Physics is like . . . physics: Teaching by analogy

There’s a quote I’ve seen attributed to John Wheeler — possibly apocryphal, but then again, aren’t all good quotes?

If you are not completely confused by quantum mechanics, you do not understand it.

This is a sensible tenet, and to be honest, if you’re willing to accept it, you’re halfway to understanding the subject! Quantum mechanics does not make sense to those of us used to living in the everyday world of people and pastries and trains and dogs and books, a world we think of as normal. Yet we know that many phenomena we observe — things appearing to be in exactly one position at any point in time, objects having definite properties — are profoundly abnormal. They don’t show us what the universe is really like.

Most people are content to simply nod at this and go about their business, until the next major physics discovery is announced and quantum mechanics becomes interesting again to the public. But there are those few who shrug aside intuition and brave the dangers of uncommon sense to try to understand the thing, if, in fact, it is possible to understand. How do they learn such a bizarre subject — or, to be more precise, how are they taught?

I am a student embarking on equally bizarre journeys into the beautiful and counterintuitive realm of physics, and so I consider myself one of those lucky few. In my first college physics course last fall — special relativity and introductory quantum mechanics — two things were emphasized: Understanding the material and understanding how to explain it to others. The job of a scientist is to figure out how the universe works, to be one of those pushing the frontiers of human knowledge. But that job is pointless if this knowledge can’t be explained, at some level, to the average person! For a good physicist, words are as good as equations when you’re trying to teach someone.

Analogies in particular seem to be a favorite tool. After all, if you can take something bizarre and connect it to something not-so-bizarre, you’ve made things much simpler. In the teacher’s battle for truth, it should be the weapon of choice. The problems, though, start when the connections fail. Consider, for instance, the wisdom of Randall Munroe:

xkcd. Image used under the Creative Commons Attribution-NonCommercial 2.5 License.

Cueball is trying to use the famous (infamous?) rubber sheet analogy:

  1. Take your favorite blanket or bedsheet. Hold it taut between four poles.
  2. Place a heavy object — preferably, a bowling ball — somewhere on the sheet.
  3. The weight of the ball will curve the sheet, just like how matter curves space-time. That’s general relativity!

Not so fast. As one of the students realizes, there’s a reason our bowling ball is pulled down: the gravity of the Earth. If you created this setup far away from any other matter, the sheet wouldn’t be bent by the bowling ball at all! No massive objects (e.g. the ball) would curve space-time (the bedsheet). J’accuse, Professor Cueball!

Yep. The analogy breaks down when you look at it too closely. That’s not to say that it isn’t a good one; it does explain, to some extent, what physicists mean when they talk about the curvature of space (although it doesn’t distinguish between intrinsic and extrinsic curvature. But it also breeds misconceptions, which are often harder to fix!

Image from Misconceptions About the Big Bang, Charles Lineweaver and Tamara Davis

Another of my favorites is the expanding-universe-as-a-balloon analogy. On large scales, our universe is expanding, and that expansion is accelerating. However, everything — again, on large scales — is moving away from everything else. This seems counterintuitive at first; where is that extra space coming from? Here, the analogy du jour is to compare the universe to the surface of a balloon being blown up. Galaxies and galaxy clusters are dots on its surface. When the balloon gets larger, all of the galaxies move away from each other, and the farther away they are, the faster they move apart.

There are two common misconceptions that I’ve seen arise from this:

  1. The universe is closed.
  2. There’s some extra dimension into which the universe is expanding.

Currently, we don’t have evidence to support the first of these, and outside theories of large extra dimensions, we have no reason to suppose the second.

It becomes even harder to make good analogies when we venture into quantum mechanics, because many phenomena simply have no real-world counterparts. You can’t mimic Schrödinger’s cat in your basement, for instance, and even the double-slit experiment doesn’t seem to make any sense. Sure, there are some good analogies for quantum mechanical behavior, but they all fall apart at some level.

Are we to give up on using analogies to try to make strange things understandable? Of course not! If physics teachers resort to simple equations without trying to make them make some sort of sense, then we lose all hope of a conceptual understanding of physics, and concepts are what transform esoteric knowledge into easier-to-understand ideas. Getting rid of analogies would set science education back substantially.

At the same time, it’s important to explain the limitations of any given explanation. It’s really easy to get confused by physics; it’s happened to me many times. To ease this confusion, though, we must be conscious of the limitations of words, and the downsides of resorting to comparisons with the “normal” world. Only then can we clear up misconceptions once and for all — before they form in the first place.

Science has no point without a scientifically literate public. That’s something that’s all too easy to forget.