There are two kinds of theoretical physicists. Some, called phenomenologists, make predictions about the real world. Others, the so-called “formal theorists”, don’t. They work with the same *kinds* of theories as the phenomenologists, quantum field theories of the sort that have been so successful in understanding the subatomic world. But the specific theories they use are different: usually, toy models that aren’t intended to describe reality.

Most people get this is valuable. It’s useful to study toy models, because they help us tackle the real world. But they stumble on another point. Sure, they say, you can study toy models…but then you should call yourself a mathematician, not a physicist.

I’m a “formal theorist”. And I’m very much not a mathematician, I’m definitely a physicist. Let me explain why, with an analogy.

As an undergrad, I spent some time working in a particle physics lab. The lab had developed a new particle detector chip, designed for a future experiment: the International Linear Collider. It was my job to test this chip.

Naturally, I couldn’t test the chip by flinging particles at it. For one, the collider it was designed for hadn’t been built yet! Instead, I had to use simulated input: send in electrical signals that *mimicked* the expected particles, and see what happens. In effect, I was using a kind of toy model, as a way to understand better how the chip worked.

I hope you agree that this kind of work counts as physics. It isn’t “just engineering” to feed simulated input into a chip. Not when the whole point of that chip is to go into a physics experiment. This kind of work is a large chunk of what an experimental physicist *does*.

As a formal theorist, my work with toy models is an important part of what a theoretical physicist *does*. I test out the “devices” of theoretical physics, the quantum-field-theoretic machinery that we use to investigate the world. Without that kind of careful testing on toy models, we’d have fewer tools to work with when we want to understand reality.

Ok, but you might object: an experimental physicist does eventually build the real experiment. They don’t just spend their career on simulated input. If someone only works on formal theory, shouldn’t that at least make them a mathematician, not a physicist?

Here’s the thing, though: after those summers in that lab, I didn’t end up as an experimental physicist. After working on that chip, I didn’t go on to perfect it for the International Linear Collider. But it would be rather bizarre if that, retroactively, made my work in that time “engineering” and not “physics”.

Oh, I should also mention that the International Linear Collider might not ever be built. So, there’s that.

Formal theory is part of physics because it cares directly about the goals of physics: understanding the real world. It is just one step towards that goal, it doesn’t address the real world alone. But neither do the people testing out chips for future colliders. Formal theory isn’t always useful, similarly, planned experiments don’t always get built. That doesn’t mean it’s not physics.

Steven MeyersonWhat about being a mathematical physicist, as in the journal by that name? What distinguishes mathematical from theoretical physicists?

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4gravitonsPost authorInterdisciplinary fields like that are hard to classify. But in general, when someone calls themselves a mathematical physicist it’s because they’re closer to the norms and interests of mathematics: more likely to prove things than calculate things, more interested in working directly with mathematicians and more up-to-date on current topics in mathematics.

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Steven MeyersonSo they might develop purely mathematical aspects of a physical theory not yet directly applicable. Given the controversy, could we describe string theorists as mathematical physicists?

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4gravitonsPost authorAgain, “mathematical physicist” vs. “formal theorist” is really more about norms than whether the theories they study are realistic or not. Some string theorists are fairly described as mathematical physicists, and would describe themselves that way, others aren’t. Whether the theory is directly applicable yet doesn’t really factor into it.

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Steven MeyersonThanks for the clarification!

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Madeleine BirchfieldBefore the 20th century, there wasn’t a clear distinction between theoretical physics and mathematics. Frequently, the theories of Newtonian mechanics and fluid mechanics would be taught under an applied mathematics department in universities, rather than in a physics department. This is partially because many of the mathematicians and theoretical physicists were largely the same people, with figures like Euler, Gauss, Laplace, Riemann, Cauchy, Hamilton, Clifford, Gibbs, and Poincare having contributed to mathematics in order to resolve issues in theoretical physics. A divide between mathematics and theoretical physics formed in the 20th century as mathematicians such as Hilbert, Russell, Peano, and Tarski turned instead to focus upon axiomatics and the foundations of mathematics, which are not of much interest to theoretical physicists.

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