GoKawiilWith this machinery, Wilson solved the mystery of why many magnets magnetize at the same rate. The zooming-out step passes through a point at which all magnets look the same, whether their atoms are arranged in cubes or tetrahedra. All that matters is that the atoms have a symmetry that lets them point in any direction. (Magnets whose atoms are pinned down to spin in a plane, for instance, magnetize at a different rate.)
Wilson’s work also clarified why a few properties, like the temperature at which the magnetization takes place, vary wildly from magnet to magnet, even when they have the same spin symmetry. These properties are related to the size of the few surviving terms.
The symmetries tell you the overall shape of the terms that stay large, but not exactly how large they are. The sizes of these terms act like threads lightly tethering the macroscopic world to the microscopic one.
Over the following decades, Wilson’s machinery seeped into many areas of physics. Physicists used Wilson’s calculations to justify the previously murky mechanics of quantum field theory, which treats each particle as a wave while washing out the less significant effects of the smallest vibrations. Wilson’s contributions also shaped modern theories of certain phases of matter, like solids.
But when it came to fluids, scientists remained stuck. Their defining symmetries weren’t yet clear.
How To Define a Fluid
The first break in the case came in the 2000s, when a group of cosmologists was using Wilsonian thinking to develop an effective field theory for the universe as a whole. As they did so, they stumbled upon a key insight: The universe’s expansion breaks a crucial symmetry in space-time.
In general, space and time have no reference point against which you can measure speed. If you’re in a windowless spaceship, you can’t tell whether you’re moving quickly, slowly, or not at all. Space-time has a symmetry with respect to speed.
But in the expanding universe, there is a special reference point against which you can discern a motion: It’s the one in which the expansion of space itself moves galaxies uniformly away from you. If you were to leave your galaxy in a spaceship and travel against this cosmic recession in a particular direction, you would see the galaxies in front of you recede more slowly than the galaxies behind you.
Fluids, the group noted, break the same symmetry. If you’re immersed in a resting liquid, you can tell you’re at rest. And if you start to swim, you’ll feel the drag of the fluid as it moves past you. The resting fluid, like the expanding universe, lacks the underlying speed symmetry of space-time. Meanwhile, it has other standard space-time symmetries; rotations and translations don’t change the fluid.
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