Tensorial Quantum Mechanics: Back to Heisenberg and Beyond

TL;DR

This paper revisits the foundations of quantum mechanics, critiques traditional formulations, and introduces a tensorial framework inspired by Heisenberg's original approach to better explain experimental phenomena.

Contribution

It proposes a novel tensorial formalism for quantum mechanics, extending matrix mechanics and aiming for a more consistent account of physical states.

Findings

Extended matrix formalism to tensorial representation

Accounted for new experimental phenomena

Critiqued the inconsistency of Dirac's axiomatic approach

Abstract

In this work we discuss the establishment of Standard Quantum Mechanics (SQM) developed through Schr\"odinger's and Dirac's wave-vectorial reformulations of Heisenberg's original matrix mechanics. We will argue that while Heisenberg's approach was consistently developed -- taking as a standpoint the intensive patterns that were observed in the lab -- as an invariant-operational formalism, Dirac's axiomatic re-formulation was, instead, developed -- taking as a standpoint Schr\"odinger's wave mechanics and the methodological guide of Bohr and logical positivists -- as an essentially inconsistent "recipe" intended (but unable) to predict (binary) measurement outcomes. Leaving SQM behind and attempting to restore the consistent and coherent account of a real state of affairs, we will present a new tensorial proposal which -- taking as a standpoint Heisenberg's original approach -- will prove capable not only to extend the matrix formalism to a tensorial representation but also to account for new experimental phenomena.