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It is not the case that Nonlinear classical mechanics systems can constrain the amplification of quantum effects, and these constraints must be evaluated on a case-by-case basis.
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
Batterman's work on asymptotic reasoning shows singular limits between quantum and classical mechanics resist smooth, case-by-case bridging.
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2.
The classical limit of quantum mechanics is mathematically discontinuous, so nonlinear classical constraints cannot straightforwardly bound quantum behavior.
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3.
Invoking classical mechanics to constrain quantum amplification presupposes the very reduction that remains philosophically contested.
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Reason for 2 of 2
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1.
Decoherence theory (Zurek, Joos) shows quantum-to-classical transitions are universal, not system-specific, undermining case-by-case evaluation.
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2.
If decoherence operates at timescales far shorter than classical chaotic amplification, nonlinear constraints become causally irrelevant.
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Reasons Against
1 perspective
Reason against
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1.
Damping due to friction can limit how quickly quantum effects are amplified before being washed out.
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2.
Local finite-time dynamics for each system may not yield any on-average growth in uncertainties.
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