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We illustrate some problems that are related to the existence of anunderlying linear structure at the level of the property lattice associatedwith a physical system, for the particular case of two explicitly separatedspin 1/2 objects that are considered, and mathematically described, as onecompound system. It is shown that the separated product of the propertylattices corresponding with the two spin 1/2 objects does not have anunderlying linear structure, although the property lattices associated with thesubobjects in isolation manifestly do. This is related at a fundamental levelto the fact that separated products do not behave well with respect to thecovering law (and orthomodularity) of elementary lattice theory. In addition,we discuss the orthogonality relation associated with the separated product ingeneral and consider the related problem of the behavior of the correspondingSasaki projections as partial state space mappingsComment: 25 page

LINEARITY AND COMPOUND PHYSICAL SYSTEMS: THE CASE OF TWO SEPARATED SPIN 1/2 ENTITIES