A Topos Perspective on the KochenSpecker Theorem: IV. Interval Valuations
Abstract
We extend the topostheoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth value to a proposition that the value of a quantity lies in a certain set $\Delta \subseteq \mathR$. Here we relate such sievevalued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectra (we call these `interval' valuations). There are two main results. First, there is a natural correspondence between these two kinds of valuation, which uses the notion of a state's support for a quantity (Section 3). Second, if one starts with a more general notion of interval valuation, one sees that our interval valuations based on the notion of support (and correspondingly, our sievevalued valuations) are a simple way to secure certain natural properties of valuations, such as monotonicity (Section 4).
 Publication:

arXiv eprints
 Pub Date:
 July 2001
 arXiv:
 arXiv:quantph/0107123
 Bibcode:
 2001quant.ph..7123B
 Keywords:

 Quantum Physics;
 General Relativity and Quantum Cosmology
 EPrint:
 Latex2e