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Classical mechanics as nonlinear quantum mechanics

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arxiv 0707.2319 v1 pith:QOUXAYP6 submitted 2007-07-16 quant-ph hep-th

classification quant-phhep-th
keywords mechanicsclassicalinterpretationnonlinearquantumequationlineararbitrary
verification ladder T0 review T1 audit T2 compute T3 formal
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All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum observables for probabilistic classical particles

    quant-ph 2026-07 conditional novelty 5.0 of 10

    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.

  2. Classical probabilistic realisation of quantum double-slit interference

    quant-ph 2026-07 conditional novelty 5.0 of 10

    Classical probability distributions over complex scalar fields realize Schrödinger dynamics and double-slit interference for a quantum particle via conserved-charge subsystems.

  3. Quantum mechanics for classical transport equations

    quant-ph 2026-05 unverdicted novelty 5.0 of 10

    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.

  4. Quantum field theory for classical fields

    quant-ph 2026-03 conditional novelty 4.0 of 10

    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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