Orthocurrence as both Interaction and Observation
Vaughan Pratt · 2005
Orthocurrence or tensor product A ⊗ B of systems A and B can be understood symmetrically as an interaction operator expressing a form of conjunction of state predicates, or asymmetrically as one of two information channels: either A−◦B ⊥ as a system consisting of A observing states of B (equivalently, conveying information about the states of B to A), or B−◦A ⊥ for the same thing in the other direction. We show how the notion of Chu space or couple arises as a natural corollary of this point of view. We conclude with a history of orthocurrence. This paper is intended to be read in conjunction with the paper by R. Rodriguez and F. Anger in this workshop [RA01]. The focus of the paper is on the intuition underlying, and history of, orthocurrence rather than on its more technically detailed aspects. For more formal definitions the impatient reader might prefer [Pra99]. One goal here is to persuade the reader that couples themselves, as well as their orthocurrence defined as tensor product, are not just artificial constructs but natural consequences of intuitively plausible aspects of interaction and observation. 1