Preparation and Measurement:Two Independent Sources of Uncertainty in Quantum Mechanics

In the Copenhagen interpretation the Heisenberg inequality ΔQ ΔP ≥ h/2 is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint measurement of incompatible observables. This interpretation was criticized a long time ago and has recently been challenged in an experimental way. These criticisms can be substantiated by using the generalized formalism of positive operato-valued measures, from which an inequality, different from the Heisenberg inequality, can be derived, precisely illustrating the Copenhagen concept of complementarity. The different roles of preparation and measurement in creating uncertainly in quantum mechanics are discussed.