Summary: A CHARACTERIZATION OF SUBSYSTEMS IN PHYSICS
DIRK AERTS and INGRID DAUBECHIES*
Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2,
B-1050 Brussel, Belgium
ABSTRACT. Working within the framework of the propositional system formalism, we use a
previous study [1 ] of the description of two independent physical systems as one big physical
system to derive a characterization of a (non-interacting) physical subsystem. We discuss the
classical case and the quantum case.
We shall follow Piron  and describe any physical system by means of the collection of its
properties, or, equivalently, of the yes-no experiments which can be carried out on this system.
In , it is shown that this collection is a propositional system, that is a complete, orthocomple-
mented, weakly modular, atomic lattice satisfying the covering law. The states of the physical
system are represented by the atoms of the lattice. For the definitions of these concepts and the
physical justification of this approach, see  or also . In what follows we shall use the
abbreviation PROP for these propositional systems.
In [1 ], we studied the description of two non-interacting physical systems as one joint
physical system. We denote these two independent systems by S~, $2, and the big physical
system containing them both by S. The corresponding PROP's are s s s From a few simple
arguments resulting from physical considerations, we arrived at the following structure (see