Do We Understand Quantum Mechanics - Finally?

TL;DR

This paper offers a unified algebraic formalism for classical and quantum systems, reviews quantum mechanics interpretations, and emphasizes the roles of dephasing and decoherence in understanding measurement and reality.

Contribution

It introduces a unified operator algebra framework for classical and quantum systems and discusses the interpretational implications of decoherence and dephasing.

Findings

Unified formalism for classical and quantum systems

Clarification of quantum measurement and interpretation

Highlighting the roles of decoherence and dephasing

Abstract

After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator algebras. We then review some basic aspects of quantum mechanics and, in particular, of its interpretation. We attempt to clarify what Quantum Mechanics tells us about Nature when appropriate experiments are made. We discuss the importance of the mechanisms of "dephasing" and "decoherence" in associating "facts" with possible events and rendering complementary possible events mutually exclusive.