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Quantum particles from coarse grained classical probabilities in phase space
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Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of the classical probabilities and choice of observables all features of a quantum particle in a potential follow from classical statistics. This includes interference, tunneling and the uncertainty relation.
Forward citations
Cited by 3 Pith papers
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Quantum observables for probabilistic classical particles
Solutions of the Liouville equation can be rewritten as a Schrödinger equation whose observables are non-commuting 'quantum' operators, reproducing the harmonic oscillator and hydrogen atom spectra as special subsystems.
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Classical probabilistic transport equations are reformulated as quantum systems whose wave function obeys Schrödinger evolution and whose observables include non-commuting operators for statistical quantities.
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Quantum field theory for classical fields
A classical Klein-Gordon field with random initial conditions, described through specially defined fluctuating observables, obeys the functional-integral rules of a quantum field theory.
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