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Is quantum mechanics based on an invariance principle?

Leon Brenig
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Abstract

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are induced by isotropic space dilations. This invariance imposes a change in the laws of classical mechanics that exactly corresponds to the transition to quantum mechanics. The Schroedinger equation appears jointly with a second nonlinear equation describing non-unitary processes. Unitary and non-unitary evolutions are exclusive and appear sequentially in time. The non-unitary equation admits solutions that seem to correspond to the collapse of the wave function.

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Leon Brenig. 2007-04-27. Is quantum mechanics based on an invariance principle?. https://doi.org/10.1088/1751-8113%2F40%2F17%2F012

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