Is quantum mechanics based on an invariance principle?

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.

15 pages

References in corpus (5)

• Quantum properties of classical Fisher information
• Schrodinger equation from an exact uncertainty principle
• Gauge Transformations in Quantum Mechanics and the Unification of Nonlinear Schrödinger Equations
• Quantum-classical transition in Scale Relativity
• Exact uncertainty approach in quantum mechanics and quantum gravity

Cited by in corpus (5)

• Generalized quantum potentials in scale relativity
• Modular Schrödinger equation and dynamical duality
• Quantum fluctuations as deviation from classical dynamics of ensemble of trajectories parameterized by unbiased hidden random variable
• On the Fractal Structure of the Universe
• Understanding quantization: a hidden variable model