3 research outputs found
Effects and Propositions
The quantum logical and quantum information-theoretic traditions have exerted
an especially powerful influence on Bub's thinking about the conceptual
foundations of quantum mechanics. This paper discusses both the quantum logical
and information-theoretic traditions from the point of view of their
representational frameworks. I argue that it is at this level, at the level of
its framework, that the quantum logical tradition has retained its centrality
to Bub's thought. It is further argued that there is implicit in the quantum
information-theoretic tradition a set of ideas that mark a genuinely new
alternative to the framework of quantum logic. These ideas are of considerable
interest for the philosophy of quantum mechanics, a claim which I defend with
an extended discussion of their application to our understanding of the
philosophical significance of the no hidden variable theorem of Kochen and
Specker.Comment: Presented to the 2007 conference, New Directions in the Foundations
of Physic
Hilbert Lattice Equations
There are five known classes of lattice equations that hold in every infinite
dimensional Hilbert space underlying quantum systems: generalised
orthoarguesian, Mayet's E_A, Godowski, Mayet-Godowski, and Mayet's E equations.
We obtain a result which opens a possibility that the first two classes
coincide. We devise new algorithms to generate Mayet-Godowski equations that
allow us to prove that the fourth class properly includes the third. An open
problem related to the last class is answered. Finally, we show some new
results on the Godowski lattices characterising the third class of equations.Comment: 24 pages, 3 figure