The Overdetermined Discharge Model: A Deterministic, Continuum Mechanics Alternative to Wavefunction Collapse

This paper introduces the Overdetermined Discharge Model (ODM), a strictly deterministic, non-local alternative to standard wavefunction collapse formulated within a continuum mechanics framework. Rather than treating quantum fields as abstract probability amplitudes, we model the vacuum as an unbroken, continuous fluid medium characterized by a global scalar field density and velocity vector field. This model resolves three foundational paradoxes in quantum theory: the measurement problem, Bell's non-locality, and double-slit interference. Apparent quantum randomness is formalized as a localized constraint satisfaction problem driven by micro-scale topological variations in the background medium, modeled via effective stochasticity in the fluid equations. Utilizing a purely spatial variational action functional, we demonstrate how the field's total energy instantly discharges along a singular, non-linear path of least resistance. This framework successfully accounts for instantaneous wave-packet grounding and discrete particle-like detector strikes without violating relativistic causality, providing full quantitative correspondence with standard Schrödinger dynamics.