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ssrn-id1006232 - Relational Quantum Mechanics and the...

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Electronic copy available at: http://ssrn.com/abstract=1006232 Relational Quantum Mechanics and the Determinacy Problem * Matthew Brown March 27, 2007 This paper is to be presented at the 15th UK and European Meeting on the Foundations of Physics (Leeds, 29-31 March 2007). It is a DRAFT version. You may cite it as such. Please do not quote directly without permission. Comments are welcome and encouraged. email: [email protected] web: http://thehangedman.com/philosophy/ Abstract Quantum mechanics describes certain systems as being in superpo- sitions 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 strat- egy 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 prob- lem 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 Jeffrey 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. 1
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Electronic copy available at: http://ssrn.com/abstract=1006232 the face of these problems. Carlo Rovelli’s relational interpretation of quantum mechanics holds that a system’s states or the values of its physical quantites as normally conceived only exist relative to a cut between a system and an observer or measuring instrument. Further- more, on Rovelli’s account, the appearance of determinate observa- tions from pure quantum superpositions happens only relative to the interaction of the system and observer. Jeffrey Barrett has pointed out that certain relational interpretations suffer from what we might call the “determinacy problem,” but the interpretations that Barrett con- siders make facts relative to branches of the universal wave function rather than to system/observer cuts. Thus, Barrett misclassifies Rov- elli’s interpretation, which differs from the interpretations that Barrett explicitly worries about and has the resources to escape his particular criticisms. Rovelli’s interpretation still leaves us with a paradox hav- ing to do with the determinacy of measurement outcomes, which can be accepted only if we are willing to give up on certain elements of the “absolute” view of the world. 1 Introduction 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
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