Built on Facts

A while back I mentioned I was starting the project of reading Neal Stephenson's rather lengthy Baroque Cycle. I'm most of the way done with the second book, so we're coming round to the 2000-page mark. It's a brilliant work thus far, though it's very difficult to summarize. The plot is rather, well, baroque. If I had to cram it into one sentence I think it might be "The world undergoes a phase transition from medieval to modern via the development of science and finance."

The series is heavily populated by actual historical people. Among these are the transcendentally brilliant Isaac Newton and a somewhat less capable and today less-well known scientist named Nicolas Fatio de Duillier. Newton developed the theory of gravitation and Fatio tried to explain its mechanism of action. This is a sticky thing to do, because it's not actually necessary for a theory to have a mechanism of action. Some do - the classic ideal gas law PV = nRT is a consequence of the fundamental properties of gas molecules bouncing around, for instance - but other properties of particles and fields just seem to be fundamental. There might be mechanisms, and mechanisms for those mechanisms, but in some cases the chain of regress does seem to terminate with a fundamental principle that is simply built into the laws of the universe. To this day, gravity as described by Newton (and refined by Einstein) is one of those things.

But Fatio gave it his best shot. He proposed that the universe was suffused with a gas of tiny and nearly undetectable particles randomly moving around in all directions just like the molecules of a gas.* A planet sitting in space has these particles crashing into it from all directions, but since the particles are moving in all directions there's no net force from any side.

But if you have two planets, then some of the particles crashing into Planet A will never make it to Planet B. Therefore Planet B has a deficit of particles hitting it from the side facing Planet A, and it feels a net force in that direction from the rest of the particles hitting it from the other side. Same thing for the other planet. Here's Wikipedia's visualization:

The farther apart the planets are, the less of the particles are blocked. In fact, if you assume some of the particles are absorbed or substantially slowed by the planet they hit, you can argue that the net loss of particles due to a planet is constant. Distribute this imbalance over an imaginary large sphere of radius r surrounding the planet and you'll see that the net-flux-per-area scales as 1/r^2, just like the force law in Newton's gravity. So maybe Fatio's theory does provide an actual mechanism for gravity without just a priori accepting the inverse square law.

But there's problems, too. There ought to be "air resistance" from the particles as the planets move through space. Then there's the fact that the force is proportional to surface area hit by the particles, not to the mass. This can be remedied by assuming a tiny interaction cross-section due to the particles, but if this is true they must be moving very fast indeed to produce the required force - many times the speed of light. And in that case the heating due to the "air resistance" of the particles would be impossibly high. Furthermore, if the particle shadows of two planets overlapped, the sun's gravity on the farther planet should be shielded. No such effect has been observed.

For these and other reasons Fatio's theory had to be rejected as unworkable. Still, like many wrong theories it wasn't a total loss. Some of the theoretical and mathematical tools used to explore the consequences of this type of gravity ended up being useful in the kinetic theory of gases and the theory of the behavior of dust in plasmas and interstellar space. We can't all be Newton, but I like to think Fatio would have at least been pleased his idea found some new life in those other forms.

*Not an unreasonable guesss; we know that this is pretty much the actual story for neutrinos and probably the story for dark matter. However, neither would work to produce the effect postulated by Fatio.