Why does Bohr nowhere discuss the projection postulate? He has the courtesy to cast at least a few disparaging words at some other notions for which he has no use, such as quantum logic. But he will not even admit the projection postulate as a subject for discussion. Another way to raise the puzzle is to point out that, although Bohr has a lot to say about measurement, he won't even recognize the existence of what has come to be called the “problem of measurement”. I have exaggerated slightly. We have one relevant comment, in the report of the discussion after Bohr's talk at the 1938 Warsaw conference: Professor Bohr wished to say, relative to the question propounded by the president, that the duality he noticed in the interpretation of the formalism of quantum mechanics was, in his opinion, a question of choosing the most adequate description of the experiment.
Why does Bohr nowhere discuss the projection postulate? He has the courtesy to cast at least a few disparaging words at some other notions for which he has no use, such as quantum logic. But he will not even admit the projection postulate as a subject for discussion. Another way to raise the puzzle is to point out that, although Bohr has a lot to say about measurement, he won't even recognize the existence of what has come to be called the “problem of measurement”. I have exaggerated slightly. We have one relevant comment, in the report of the discussion after Bohr's talk at the 1938 Warsaw conference: Professor Bohr wished to say, relative to the question propounded by the president, that the duality he noticed in the interpretation of the formalism of quantum mechanics was, in his opinion, a question of choosing the most adequate description of the experiment.
I propose now to examine Bohr's informal theory of measurement from a somewhat more formal point of view, and to consider how his theory relates to the orthodox theory of measurement in quantum mechanics. This is a difficult task, since Bohr nowhere discusses the theory of measurement in formal terms. My discussion, therefore, will be less closely tied to Bohr's own statements. I shall also consider some important objections to the theory. The objective-values theory of measurement Before we look into this theory, it will be useful to have a brief sketch of some of the relevant formal elements of quantum mechanics. In the Hilbert space formulation of quantum mechanics the measurable physical properties (‘observables’) of an object are represented by linear Hermitian operators A , B , … which have complete orthonormal sets of eigenvalues a n , b n , … corresponding to the subspaces (closed linear manifolds) of a Hilbert space H . These operators are in one-to-one correspondence with the projection measures P A , P B , … on the Hilbert space such that P A = Σ n a n P n , where P n are the projections of the eigenvectors ψ n belonging to the eigenvalues a n of A , and a n are discrete, non-degenerate values (for simplicity I shall deal only with operators which have such values, and shall denote observables and the corresponding operators by the same symbols).
An interpretation of quantum mechanics that rejects hidden variables has to say something about the way measurement can be understood as a transformation on states of individual systems, and that leads to the core of the interpretive problems posed by Luders' projection rule: What, if any, is its physical content? In this paper I explore one suggestion which is implicit in usual interpretations of the rule and show that this view does not stand on solid ground. In the process, important aspects of the role played by the projection postulate in the conceptual structure of quantum mechanics will be clarified. It will be shown in particular that serious objections can be raised against the (often implicit) view that identifies the physical relation of compatibility preserved by Luders' rule with the relation of simultaneous measurability.
The field of interpretation of quantum mechanics emerged in an attempt to solve the measurement problem. This turned on the perception that Niels Bohr avoided addressing the measurement problem by taking an instrumentalist view of quantum mechanics. I argue that this view is mistaken and Bohr's interpretation of quantum mechanics is realist. Moreover, Bohr's interpretation, which is different from textbook quantum mechanics (which is due more to Von Neumann and Paul Dirac), succeeds in solving the measurement problem. While the claim that Bohr dissolves the measurement problem within the limits of the epistemological framework he assumes has been made by a few authors, rarely has the case been made that Bohr's project unambiguously and completely overcomes the measurement problem. I make the strong case that Bohr eliminated the measurement problem altogether. For this, I put forward two new postulates through which to make sense of Bohr's interpretation. The article thus seeks to single out Bohr's interpretation from the various views that go together under the umbrella of orthodox quantum mechanics, and which have been traditionally considered susceptible to the measurement problem. It shows that Bohr's interpretation should be classified along with those like hidden variable theories, collapse models, modal interpretations etc., which offer a solution to the measurement problem and are committed to a realist ontology.
Wonderful news from Copenhagen Heisenberg and Schrödinger invented mathematical formalisms that provided correct answers to all the various problems of (non-relativistic) quantum theory. It was Bohr who uncovered the underlying significance of the theory; in particular he showed how the profound conceptual difficulties encountered as the theory developed – the so-called wave–particle duality, the totally unclassical nature of the uncertainty principle – could be neutralised by a revision, or more accurately a generalisation, of our use of physical concepts. Such was the generally accepted view of things from soon after 1927, when Bohr first put forward his ideas on complementarity at an international meeting of physicists at Como, through the 1930s, when it was felt that Bohr destroyed Einstein's contrary opinions, and certainly up to the time of Bohr's death in 1962. Bohr's analysis is usually spoken of as the Copenhagen interpretation of quantum theory, though it is instructive to realise that such a term was frowned upon by those closest to Bohr, since it appears to suggest that the interpretation is just one among (conceivably) many. Let us examine, for example, the words of Léon Rosenfeld, Bohr's disciple and long-term collaborator, as expounded at a conference in 1957 [52]. Rosenfeld maintained that any idea of ‘interpreting a formalism’ was a ‘false problem’, that in a good theory, the ‘ordinary language (spiced with technical jargon for the sake of conciseness)’ in which it is described, is ‘ inseparably united … with whatever mathematical apparatus is necessary’, that ‘we are here not faced with a matter of choice between two possible languages or two possible interpretations, but with a rational language intimately connected with the formalism and adapted to it, on the one hand, and with rather wild, metaphysical speculations … on the other’.
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.
Niels Bohr's philosophical view of quantum mechanics has been the subject of extensive scholarship for the better part of five decades. Yet Bohr’s writings have remained obscure, as evidenced by the variety of different scholarly interpretations of his work. In this chapter, I review the historiography of Bohr scholarship, arguing that his meaning has remained elusive because his central preoccupations lay not so much with an interpretation of the quantum-mechanical formalism, which many commentators see as the problem of quantum theory, but rather with the epistemological question of how we can acquire empirical knowledge of quantum objects by means of experiment. Bohr’s doctrine of classical concepts, I argue, is therefore best understood as a philosophy of experiment.