Dirac Book The Principles Of Quantum Mechanics as presenting the alternative organization of a theory

TL;DR

This paper analyzes Dirac's book on quantum mechanics, highlighting its non-axiomatic organization aimed at relating quantum to classical mechanics, and discusses the shift towards an axiomatic approach in later editions.

Contribution

It reveals that Dirac's original formulation employed a non-axiomatic, analogy-based organization, contrasting with the later axiomatic approach, offering insights into the foundational structure of quantum mechanics.

Findings

Dirac's initial formulation was non-axiomatic and analogy-based.

The text aims to relate quantum mechanics to classical mechanics.

Later editions shifted towards an axiomatic formulation.

Abstract

Authoritative appraisals qualified this book as an axiomatic theory. However, being its essential content no more than an analogy, its theoretical organization cannot be an axiomatic one. In fact, in the first edition Dirac declares to avoid an axiomatic presentation. Moreover, I show that the text is aimed at solving a basic problem: How quantum mechanics is similar to classical mechanics. A previous paper analyzed all past theories of physics, chemistry and mathematics, presented by the respective authors in a non-axiomatic way. Four characteristic features of a new model of organizing a theory have been recognized. An accurate inspection of Dirac text proves that it actually applied this kind of organization of a theory. This fact gives a formal reason of what Kronz and Lupher suggested through intuitive categories, pragmatism and rigor, i.e. Dirac formulation of Quantum mechanics represents a distinct theoretical attitude from von Neumann axiomatic attitude. However, since the second edition Dirac changed his attitude; although relying again on an analogy, his theory was referred to the axiomatic method. Some considerations on the odd paths which led to the present formulation of QM are added. They suggest to look for a new foundation of this theory.