I did my PhD in the Eöt-Wash group  at the University of Washington, where many of the "world's best" torsion balance experiments have be done: tests of the equivalence principle, measurement of gravity at short distances, measurement of the gravitational constant, and others. The 3 professors in the group won the Breakthrough Prize in Physics last year.
When this article came out a few months ago I was surprised it got so much press. If I'd had any idea it would get so much attention (and merit a paper in Nature) I would have pushed for us to do it :) The authors did a great job doing the experiment and addressing the possible systematics--doing torsion balance experiments the right way is difficult--but there doesn't seem to be anything too new here.
“The motion of the rod was only about 0.16 inches (4.1 mm)”
At first sight, I find that surprisingly large. Thinking of it, he used heavy objects (300kg in total), it isn’t hard to twist a wire, and falling down even a meter hurts, so perhaps it isn’t that surprising.
Those are really for coherent gravitational waves (the same across locations across the world) not for interactions between individual small objects. Since they're looking for any defect in the inverse square law (e.g. due to extra dimensions of string theory) these would screw it up.
Light actually exerts a force (even like tweezers) so it's not a good choice for this kind of measurement.
They must have done an amazing job of removing any electrostatic or magnetic effects since those so quickly dominate at these dimensions. The gold ball isn't so bad to discharge, but typically glass fibers are used, which can build up charges. My expectation is that they used radically different frequencies on the two ball supports and very high oscillator Q (they're pendulums in a vacuum) to separate them mechanically since they have to be in the same chamber.
People have tried placing "screening materials" between the masses to reduce electro-magnetic coupling, but those tended to cause their own non-gravitational effects.
It’s not dumb at all and perhaps some incredibly advanced civilisation would do exactly that. However space time is exceedingly stiff, the energies required to create measurable ripples are enormous. Targeted neutrino based communication would probably make more sense though.
It's not very practical. We've been able to detect gravitational waves from black holes (or maybe neutron stars? Something like that anyways...) falling into each other, so in theory we could send a message across the galaxy using non-electromagnetic means if we could deliberately cause a similar event.
I'm not sure why we'd want to even if we could, though I guess "hey look at this, I can push a black hole into another one" would likely be regarded as a rather meaningful kind of message on its own to anyone with the technology to hear it.
Gravitons  are the only particles that would be able to travel in higher dimensions, so yes if they do exist along with higher dimensions that you find yourself in need of communicating with then gravity would be pretty useful . You do need to move around a planet or at least a moon to generate the signals though.
If the BMV effect is observed it would falsify Penrose's conjecture that something unusual and nonlinear happens around the Planck mass (conversely the experiment could also begin to probe and measure that regime and find Penrose was on to something).
Could any experiment like this ever measure how the dark energy driven expansion of the universe affects gravitationally bound systems?
Of course I understand it's beyond any reasonable measurement capability --masses should be infinitesimal and the system be isolated from any other interactions, the question is about if it's theoretically possible. Like, "it's impossible because masses should be below the Planck mass"
"Abstract. This paper describes gravity experiments, where the outcome
depends upon both the gravitational acceleration g and the Planck constant h¯ .
We focus on the work performed with an elementary particle, the neutron"
Excellent idea! Also this whole experiment is really exciting. I'd heard of quantum entanglement being demonstrated with larger objects, but this is the first I've heard of measuring gravity between small objects. It seems like this must eventually lead to quantum gravity, or. . . something else!
The issue is that gravity and quantum mechanics contradict each other only when the curvature of spacetime is significant, which is not the case here. Still, it would be amazing to measure gravitational field from an entangled object... But I do not expect to see this during my natural lifetime.
I believe QM and GR contradict each other for any curvature, but measuring the extremely small curvature/gravitational effects caused by a single particle would require enormous amounts of energy. Specifically the problem is the way that the uncertainty principle interacts with GR's assumptions.
I don't believe that is true. For example, if this experiment can be carried out with much smaller masses, they could find that the attractive force isn't smooth but is instead stair-stepped, which would imply some kind of quantization in space or gravity.
It's "really measuring" the deflection of a beam of light by a mirror connected to a wire connected to a weight. Everything else is a matter of modeling.
The best model that explains all of the data is the Einstein Field Equations. The most useful way to interpret the model is to think of space and time geometrically (albeit a very weird kind of geometry in which one of the dimensions has the bizarre property that a straight line is the longest distance between two points). If you view it that way, the geometry acts as if it has intrinsic curvature: otherwise straight lines (like beams of light) don't go straight.
So... it doesn't get to directly measure curvature. It's not even clear if it's meaningful to "really" measure curvature. Push on the whole notion of "measure" hard enough and it turns out that it's not nearly as clear as we think it is. Everything is "theory laden": a measurement is always a matter of interpretation, even the most straightforward ones.
I think of it as internally, where space and time converge to the same medium, each grain of gold has it's own filmstrip with very similar, yet still different frame rates.
For example, the Sun is on a slower frame rate than the Earth. The Earth needs to do something in those frames yet still conserve spacetime. So the Earth orbits it. You floating in space are on a much faster frame rate than Earth. You might look like you are going to float by it. But you need to fill those frames while the Earth doesn't. You crash in, sync frame rates, and feel that impact.
Those two grains are orbiting each other at really really small angles. It doesn't happen though as convection or electrical conduction fills the frames.
There could be gravity applications, as in using a tremendous amount of energy, all the energy that exists, to generate a particle. That could be considered communication.
The following link discusses the same experiment and has more specifics (does not discuss mass only in terms grains of rice or eyelashes - TL;DR 92mg). It also includes a clearer discussion of how well the results match Newton's equation (F=Gm1m2/r^2) vs the uncertainty of the experimental setup (TL;DR - this was inconclusive).