- 94-300 Bona P.
- On the Problem of Universality of Quantum Theory.
Sep 28, 94
(auto. generated ps),
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Abstract. Two aspects of the problem of ``objectification'' in quantum mechanics (QM)
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)
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
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.