Fluids ran for 200 years on math that ignores atoms, until a rebuild from symmetry
The old math ignores atoms, but a 20-year effort defines fluids by symmetry and shows where the old equations come from.
Quanta Magazine · Theory of Fluids Enters the 21st CenturyPhysics spent the late 1900s getting rewritten from the bottom up. Scientists learned that everyday matter emerges from molecules, which emerge from subatomic particles, which emerge from still stranger stuff, and they rebuilt their theories to match.
Fluids missed that update. They are still governed by the Navier-Stokes equations, a 19th-century set of rules that predicts how liquids and gases flow and swirl.
Those equations work remarkably well, but they leave out the atomic detail. They assume a fluid is perfectly smooth and continuous, no matter how far you zoom in. Real water and air are made up of molecules and atoms, and that grainy nature creates tiny blips in the flow that the classic equations lop off.
As Michael Landry, a physicist at the Massachusetts Institute of Technology, puts it, "Navier-Stokes is very much an approximation," not an exact equation. That left fluid theory an outlier, still not rebuilt around atoms.
Now, after about 20 years of work, physicists have rebuilt it from the ground up. They define a fluid by its symmetries, the basic properties that stay the same under change, and show that the Navier-Stokes equations follow from those symmetries, a result that explains the old equations and points to new fluid behavior beyond them.
Questions people ask
If the old equations ignore atoms, why do they still work so well?
At the scale of wings, weather, and pipes, countless tiny molecular motions largely cancel out on average. The smooth average is so close to what we measure that engineers can design and forecast with it.
What does it mean to pretend a fluid is perfectly smooth?
It means you could keep magnifying a small piece of fluid forever and never find anything lumpy. In reality, magnification eventually reveals molecules and atoms, so the flow has fine grain that the old math smooths away.
Who were Navier and Stokes?
Claude-Louis Navier was a French engineer and George Gabriel Stokes was an Irish physicist and mathematician. In the early 1800s, they upgraded Leonhard Euler's equations from the 1750s, which described perfect fluids with no viscosity, or intrinsic stickiness, to include viscosity and friction, so they could handle real liquids and gases.