  This chapter explores a deterministic hydrodynamically-inspired ensemble
interpretation for free relativistic particles, following the original pilot
wave theory conceptualized by de Broglie in 1924 and recent advances in
hydrodynamic quantum analogs. We couple a one-dimensional periodically forced
Klein-Gordon wave equation and a relativistic particle equation of motion, and
simulate an ensemble of multiple uncorrelated particle trajectories. The
simulations reveal a chaotic particle dynamic behavior, highly sensitive to the
initial random condition. Although particles in the simulated ensemble seem to
fill out the entire spatiotemporal domain, we find coherent spatiotemporal
structures in which particles are less likely to cross. These structures are
characterized by de Broglie's wavelength and the relativistic modulation
frequency kc. Markedly, the probability density function of the particle
ensemble correlates to the square of the absolute wave field, solved here
analytically, suggesting a classical deterministic interpretation of de
Broglie's matter waves and Born's rule.
