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Summary: Linearity and compound physical systems: the case
of two separated spin 1/2 entities
Diederik Aerts and Frank Valckenborgh
Center Leo Apostel (CLEA) and
Foundations of the Exact Sciences (FUND),
Brussels Free University, Krijgskundestraat 33,
1160 Brussels, Belgium.
diraerts@vub.ac.be, fvalcken@vub.ac.be
Abstract
We illustrate some problems that are related to the existence of an
underlying linear structure at the level of the property lattice associ-
ated with a physical system, for the particular case of two explicitly
separated spin 1/2 objects that are considered, and mathematically
described, as one compound system. It is shown that the separated
product of the property lattices corresponding with the two spin 1/2
objects does not have an underlying linear structure, although the
property lattices associated with the subobjects in isolation manifestly
do. This is related at a fundamental level to the fact that separated
products do not behave well with respect to the covering law (and or-
thomodularity) of elementary lattice theory. In addition, we discuss
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