I study a theory called N=4 super Yang-Mills.

When I say this to someone, I have a pretty good idea of how the conversation will go. First, the person will spend a few moments trying to pronounce the theory’s name. Giving up, they'll then try to bring things back to something they’ve heard of.

“N=4 super… umm… so, is that something they’re testing at the Large Hadron Collider?”

“Well, not really, no.”

“Is it astrophysics? Could you see it through a telescope?”

“No, nothing like that.”

“So… what sorts of experiments do you use to test it then?”

“None.”

There are no experiments that could test N=4 super Yang-Mills. Nor will there ever be, because N=4 super Yang-Mills doesn’t describe reality. In an everyday sense, N=4 super Yang-Mills is not “true.”

Yes, I study a theory that isn’t true.

Wait, what? How do you know...

First of all, N=4 super Yang-Mills involves supersymmetry. Some forms of supersymmetry are being searched for by the Large Hadron Collider. But those forms involve symmetries that are broken, which allow the particles to have distinctive characters.

In N=4 super Yang-Mills, supersymmetry is unbroken. Every particle has the same mass and the same charge. Furthermore, in N=4 super Yang-Mills that mass is equal to zero; like photons, the particles of N=4 super Yang-Mills would all travel at the speed of light.

There is no group of particles like that in the Standard Model. They can’t be undiscovered particles, either. Particles that travel at the speed of light are part of the everyday world if they have any interaction with normal matter whatsoever, so if the particles existed, we’d know about them. Since they don’t in N=4 super Yang-Mills, we know the theory isn't “true.”

Even with this knowledge, there is an even more certain way to know that N=4 super Yang-Mills isn't “true": it was never supposed to be true in the first place.

A theory by any other name

More than a few of you are probably objecting to my use of the word “theory” in the last few paragraphs. If N=4 super Yang-Mills isn't part of the real world, how could it possibly be a theory? After all, a scientific theory is "a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment.”

That's courtesy of the American Association for the Advancement of Science. Confused? You must have been talking to the biologists again. Let’s explain.

In biology, a theory is indeed the confluence of multiple lines of real-world observations and evidence. That's precisely what scientists mean when they refer to evolution as a theory. And this is how it works in most other areas of science, from the germ theory of disease to the theory of plate tectonics to the big bang theory. But just because a term is used one way, that doesn't mean it isn't also frequently applied in another.

When something is called a theory, it is being compared to the other great theories of the past. In the case of something like the theory of evolution or the germ theory of disease, this comparison is saying that, like the theory of general relativity or evolution, a theory is so well-tested and so thoroughly incorporated into its field that it comes as close as science gets to final truth. Theoretical physics, on the other hand, often uses a different comparison; like general relativity, a theory in theoretical physics is a mathematical framework, a set of rules that describe the behavior of some system. Unlike general relativity, these systems don’t need to be grounded in experiment and they usually aren't even meant to describe the real world. N=4 super Yang-Mills isn't alone; check out Chern-Simons theory, Topological Quantum Field theories, or N=2 Superconformal Field theories.

What these theories do share is a certain level of rigor. Rather than being arbitrary, they involve precisely defined conditions that collectively give rise to interesting properties. While a theory in the theoretical physics sense isn't “true” in that it doesn’t describe the real world, it is “true” in that two researchers will agree on the theory’s properties. This allows interested parties to build off each other’s work.

While this sort of definition is perhaps most jarring in physics, other fields also define "theory" in a similar way. Essentially, every theory in mathematics is a theory in this sense (see Group theory and Category theory). The same is often true in closely related fields like computer science (Type theory, anyone?).