From Robustness to Stabilization: Why the Physical World Requires Nonlinear Dynamics
Abstract
We argue that the existence of robust, reproducible physical properties — the minimal condition for empirically grounded physics — requires a nonlinear generative dynamics. The argument proceeds in three steps. First, the objectivity postulates (established in [33]) demand that properties form *robustness classes*: equivalence classes of configurations yielding the same macroscopic outcome (Definition 1, MRL). Second, the dispersive instability theorem (RAGE) entails that no linear evolution on unbounded domains can sustain such classes; decoherence presupposes the robust structures it purports to explain. The only resolution is active nonlinear stabilization (Definition 2, SSR). Third, a self-trapped excitation acquires a discrete vibrational spectrum, so quantization emerges as a *consequence* of stabilization (Corollary 1, EDC). Applying the SSR as a filter within a *Dynamical Ledger* — five independently motivated constraints — and invoking the Derrick–Hobart virial identity and the Gisin–Polchinski no-signaling bound, we eliminate all candidate field theories but three (Theorem 2): nonlinear Dirac (Soler), chiral sigma (Skyrme), and their self-consistent coupling (CQSM). Six competing interpretive frameworks are likewise eliminated (Propositions 4–9). We conclude that ψ is injective (ψ-ontic), non-surjective (incomplete), and operationally epistemic within the Harrigan–Spekkens framework.
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BibTeX
@misc{dechery2026from,
title = {{From Robustness to Stabilization: Why the Physical World Requires Nonlinear Dynamics}},
author = {Fabien Déchery},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05854377v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - From Robustness to Stabilization: Why the Physical World Requires Nonlinear Dynamics
AU - Fabien Déchery
PY - 2026
DA - 2026/10/29
PB - HAL
UR - https://hal.science/hal-05854377v1
AB - We argue that the existence of robust, reproducible physical properties — the minimal condition for empirically grounded physics — requires a nonlinear generative dynamics. The argument proceeds in three steps. First, the objectivity postulates (established in [33]) demand that properties form *robustness classes*: equivalence classes of configurations yielding the same macroscopic outcome (Definition 1, MRL). Second, the dispersive instability theorem (RAGE) entails that no linear evolution on unbounded domains can sustain such classes; decoherence presupposes the robust structures it purports to explain. The only resolution is active nonlinear stabilization (Definition 2, SSR). Third, a self-trapped excitation acquires a discrete vibrational spectrum, so quantization emerges as a *consequence* of stabilization (Corollary 1, EDC). Applying the SSR as a filter within a *Dynamical Ledger* — five independently motivated constraints — and invoking the Derrick–Hobart virial identity and the Gisin–Polchinski no-signaling bound, we eliminate all candidate field theories but three (Theorem 2): nonlinear Dirac (Soler), chiral sigma (Skyrme), and their self-consistent coupling (CQSM). Six competing interpretive frameworks are likewise eliminated (Propositions 4–9). We conclude that ψ is injective (ψ-ontic), non-surjective (incomplete), and operationally epistemic within the Harrigan–Spekkens framework.
ER -