20. The Realm of Quantum Mechanics in a Nutshell

Quantum mechanics (QM), as well as mechanics in general since the time of Isaac Newton, is concerned with motions, and changes of motions of bodies, and with their generating causes, the so-called forces or energies. The scientific aim of mechanics consists in defining motions (or momenta), and the relations to their causes not conceptually, but by means of mathematics in a quantitative manner. The paper lists the mathematical terms for "momentum", and for "energy" which the current theory of QM is based on, bringing to light a mathematical difference between linear and squared energy-momentum relations of consequence for the appear-ance of QM as to indeterminism (true causality) or determinism.

By means of Euclidean proportion theory it is shown how Heisenberg's indeterminacy relati-ons can be derived from a foundation of QM on the indeterministic linear energy-momentum relation (the proportionality of energy and momentum) only. This approach also explains the non-commutativity of QM operators, and yields a QM theory based on only one natural con-stant, c (dimensions space over time).

In considering Schrödinger's approach to wave mechanics, by application of geometric prin-ciples the paper shows how the Schrödinger equation rests on the squared energy-momentum relation (the classical concept of kinetic energy) only. Thus the deterministic feature of wave mechanics is understood, and the non-locality problem solved. Moreover, the way for a unification of QM and special relativity, and for a quantum theory of gravitation is paved.

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