A Simple Violation of Determinism in Newtonian Mechanics: The Dome
2025-01-03
This paper presents a counterintuitive example in Newtonian mechanics where determinism fails: a mass resting at the apex of a specially shaped dome spontaneously moves without any external intervention. The author demonstrates, through mathematical solutions and physical reasoning, that this system allows for multiple solutions, some of which depict the mass initiating motion at an arbitrary time, with no Newtonian prediction for when or in what direction. Even simple Newtonian systems can exhibit acausal events, challenging the universality of causality in classical physics.