The author begins by stating that while theories like quantum mechanics and general relativity violate our expectations of causation and determinism, Newtonian mechanics is presumed to only violate these expectations in extreme circumstances. However, the author argues that even simple Newtonian systems can exhibit uncaused events and events for which probabilities cannot be determined. They provide an example of a mass on a dome that remains at rest for an arbitrary amount of time and then spontaneously moves off in an arbitrary direction, with no external intervention or change in the physical environment. The author explains the mathematical analysis behind this phenomenon and addresses concerns about violating Newton’s First Law. They also discuss the time reversal trick and the limitations of the dome shape.
https://sites.pitt.edu/~jdnorton/Goodies/Dome/