An Introduction to Consistent Quantum Theory

TL;DR

This paper introduces Consistent Quantum Theory (CQT), emphasizing the role of incompatible frameworks in quantum mechanics and explaining how the single framework rule accounts for quantum phenomena.

Contribution

It provides an elementary, clear exposition of CQT, highlighting its novel approach of using incompatible frameworks to interpret quantum mechanics.

Findings

Multiple incompatible frameworks are essential to quantum behavior.

The single framework rule prevents meaningless combinations of incompatible descriptions.

Quantum phenomena like entanglement and wave function collapse follow logically within CQT.

Abstract

This paper presents an elementary introduction to Consistent Quantum Theory (CQT), as developed by Griffiths and others over the past 25 years. The theory is a version of orthodox(Copenhagen) quantum mechanics, based on the notion that the unique and mysterious feature of quantum, as opposed to classical, systems is the simultaneous existence of multiple incompatible representations of reality, referred to as "frameworks". A framework is a maximal set of properties of a system for which probabilities can be consistently defined. This notion is expressed by saying that a framework provides an exhaustive set of exclusive alternatives (ESEA), but no single framework suffices to fully characterize a quantum system. Indeed, the existence of multiple incompatible frameworks is the hallmark of quantum mechanical behavior. Any prediction of the theory must be confined to a single framework and combining elements from different frameworks leads to quantum mechanically meaningless statements. This "single framework rule" is the precise mathematical statement of Bohr's complementarity. It is shown that if the microscopic description is assumed to incorporate these elements in a local setting, then distant entanglements, macroscopic measurements, wave function collapse and other mysterious features of quantum behavior follow in a logical manner. The essential elements of the theory are first explained using the simplest quantum system, a single spin-1/2 degree of freedom at one time.