Value Assignments to Observables Depending on a History of Context Change

Abstract

The functional composition principle is generalized by taking into account of history of context change. Analysis of Peres' example shows hysteresis of value assignments. It is shown that value assignments which depend on the history of context change are possible in the case that the Hilbert space of state vectors is finite dimensional.Comment: 22 pages. Errors in the previous proof of Proposition 5 were corrected. This is the full version of "On Hysteresis of Value Assignments to Observables during Changes of Context" in Foundations of Probability and Physics - 4, eds. A. Yu. Khrennikov et al., AIP Conf. Proc. 889, 2007, pp. 422-42