FUZZINESS IN QUANTUM-MECHANICS

It is shown that quantum mechanics can be regarded as what one could c all a ''fuzzy'' mechanics, that is, the mechanics whose underlying log ic is not Aristotelian binary logic of classical mechanics but, rather , fuzzy logic. From this point of view, classical mechanics is a crisp limit of a more general quantum mechanics based on the fuzzy logic. U sing such an approach, the Schrodinger equation is derived from the Ha milton-Jacobi equation. The deep underlying unity between these equati ons is connected to the fact that a unique ''crisp'' trajectory of a c lassical particle is ''selected'' out of many-continuum paths accordin g to the principle of least action. This can be interpreted as a conse quence of the assumption that a classical particle ''resides'' in ever y path of a set of many-continuum paths that collapse to a single traj ectory of an observed classical motion. The wave function is treated a s a quantity describing a deterministic entity possessing a fuzzy char acter. As a logical consequence of such an interpretation, the complem entarity principle and wave-particle duality concept can be abandoned in favor of an idea of a fuzzy deterministic microobject. In optical c omputing the undetectable quantum phase and its global information are lost in the process of defuzzification leading to its ''final'' produ ct, that is, the probability density. Since in optical computing we ar e interested only in this product, we do not need to register all the intermediate results that contribute to the generation of the product. The lost information then can be viewed as ''garbage.''