Reconstructing the formalism of quantum mechanics in the ``contextual objectivity" point of view

TL;DR

This paper develops an axiomatic formulation of quantum mechanics based on the 'contextual objectivity' perspective, emphasizing the physical definition of quantum states and their relation to measurement apparatus transformations.

Contribution

It introduces a new axiomatic approach linking quantum structure to the non-commutative group of measurement transformations within the 'contextual objectivity' framework.

Findings

Quantum states are defined in physical terms with objective reality.

The structure of QM arises from non-commutative geometrical transformations.

A possible axiomatic foundation for QM is proposed based on system dimensionality.

Abstract

In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in such a way that it may be given an "objective reality". Here we use some ideas about the system dimensionality, taken from quant-ph/0101012, to propose a possible axiomatic approach to QM. In this approach the structure of QM appears as a direct consequence of the non-commutative character of the (classical geometrical) group of "knobs transformations", that relate between themselves the different positions of the measurement apparatus.