TIME-SYMMETRICAL FORMULATION OF QUANTUM-MECHANICS

We explore further the suggestion to describe a pre- and postselected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic opera tions, we systematically recast the basics of quantum mechanics-dynami cs, observables, and measurement theory-in terms of two-states as the elementary quantities. We find a simple and suggestive formulation tha t ''unifies'' two complementary observables: probabilistic observables and nonprobabilistic ''weak'' observables. Probabilities are relevant for measurements in the ''strong-coupling regime.'' They are given by the absolute square of a two-amplitude (a projection of a two-state). Nonprobabilistic observables are observed in sufficiently weak measur ements and are given by linear combinations of the two-amplitude. As a subclass they include the ''weak values'' of Hermitian operators. We show that in the intermediate regime, one may observe a mixing of prob abilities and weak values. A consequence of the suggested formalism an d measurement theory is that the problems of nonlocality and Lorentz n oncovariance, of the usual prescription with a ''reduction,'' may be e liminated. We exemplify this point for the Einstein-Podolsky-Rosen exp eriment and for a system under successive observations.