94-300 Bona P.

On the Problem of Universality of Quantum Theory. (37K, TeX) Sep 28, 94

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Abstract. Two aspects of the problem of ``objectification'' in quantum mechanics (QM) are considered: 1) The question of description of the usually requested nonexistence of interference of macroscopically different states, 2) the possibility of distinction of Genuine mixture (or ``Gemenge'') from the Elementary mixture (or ``improper mixture''). It is argued that some restriction of the set of the usually theoretically postulated quantal ``observables'' of large systems (e.g. measuring apparatuses) is not only useful, but also, perhaps, necessary for their adequate description. Such a restriction was anticipated in a rather hidden way in algebraic description of infinite quantal systems. Conscious acceptance of this condition (of restriction of the set of ``observables'') could give us possibility of description of quantal measurement process in framework of systems with finite number of degrees of freedom. This would need, however, an analysis of dynamics of actually used (and/or possibly constructed) apparatuses. The above considerations are supplied by an idealised solvable model of measurement process in quantum theory. It is argued, that the transition of superposition to (at least effective) Genuine mixture is connected with appearance of correlations with macroscopically distinguishable states. Such a correlation could be acompanied with interaction of the considered system (e.g. a microsystem) with a macrosystem leading to its dynamics in an external field. This can lead to an effective nonlinearity of the system's evolution distinguishing the Genuine mixture from the corresponding (kinematically equivalent) Elementary one. ``Relative isolation'' of quantal systems is defined in this connection. A nonlinear version of quantum mechanics (a consistent generalisation of the Weinberg's one) describing the last mentioned evolution is presented. Statistical interpretation of this nonlinear theory -- if taken seriously as a basic theory -- leads naturally to several modifications (resp. extensions) of the concepts of the standard linear quantum mechanics. Such a theory contains more ``states'' and ``observables'' then linear QM does: It includes also various (semi-)classical observables, distinguishes between ``observables'' and ``generators'', some ``quasiclassical'' or ``approximate'' theories (like the Time Dependent Hartree-Fock Theory) are here included as specific subtheories (without any approximations), distinction between Elementary and Genuine mixtures naturally appears, etc.

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