We explore the hypothesis that both Newtonian and relativistic gravitational phenomena may emerge from critical dynamics in nonlinear relativistic wave fields, in analogy with wave–particle duality in quantum systems. Using a general nonlinear self-adjoint wave Hamiltonian, we construct a set of illustrative toy models in which increasing interaction strength drives a transition from extended, oscillatory waves to localized particle-like excitations. In this framework, gravitational and cosmological effects—including redshift—arise as collective, near-critical wave phenomena rather than as properties of a predefined spacetime geometry. The constancy of the speed of light emerges from nonlinear terms in the dispersion relation, and wave localization provides a common origin for inertial and gravitational mass without requiring a separate equivalence principle. These models also exhibit the absence of singularities (e.g., at the Schwarzschild radius or at r = 0 ) and suggest potential connections between local gravitational behavior and large-scale structure. As a proof of concept, we show how critical-wave effects may alleviate the observed tension between Planck CMB inferences and supernova/Cepheid distance measurements without assuming FLRW metrics or Λ CDM dynamics; the same mechanism provides an alternative simple explanation for the BAO peak in the galaxy distribution function. We emphasize that these results are not proposed as a replacement for general relativity or standard cosmology, but as a conceptual demonstration that nonlinear wave dynamics can reproduce qualitative gravitational and cosmological features, motivating further investigation into emergent-gravity scenarios.
Galinsky et al. (2026) studied this question.