What do you think of this paper? Is classical physics actually non-deterministic?
When contrasting quantum mechanics with classical physics, it is often said that the latter is deterministic. However, in [this paper](https://sites.pitt.edu/~jdnorton/papers/003004.pdf) an example of a classical physical system is shown where that is not the case.
Consider a frictionless dome of height h=(2/3)r^(3/2) and let a ball be at rest on top of the dome. In this case, the equations of motion allow for multiple solutions: the ball could stay perfectly still, but it could also start rolling down at any time t. This is not surprising because classical mechanics is governed by differential equations, and the solution to differential equations is not always unique (x'=F(x) is only deterministic if F is Lipschitz continuous).
Aside from the phylosophical talk in the paper, what is the physics actually saying? Is the current understanding of physics able to determine what will be the actual behavior of the system described in the paper?
I know in real life the dome will never be perfectly frictionless or have that perfect shape, however this answer is not satisfying to me because if classical mechanics is truly fundamentally deterministic, then the mathematical axioms we use to describe it should also lead to determinism.
Were you familiar with this paradox. I personally found it surprising and rarther intriguing.
EDIT: The discussion of the actual physical example in the paper begins at page 8.