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Quantum axiomatics and a theorem of M.P. Sol`er Diederik Aerts, Bart Van Steirteghem
 

Summary: Quantum axiomatics and a theorem of M.P. Sol`er
Diederik Aerts, Bart Van Steirteghem
Foundations of the Exact Sciences (FUND),
Department of Mathematics, Brussels Free University,
Pleinlaan 2, B­1050 Brussels, Belgium;
diraerts@vub.ac.be, bvsteirt@vub.ac.be
Abstract
Three of the traditional quantum axioms (orthocomplementation, ortho-
modularity and the covering law) show incompatibilities with two prod-
ucts introduced by Aerts for the description of joint entities. Inspired
by Sol`er's theorem and Holland's AUG axiom, we propose a property of
`plane transitivity', which also characterizes classical Hilbert spaces among
infinite­dimensional orthomodular spaces, as a possible partial substitute
for the `defective' axioms.
1 Introduction
In his axiomatization of standard quantum mechanics Holland (1995) introduces
the Ample Unitary Group axiom (cf. (2) in Proposition 1 of this paper). It hints
at an evolution axiom but has the shortcoming that it is not lattice theoreti-
cal. In particular, it cannot be formulated for property lattices --complete,
atomistic and orthocomplemented lattices-- which play a central role in the

  

Source: Aerts, Diederik - Leo Apostel Centre, Vrije Universiteit Brussel

 

Collections: Multidisciplinary Databases and Resources; Physics