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Physics  2015 

The Madelung Picture as a Foundation of Geometric Quantum Theory

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Abstract:

Despite its age quantum theory remains ill-understood, which is partially to blame on its deep interwovenness with the mysterious concept of quantization. In this article we argue that a quantum theory recoursing to quantization algorithms is necessarily incomplete. To provide a new axiomatic foundation, we give a rigorous proof showing how the Schr\"odinger equation follows from the Madelung equations, which are formulated in the language of Newtonian mechanics. We show how the Schr\"odinger picture relates to this Madelung picture and how the "classical limit" is directly obtained. This suggests a reformulation of the correspondence principle, stating that a quantum theory must reduce to a probabilistic version of Newtonian mechanics for large masses. We then enhance the stochastic interpretation developed by Tsekov, which speculates that quantum mechanical behavior is caused by random vibrations in spacetime. A new, yet incomplete model of particle creation and annihilation is also proposed.

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