Is quantum mechanics based on an invariance principle?
Oct, 2006Citations per year
Abstract: (arXiv)
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.Note:
- 15 pages
- 03.65.Ta
- Dilatations
- Heisenberg inequality
- invariance
- classical mechanics
- quantum mechanics
- space-time geometry
- mechanics: classical
- space-time: geometry
- quantum mechanics: nonrelativistic
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