Why is the Solar System flat?
Our sun and the earth, and all the planets and moons and dwarf planets and asteroids and comets... The Solar System in short formed about 4.6 billion years ago from a nebulous cloud of swirling gas and dust which coalesced thanks to the irresistibly attractive force of gravity. However, this nebula started off more or less as a big shapeless blob. So how did our solar system end up with all the planets and their moons orbiting in a flat disk? I mean, we've all seen the planetary model of the atom, which is definitely wrong when applied to atoms. But it also kind of suggests that planets might revolve around the sun every which way. So is our solar system somehow special in its flatness? Or is the planetary model of the atom doubly wrong? Well, our solar system definitely isn't alone. Many exoplanets' star systems are flat, a lot of galaxies are flat, black hole accretion disks are flat, Saturn's rings are flat, etc. So why, when there's all of 3D space to fill, does the universe have this preference for flatness? The answer has to do with two things: collisions and the fact that we live in three dimensions. Bear with me. Anytime a bunch of objects held together by gravity are zooming and circling around, their individual paths are nearly impossible to predict. And yet, collected together, they have a single total amount that they spin about their center of mass. It may be hard to figure out exactly what direction that rotation is in, but the mathematics implies there must be some plane in which the cloud, taken as a whole, spins. Now, in two dimensions, a cloud of particles rotating in a plane is flat by definition, it's in two dimensions. But in three dimensions, even though the rotation of the cloud is given by one plane, particles can whiz around far up and down from that plane. As the particles bump into each other, all the up and down motion tends to cancel out. It's energy lost in crashing and clumping. Yet, the whole mass must continue spinning inexorably, because in our universe, the total amount of spinning in any isolated system always stays the same. So over time, through collisions and crashes, the cloud loses its loft and flattens into a spinning, roughly 2 dimensional disk shape, like a solar system or a spiral galaxy. However, in 4 spacial dimensions, the math works out such that there can be two separate and complementary planes of rotation, which is both really really hard for our 3D-thinking brains to picture and also means there's no up and down direction in which particles lose energy by collisions. So a cloud of particles can continue being just that... a cloud. And thus, only in three dimensions can a nebula or infant galaxy start out not flat and end up flat which is definitely a good thing, because we need all that matter to clump together in order for stars and planets to form, and for us, even those of us who think atoms look like this, to exist.
