The Problem of Formulating an Axiomatics for Quantum Mechanics

Günther Ludwig

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.

Luca Salasnich

Rodolfo Gambini, Luis Pedro García-Pintos, Jorge A. Pullin

We make a first attempt to axiomatically formulate the Montevideo interpretation of quantum mechanics. In this interpretation environmental decoherence is supplemented with loss of coherence due to the use of realistic clocks to measure time to solve the measurement problem. The resulting formulation is framed entirely in terms of quantum objects without having to invoke the existence of measurable classical quantities like the time in ordinary quantum mechanics. The formulation eliminates any privileged role to the measurement process giving an objective definition of when an event occurs in a system.

Honors Thesis

Jiří Souček

From the dichotomy nonlocality vs which is the consequence of Bell Inequalities (BI) we shall choose the non-realism. We shall present here the modified Quantum Mechanics (modQM) in the axiomatic form. ModQM was introduced in [5] and we shall show its non-realism in the description of an internal measurement process. ModQM allows the restoration of locality, since BI cannot be derived in it. In modQM it is possible to solve: the measurement problem, the collapse problem, the problem of a local model for EPR correlations (see[5]). ModQM is a unique explicit realization of non-realism in QM. ModQM should be preferred as an alternative to the standard QM mainly since it restores the locality.