Abstract
The recently developed technique of Bohrification associates to a (unital) C*-algebra A 1. the Kripke model, a presheaf topos, of its classical contexts; 2. in this Kripke model a commutative C*-algebra, called the Bohrification of A; 3. the spectrum of the Bohrification as a locale internal in the Kripke model. We propose this locale, the 'state space', as a (n intuitionistic) logic of the physical system whose observable algebra is A. We compute a site which externally captures this locale and find that externally its points may be identified with partial measurement outcomes. This prompts us to compare Scott-continuity on the poset of contexts and continuity with respect to the C*-algebra as two ways to mathematically identify measurement outcomes with the same physical interpretation. Finally, we consider the not-not-sheafification of the Kripke model on classical contexts and obtain a space of measurement outcomes which for commutative C*-algebras coincides with the spectrum. The construction is functorial on the category of C*-algebras with commutativity reflecting maps.
| Original language | English |
|---|---|
| Journal | Foundations of Physics |
| Volume | 42 |
| Issue | 7 |
| Pages (from-to) | 896-908 |
| Number of pages | 13 |
| ISSN | 0015-9018 |
| DOIs | |
| Publication status | Published - 1 Jul 2012 |
| Externally published | Yes |
Keywords
- Bohrification
- Boolean valued models
- Measurement
- Sheaves