Bohmian mechanics
Bohmian mechanics is the fully worked-out, mathematically precise version of pilot-wave theory, developed in detail by David Bohm and later sharpened by John Bell and others. It is a complete hidden-variable theory in the original sense Einstein hoped for: the wavefunction is supplemented by extra variables — the actual positions of all the particles — so that the world has a definite state at every instant, whether or not anyone is measuring.
The theory has exactly two equations. The wavefunction obeys the ordinary Schrodinger equation, exactly as in standard quantum mechanics. The particle positions obey a separate guidance equation that reads off their velocities from the wavefunction. Together these say everything: there is no separate collapse postulate, no special measurement axiom, and no need to invoke an observer. Measurement is just an ordinary physical interaction between particles, governed by the same two laws.
Bohmian mechanics is valuable as a clean existence proof: it shows, against decades of loose claims, that a deterministic theory of particles with definite trajectories can reproduce every prediction of quantum mechanics. Its honest costs are an explicit, irreducible nonlocality and a privileged role for position over other quantities. It is not a fringe escape from quantum weirdness so much as a precise, if unfashionable, way of facing it.
Two laws and nothing else: the Schrodinger equation for ψ, the guidance equation for the real positions Q.
Pictures of smooth Bohmian trajectories can be drawn, but those exact paths are not directly observable; measuring a particle's path disturbs it, so the trajectories are a feature of the theory, not a thing you can photograph.