I Must Be Missing Something

This experiment amounts to a way to measure gravity much more precisely than ever before. This article on the experiment claims that it is a step towards unifying quantum theory and Einstein's descriptions of gravity in his relativity theory. How? I guess in the very general sense, more precise data will always be helpful, but what specifically does it do to aid unification?

For those who don't know, I'll give my history major's thumbnail sketch of gravity. Einstein's theory said that gravity was not some mysterious force that acted within the framework of space. Rather, gravity is a RESULT of the framework of space. Space itself is curved by large objects like stars or planets (and by smaller objects too, but we don't notice them) and what we see as gravity is actually this curved geometry of space sliding objects around. A good way to picture it is to imagine your mattress as space. When you place a "star" (heavy object) on the mattress, its mass causes the mattress to sink underneath it, creating "gravity" (a depression). Any small object placed nearby will roll towards the heavy object because of this depression. Now, add an extra dimension and a bunch of fancy math and you have Einstein's theory.

This worked beautifully until quantum physics came along and insisted that the big deal at the bottom of everything cool were particles. Photons, muons, bozons, electrons, etc. The cool kids were all particles, and gravity wanted to fit in. So, the competing quantum theory is that massless particles called "gravitons" are the ones doing all of the work of Einstein's depressed mattress. Both theories mostly work mathematically (gravitons don't in some cases), and seem to have equal explanatory force. I personally like Einstein's theory better, but that's because I'm completely unqualified to make any judgements about quantum gravitational theory, while the handy mattress analogy makes me an expert on Einstein.

So, to reiterate, I don't quite see how we come any closer to squaring the "invisible mattress versus tiny particles" argument by simply doing more precise measurements. If anyone has any thoughts that are expressible in terms that won't shatter my tiny, math-averse brain, feel free to pass them along.