Complementary Observables and Non-Boolean Logic Outside Quantum Physics

TL;DR

This paper explores how non-Boolean logic and complementarity, typically associated with quantum systems, can also apply to classical systems and even mental processes, especially when certain stability criteria are not met.

Contribution

It demonstrates that non-Boolean propositional lattices and complementarity can arise in classical and nonlinear dynamical systems under specific conditions.

Findings

Complementarity can exist in classical systems with certain partitions.

Non-Boolean logic applies to non-generating partitions of dynamical systems.

Implications extend to mental processes and systems outside quantum physics.

Abstract

The concept of complementarity in combination with a non-Boolean calculus of propositions refers to a pivotal feature of quantum systems which has long been regarded as a key to their distinction from classical systems. But a non-Boolean logic of complementary features may also apply to classical systems, if their states and observables are defined by partitions of a classical state space. If these partitions do not satisfy certain stability criteria, complementary observables and non-Boolean propositional lattices may be the consequence. This is especially the case for non-generating partitions of nonlinear dynamical systems. We show how this can be understood in more detail and indicate some challenging consequences for systems outside quantum physics, including mental processes.