NASA held a big press conference yesterday to announce that the Gravity Probe B experiment had confirmed a prediction of General Relativity that spacetime near Earth should be “twisted” by the Earth’s rotation. A lot of the coverage has focused on the troubled history of the mission (as did the press conference, apparently), but scientifically it’s very impressive.

The shift measured is very, very small– 0.04 arcseconds over the course of a year, or 0.000011 degrees– but agrees nicely with the predictions of relativity. I’m not sure whether to try to work this into the book-in-progress as I revise it– I suspect it’s too complicated to fit into a sentence or two, and I don’t want to take much more space– but it got me thinking about something that does get said quite a bit, namely relativity’s status as one of the best-tested theories in the history of science.

When you get down to it, there are really only two theories in the running for the title of “The Most Precisely Tested Theory in the History of Science”: relativity and quantum mechanics, specifically quantum electro-dynamics (QED). Both theories predict tiny shifts in quantities that are well known from other theories– the rate of ticking of a clock, or the energy difference between two states of an atom– and in both cases, those predictions have withstood a huge battery of experimental tests. There is no question that both general relativity and QED are correct theories, at least within their well-understood limits. (Somewhat embarrassingly, the two don’t play nice together, so neither works well in contexts where both gravity and quantum effects are important. We can’t access any of those contexts experimentally at present, though.)

So, which of the two is *The* Most Precisely Tested Theory in the History of Science?

It’s a little tough to quantify a title like that, but I think relativity can claim to have tested the smallest effects. Things like the aluminum ion clock experiments showing shifts in the rate of a clock set moving at a few m/s, or raised by a foot, measure relativistic shifts of a few parts in 10^{16}. That is, if one clock ticks 10,000,000,000,000,000 times, the other ticks 9,999,999,999,999,999 times. That’s an impressively tiny effect, but the measured value is in good agreement with the predictions of relativity.

In the end, though, I have to give the nod to QED, because while the absolute effects in relativity may be smaller, the precision of the measurements in QED is more impressive. Experimental tests of relativity measure tiny shifts, but to only a few decimal places. Experimental tests of QED measure small shifts, but to an absurd number of decimal places. The most impressive of these is the “anomalous magnetic moment of the electron,” expressed is terms of a number *g* whose best measured value is:

g/2 = 1.001 159 652 180 73 (28)

Depending on how you want to count it, that’s either 11 or 14 digits of precision (the value you would expect without QED is exactly 1, so in some sense, the shift really starts with the first non-zero decimal place), which is just incredible. And QED correctly predicts all those decimal places (at least to within the measurement uncertainty, given by the two digits in parentheses at the end of that).

The Lamb shift in hydrogen hasn’t been measured quite as well, but is also known to many digits, with a measured value of 1057.864 MHz according to this page, which was the clearest statement a quick Google turned up. And there are some other shifts and corrections that have been measured to similar precision.

Now, admittedly, I’m a little biased, in that the QED experiments are closer to my own areas of physics, but for my money, it’s a more impressive accomplishment to correctly predict a small shift to ten decimal places than a tiny shift to two. So, if I had to name one of the two theories as *The* Most Precisely Tested Theory in the History of Science, Einstein loses to Feynman, Schwinger, and Tomonaga. They’re both amazing accomplishments, though, and nothing else comes close.

(Of course, it should be noted that the two theories are not completely distinct– QED is the result of combining quantum mechanics with special relativity, so Einstein had a hand in both, albeit indirectly. General relativity, though, while it incorporates special relativity, is its own thing, and doesn’t mesh well with QED at all.)