Re:Norton’s Dome: A simple violation of determinism in Newto...
by tsimionescu on Saturday August 05, 2023 @12:11PM
(#37013432)
> Because once you properly set the initial state of the ball (force=velocity=0, or any other values), then the solution becomes unique and that’s it, there is one possible trajectory.
As the linked article points out, that is not true. Even for force = velocity = 0, there are solutions for which the ball starts rolling. Additionally, even adding the first law does not help, since the body has F = v = a = 0 at any time before T, and it has a > 0 only for times where it also has F > 0. So the body spontaneously starting to move is perfectly consistent with classical mechanics.
A better attack on the example is that the shape of the dome may not be possible to construct from actual matter. The math only works with a shape that has a certain type of infinite smoothness with a single bump, which is probably not possible even in principle to construct from real matter.
As the linked article points out, that is not true. Even for force = velocity = 0, there are solutions for which the ball starts rolling. Additionally, even adding the first law does not help, since the body has F = v = a = 0 at any time before T, and it has a > 0 only for times where it also has F > 0. So the body spontaneously starting to move is perfectly consistent with classical mechanics.
A better attack on the example is that the shape of the dome may not be possible to construct from actual matter. The math only works with a shape that has a certain type of infinite smoothness with a single bump, which is probably not possible even in principle to construct from real matter.