Is quantum mechanics based on an invariance principle?

Details Is quantum mechanics based on an invariance principle? Is quantum mechanics based on an invariance principle?

2006-10-27

arxiv.org/abs/gr-qc/0610142v2

J.Phys.A40:4567-4584,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages

Scientific paper

10.1088/1751-8113/40/17/012

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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