Tensorial Quantum Mechanics: Back to Heisenberg and Beyond

In this work we discuss the establishment of Standard Quantum Mechanics (SQM) developed through Schrödinger’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 Schrödinger’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.