Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
A phenomenological solution to the measurement problem? Husserl and the foundations of quantum mechanics
Section snippets
The measurement problem in quantum mechanics
The measurement problem runs like a crack through the foundations of quantum mechanics (QM). Briefly put, the problem is the following. According to the formalism, if two systems interact, the state of the joint system will be a superposition of states of each system and, as the joint system evolves in time, its joint state will remain a superposition. If the formalism is taken to apply to all physical systems, including measurement apparatuses, then when such an apparatus interacts with
The von Neumann–London–Bauer ‘solution’
The orthodox solution can be decomposed into two aspects: the formal and the philosophical. The formal is represented by von Neumann's division of all processes into the following (see, for example, Jammer, 1974, pp. 474–479; Barrett, 1999, pp. 30–37):
Processes of the first kind: these are the processes involved in measurement (von Neumann referred to them as ‘arbitrary changes’) and are discontinuous, non-causal, and irreversible;
Processes of the second kind: these are the processes (or
Putnam's and Shimony's criticisms
The early 1960s saw the publication of two sets of criticisms of the above ‘orthodox’ solution that came to be seen as definitive.
The first criticism originated with Putnam, who expressed concern about the central role given to the observer in this solution to the measurement problem, and argued that quantum mechanics could not jointly incorporate two conditions: first, that a measurement requires an interaction with an ‘outside’ system; and, secondly, that the ‘whole universe’ can be treated
London's philosophical roots
London was,14
The phenomenological construction of the ego
There is, of course, an enormous body of literature on phenomenology in general and Husserl's work in particular. Here I simply want to emphasize certain important points, particularly regarding the conception of the ego, that will help illuminate the London and Bauer analysis.
As Smith and Woodruff Smith suggest, a ‘preliminary orientation’ of Husserl's work can be obtained by conceiving of it as evolving through three stages: the first consists in the rejection of the psychologistic
The re-discovery of the ego
As we shall see, the passages above provide the key to understanding the London and Bauer account of the measurement situation. There is a problem, however, and it is summed up in a footnote, inserted by Husserl in the second edition of The Logical Investigations and attached to the above claim, that he is “…quite unable to find this ego, this primitive, necessary centre of relations”:
I have since managed to find it, i.e. have learnt not to be led astray from our grasp of the given through
The reconciliation
The ‘reflective regard’, then, is a kind of tool for exploring the ‘infinite field of absolute mental processes’, and it is only through using this tool, through effecting acts of reflection, that we arrive at the field of phenomenology in the first place (Husserl, 1982, p. 174). All such acts necessarily have the form of the ‘cogito’, and it is of the nature of such acts of reflection that they are not only directed towards some object, but that they include a reference to an ego (otherwise,
London and Bauer revisited
Let us finally turn to the London and Bauer analysis of measurement, which begins in what appears to be traditional fashion (London & Bauer, 1983, p. 250) by considering the measurement of some quantity F(x,p) of a system in the state ψ=Σkψkuk(x), where uk is an eigenfunction corresponding to the value fk of F. The system is then coupled with an apparatus capable of measuring F, where G(y,py) is the coordinate specifying the position of the apparatus ‘needle’, and g0,g1,…,gρ its eigenvalues,
Objectivity and the ‘Regard’
There is a further concern, however: In what sense can we now say that the process of measurement is objective? London and Bauer begin their final section, ‘Scientific Community and Objectivity’, by acknowledging that “At first sight it would appear that in quantum mechanics the concept of scientific objectivity has been strongly shaken” (London & Bauer, 1983, p. 258), and it looks as if quantum mechanics drives us towards solipsism. However, they insist, “No physicist has retired into a
Conclusion
London himself never elaborated any further on the ideas contained in the monograph and appears to have regarded the measurement problem as solved (Gavroglu, private email). Is it? Obviously ‘No’ if one insists that any putative solution must be broadly physicalistic. Everett, for example, in originally presenting his ‘relative state’ alternative to what he took to be the orthodox solution, characterized the observer as a physical system only, such as a photoelectric cell or a photographic
Acknowledgements
I am grateful to a number of colleagues for comments, advice, and encouragement, including, in particular, Otávio Bueno, James Ladyman, and Simon Saunders. I am especially indebted to Richard Francks for detailed commentary, and Matt Taylor for letting me have advance copies of chapters from his Ph.D. dissertation. My reliance on those chapters, and also on Kostas Gavroglu's biography of London, should be apparent. Earlier versions of this paper were presented at the Informal Research Workshop
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