Solitons are stable localized solutions of nonlinear field theories that exhibit many particle-like properties, including well-defined energy, momentum, and inertial mass. Whether quantum dynamics can emerge from such classical field configurations remains an open question. Here we consider a relativistic nonlinear field theory that supports stable solitons and show analytically that a self-generated spatiotemporally chaotic background induces fluctuations in the soliton's momentum and position that satisfy an exact uncertainty relation. The value of the effective Planck constant is determined by the amplitude of the background fluctuations and is independent of the soliton properties. By analogy with the non-relativistic case, from this uncertainty principle one can argue that ensembles of classical relativistic particles obeying such a relation could exhibit relativistic quantum dynamics. We test this prediction by comparing the evolution of large ensembles of solitons moving on a spatiotemporally chaotic background with the corresponding solution of the Klein–Gordon equation. The agreement is found to be excellent over the entire evolution of relativistic Gaussian wave packets. Our results provide a concrete nonlinear field-theoretic realization of the exact uncertainty principle and establish a connection between relativistic soliton dynamics, spatiotemporal chaos, and quantum ensemble behavior.
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