Status: Preprint (not peer reviewed)
Author: Robert W. Harrison
Plain-English Summary
Quantum mechanics is extraordinarily successful at prediction, but after a century it remains interpreted rather than understood. We can calculate what will happen without knowing why it happens. The wave function lives in abstract mathematical space, measurement “collapses” superpositions through mechanisms no one can specify, and entangled particles correlate across space through what Einstein called “spooky action at a distance.”
This paper argues that these mysteries dissolve when quantum mechanics is recognised as fluid dynamics with one additional term. Using the Madelung transformation — a mathematically exact rewriting of the Schrödinger equation published just one year after Schrödinger’s original (1927) — the quantum wave function decomposes into a density field and a velocity field obeying classical fluid equations, plus a “quantum potential” Q that acts as dispersive stress in the medium.
Within the Hydrodynamic Quantum Gravity (HQG) framework, the wave function is identified with the physical order parameter of a dynamic vacuum — not a material substance filling space, but empty space possessing dynamical properties that can be modelled using superfluid mathematics. In this picture, particles are stable wave patterns (oscillons) in the vacuum, the uncertainty principle is wave packet dispersion plus vacuum fluctuation noise, quantisation arises from topological phase constraints (the wave must close on itself), spin is vortex circulation, entanglement is phase coherence through a connected medium, tunnelling is evanescent wave coupling, and measurement “collapse” is bifurcation into attractor basins.
The paper completes a four-paper series covering gravity, electromagnetism, and quantum mechanics as emergent phenomena within a single hydrodynamic framework.
What This Paper Claims (High Level)
- The Schrödinger equation is mathematically equivalent to classical Euler fluid dynamics plus a dispersive stress term (the quantum potential Q), via the exact Madelung transformation.
- The wave function Ψ is identified with the physical order parameter of a dynamic vacuum — its amplitude gives condensate density, its phase gradient gives velocity — and the Born rule (|Ψ|² as probability) emerges from the statistics of defect distribution in the medium.
- Quantisation arises from topology, not operator algebra: charge, angular momentum, and energy levels all follow from the requirement that the phase field be single-valued around closed loops (Onsager-Feynman quantisation).
- Spin is quantised vorticity — fermions are half-quantum vortices, bosons are integer vortices — and the Pauli exclusion principle is topological obstruction rather than arbitrary rule.
- Entanglement is phase coherence through a connected vacuum field, consistent with Bell’s theorem (which rules out local hidden variables but permits the non-local vacuum field).
- Measurement collapse is hydrodynamic bifurcation into attractor basins, requiring no conscious observer — the Born rule emerges as the natural measure over basins of attraction.
Why It Might Matter
If correct, this reinterpretation dissolves the major conceptual puzzles of quantum mechanics — wave-particle duality, the measurement problem, non-locality, and the uncertainty principle — by grounding them in the physical dynamics of empty space rather than abstract postulates. The Madelung transformation is mathematically exact, so all standard quantum predictions are preserved. But in extreme regimes the framework suggests testable deviations: modified inertial mass inside Casimir cavities (if inertia arises from zero-point field interaction), nonlinear corrections at extreme densities, and potential Born rule violations far from equilibrium. The paper completes a four-paper programme deriving gravity, electromagnetism, and quantum mechanics from a single hydrodynamic framework.
Links
PDF (this site):
DOI (Zenodo):
https://doi.org/10.5281/zenodo.18230975
Keywords / Topics
Madelung transformation, quantum potential, Bohm potential, superfluid vacuum, order parameter, wave function ontology, pilot wave, uncertainty principle, zero-point field, quantised vorticity, spin-½, half-quantum vortex, entanglement, phase coherence, quantum tunnelling, evanescent wave, measurement problem, bifurcation dynamics, Born rule, Onsager-Feynman quantisation, walking droplets, Stochastic Electrodynamics
Note: This is a technical preprint made available for discussion and critique. If you have relevant expertise and would like to comment, please reach out.