The Dome: A Simple Violation of Determinism in Newtonian Mechanics

I felt that the "Still not happy?" section at the end was a bit clearer. You can roll a ball up a hill and have it perfectly perch at the top. If you film that and run it in reverse, it looks like a ball just sitting there, then deciding for no reason whatsoever to roll in some random direction. It breaks no laws of physics; it's a valid solution.

The energy of this works out, but I'm not sure that momentum does. The article doesn't mention the word. When you roll the ball up the hill it goes from having momentum to having zero momentum. That momentum went somewhere -- into the hill (or the planet that the hill is part of). If you run the tape in reverse, you'll see that there's a tiny, tiny push from the planet.

So I think that the conclusion is not "Newtonian mechanics is indeterminate" but "There are no immovable objects". If you had one you could indeed make asymmetries, because it would violate the conservation laws. You just need to be really, really careful about tracking all of your conserved quantities.

If you do, I'm not sure you actually can get a ball to perch on top of a hill like that without some friction. The ball will exert horizontal force on the planet as it rolls, putting it in rotation. That rotation will make it impossible for the ball to completely come to rest. The situation won't be symmetric, reflecting the asymmetry of the ball having horizontal momentum in the first place.

Which makes me wonder... what is the point of this article? For the reader to find the hidden asymmetry? Or is this journal article by a historian and philosopher doing invalid physics to make an incorrect epistemological point?