Linkages Between the Calculable and the Incalculable in Quantum Theory

Abstract

Seemingly disparate phenomena-e.g., the optimal reception of light signals, experimental designs to rule out hidden-parameter theories, and the triggering that is essential to the demonstration of wave-particle duality-involve a common but previously overlooked thread. The common thread is a quantum Field that defines several measurement steps, leading to several spatio-temporally distinct outcomes. In the ease of light reception, this operator field has values at later spacetime points influenced by incalculable outcomes at earlier spacetime points; these outcomes are outcomes of measurement steps defined by values of the field itself at earlier spacetime points. This field, called a linkage field, is defined carefully to show the coupling between random, incalculable outcomes, on the one hand, and the propagation of calculable field values on the other. We inquire into the necessity of this field for optimal measurements. Assumptions implicit in quantum decision theory are stated, pertaining to; I) the expression of possibilities by random variables, and 2) the locating of outcomes of measurements. A proposition is stated and proved that such a randomly influenced linkage field is necessary to the optimal measurement of binary coherent light signals. Other examples of linkage fields and their applications are discussed briefly.