Vortices in the Quantum World ✎ express

Original: "The Schr\"{o}dinger equation in the complex plane and quantum entanglement"
· Vassiliy Lubchenko
arXiv:2606.28640 · 2026-06-26 · arXiv non-exclusive · independent analysis · 1 min
In a quantum fluid, probability zeros are whirlpools that govern the flow of energy.

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A regular object moves along a predictable path, like a ball. In the quantum world, a particle is smeared into a probability cloud. To find order in this fog, scientists have recast Schrödinger's equation in the language of flowing water.

The points where the probability of finding a particle is exactly zero turned into whirlpools. Around these funnels, the probability current swirls like water down a drain.

The number of such vortices is always an integer, and that's all you need for precise energy quantization. Previously, level calculations relied on the approximate Bohr–Sommerfeld rule, which often failed. In the new picture, the integer nature of vortices automatically yields the correct spectrum. It also clarifies the origin of the eternal jitter even in a 'still' particle: it's the swirling flow around the zeros. Vortices exist at every point where the particle cannot be, and it is they that determine its energy — much like an invisible whirlpool in a mountain lake sets the water level.

The number of vortex-zeros is always an integer, like the set of notes in a chord determines its sound.

In Dune, navigators manipulate probabilities; perhaps vortex-zeros are knobs you can tug to pull the fabric of reality.

\oint p \, dx = n h
The integral of momentum p over a closed loop equals an integer n times Planck's constant h.
Scientists
Erwin SchrödingerHugh Everett IIIMax BornJulian SchwingerBryce DeWittCarlo Rovelli
Concepts
Schrödinger equation time evolution Bloch's theorem angular momentum field quantum jitters momentum space boundary conditions Birkhoff's theorem Gross–Pitaevskii equation hamiltonian Schwinger effect continuum classical physics position potential hydrodynamics von klitzing constant Heisenberg uncertainty principle quantum state