A matter of gravity

Gravity remains an enduring challenge in physics.  Newton had the insight that he could understand many phenomena (e.g., the falling of an apple, the orbit of Halley's comet) if the gravitational interaction between two objects is an attractive force proportional to the product of the objects' masses, and inversely proportional to the square of the distance between them ( \(F = - G M_{1}M_{2}/r^{2}\) ), and acts along the line between the objects.  The constant of proportionality, \(G\), is Newton's gravitational constant.   About 225 years later, Einstein had the insight that in more generality one should think of gravity as actually distorting space-time; what looks like a force is really a case of freely falling objects moving in the (locally) straightest trajectories that they can.  (Obligatory rubber sheet analogy here.)  In that theory, general relativity (GR), Newton's constant \(G\) again appears as a constant of proportionality that basically sets the scale for the amount of space-time distortion produced by a certain amount of stress-energy (rather than just good old-fashioned mass).  GR has been very successful so far, though we have reasons to believe that it is the classical limit of some still unknown quantum theory of gravity.  Whatever that quantum theory is, \(G\) must still show up to set the scale for the gravitational interaction.

It makes sense that we would like to know the numerical value of \(G\) as accurately and precisely as possible - seems like the first thing you'd like to understand, right?  The challenge is, as I've explained before, gravity is actually an incredibly weak force.  To measure it well in absolute numbers, you need an apparatus that can measure small forces while not being influenced by other, faaaaaar stronger forces like electromagnetism, and you need to do something like measure the force (or the counter-force that you need to apply to null out the gravitational force) as a function of different configurations of test masses (such as tungsten spheres). 

I'm revisiting this because of a couple (1, 2) of interesting papers that came out recently.  As I'd said in that 2010 post, the challenge in measuring \(G\) is so difficult that different groups have obtained nominally high precision measurements (precise out to the fourth decimal place, such as \(G = 6.6730 \pm 0.00029 \times 10^{-11}\) Nm²/kg²) that are mutually inconsistent with each other.  See this plot (Fig. 1 from arxiv:1505.01774).  The various symbols correspond to different published measurements of \(G\) over the last 35 years (!).  The distressing thing is that there does not seem to be much sign of convergence.  The recent papers are looking to see whether there is actually some periodicity to the results (as hinted by the sinusoid on the plot).  To be clear:  The authors are not suggesting that \(G\) really varies with a several year period - rather, they're exploring the possibility that there might be some unknown systematic effect that is skewing the results of some or all of the various measurement approaches.  As both teams of authors say, the best solution would be to come up with a very clean experimental scheme and run it, undisturbed, continuously for years at a time.  That's not easy or cheap.  It's important to note that this is what real, careful measurement science looks like, not some of the stuff that has made web headlines lately.