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Zooming out erases the atoms
A puzzle about metals
Since the 1960s, physicists had puzzled over a property of metals. When a metal is cooled, its atoms eventually align and the metal magnetizes, and the alignment always happens at precisely the same speed, whether the metal is iron, nickel, or cobalt. In the 1970s, Kenneth Wilson, a physicist at Cornell University, developed the method that explained it, a way of building theories called effective field theories. It won him a Nobel prize.
Starting from symmetries
A symmetry is a change that doesn't matter. Rotate a square by 90 degrees and no one will notice, and rotate a circle by any angle at all with the same result. Wilson's method starts by listing the symmetries of a system at the most microscopic level understood. In a magnet, the atoms sit on a grid, so the magnet has to move by one lattice space to look the same, and each atom is free to point in any direction. Symmetries like these fix exactly which mathematical terms belong in the theory.
Zooming out
Then the math zooms out toward the macroscopic level and shows whether each term grows or shrinks. Most shrink nearly to zero, because the mathematical vision blurs and details of individual atoms, or small groups of atoms, become too small to matter. Only the terms tracking broad trends survive, which leaves a short theory of magnetism with almost none of the atomic detail.
Why do different metals magnetize in the same way?
Physicists call this universality. Near the temperature where magnetization appears, atoms are correlated across stretches much longer than the spacing between them, so the quirks of any one atom average away. What remains depends on broad features such as the number of spatial dimensions and the symmetry of the magnetization. The metals still differ in where the transition happens: the Curie temperature is roughly 1040 kelvin for iron, 630 for nickel, and 1390 for cobalt.
How did Wilson turn zooming out into math?
Wilson's approach, known as the renormalization group, repeats one step: average over small blocks of the system, rescale the picture, and rewrite the theory for the blurred version. After each round, some terms in the theory grow and others shrink away. The terms that shrink are called irrelevant, and the ones that grow are called relevant. Wilson received the 1982 Nobel Prize in Physics for this work on critical phenomena.
Where else do effective field theories show up?
Enrico Fermi's 1930s theory of beta decay treated the weak nuclear force as a direct contact between particles. It worked well at low energies, which is what an effective theory does. The full picture, with heavy W and Z bosons carrying the force, was confirmed when those particles were observed at CERN in 1983.
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