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Simultaneous measurement and joint probability distributions in quantum mechanics

Willem M. de Muynck, Peter A. E. M. Janssen & Alexander Santman

Foundations of Physics 9 (1-2):71-122 (1979)

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The inaccuracy principle.Hans Martens & Willem M. de Muynck - 1990 - Foundations of Physics 20 (4):357-380.details The problem of joint measurement of incompatible observables is investigated. Measurements are represented by positive operator-valued measures. A quantitative notion of inaccuracy is defined. It is shown that within this framework joint inaccurate measurements are possible for arbitrary maximal projection-valued measures on finite-dimensional spaces. The accuracy of such measurements is limited, as is shown by an inaccuracy inequality we derive. This new type of uncertainty relation can be unambiguously interpreted as referring to measurement precision rather than preparative quality. Several recent (...) Download Export citation Bookmark 8 citations
On the relation between the Einstein-Podolsky-Rosen paradox and the problem of nonlocality in quantum mechanics.Willem M. de Muynck - 1986 - Foundations of Physics 16 (10):973-1002.details The EPR problem is studied both from an instrumentalistic and from a realistic point of view. Bohr's reply to the EPR paper is analyzed and demonstrated to be not completely representative of Bohr's general views on the possibility of defining properties of a microscopic object. A more faithful Bohrian answer would not have led Einstein to the conclusion that Bohr's completeness claim of quantum mechanics implies nonlocality. The projection postulate, already denounced in 1936 by Margenau as the source of the (...) Download Export citation Bookmark 5 citations
A derivation of local commutativity from macrocausality using a quantum mechanical theory of measurement.W. M. de Muynck & J. P. H. W. van den Eijnde - 1984 - Foundations of Physics 14 (2):111-146.details A theory of the joint measurement of quantum mechanical observables is generalized in order to make it applicable to the measurement of the local observables of field theory. Subsequently, the property of local commutativity, which is usually introduced as a postulate, is derived by means of the theory of measurement from a requirement of mutual nondisturbance, which, for local observables performed at a spacelike distance from each other, is interpreted as a requirement of macrocausality. Alternative attempts at establishing a deductive (...) Download Export citation Bookmark 4 citations
Some realizable joint measurements of complementary observables.Paul Busch - 1987 - Foundations of Physics 17 (9):905-937.details Noncommuting quantum observables, if considered asunsharp observables, are simultaneously measurable. This fact is exemplified for complementary observables in two-dimensional state spaces. Two proposals of experimentally feasible joint measurements are presented for pairs of photon or neutron polarization observables and for path and interference observables in a photon split-beam experiment. A recent experiment proposed and performed by Mittelstaedt, Prieur, and Schieder in Cologne is interpreted as a partial version of the latter example. Download Export citation Bookmark 19 citations

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