanding of 'physical theories' in which 'observation' is considered as derived from theoretical presuppositions. It is from this standpoint that we discuss a new non-classical conceptual representation which allows us to understand quantum phenomena in an intuitive (anschaulicht) manner. Leaving behind the projection postulate, we discuss the general physical conditions for measuring and observing quantum superpositions.
If we take the state function of quantum mechanics to describe belief states, arguments by Stairs and Friedman-Putnam show that the projection postulate may be justified as a kind of minimal change. But if the state function takes on a physical interpretation, it provides no more than what I call a fortuitous approximation of physical measurement processes, that is, an unsystematic form of approximation which should not be taken to correspond to some one univocal “measurement process” in nature. This fact suggests that the projection postulate does not provide a proper locus for interpretive investigation. Readers will also find section 3's analysis of fortuitous approximations of independent interest and presented without the perils of quantum mechanics.
It has been suggested that the Modal Interpretation of Quantum Mechanics (QM) is "incomplete" if it lacks a dynamics for possessed values. I argue that this is only one of two possible attitudes one might adopt toward a Modal Interpretation without dynamics. According to the other attitude, such an interpretation is a complete interpretation of QM as standardly formulated, an interpretation whose innovation is to attempt to make sense of the quantum realm without the expedient of novel physics. Then I explain why this attitude, though available, is unattractive. Without dynamics, the Modal Interpretation vanquishes the measurement problem only, it seems, to succumb to the problem of state preparation. On this view, the Modal Interpretation needs dynamics not to be an interpretation at all, but to be an adequate one. I review reasons to suspect that the dynamics which would best suit the Modal Interpretation--a dynamics equivalent to a set of two time transition probabilities of the sort used to solve the preparation problem--is not a dynamics the interpretation can have. I close with a brief discussion of versions of the Modal Interpretation that may not succumb to the considerations presented here.