Effective Theory

People can disagree about many deep and fundamental questions, but we are all pretty confident that when we sit on a hard wooden chair it will support us, and that when we take a breath on the surface of the Earth we will take in the oxygen we need to survive.

Yet, ultimately that chair is made of molecules, which are made of atoms composed of nuclei—protons and neutrons—with electrons orbiting them with probability functions in agreement with quantum mechanical calculations. Those electrons are on average very far from the nuclei, meaning from a perspective of matter, they are mostly empty space. And those protons and neutrons are made of quarks bound together by the dynamics of the strong force.

No one knew about quarks until the second half of the 20th century. And despite the wisdom of the ancient Greeks, no one really knew about atoms either until at best a couple of hundred years ago. And of course air contains oxygen molecules and many others, too. Yet people had no trouble breathing air before this was known.

How is that possible? We all work in terms of effective theories. We find descriptions that match what we actually see, interact with, and measure. The fact that a more fundamental description can underlie what we observe is pretty much irrelevant until we have access to any effects that differentiate that description. A solid entity made from wood is a pretty good description of a chair when we go about our daily lives. It’s only when I want to know more about its fundamental nature that we bother to change our description. Really it’s only when we have the technological tools to study those questions that we can test whether our ideas about its underlying nature are correct.

Effective theory is a valuable concept when we ask how scientific theories advance, and what we mean when we say something is right or wrong. Newton’s laws work extremely well. They are sufficient to devise the path by which we can send a satellite to the far reaches of the Solar System and to construct a bridge that won’t collapse. Yet we know quantum mechanics and relativity are the deeper underlying theories. Newton’s laws are approximations that work at relatively low speeds and for large macroscopic objects. What’s more is that an effective theory tells us precisely its limitations—the conditions and values of parameters for which the theory breaks down. The laws of the effective theory succeed until we reach its limitations when these assumptions are no longer true or our measurements or requirements become increasingly precise.

This notion of effective theory extends beyond the realm of science. It’s really how we approach the world in all its aspects. We can’t possibly keep track of all information simultaneously. We focus on what is accessible and relate those quantities. We use a map that has the scale we need. It’s pointless to know all the small streets around you when you’re barreling down a highway.

This notion is practical and valuable. But we should be wary since it also makes us miss things in the world—and in science. What’s obvious is what’s in our effective theory. What lies beyond might be the more fundamental truth. Sometimes it’s only a little prodding that takes us to a richer, more inclusive understanding. Getting outside our comfort zone is how science and ideas advance and what ultimately yields a richer understanding of the world.