Do you understand the difference between Norton's dome and other domes with balls at rest on the top? The very point of non-determinism is that the next state

Do you understand the difference between Norton's dome and other domes with balls at rest on the top? The very point of non-determinism is that the next state doesn't follow uniquely from the current state, causality is broken. Thus there is no "cause" for one or the other trajectory. This is a feature of the Newtonian equations, whether you like it or not.