Norton's dome is a thought experiment devised by John D. Norton in 2003 that demonstrates non-determinism within Newtonian mechanics. A frictionless dome allows a particle at its apex to either remain stationary indefinitely or spontaneously slide down after any arbitrary time, both solutions satisfying the same initial conditions and equations of motion. This paradox suggests Newtonian mechanics may be non-deterministic, though critics dispute whether the scenario violates physical principles like Lipschitz continuity or symmetry.