Summary: Operator structure of a non quantum and a non classical system
Diederik Aerts and Bart D'Hooghe
Department of Theoretical Physics, Brussels Free University,
Pleinlaan 2, 1050 Brussels, Belgium.
There exists a connection between the vectors of the PoincarŽe-sphere and the elements of the complex
Hilbert Space C2
. This latter space is used to describe spin-1
measurements. We will now use this
connection to study the intermediate cases of a more general spin-1
measurement model which has
no representation in a Hilbert Space. We will construct the set of operators of this general model, and
investigate under which circumstances it is possible to define linear operators. Because no Hilbert
Space structure is possible for these intermediate cases, it can be expected that no linear operators
are possible and it is shown that under very plausible assumptions this is indeed the case.