Is quantum mechanics based on an invariance principle?

Oct, 2006
9 pages
Published in:
  • J.Phys.A 40 (2007) 4567-4584
e-Print:

Citations per year

200620072008021
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