The model doesn't have to apply here, it's ladders and ladders of extrapolation ahead of any data. At, what, six orders of magnitude of difference is like administering WAIS IQ test to a nonlinear being existing outside time. A tangent, one I've been on and off procrastinating my PhD over for a while now: Fluffy: Quantum physicists measure the smallest gravitational force yet Meaty: Measurement of Gravitational Coupling between Millimeter-Sized Masses; PDF; Nature paywalling the same thing The reason those measurements are not just necessary but are looked into with bated breath is because this is the closest we can hope to get to testing gravity on quantum scales in the foreseeable future. Or, to be precise, mesoscales -- it's a long road to quantum. Just because Newton's model works at scales in the article doesn't mean it'll keep doing so (EDIT: or that it should have been assumed it would do so without a need for testing), and very serious basic physicists know it has to be tested at all intermediate distances and masses. Yes. Newton's gravity. It's still hawt and exciting, exactly because it finally gets thorough, reliable, repeatable tests at lower end of the parameter space. I'm saying it because while I absolutely can appreciate and play with likely-false hypotheses... even neo-rationalists should know the need for rigour. Ho-ho, I too can be cheeky about imagined opponents! No binding promises are made, but I'll try to dissect this soon-ish rather than later-ish.Log scaling is really poor, but as the NYT reminds us, we’re talking about really extreme levels of wealth here. Sure, you only gain a few more points of happiness between an income $75,000 and $160,000, but Jeff Bezos is sitting comfortably at a net worth of $211,000,000,000. Our intuitions just don’t apply very well here.
Step 1: Construct a tiny Cavendish pendulum with two solid gold BBs hanging from a silica fiber. A perturbation, perhaps a truck passing a kilometer off, or an earthquake near the Canary Islands, will set it oscillating, that is, swaying to and fro once every five minutes, so wait until the Christmas season when things are quiet. Set aside three weeks for observations. Step 0: Don't forget to do this in a hard vacuum: 0.0000000006 bar. PV = nRT n = (0.0000000006 bar)(1 liter) / (0.08314 L⋅bar/K⋅mol)(293 K) moles of gas n = 0.000000000024629 moles or just about a billion molecules of gas per liter flying around the hypersensitive pendulum in your vacuum chamber, hopefully not adding too much noise to the signal. Don't forget air springs and Viton™ rubber feet to dampen vibrations. Step 3, etc.: Jiggle a third tiny gold ball mounted on a thin wire near the pendulum very carefully to induce oscillations, and observe. Thanks, that was fascinating, but I didn't get far enough along to see how they imagine possibly scaling this down below the gram scale, to say nothing of the Planck mass.
In principle? It could go to the nanoscale, so tens of atoms, before tunneling and Casimir effect influence would be too much to ignore. In practice? I think there'll be a plateau around tens of thousands of atoms due to the electrical charge becoming a growing concern and quantum effects surfacing their ugly heads. I'm very happy you liked it.