{"id": "card_n_810d857d886e", "kind": "note", "title": "Madelung hydrodynamics — quantum mechanics as a probability fluid", "body": "Write ψ = √ρ·e^(iS/ħ) and the Schrödinger equation becomes fluid dynamics of the probability\ndensity ρ = |ψ|²: a continuity equation with velocity v = ∇S/m, plus an Euler equation carrying a\n'quantum potential.' The interference and tunnelling of QM are the flow of this fluid. Which fluid\nis ontologically real (Bohmian pilot-wave) is an interpretation — refused as unsealable.", "source": {"label": "Concordance assay — 2026-07-08", "url": "https://narrowhighway.com/s/8a3d0e4b4c8af33851fc97658b7af1f9631e8a770708a245234f2226f076d694", "ref": "madelung", "authority_tier": "engine_derived"}, "shelf": "science", "box": "fluid_probability_dynamics", "bands": ["madelung", "quantum hydrodynamics", "schrodinger", "bohmian", "pilot wave", "quantum potential"], "connections": [{"to_card_id": "card_n_8530c72a2201", "relationship": "instantiates", "origin": "assay_2026_07_08"}], "author": "engine", "created_at": "2026-07-09T21:52:14.887408+00:00", "updated_at": "2026-07-09T21:52:14.887408+00:00", "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "metrics": {"paperclips_count": 0, "helpful_count": 0, "not_helpful_count": 0, "cite_count": 0, "walks_through_count": 0, "flagged_count": 0}, "source_hash": "a18c06333f9f1a92eabb515b66c43f09407763540b8c8c6259db549068964d68"}