  Sequential measurements of non-commuting observables produce order effects
that are well-known in quantum physics. But their conceptual basis, a
significant measurement interaction, is relevant for far more general
situations. We argue that non-commutativity is ubiquitous in psychology where
almost every interaction with a mental system changes that system in an
uncontrollable fashion. Psychological order effects for sequential measurements
are therefore to be expected as a rule. In this paper we focus on the
theoretical basis of such effects. We classify several families of order
effects theoretically, relate them to psychological observations, and predict
effects yet to be discovered empirically. We assess the complexity, related to
the predictive power, of particular (Hilbert space) models of order effects and
discuss possible limitations of such models.
