And by “we” I really mean the first author (Steve) who did all legwork of analyzing the copious clock data we generate, and had realized that our continuously-running clocks had an advantage over other groups who have been doing these measurements over longer intervals. I helped out a bit with the clock-building (and clock building-building) and thus data generation, and some feedback.

The arXiv version of “Tests of LPI Using Continuously Running Atomic Clocks” was posted (some time ago, sorry this is late) so you can follow along with the home version of the game, if you wish. Keep in mind that I am an atomic physicist, Jim, and not someone who really works with general relativity past the point of including gravitational time dilation in discussions about timekeeping.

One of the tests of general relativity, or specifically of the Einstein equivalence principle, is that of local position invariance. That is, local physics measurements not involving gravity must not depend on one’s location in space-time. Put another way, there shouldn’t be any effects other than gravitational ones if you do an experiment in multiple locations — the gravitational fractional frequency shift should only depend on the gravitational potential: \(frac{Delta f}{f} = frac{Phi^2}{c^2}\)

So you look for a variation in this. One possibility of investigation is to compare co-located clocks of different types as the move to a new location, that could behave differently if LPI were violated. This can arise if the electromagnetic coupling, i.e. the fine structure constant, weren’t the same everywhere. Then clocks using different atoms would deviate from the predicted behavior. Since we’re looking at transitions involving the hyperfine splitting, nuclear structure is involved, so the other possibilities that can be tested are variations in the electron/proton mass ratio and the the ratio of the light quark mass to the quantum chromodynamics length scale. One need not do any kind of (literal) heavy lifting of moving the clocks into different gravitational potentials because the earth does it for us by having an elliptical orbit — we sample different gravitational potentials of the sun over the course of the year.

In order to get the statistics necessary to put good limits on the deviation, other groups have done measurements over the span of several years, but this was because their devices were primary frequency standards, which (as I’ve pointed out before, probably ad nauseum) don’t run all the time, so you only get a handful of data points each year. Continuously running clocks, on the other hand, allow you to do a good measurement in significantly less time. You want to sample the entire orbit along with some overlap — about 1.5 years does it (as opposed to a few measurements per year, where you really need several years’ worth of data to try and detect a sinusoidal variation).

Another key is having a boatload of clocks. Having a selection is especially important for Hydrogen masers, since they have a nasty habit of drifting, and sometimes the drift changes. Having several from which to choose allows one to pick ones that were well-behaved over the course of the experiment. Having lots of Cesium clocks, which are individually not as good (but don’t misbehave as often), allows one to average them together to get good statistics. Finally, having four Rubidium fountains, which are better than masers in the long-term, adds in another precise measurement.

All of the clocks are continually measured against a common reference, so you can compare any pair of clocks by subtracting out the common reference, so we have relative frequency information about all the clocks. The basic analysis was to take the clock frequency measurements and remove any linear drift that was present in the frequency, and check the result for an annually-varying term. The result isn’t zero, because there’s always noise and some of that noise will have a period of a year, but the result is small with regard to the overall measurement error such that it’s consistent with zero (and certainly does not exclude zero in a statistically significant way).

We’ve pushed the limit of where any new physics might pop up just a little further down the experimental road — relativity continues to work well as a description of nature.