Quantum mechanics describes certain systems as being in superpositions of their properties, yet every measurement on every system that we are able to perform yields a determinate result. The “orthodox” formulation of the theory builds this in by including a postulate that such superpositions “collapse” at the time of measurement. This strategy fails to really explain why such measurements are determinate, is unacceptably imprecise, and makes observation basic in fundamental physical theory, which looks like the wrong sort of process for the job. The problem of the interpretation of quantum mechanics is the problem of finding a more satisfactory understanding of the formalism in This project began in an independent study with Craig Callender, who provided much help in terms of direction, discussion, comments, and continuing support. Thanks also to Jerey Barrett for reading and commenting on an earlier draft of this paper, including helping me find some clearer and more economical way of putting some crucial points.
Quantum mechanics describes certain systems as being in superpositions of their properties, yet every measurement on every system that we are able to perform yields a determinate result. The “orthodox” formulation of the theory builds this in by including a postulate that such superpositions “collapse” at the time of measurement. This strategy fails to really explain why such measurements are determinate, is unacceptably imprecise, and makes observation basic in fundamental physical theory, which looks like the wrong sort of process for the job. The problem of the interpretation of quantum mechanics is the problem of finding a more satisfactory understanding of the formalism in This project began in an independent study with Craig Callender, who provided much help in terms of direction, discussion, comments, and continuing support. Thanks also to Jerey Barrett for reading and commenting on an earlier draft of this paper, including helping me find some clearer and more economical way of putting some crucial points.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
Despite its enormous practical success, quantum theory is so contrary to intuition that, even after 45 years, the experts themselves still do not all agree what to make of it. The area of disagreement centers primarily around the problem of describing observations. Formally, the result of a measurement is a superposition of vectors, each representing the quantity being observed as having one of its possible values. The question that has to be answered is how this superposition can be reconciled with the fact that in practice we only observe one value. How is the measuring instrument prodded into making up its mind which value it has observed?
Abstract On the orthodox (Diracvon Neumann) interpretation1 of quantum mechanics, an observable has a determinate (definite, sharp) value for a system in a given quantum state if and only if the state is an eigenstate of the observable. So, the orthodox interpretation selects a particular set of observables that have determinate values in a given quantum state; equivalently, a particular set of idempotent observables or propositions, represented by projection operators, Thanks to Guido Bacciagaluppi and Michael Dickson for helpful critical comments on a draft version of the paper. R. C. would like to thank the Social Sciences and Humanities Research Council of Canada for research support.
Despite its enormous practical success, quantum theory is so contrary to intuition that, even after 45 years, the experts themselves still do not all agree what to make of it. The area of disagreement centers primarily around the problem of describing observations. Formally, the result of a measurement is a superposition of vectors, each representing the quantity being observed as having one of its possible values. The question that has to be answered is how this superposition can be reconciled with the fact that in practice we only observe one value. How is the measuring instrument prodded into making up its mind which value it has observed?
The interpretation of quantum mechanics in the context of measurements, and concepts such as state “collapse,” have troubled physicists since the inception of quantum theory. Pushed to their logical extreme, such issues become entangled (in the colloquial sense) with questions of consciousness, reality, etc. Bell’s theorem eliminated possible ways out of this tangle via any (halfway reasonable) classical underlying theory, and the success of quantum mechanics forces us to adopt it as a fundamental theory and face the logical consequences.
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.