Excellent Approximations and Lying to Children

In which I talk about the common complaint that we teach students physics that “isn’t true,” and the limits on that statement.

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Frequent commenter Ron sent me an email pointing to this post by David Reed on “What we “know” that t’aint so…. and insist on teaching to kids!”:

he science we teach is pretty old. Mostly 19th century ideas about the world around us are taught as “facts” with little but anecdotal data to support it. We teach it via an ontology that replays the history of science, thus the newest and most powerful scientific understandings are viewed as “too advanced”. If it weren’t so widely discredited, we would be teaching K-12 kids about phlogiston first, and general chemical oxidation reactions second, just as one example of that.

We don’t teach kids ancient Greek and French cave drawing first, do we?

I’ve heard lots of reasons for teaching “old” science, and old models and definitions taught as facts, over the years, and the reasonsnever really made a lot of sense. They certainly don’t make sense today. If we rethink the whole enterprise of what we teach as science, we have a real opportunity – perhaps a bigger opportunity than the big postwar drive towards science surrounding the Kennedy space program.

This is a complaint that comes up a lot, particularly in physics, which is more prone to a historical approach than some other sciences. It’s got a certain appeal– the reason I’m a professional physicist is quantum mechanics, not blocks sliding on inclined planes. But in the end, I think it’s misguided, because it relies on the common misconception that approximations are wrong.

To see what I mean, let’s look at his two examples of failures of the historical approach:

1) Is the Universe’s geometry Euclidean? We teach Euclidean geometry under the unadorned name “Geometry” as if it were foundationally correct. And we teach physics (including elementary astrophysics and cosmology) as if the universe were Euclidean. But by the end of the 20th century it’s become pretty clear that the universe’s geometry is non-Euclidean. That’s what Einstein proposed in the first decade of the 20th century, and more than 100 years later, it’s pretty clear that he was right in rejecting Euclid. Many (but not necessarily all) of the theorems taught in High School geometry also can be derived without using the parallel postulate in their proof – and non-Euclidean geometry need *only* be complicated to people who have learned Euclidean geometry first.. That postulate, however, is almost certainly *scientifically* wrong…. do we teach geometry according to Euclid because it’s always been taught that way? If so, we should put a caveat in the front of the book that we are teaching something that kids should forget about when they learn more about physics? [Euclidean geometry is a consistent formal theory, but teaching it first is profoundly misleading, if our universe is not that way.]

First of all, the initial question is too vague to do much with. Is the geometry of the universe Euclidian? On what scale? On very small scales, geometry will always appear Euclidean– that’s one way of phrasing the principles of general relativity. Any observer, no matter where they are, will see space inn their immediate vicinity as flat (granted, the range that qualifies as “immediate vicinity” can get very small near a black hole…). On the very largest scales, to the best of our ability to measure it, Euclidian geometry also appears to work– the universe as a whole is extremely close to flat, and there are reasons to believe that there is no overall curvature to space.

So the question only makes sense on a sort of intermediate scale, about the size of planets and stars and things. And there, it’s true, space is curved by the presence of mass. We have any number of experimental measurements confirming the predictions of general relativity, to exquisite precision.

In a narrow, technical sense, then, it’s true that the geometry of the universe is not Euclidian. But the thing is, Euclidian geometry is an outstanding approximation. You need to go to fairly extreme circumstances to see any appreciable effects of the curvature of spacetime. The effect on the perihelion shift of Mercury is a bit less than 10% of the prediction you would get from classical physics (the gravitational influence of all the other planets), and that’s pretty much the biggest effect of spacetime curvature you can see within the solar system. Other sorts of things you can measure are the effect of the Sun’s gravity on radio signals from the Cassini probe, where general relativity shifts the frequency of the 8,000,000,000 Hz carrier by about 4 Hz. If you don’t want to leave Earth, you’ll need an ultra-precise atomic clock to measure the gravitational time dilation, or a tall building and a Mössbauer spectrometer.

So, yes, it’s true that Euclidian geometry is only a special case of the mroe general geometry of spacetime. But it’s an amazingly good approximation to any situation you will ever encounter. Which is why we teach it to children– because it’s vastly simpler, and the cases where it doesn’t work are very far from everyday experience.

Reed’s other example isn’t much better:

2) Is there nothing? One of the most painful parts of physics teaching these days is the conceit used in its teaching that a true “vacuum” exists or that experiments can be perfectly isolated… Teaching kids the idea that they can create conditions of complete vacuum, with no fields, no matter/energy, … except for, say, a couple of billiard balls representing masses has a real downside. The downside is that we have no evidence that such a vacuum exists or can exist.

Again, strictly speaking, it’s true that there’s no such thing as perfectly empty space– quantum electrodynamics tells us that the vacuum necessarily contains a vast number of virtual particles fluctuating their way in and out of existence. But the practical consequences of this are minimal for any situation you’re likely to ever encounter. The Casimir effect is real, and the electron g-factor isn’t exactly 2, and we can measure these things to extremely good precision. But none of these effects will have any measurable impact on the motion of everyday objects.

There’s something closer to a good point here, when Reed notes that “It’s very hard to differentiate “nothing” from “I haven’t found any way to measure all aspects of reality yet, but maybe there is something there that we haven’t managed to notice.”” But again, this is a narrow technical point, and does not change the fact that treating space with no macroscopic objects in it as empty is an excellent approximation.

And this is the point. We teach kids “obsolete” physics because it works. There are important situations where classical physics breaks down, true, but they’re limited in number, and not really important for most of the situations people learning physics will ever encounter. Even people who routinely make use of physical science in their work will almost never need to use non-Euclidian geometry or think about QED.

I’ve talked before about the concept, borrowed from The Science of Discworld of lies-to-children, namely the simplified versions of how the world works that we teach to kids who aren’t quite ready to handle the full thing. These provide the basic understanding that they need right away, and leave the greater complexity for a time when they’re ready for it. My usual example of this is the “How a bill becomes a law” civics explanation American schoolchildren get in grade school: both houses of Congress pass a bill, the President signs it, and it becomes a law. That’s the basic level of knowledge you need when you’re in elementary school, and all the stuff about cloture motions and reconciliation rules and conference committees can come later.

Classical physics is like that, only a billion times more so. The “Schoolhouse Rock” model of the legislative process fails pretty dramatically these days, because you can’t really understand the news without knowing something about the filibuster. Classical physics, though, will work for the vast majority of situations any student is likely to encounter (really, the only place it breaks down that’s at all significant is when you start talking about the interaction of light and matter). And it’s vastly easier to work with.

As I said at the start of this post, there is a certain appeal to the idea that we need to reinvent physics instruction to be more “modern” from the beginning. There’s definitely some value in reconfiguring college physics to look less like high school physics with a more casual attendance policy, and there are places where you can put in some hooks to let students know they’re not getting the whole story. But the idea that we’re doing students a disservice by teaching them classical physics is just nonsense. Classical physics may not be a complete theory of reality, but it’s an excellent approximation of reality.

And while I probably bear some responsibility for promoting the general idea that classical physics has been superseded, by writing books emphasizing the weird and counterintuitive stuff in relativity and quantum mechanics, I’ve come to think that it’s a mistake to think of modern topics as the only attractive elements of physics. While quantum mechanics and relativity are some of the weirdest and coolest things around, you can do an awful lot of neat stuff with just classical physics. If you don’t believe me, go read Rhett Allain’s Dot Physics, which is full of awesome stuff that rarely if ever requires physics beyond basic classical mechanics.