OBSERVABLES AND DERIVABLES PART II: UNIQUENESS AND EXISTENCE PROPERTIES.
Abstract
Certain uniqueness and existence properties of bounded observables are discussed. The uniqueness problem considers the question: if two bounded observables have the same expectations in every state, are the observables equal. We say that an observable z is the sum of two bounded observables x and y if the expectation of z is the sum of the expectations of x and y for every state. The existence problem poses the question: does the sum of two bounded observables exist. Only partial answers to these questions have been found. It is shown that the uniqueness property holds for simultaneous observables and certain classes of non-simultaneous or complementary observables. The existence property holds for simultaneous observables and a counterexample is given which shows that this property does not hold in general. Logics in which the uniqueness and existence properties hold are considered. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1965
- Accession Number
- AD0623743
Entities
People
- Stanley P. Gudder