This crucial point...implies the impossibility of any sharp separation between the behaviour of atomic objects [i.e., objects governed by quantum mechanics] and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear.... Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects.
Typically, one is taught that this means that an electron can either be a particle or a wave, depending on the circumstances. As we've gotten more used to using quantum mechanics, those qualitative descriptions seem less and less relevant. The electron's (or other small object's) behavior is governed by a wave-like equation at all times. The behavior that emerges at large scales involves the apparent disappearance of part of the resulting wave-like state. There remain some serious questions about the interpretation of that stage, but the complementarity principle is not really of any use in addressing these questions. The issues that it once helped with are now dealt with by descriptions of a process called decoherence, an intrinsic implication of the quantum theory without any extra philosophical baggage.
(published on 06/18/12)