Abstract
A relation ≺ϕ between noncommuting 1-0 quantum observables (i.e., projections) is introduced, ϕ being the state vector of the system. This relation extends the empirical implication between commuting projections. An operational interpretation of the new relation is given, which can be expressed also in counterfactual terms. It is shown that a relation proposed some years ago by Hardegree, namely the Sasaki arrow ↪ϕ, can be interpreted in terms of the relation ≺ϕ; furthermore, this new relation turns out to be successful also in cases in which the Sasaki arrow fails.
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References
G. Hardegree,Synthese 29, 63–80 (1974).
G. Hardegree, inThe Logico-Algebraic Approch to Quantum Mechanics II, C. A. Hooker, ed. (Reidel, Dordrecht, 1979), pp. 49–108.
P. Busch, P. Lahti, and P. Mittelsteadt,The Quantum Theory of Measurement (Springer, Berlin, 1991).
P. Halmos,Trans. Am. Math. Soc. 144, 381 (1969).
G. NisticÒ and M. C. Romania,J. Math. Phys. 35, 4534–4546 (1994).
D. Lewis,Counterfactuals (Basil Blackwell, Oxford, 1973).
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NisticÒ, G. Empirical relations between noncommuting observables. Found Phys 25, 1757–1767 (1995). https://doi.org/10.1007/BF02057887
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DOI: https://doi.org/10.1007/BF02057887