Reductionism Is Not Fundamentalism

Ashutosh Jogalekar has a response to my post from yesterday complaining about his earlier post on whether multiverses represent a philosophical crisis for physics. I suspect we actually disagree less than that back-and-forth makes it seem-- he acknowledges my main point, which was that fundamental theoretical physics is a small subset of physics as a whole, and I don't disagree with his point that physics as a discipline has long been characterized by a reductionist sort of approach-- always trying to get to smaller numbers of fundamental principles.

Our real point of disagreement, I think, is more subtle, and has to do with the implications of that reductionist approach. He seems to take the view that this necessarily entails always striving for greater simplicity, while I'm happy to stop at a somewhat higher level. Not to put words in his mouth, but a kind of extreme version of this line of thought is seen in the comment from RM, putting words in the mouth of a certain class of other physicists, who would claim that the sort of physics I do isn't really physics, but stamp collecting.

Jogalekar isn't that crass, but goes for more high-class antecedents, telling a story about Oppenheimer, who felt thatfinding fundamental equations was the only real physics, and "the study of particular solutions of the equations would be a routine exercise for second-rate physicists or graduate students." My feeling is that this probably says more about Oppenheimer and his character flaws than it does about physicists in general, but I will also admit that I don't know all that much about Oppenheimer.

(It's kind of weird, really-- he's an important figure in 20th century physics, and plays a peripheral role in the stories of a lot of people I find more interesting, but somehow, Oppenheimer himself has never seemed all that compelling to me. I'd like to read a good biography of Pauli at some point, but despite the ready availability of a new and fairly well regarded Oppenheimer bio, I'm just not that interested.)

This does raise an interesting question, though, about what exactly characterizes the mindset of a physicist, as distinct from those other, stamp-collecting disciplines. Obviously, I have an interest in avoiding any definition that has those of us who study whole atoms (let alone large collections thereof) classed as chemists with delusions of grandeur, but if I'm not willing to go down the rabbit hole of endless searching for more fundamental laws, what is it that defines physicists?

I spent a bunch of time Wednesday thinking about this, and ended up offering a few comments on it to the general bafflement of my students in introductory E&M, who almost certainly don't read this blog. If you want a bumper-sticker version, though, you can probably go with a line often found pasted over photographs of Einstein in various social-media things, namely that everything should be made as simple as possible, but no simpler.

I've gone on about this before, but when I think about what it means to think like a physicist, I keep circling around the idea of doing the best that you can with the smallest number of inputs. Physicists will treat cows as spherical because you can capture a surprising amount of the essential elements of cow behavior while operating under that approximation. A more complicated model will pick up some additional details, but the spherical model allows a more universal and elegant approach, and gets at the things that cows have in common with horses, sheep, and donkeys (all of which can also be approximated as spheres, to lowest order).

But that commitment to simple rules and general principles does not imply a need to follow that all the way down, or any kind of spiritual connection to people who do. I'm not bothered by the inability of string theorists to come up with an equation for everything that fits on a cocktail napkin, because I can write the Schrödinger equation on the back of a business card, and it's as much of a theory of everything as I need to fill an entire career.

You can take a reductionist approach without reducing things all the way to the Standard Model-- even when they're spherical, after all, cows are composite particles. Working out the consequences of lots of simple particles interacting via simple rules is a fascinating field in itself, and does not entail the abandonment of an essentially reductionist approach. Reducing the rules and particle properties to their essential core is reductionist already.

An anecdote from class Wednesday that might help to illustrate what I'm talking about. We're in the third week of intro E&M, talking about the electric fields of various charge distributions. I pointed out that, really, all you need to know to understand electrostatics is how to calculate the electric field of a point charge; the rest is just calculus. Then we worked through a few examples of how to find the field of some simple symmetric shapes by adding up lots of point charges.

When we were done going over the field from a ring of charge, one of the students, a mechanical engineering major, asked "Why don't you just give us the formula for calculating this for a charge density distribution? Why are we talking about these shapes? I mean, if there's a tiny bump on one side, that formula isn't any good any more."

I tried to explain that the point isn't just to have a process that lets you turn the crank and get an answer, but to get some insight into the essential behavior. It's perfectly true that the formula for the field from a ring of charge doesn't work for a ring of charge with a bump on one side. But if you know how to find the field of a ring, then you can approximate the ring-with-a-bump as a ring with a point charge next to it. And knowing the simple cases gives you a sense of what you ought to expect from the complicated scenario when you turn the crank on the more detailed method. And yeah, the exact details of the final answer might depend on the exact shape of the bump on the side of the ring, but the simple approximation will get you a basic idea, and provides an essential sanity check.

I'm not sure that really convinced him that this was worthwhile, but then, that's probably the difference between the worldview of a physicist and an engineer right there. As a physicist, I want to model cows as spheres and sticky tapes as point charges, and leave the fiddly details to the engineers.

(Meanwhile, the chemistry majors in the class want a comprehensive and memorizable list of formulae covering all the possible shapes we might ask about...)

As to the question of whether multiverses pose a fundamental philosophical problem for physics, I just don't see it. I find the whole thing a little silly, particularly in its more extravagant forms, but I don't think it represents any kind of existential crisis. It's a phase that will shake itself out eventually-- the more precisely defined multiverse models will eventually make predictions, and clever observers and experimentalists will figure out something to test those, and everybody will move on. The less precisely defined and the essentially undefinable forms will fade away, or become philosophy.

Even if I'm wrong, though, if the fundamentalist subfield remains forever as murky as pot smoke in a dorm room, that has essentially zero impact on what people in my field, or the many other thriving subfields of physics, do with our lives. There's a common worldview of sorts, but we're really not drawing philosophical inspiration from quantum gravity theorists. We're too busy doing physics for that.