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arXiv · 2410.09535

Tensorial Quantum Mechanics: Back to Heisenberg and Beyond

Christian de Ronde·Raimundo Fernández Mouján·César Massri
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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.

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Christian de Ronde, Raimundo Fernández Mouján, César Massri. 2024-10-12. Tensorial Quantum Mechanics: Back to Heisenberg and Beyond. https://arxiv.org/abs/2410.09535

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