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Independently motivating the KochenDieks modal interpretation of quantum mechanics

Rob Clifton, Jeremy Butterfield, Hans Halvorson

Published Sep 23, 2009• 0 citations

Abstract

Abstract All interpretations of quantum mechanics still face the issue vigorously debated by Einstein and Bohr in the 1930s: do the theory’s mere probabilistic predictions for measurement outcomes indicate that observables lack definite values prior to measurement? Or is it just that the theory is lacking, making it currently not possible to know with certainty what the true values are until they are measured? Kochen (1985) and Dieks (1989), or ‘KD’ for short, embrace the For countless useful comments and often penetrating criticism, I would like to thank Guido Bacciagaluppi, John L. Bell, Harvey Brown, Jeffrey Bub, Bill Demopoulos, Michael Dickson, Dennis Dieks, Arthur Fine, Martin Jones, Simon Kochen, Richard Healey, Meir Hemmo, David Malament, Hamar Pitowsky, Laura Ruetsche, Abner Shimony, and Howard Stein. (This is not a list of ‘endorsements’.) And I wish to express gratitude to the Social Sciences and Humanities Research Council of Canada for their continued generous support.

DOI: 10.1093/oso/9780199270156.003.0001

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The distinguishing feature of ‘modal’ interpretations of quantum mechanics is their abandonment of the orthodox eigenstate–eigenvalue rule, which says that an observable possesses a definite value if and only if the system is in an eigenstate of that observable. Kochen's and Dieks' new biorthogonal decomposition rule for picking out which observables have definite values is designed specifically to overcome the chief problem generated by orthodoxy's rule, the measurement problem, while avoiding the no-hidden-variable theorems. Otherwise, their new rule seems completely ad hoc.The ad hoc charge can only be laid to rest if there is some way to give Kochen's and Dieks' rule for picking out which observables have definite values some independent motivation. And there is, or so I will argue here. Specifically, I shall show that theirs is the only rule able to save Schrödinger's cat from a fate worse than death, and sidestep the Bell–Kochen–Specker no-hidden-variables theorem, once we impose four independently natural conditions on such rules

Orthodox quantum mechanics includes the principle that an observable of a system possesses a well-defined value if and only if the presence of that value in the system is certain to be confirmed on measurement. Modal interpretations reject the controversial ‘only if’ half of this principle to secure definite outcomes for quantum measurements that leave the apparatus entangled with the object it has measured. However, using a result that turns on the construction of a Kochen–Specker contradiction, I argue that modal interpretations cannot deliver a metaphysically tenable conception of properties in quantum mechanics unless they also abandon the less controversial ‘if’ half of the orthodox principle.

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.

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