Quantum observables for probabilistic classical particles
- URL: http://arxiv.org/abs/2607.13937v1
- Date: Wed, 15 Jul 2026 15:19:49 GMT
- Title: Quantum observables for probabilistic classical particles
- Abstract summary: We propose the use of more robust quantum observables for probabilistic classical particles.<n>The quantum observables are statistical observables which do not take fixed values for a given classical position and momentum.<n>We demonstrate for a general potential how a quantum system emerges from classical statistics.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The classical observables of position and momentum are not well adapted to particles in a microphysical situation where typical probability distributions are characterized by a substantial dispersion. We propose the use of more robust quantum observables for probabilistic classical particles. The quantum observables are statistical observables which do not take fixed values for a given classical position and momentum. Solutions of the Liouville equation are discussed in the quantum formalism for classical statistics. Statistical observables are represented by non-commuting operators. No classical correlation function is defined for these observables and Bell's inequalities do not apply. We demonstrate for a general potential how a quantum system emerges from classical statistics. For the particular cases of a harmonic potential and a Coulomb potential we investigate subsystems which describe all features of a quantum particle. This covers the discrete energy spectrum of the hydrogen atom and quantum harmonic oscillator. We discuss the interference for the double-slit experiment. Conserved statistical observables may also be relevant for the probabilistic dynamics of dust or planets.
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