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associated probabilities that is in agreement with the
additional collapse postulate to account for definite mea-
results of unitary quantum mechanics would presum-
surement results. Of course, this immediately raises the
ably be easier than in a model of property ascription
question of how physical properties that are perceived
where the set of possibilities does not arise dynami-
through measurements and measurement results are con-
cally via the Schrödinger equation alone (for a detailed
nected to the state, since the bidirectional link between
proposal for modal dynamics of the latter type, see
the eigenstate of the observable (that corresponds to the
Bacciagaluppi and Dickson, 1999). The need for explicit
physical property) and the eigenvalue (that represents
dynamics of property states in modal interpretations is
the manifestation of the value of this physical property
controversial. One can argue that it suffices to show
in a measurement) is broken. The general goal of modal
that each instant of time, the set of possibly possessed
interpretations is then to specify rules that determine a
properties that can be ascribed to the system is empiri-
catalogue of possibilities for the properties of a system
cally adequate in the sense of containing the properties
that is described by the density matrix Á at time t. Two
of our experience, especially with respect to the proper-
different views are typically distinguished: a semantic
ties of macroscopic objects (this is essentially the view
approach that only changes the way of talking about the
of, for example, van Fraassen, 1973, 1991). On the other
connection between properties and state; and a realistic
hand, this cannot ensure that these properties behave
view that provides a different specification of what the
over time in agreement with our experience (for instance,
possible properties of a system really are, given the state
that macroscopic objects that are left undisturbed do
vector (or the density matrix).
not change their position in space spontaneously in an
Such an attribution of possible properties must fulfill observable manner). In other words, the emergence of
certain desiderata. For instance, probabilities for out- classicality is not only to be tied to determinate prop-
comes of measurements should be consistent with the erties at each instant of time, but also to the existence
usual Born probabilities of standard quantum mechan- of quasiclassical  trajectories in property space. Since
ics; it should be possible to recover our experience of decoherence allows one to reidentify components of the
classicality in the perception of macroscopic objects; and decohered density matrix over time, this could be used
an explicit time evolution of properties and their prob- to derive property states with continuous, quasiclassi-
abilities should be definable that is consistent with the cal trajectory-like time evolution based on Schrödinger
results of the Schrödinger equation. As we shall see in dynamics alone. For some discussions into this direc-
the following, decoherence has frequently been employed tion, see Hemmo (1996) and Bacciagaluppi and Dickson
in modal interpretations to motivate and define rules for (1999).
property ascription. Dieks (1994a,b) has argued that one
of the central goals of modal approaches is to provide an
interpretation for decoherence.
The fact that the states emerging from decoherence
and the stability criterion are sometimes nonorthogonal
or form a continuum will presumably be of even lesser
1. Property ascription based on environment-induced relevance in modal interpretations than in Everett-style
superselection
interpretations (see Sec. IV.C) since the goal is here solely
to specify sets of possible properties of which only one
The intrinsic difficulty of modal interpretations is to set gets actually ascribed, such that an  overlap of the
avoid any ad hoc character of the property ascription, sets is not necessarily a problem (modulo the potential
yet to find generally applicable rules that lead to a selec- difficulty of a straightforward ascription of probabilities
tion of possible properties that include the determinate in such a situation).
27
2. Property ascription based on instantaneous Schmidt 3. Property ascription based on decompositions of the
decompositions decohered density matrix
Other authors therefore appealed to the orthogonal
However, since it is usually rather difficult to ex-
decomposition of the decohered reduced density matrix
plicitely determine the robust  pointer states through
(instead of the decomposition of the instantaneous den-
the stability (or a similar) criterion, it would not be easy
sity matrix) which has led to noteworthy results. For
to comprehensively specify a general rule for property
the case of the system being represented by an only fi-
ascription based on environment-induced superselection.
nite-dimensional Hilbert space, and thus for a discrete
To simplify this situation, several modal interpretations
model of decoherence, the resulting states were indeed
have restricted themselves to the orthogonal decomposi-
found to be typically close to the robust states selected
tion of the density matrix to define the set of properties
by the stability criterion (for macroscopic systems, this
that can be ascribed (see, for instance, Bub, 1997; Dieks,
typically means localization in position space), unless
1989; Healey, 1989; Kochen, 1985; Vermaas and Dieks,
again the final composite state was very nearly degen-
1995). For example, the approach of Dieks (1989) rec-
erate (Bacciagaluppi and Hemmo, 1996; Bene, 2001; see
ognizes, by referring to the decoherence program, the
also Sec. III.E.4). Thus in sufficiently nondegenerate
relevance of the environment by considering a compos-
cases decoherence can ensure that the definite properties
ite system environment state vector and its diagonal
selected by modal interpretations of the Dieks type when
"
Schmidt decomposition, |È = pk |ÆS |ÆE , which
k k k
based on the orthogonal decomposition of the reduced
always exists. Possible properties that can be ascribed
decohered density matrix will be appropriately close to
to the system are then represented by the Schmidt pro-
the properties corresponding to the ideal pointer states
jectors Pk = »k|ÆS ÆS|. Although all terms are present
k k selected by the stability criterion.
in the Schmidt expansion (that Dieks calls the  math-
On the other hand, Bacciagaluppi (2000) showed that
ematical state ), the  physical state is postulated to
when the more general and realistic case of an infinite- [ Pobierz całość w formacie PDF ]