# Thanksgiving

This year we give thanks for an idea that is absolutely crucial to how our understanding of nature progresses: effective field theory. (We’ve previously given thanks for the Standard Model Lagrangian, Hubble’s Law, the Spin-Statistics Theorem, and conservation of momentum.)

“Effective field theory” is a technical term within quantum field theory, but it is associated with a more informal notion of extremely wide applicability. Namely: if we imagine dividing the world into “what happens at very short, microscopic distances” and “what happens at longer, macroscopic distances,” then *it is possible to consistently describe the macroscopic world without referring to (or even understanding) the microscopic world*. This is not always true, of course — our macroscopic descriptions have very specific domains of applicability, past which the microscopic details begin to matter — but it’s true very often, for a wide variety of situations with direct physical relevance.

The most basic examples are thermodynamics and fluid mechanics. You can talk about gasses and liquids very well without having any idea that they are made of atoms and molecules. Once you get deep into the details, we start talking about effects for which the atomic granularity really matters; but there is a very definite and useful regime in which it is simply irrelevant that air and water are “really” made of discrete units rather than being continuous fluids. Fluid mechanics is the “effective field theory of molecules” in the macroscopic domain.

How awesome is that? If it weren’t for the idea of effective field theory, it’s hard to imagine how we would ever make progress in physics. You wouldn’t be able to talk about atmospheric science without knowing all the details of microscopic physics (known in the trade as the ultraviolet completion), all the way down to the Planck scale! Fortunately, the universe is much more kind to us.

In particle physics, this idea is absolutely central. Protons, neutrons, and pions constitute an effective field theory that describes how quarks and gluons behave over sufficiently large distances. Another great example comes from Enrico Fermi’s theory of the weak interactions. Back in the 1930’s, Fermi proposed a theory that made use of the new “neutrino” particle. It involved processes that looked like this interaction of a proton plus electron converting into a neutron plus neutrino.

Nowadays we know better. What’s really going on is that the proton is made of two up quarks and a down quark, while the neutron is made of two downs and an up. The electron exchanges a *W* boson with one of the quarks, converting into an electron neutrino in the process.

But the miracle is: it doesn’t matter. Knowing that the weak interactions are “really” carried by *W* bosons is completely irrelevant, as long as we are concerned only with large distances. In quantum mechanics, large distances correspond to low energies. (Remember that the energy of a wave decreases as its wavelength increases; quantum mechanics is all about waves.) So for low-energy processes, the effective field theory provided by Fermi is all you need to know about the weak interactions.

The universe is kind, but that kindness comes at a price. Sometimes you *want* to care about the microscopic realm — for example, if you’re a physicist trying to figure out what is going on down there. When we look at spacetime on length scales of 10^{-33} centimeters, do we see vibrating strings, or noncommuting matrices, or spin networks, or what? Hard to tell, because it makes no difference at all to the large-distance/low-energy physics we can actually observe.

That’s okay. A world described by a succession of effective field theories of ever-higher resolution helps us make sense of the world, while leaving physicists plenty of puzzles to think about. Very deserving of our thanksgiving.

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