What’s the difference between a model and an explanation?

Suppose you cared about dark matter. You observe that things out there in the universe don’t quite move the way you would expect. There is something, a consistent something, that changes the orbits of galaxies and the bending of light, the shape of the early universe and the spiderweb of super-clusters. How do you think about that “something”?

One option is to try to model the something. You want to use as few parameters as possible, so that your model isn’t just an accident, but will actually work to predict new data. You want to describe how it changes gravity, on all the scales you care about. Your model might be very simple, like the original MOND, and just describe a modification to Newtonian gravity, since you typically only need Newtonian gravity to model many of these phenomena. (Though MOND itself can’t account for all the things attributed to dark matter, so it had to be modified.) You might have something slightly more complicated, proposing some “matter” but not going into much detail about what it is, just enough for your model to work.

If you were doing engineering, a model like that is a fine thing to have. If you were building a spaceship and wanted to figure out what its destination would look like after a long journey, you’d need a model of dark matter like this, one that predicted how galaxies move and light bends, to do the job.

But a model like that isn’t an explanation. And the reason why is that explanations generalize.

In practice, you often just need Newtonian gravity to model how galaxies move. But if you want to model more dramatic things, the movement of the whole universe or the area around a black hole, then you need general relativity as well. So to generalize to those areas, you can’t just modify Newtonian gravity. You need an explanation, one that tells you not just how Newton’s equations change, but how Einstein’s equations change.

In practice, you can get by with a simple model of dark matter, one that doesn’t tell you very much, and just adds a new type of matter. But if you want to model quantum gravity, you need to know how this new matter interacts, not just at baseline with gravity, but with everything else. You need to know how the new matter is produced, whether it gets its mass from the Higgs boson or from something else, whether it falls into the same symmetry groups as the Standard Model or totally new ones, how it arises from tangled-up strings and multi-dimensional membranes. You need not just a model, but an explanation, one that tells you not just roughly what kind of particle you need, but how it changes our models of particle physics overall.

Physics, at its best, generalizes. Newton’s genius wasn’t that he modeled gravity on Earth, but that he unified it with gravity in the solar system. By realizing that gravity was universal, he proposed an explanation that led to much more progress than the models of predecessors like Kepler. Later, Einstein’s work on general relativity led to similar progress.

We can’t always generalize. Sometimes, we simply don’t know enough. But if we’re not engineering, then we don’t need a model, and generalizing should, at least in the long-run, be our guiding hope.