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Foundations of Science

Dirac’s Book The Principles of Quantum Mechanics as an Alternative Way of Organizing a Theory

Antonino Drago

Published Mar 22, 2022• 4 citations
Publisher
DOI
10.1007/s10699-022-09835-3

Related papers

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

Antonino Drago

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.

arXiv:2101.09565•Jan 23, 2021•0 citations

Paul A.M. Dirac’s The Principles of Quantum Mechanics

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Three-particle symmetry classifications according to the method of Dirac

Paul E. Hussar, Y. S. Kim, Marilyn E. Noz

It is shown that the method of Dirac is an effective way of teaching three-particle symmetry classifications to students in the first-year quantum mechanics class, who wish to understand the symmetry properties associated with elementary particles before or without learning group theory. According to the method spelled out for the N-particle case by Dirac in Secs. 55 and 56 of his classic book Principles of Quantum Mechanics, explicit calculations are carried out for three particles. It is shown that this method leads to the three-particle wave functions and their symmetric combinations as given by Feynman et al. In the following paper, the general principles derived here are applied to the quark model of hadrons.

American Journal of Physics•Dec 1, 1980•11 citations

Paul Dirac and The Principles of Quantum Mechanics

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Quirks of the Quantum Mind by Robert G. Jahn and Brenda J. Dunne

Sky Estabrook Nelson

Quirks of the Quantum Mind accomplishes something that no other book to my knowledge has done. Using extensive data from the authors’ multiple decades of unique field research, Quirks synthesizes a “metaphor” which serves as a model for understanding consciousness-related anomalies. The book coherently presents a parallel between the principles of quantum mechanics and the psychic behavior observed in the research done at the Princeton Engineering Anomalies Research Laboratory.The authors do not presume to create a “theory” connecting quantum mechanics with consciousness. The authors steadfastly stick to the notion that quantum mechanics may serve as a metaphor for psychic phenomena. Yet they also make clear that the formalism of quantum mechanics itself is ultimately a reflection of the way we think. They point out that "common concepts of physical theories, such as mass, momentum and energy, electric charge and magnetic field, the quantum and the wave function, and even distance and time, are not more than useful organizing strategies consciousness has developed [for organizing its world]."

Journal of Scientific Exploration•Jun 1, 2013•0 citations

The Principles of Quantum Theory, Dirac’s Equation, and the Architecture of Quantum Field Theory

Arkady Plotnitsky

Springer eBooks•Jan 1, 2016•2 citations
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.
It is shown that the method of Dirac is an effective way of teaching three-particle symmetry classifications to students in the first-year quantum mechanics class, who wish to understand the symmetry properties associated with elementary particles before or without learning group theory. According to the method spelled out for the N-particle case by Dirac in Secs. 55 and 56 of his classic book Principles of Quantum Mechanics, explicit calculations are carried out for three particles. It is shown that this method leads to the three-particle wave functions and their symmetric combinations as given by Feynman et al. In the following paper, the general principles derived here are applied to the quark model of hadrons.
Quirks of the Quantum Mind accomplishes something that no other book to my knowledge has done. Using extensive data from the authors’ multiple decades of unique field research, Quirks synthesizes a “metaphor” which serves as a model for understanding consciousness-related anomalies. The book coherently presents a parallel between the principles of quantum mechanics and the psychic behavior observed in the research done at the Princeton Engineering Anomalies Research Laboratory.The authors do not presume to create a “theory” connecting quantum mechanics with consciousness. The authors steadfastly stick to the notion that quantum mechanics may serve as a metaphor for psychic phenomena. Yet they also make clear that the formalism of quantum mechanics itself is ultimately a reflection of the way we think. They point out that "common concepts of physical theories, such as mass, momentum and energy, electric charge and magnetic field, the quantum and the wave function, and even distance and time, are not more than useful organizing strategies consciousness has developed [for organizing its world]."