7.7 On the “Measurement Problem” in QM
213
specific dynamics of the considered processes. They are often mathematically highly
elaborated, very elegant and probably also useful from the point of view of applications of QM. We were not concentrating ourselves here on these approaches and
on the questions motivating them. The avoidance of the problems with the dynamics
of the interaction of the measured microsystems with the measuring macroscopic
apparatuses indicates that in these phenomenological works one assumes, at least
implicitly, the existence of some unknown mechanism of the “wave packet reduction”, or equivalently “wave packet collapse”. This is acceptable from the ‘practical
point of view’, because in the usual praxis of manipulations with microsystems (e.g.
measurements on them) it is possible to deal with the results (e.g. the outcomes of
the measurements) as if the “wave packet reduction” really happened. We are here,
however, interested in the problem how this process can be included into a noncontradictory quantum theory. An extensive discussion of these problems by the leading
physicists up to 1980’s contains [331].
The last decades, on the other hand, have seen experiments whose results indicate that the interference of macroscopically different states is possible in suitable
conditions, cf. e.g. [195, 196]. These ‘suitable conditions’ consist, first of all, in sufficient isolation of the considered quantum macro-system from any interactions with
surrounding environment, then, of course, in the ability of experimenters to discover
some suitable ‘macrointerference detecting’ observable quantity, and finally in the
inventiveness of experimenters when constructing the desired measuring apparatus.
Our models described in the Sects. 7.3, 7.4 and 7.5 of this chapter, mainly inspired
by the ideas published in [153], show that in the limit t m → ∞ the classical-like
probability distributions of the measurement results (i.e. probability without mutual
interferences of results) can be reached. In these models, apparatuses are treated as
quantum collections of infinitely many “small” subsystems, and the time necessary
for reaching the “reduction of the wave packet” is infinitely long; also, the convergence to the final states of the apparatuses of “proper mixtures”-type is in these
simple models—contrary to the ideal requirements—very slow.
The last of our models described in Sect. 7.6 shows, however, that if we construct
an “apparatus” as a large but finite collection of microsystems, interacting, moreover,
with the environment by radiating a particle, the convergence proceeds fast enough—
in the sense ‘almost exponentially’. The problem here is nonvanishing possibility of
interference of states with different pointer positions, although such a possibility
would be for ‘sufficiently large’ apparatuses very improbable. Again, an opened
question is the existence and location of a possible borderline for the validity of
QM. A mathematically clear formulation of the dependence of possible interferences
between macroscopic states of a “large system” on its size will be, probably, a subject
of future investigations in theoretical physics. One cannot exclude, however, that
there is no sharp borderline between QM and CM, and instead, there is a continuous
transition from QM to CM dependent on more parameters than just the size of the
measuring apparatus. Or, that there is no borderline at all, QM is a universal theory,
but our understanding of its possible applications requires some completions.
213
specific dynamics of the considered processes. They are often mathematically highly
elaborated, very elegant and probably also useful from the point of view of applications of QM. We were not concentrating ourselves here on these approaches and
on the questions motivating them. The avoidance of the problems with the dynamics
of the interaction of the measured microsystems with the measuring macroscopic
apparatuses indicates that in these phenomenological works one assumes, at least
implicitly, the existence of some unknown mechanism of the “wave packet reduction”, or equivalently “wave packet collapse”. This is acceptable from the ‘practical
point of view’, because in the usual praxis of manipulations with microsystems (e.g.
measurements on them) it is possible to deal with the results (e.g. the outcomes of
the measurements) as if the “wave packet reduction” really happened. We are here,
however, interested in the problem how this process can be included into a noncontradictory quantum theory. An extensive discussion of these problems by the leading
physicists up to 1980’s contains [331].
The last decades, on the other hand, have seen experiments whose results indicate that the interference of macroscopically different states is possible in suitable
conditions, cf. e.g. [195, 196]. These ‘suitable conditions’ consist, first of all, in sufficient isolation of the considered quantum macro-system from any interactions with
surrounding environment, then, of course, in the ability of experimenters to discover
some suitable ‘macrointerference detecting’ observable quantity, and finally in the
inventiveness of experimenters when constructing the desired measuring apparatus.
Our models described in the Sects. 7.3, 7.4 and 7.5 of this chapter, mainly inspired
by the ideas published in [153], show that in the limit t m → ∞ the classical-like
probability distributions of the measurement results (i.e. probability without mutual
interferences of results) can be reached. In these models, apparatuses are treated as
quantum collections of infinitely many “small” subsystems, and the time necessary
for reaching the “reduction of the wave packet” is infinitely long; also, the convergence to the final states of the apparatuses of “proper mixtures”-type is in these
simple models—contrary to the ideal requirements—very slow.
The last of our models described in Sect. 7.6 shows, however, that if we construct
an “apparatus” as a large but finite collection of microsystems, interacting, moreover,
with the environment by radiating a particle, the convergence proceeds fast enough—
in the sense ‘almost exponentially’. The problem here is nonvanishing possibility of
interference of states with different pointer positions, although such a possibility
would be for ‘sufficiently large’ apparatuses very improbable. Again, an opened
question is the existence and location of a possible borderline for the validity of
QM. A mathematically clear formulation of the dependence of possible interferences
between macroscopic states of a “large system” on its size will be, probably, a subject
of future investigations in theoretical physics. One cannot exclude, however, that
there is no sharp borderline between QM and CM, and instead, there is a continuous
transition from QM to CM dependent on more parameters than just the size of the
measuring apparatus. Or, that there is no borderline at all, QM is a universal theory,
but our understanding of its possible applications requires some completions.