The Principles of Quantum Mechanics. II. The Postulates of Quantum Mechanics

Oscar Diego

In this paper we are going to introduce a new dynamical postulate in Quantum Mechanics. This new principle is defined using path integrals over the set of normalized wave functions. We will show in a qualitative way that this postulate is equivalent to the Schrodinger equation and to the measurement postulates. Then we propose a new set of fundamental postulates for Quantum Mechanics. In this approach to Quantum Mechanics we separate the fundamental postulates and the physical interpretation. The fundamental postulates are abstract mathematical principles. Their physical interpretation depend on the physical system under study. These postulates do not use the concepts of measurement device and observer.

Gregory L. Naber

Laurent Nottale A, Marie-Noëlle Célérier

Quantum mechanics is based on a series of postulates which lead to a very good description of the microphysical realm but which have, up to now, not been derived from first principles. In the present work, we suggest such a derivation in the framework of the theory of scale relativity. After having analyzed the actual status of the various postulates, rules and principles that underlie the present axiomatic foundation of quantum mechanics (in terms of main postulates, secondary rules and derived 'principles'), we attempt to provide the reader with an exhaustive view of the matter, by both gathering here results which are already available in the literature, and deriving new ones which complete the postulate list.

Luigi E. Picasso

Andrei Yu. Khrennikov

This note is a part of my efforts for getting rid of nonlocality from quantum mechanics (QM). Quantum nonlocality is two faced Janus, one face is apparent quantum mechanical nonlocality (assigned with projection postulate), another face is nonlocality of Bell's model with the hidden variables. This paper is directed against the latter. The main casualty of Bell's model is that it contradicts to the Heinsenberg's uncertainty and Bohr's complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the {\it quantum postulate}: the existence of indivisible quantum of action given by the Planck constant. Bell's model by contradicting to the basic principles of QM implies rejection of this postulate. Thus, it contradicts not only to the QM-formalism, but also to the fundamental feature of the quantum world that was initially discovered by Planck.