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thus typically eigenstates of position). This case possible quantum mechanical superpositions is reduced
corresponds to the typical quantum measurement so much because the laws governing physical interactions
setting; see, for example, the model by Zurek (1981, depend only on a few physical quantities (position, mo-
1982) and its outline in Sec. III.D.2 above. mentum, charge, and the like), and the fact that pre-
cisely these are the properties that appear determinate
2. When the interaction with the environment is weak to us is explained by the dependence of the preferred ba-
and HS dominates the evolution of the system sis on the form of the interaction. The appearance of
(namely, when the environment is slow in the classicality is therefore grounded in the structure of
above sense), a case that frequently occurs in the physical laws certainly a highly satisfying and rea-
the microscopic domain, pointer states will arise sonable approach.
15
The above argument in favor of the approach of on a larger and more general scale, i.e., when larger
environment-induced superselection could of course be parts of the universe are considered where the split into
considered as inadequate on a fundamental level: All subsystems is not suggested by some specific system
physical laws are discovered and formulated by us, so apparatus surroundings setup.
they can solely contain the determinate quantities of our
To summarize, environment-induced superselection of
experience because these are the only quantities we can
a preferred basis (i) proposes an explanation why a par-
perceive and thus include in a physical law. Thus the
ticular pointer basis gets chosen at all namely, by argu-
derivation of determinacy from the structure of our phys- ing that it is only the pointer basis that leads to stable,
ical laws might seem circular. However, we argue again
and thus perceivable, records when the interaction of the
that it suffices to demand a subjective solution to the
apparatus with the environment is taken into account;
preferred basis problem that is, to provide an answer
and (ii) it argues that the preferred basis will correspond
to the question why we perceive only such a small sub- to a subset of the set of the determinate properties of
set of properties as determinate, not whether there really
our experience, since the governing interaction Hamilto-
are determinate properties (on an ontological level) and
nian will solely depend on these quantities. But it does
what they are (cf. the remarks in Sec. II.B.3).
not tell us in general what the pointer basis will precisely
be in any given physical situation, since it will usually
We might also worry about the generality of this
be hardly possible to explicitely write down the relevant
approach. One would need to show that any such
interaction Hamiltonian in realistic cases. This also en-
environment-induced superselection leads in fact to pre-
tails that it will be difficult to argue that any proposed
cisely those properties that appear determinate to us.
criterion based on the interaction with the environment
But this would require the precise knowledge of the sys-
will always and in all generality lead to exactly those
tem and the interaction Hamiltonian. For simple toy
properties that we perceive as determinate.
models, the relevant Hamiltonians can be written down
explicitely. In more complicated and realistic cases, this More work remains therefore to be done to fully explore
will in general be very difficult, if not impossible, since the general validity and applicability of the approach of
the form of the Hamiltonian will depend on the particu- environment-induced superselection. But since the re-
lar system or apparatus and the monitoring environment sults obtained thus far from toy models have been found
under consideration, where in addition the environment to be in promising agreement with empirical data, there
is not only difficult to precisely define, but also constantly is little reason to doubt that the decoherence program
changing, uncontrollable and in essence infinitely large. has proposed a very valuable criterion to explain the
emergence of preferred states and their robustness. The
But the situation is not as hopeless as it might sound,
fact that the approach is derived from physical principles
since we know that the interaction Hamiltonian will in
should be counted additionally in its favor.
general be based on the set of known physical laws which
in turn employ only a relatively small number of physical
quantities. So as long as we assume the stability crite-
rion and consider the set of known physical quantities as
4. Pointer basis vs. instantaneous Schmidt states
complete, we can automatically anticipate the preferred
basis to be a member of this set. The remaining, yet very
The so-called Schmidt basis , obtained by diagonal-
relevant, question is then, however, which subset of these
izing the (reduced) density matrix of the system at each
properties will be chosen in a specific physical situation
instant of time, has been frequently studied with respect
(for example, will the system preferably be found in an
to its ability to yield a preferred basis (see, for exam-
eigenstate of energy or position?), and to what extent this
ple, Albrecht, 1992, 1993; Zeh, 1973), having led some to
matches the experimental evidence. To give an answer,
consider the Schmidt basis states as describing instan-
a more detailed knowledge of the interaction Hamilto-
taneous pointer states (Albrecht, 1992). However, as it
nian and of its relative strength with respect to the self-
has been emphasized (for example, by Zurek, 1993), any
Hamiltonian of the system will usually be necessary in
density matrix is diagonal in some basis, and this ba-
order to verify the approach. Besides, as mentioned in
sis will in general not play any special interpretive rôle.
Sec. III.E, there exist other criteria than the commutativ-
Pointer states that are supposed to correspond to qua-
ity requirement, and it is not at all fully explored whether
siclassical stable observables must be derived from an
they all lead to the same determinate properties.
explicit criterion for classicality (typically, the stability
criterion); the simple mathematical diagonalization pro-
Finally, a fundamental conceptual difficulty of the
decoherence-based approach to the preferred basis prob- cedure of the instantaneous density matrix will gener-
ally not suffice to determine a quasiclassical pointer basis
lem is the lack of a general criterion for what defines
(see the studies by Barvinsky and Kamenshchik, 1995;
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