Viewed another way, the hill beside our lab deflects the direction of "down" by about 50 nanoradians for every meter you move vertically in the lab. (If you kept the hill, and got rid of the earth, a satellite would orbit the hill.)
The really crazy thing about the experiments described in the article is that they depend on the difference in potential, which is much harder to estimate. As these clock-based experiments reach still-higher sensitivities, we're going to see improved and interesting tests of gravity emerge alongside the increasingly-difficult problems of time-transfer at these levels of precision.
(We care about this difference-in-the-direction-of-down because we need to lock one of our turntables to "local vertical" with nanoradian stability. It was initially a surprise, before my time, when it was realized that it was impossible to do so simultaneously for two sensors on the same turntable but at different locations on the turntable axis.)
Also, if you think that's cool, depending on your latitude, the "down" you experience doesn't point in the direction of the center of the earth. The earth is rotating, so there is a substantial centrifugal contribution to the acceleration you experience. Off the top of my head, I believe the effect here in Seattle is about 14 milliradians. It is zero at the pole and equator (the apparent centrifugal acceleration makes you effectively lighter!), though :).
Holy moly. Just what kind of measurements are you doing in your lab?
Our most-recent measurement: https://news.ycombinator.com/item?id=22797729
Once you know how, it's not as hard as you'd expect to measure a nanoradian ;).
Gravity is, by most measures, our oldest force, and while GR is a very successful theory, we know essentially nothing about the underlying mechanism. This is very much unlike the rest of the Standard Model, where we have very-successful quantum theories.
https://www.hartenergy.com/exclusives/gravity-and-magnetic-g...
https://en.wikipedia.org/wiki/Schiehallion_experiment
"The Royal Society formed the Committee of Attraction to consider the matter, appointing Maskelyne, Joseph Banks and Benjamin Franklin amongst its members"