The Madelung translation

RSI anchors its fluid reading of quantum mechanics in the Madelung transformation (quantum hydrodynamics). It shows that the Schrödinger equation, which governs the wavefunction ψ, can be rewritten exactly as a set of equations for a continuous fluid.

The wavefunction is split into two parts. Its amplitude, R, maps to the fluid density ρ of the Eternal Consonance. Its phase, S, maps to the velocity potential of the fluid's flow. The mathematics then separates into two classical laws.

First is the continuity equation, ∂ρ/∂t + ∇·(ρv) = 0. Standard theory reads it as conservation of probability. RSI reads it as conservation of the medium, which cannot be created or destroyed. The second is the Euler equation, which governs how the fluid moves under external pressure gradients V and internal tension Q. The fluid velocity is the gradient of the phase divided by mass. In RSI, the Aharonov-Bohm phase shift is therefore a shift in the velocity of the medium itself.