Derivation of the postulates of quantum mechanics from the first principles of scale relativity

TL;DR

This paper derives the fundamental postulates of quantum mechanics from the principles of scale relativity, aiming to ground the theory in first principles rather than axiomatic assumptions.

Contribution

It provides a comprehensive derivation of quantum postulates within the scale relativity framework, combining existing results with new derivations to deepen foundational understanding.

Findings

Derivation of quantum postulates from scale relativity

Analysis of the axiomatic structure of quantum mechanics

New results completing the set of foundational postulates

Abstract

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.