The construction of quantum mechanics from electromagnetism. Theory and hydrogen atom

Abstract

We reconstruct Quantum Mechanics in a way that harmonises with classical mechanics and electromagnetism, free from mysteries or paradoxes as the \emph{collapse of the wave-function} or \emph{Schr\"odinger's cat.} The construction is inspired by de Broglie's and Schr\"odinger's wave mechanics while the unifying principle is Hamilton's principle of least action, which separates natural laws from particular circumstances such as initial conditions and leads to the conservation of energy for isolated systems. In Part I we construct the Quantum Mechanics of a charged unitary entity and prescribe the form in which the entity interacts with other charged entities and matter in general. In Part II we address the quantum mechanics of the hydrogen atom, testing the correctness and accuracy of the general description. The relation between electron and proton in the atom is described systematically in a construction that is free from analogies or ad-hoc derivations and it supersedes conventional Quantum Mechanics (whose equations linked to measurements can be recovered). We briefly discuss why the concept of isolation built in Schr\"odinger's time evolution is not acceptable and how it immediately results in the well known measurement paradoxes of quantum mechanics. We also discuss the epistemic grounds of the development and provide a criticism of instrumentalism, the leading philosophical perspective behind conventional Quantum Mechanics.