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Norton's Dome is only non-deterministic because it assumes perfect spheres exist. One does not need to go to atomic theory for this assumption to be wrong in r
by xqcgrek2 2y ago
Norton's Dome is only non-deterministic because it assumes perfect spheres exist.
One does not need to go to atomic theory for this assumption to be wrong in reality.
- cesaref 2y agoThe question is about classical (newtonian) physics, which is a mathematical model, rather than the real world. The question is asking when is there non-determinism in the newton mathematical model. In the model, you have perfect spheres...
- xqcgrek2 2y agoNewtonian theory has no assumptions or requirements for perfect spheres.
- munchler 2y agoYou've got it backwards. Newtonian theory does not rule out perfect spheres (or any other mathematically perfect shape), hence the possibility of non-determinism.
- wruza 2y agoIt also better rule out general fractals as well, cause some shit will happen between these as well. Not fully sure, but it feels like Newtonian doesn’t really work with anything non-finitely jagged, cause geometry has extremums or simply insane behavior at everything non-linear non-finite.
- munchler 2y agoNorton's Dome isn't spherical, so it's a bit more sophisticated than you imply. In classical physics, you could roll a ball up the dome so that it comes to a rest at the apex in finite time. Thus, due to time symmetry, it's also theoretically possible for a ball at rest on the apex to suddenly roll down the hill in a non-deterministic way. This is certainly unrealistic, as you say, but that's what classical physics predicts. https://en.wikipedia.org/wiki/Norton%27s_dome https://en.wikipedia.org/wiki/Norton%27s_dome
- moralestapia 2y ago>but that's what classical physics predicts How? I've only seen "magical wand" arguments. Norton's Dome is nonsense to me.
- Certhas 2y agoWhat is "magical wand" here? This is simply Newton's equation and a specific dome shape. Trivially no perfect bodies can be built experimentally, and it's specific properties are not robust to perturbation, but there is absolutely nothing magical or strange going on here.
- moralestapia 2y ago>What is "magical wand" here? Whatever takes the ball out from its state of equilibrium/rest.
- Certhas 2y agoDo 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.
- naasking 2y agoRather than accepting non-determinism, this could also entail that the existence of non-deterministic classical solutions implies that such configurations don't actually exist, eg. you can't construct Norton's Dome. It turns out that that's correct, and the same with the space invader example, eg. no such thing as unbounded acceleration.
- thechao 2y agoYou mean, like electrons? At the bottom of physics is a bunch of spherical cows.