Abstract
Any attempt to introduce probabilities into quantum mechanics faces difficulties due to the mathematical structure of Hilbert space, as reflected in Birkhoff and von Neumann's proposal for a quantum logic. The (consistent or decoherent) histories solution is provided by its single framework rule, an approach that includes conventional (Copenhagen) quantum theory as a special case. Mermin's Ithaca interpretation addresses the same problem by defining probabilities which make no reference to a sample space or event algebra (“correlations without correlata”). But this leads to severe conceptual difficulties, which almost inevitably couple quantum theory to unresolved problems of human consciousness. Using histories allows a sharper quantum description than is possible with a density matrix, suggesting that the latter provides an ensemble rather than an irreducible single-system description as claimed by Mermin. The histories approach satisfies the first five of Mermin's desiderata for a good interpretation of quantum mechanics, including Einstein locality, but the Ithaca interpretation seems to have difficulty with the first (independence of observers) and the third (describing individual systems).
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Griffiths, R.B. Probabilities and Quantum Reality: Are There Correlata?. Foundations of Physics 33, 1423–1459 (2003). https://doi.org/10.1023/A:1026092212820
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DOI: https://doi.org/10.1023/A:1026092212820