The Physical Principles of Quantum Mechanics. A critical review

TL;DR

This paper critically reviews the foundational principles of quantum mechanics, proposing a simpler, more physically motivated formulation that emphasizes operationally testable complementarity over traditional uncertainty relations.

Contribution

It introduces a geometrical approach to quantum principles, challenging traditional Dirac quantization and clarifying the role of non-commuting observables.

Findings

Operationally testable complementarity relations explain non-commuting observables.

A geometrical formulation avoids Dirac's canonical quantization issues.

Simplifies the conceptual understanding of quantum mechanics.

Abstract

The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approach.