Relational observables, reference frames, and conditional probabilities

Topos Theoretical Reference Frames on the Category of Quantum Observables

An observable effects a schematization of the Quantum event structure by correlating Boolean algebras picked by measurements with the Borel algebra of the real line. In a well-defined sense Boolean observables play the role of coordinatizing objects in the Quantum world, by picking Boolean figures and subsequently opening Boolean windows for the perception of the latter, interpreted as local me...

Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox “absolute” quantities are good representatives of observable relative quantitie...

Probabilities of Conditionals and Conditional Probabilities Ii

A dams's thesis about indicative conditionals is that their assertIlability goes by the conditional subjective probability of the consequent given the antecedent, in very much the same way that assertability normally goes by the subjective probability of truth.' The thesis is well established; the remaining question is how it may best be explained. The nicest explanation would be that the truth...

Propensities and conditional probabilities

The present paper deals with the objection that Paul Humphreys raised against the propensity interpretation of probability "Humphreys' paradox". An update on existing solutions is o ered, and it is concluded that none of them is completely satisfactory in view of Humphreys' 2004 rejoinder. Positively, an original solution is formulated and discussed.

Quantum Conditional Probabilities Are Not Probabilities of Quantum Conditional