The problem of simultaneous measurement of incompatible observables in quantum mechanics is studied on the one hand from the viewpoint of an axiomatic treatment of quantum mechanics and on the other hand starting from a theory of measurement. It is argued that it is precisely such a theory of measurement that should provide a meaning to the axiomatically introduced concepts, especially to the concept of observable. Defining an observable as a class of measurement procedures yielding a certain prescribed result for (...) the probability distribution of the set of values of some quantity (to be described by the set of eigenvalues of some Hermitian operator), this notion is extended to joint probability distributions of incompatible observables. It is shown that such an extension is possible on the basis of a theory of measurement, under the proviso that in simultaneously measuring such observables there is a disturbance of the measurement results of the one observable, caused by the presence of the measuring instrument of the other observable. This has as a consequence that the joint probability distribution cannot obey the marginal distribution laws usually imposed. This result is of great importance in exposing quantum mechanics as an axiomatized theory, since overlooking it seems to prohibit an axiomatic description of simultaneous measurement of incompatible observables by quantum mechanics. (shrink)

Ekstein has shown that causal independence neither implies nor is implied by commutativity in an infinite-dimensional, reducible construction. DeFacio and Taylor have presented a finite-dimensional irreducible example of Ekstein's proposition. Avishai and Ekstein have shown that the original question regarding locality for algebraic quantum field theories remainsopen. We concur with that claim and offer additional arguments. A new denumerably infinite-dimensional, irreducible example is presented here which shows that a sort of “orthogonality” among operators is involved. Some observations on localC*-andW*-algebras are (...) given. (shrink)

Causal independence of the simultaneous positions and momenta of two distinguishable particles in nonrelativistic physics and causal independence of events in two relatively spacelike regions of space-time in relativity are analyzed and discussed. This review paper formulates causal independence in a general and operational way and summarizes the inferences drawn from it in non-relativistic quantum mechanics, classical relativistic point mechanics, quantum field theory, and classical field theory. Special attention is given to the open question of the relationship between local independence (...) and commutativity in quantum field theory. (shrink)