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 Schrödinger 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 wavefunction.
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