Investigation of the basic aspects of an axiomatic non-linear quantum mechanics

Diederik Aerts, Bart D’Hooghe

Stanley Gudder

Tapan Kumar Das

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.

Xijia Wang

Any scientific system has a unified basic theory. But physics has no unified basic theory in the modern sense. Classical mechanics, relativity and quantum mechanics have their own basic concepts, categories and principles, so none of them can be regarded as true basic theories of physics. Cosmic Continuum Theory holds that the continuity and discreteness of the universe are fundamental issues related to the unification of physics. Because the contradiction between quantum non-locality and local reality is the fundamental obstacle to the unification of physics, while locality and non-locality correspond to the continuity and discreteness of physical reality respectively. The cosmic continuum theory introduces mathematical continuum and axiomatic ideas to reconstruct the basic theory of physics, and by the correspondence of existence and its dimensions to achieve the unification of the essence of physical reality, by introducing the cosmic continuum hypothesis to achieve the unification of the continuity and discreteness of physical reality, by introducing axiomatic methods to achieve formal unification of the foundations on physics. From the perspective of Cosmic Continuum, classical mechanics, relativity and quantum mechanics are no longer the basic theories of physics, but three branch theories of physics that are respectively applicable to macroscopic, cosmoscopic and microcosmic systems.

Nelson Enrique Bolivar, Gabriel Abellán

This volume will act as a guide through the various aspects of quantum mechanics. It not only covers the basics but also addresses new themes developed in the field of quantum mechanics in recent years. These include quantum mechanics in relation to electronics, quantum dots, spintronics, cryptography, and other more theoretical aspects, such as the path integral formulation and supersymmetric quantum mechanics. The volume presents a number of mathematical tools and physical consequences derived from quantum mechanics. The starting point of the volume is a very brief review of the phenomenology associated with the origins of quantum theory, as the branch of science was understood in the beginning of the 20th century, leading to an interpretation of the results at that time. Key features: • Provides understanding and demystification of the quantum theory • Presents applications to information theory and encryption • Introduces applications to medicine, in both treatment and diagnosis • Covers applications to modern communications systems • Looks at the philosophical implications of quantum mechanics, its reality, and its perception • Describes the application to the basics of solid state devices