The emergence of probabilities in anhomomorphic logic

TL;DR

This paper explores how probabilities can emerge within anhomomorphic logic, a quantum interpretation that assigns truth values to questions, using the Cournot principle and examples like the double slit experiment.

Contribution

It demonstrates how probabilistic predictions can be derived in anhomomorphic logic through the use of the Cournot principle and approximate preclusions, extending the interpretation of quantum measure theory.

Findings

Probabilities arise from preclusive co-events and the quantum measure.

Application to the double slit experiment illustrates the approach.

Uses weak Cournot principle to interpret quantum probabilities.

Abstract

Anhomomorphic logic is a new interpretation of Quantum Theory (due to R. Sorkin). It is a histories formulation (c.f. consistent histories, quantum measure theory). In this approach, reality is a co-event, which is essentially an assignment of a truth value {True, False} to each question. The way this assignment is done mimics classical physics in as much as possible allowing however for sufficient flexibility to accommodate quantum 'paradoxes', as is shown by the analysis of Kochen-Specker theorem. In this contribution, after briefly reviewing the approach, we will examine how probabilistic predictions can arise. The Cournot principle and the use of approximate preclusions will play a crucial role. Facing similar problems in interpreting probability as in classical probability theory, we will resort to the weak form of Cournot principle, where possible realities will be preclusive co-events and the quantum measure is used to obtain predictions. Examples considered, includes the fair coin and the double slit pattern arguably one of the most important paradigms for quantum theory.