| > So many significant digits includes a level of self-consistency of the model No, that's incorrect. The specific measurement -the most accurate scientific prediction humans have ever made, the anomalous magnetic moment- is only to 1 in 10 trillion. The magnetic moment (think moment of inertia) is the ratio of force from the magnetic field to the mass of the electron. You put an electron into a magnetic field, and it'll turn to face the field at a certain speed. If you stick the electron in a vacuum, it overshoots (because of rotational momentum) and ends up wobbling back and forth at a specific frequency. That's how MRIs work; they make a big magnetic field (stronger on one end) and then measure how many electrons are wobbling in different areas, since the electrons in high-strength fields wobble faster. Specifically, you expect the wobble to get ~2.8025 GHz (similar to a microwave oven) faster for every 1000 gauss (please, no jokes about teslas). It's very convenient to measure a difference in frequency, since you can just measure the drift over time. Because that frequency is relatively high it takes about 30 minutes for the frequency to drift off by a half-cycle and totally cancel out your reference. And it's super easy to get a reference frequency, too. It's just the charge of an electron divided by 2x the mass of an electron. Did you do this experiment in physics class? https://www.youtube.com/watch?v=Kcn2VgBNJjg Then you measured the charge/mass ratio of an electron. A clock that's accurate to 1 in 10 trillion is also not a big deal, although unless you have an oscilloscope in your house its probably more accurate than any clock you own. Still, you can buy a better Phase Locked Loop for a couple bucks. If you just wanted to measure the difference, you don't need that much precision, though. The correction from quantum mechanics is pretty large, relatively speaking: ~0.16%. Even the next several digits are super easy, and it's only those last ones that you really need to bust out the liquid helium. Lawrence and Livingston made the first cyclotron out of literal junk: https://upload.wikimedia.org/wikipedia/commons/6/61/4-inch-c... And it really doesn't take much more than junk to get to that 0.16% accuracy that lets you see that a classical prediction of the electron is just VERY wrong. But if you listen to those wizards with the bongos, suddenly they're really, really right about what that difference is: https://en.wikipedia.org/wiki/Vertex_function |
