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Except Newtonian mechanics doesn't say anything about causation, it simply says which equations are valid solutions. Most people find it counter-intuitive, but
by xvedejas 9y ago
Except Newtonian mechanics doesn't say anything about causation, it simply says which equations are valid solutions. Most people find it counter-intuitive, but it's totally possible for multiple solutions to exist in the Newtonian framework for some circumstances.
- kobeya 9y agoNo what I'm saying is that the single Newtonian solution in this problem is no motion. The ball stays at the top of the dome. If there is a problem with multiple Newtonian solutions, this isn't it.
- xvedejas 9y agoHow did you determine that? There are infinitely many solutions that follow all laws of Newtonian mechanics. The burden of proof is yours to show uniqueness of a solution here, which I'm certain you cannot do with the canonical Newtonian laws alone.
- kobeya 9y agoBecause moving in any direction down the dome requires epsilon momentum from an application of epsilon force, which is not present in the assumed setup.
- xvedejas 9y agoThere is an explanation in the article as to why a causative force is not required to obey Newtonian mechanics. At every moment that the ball is moving, there is indeed an external force due to gravity.
- eru 9y agoIndeed. If you want to challenge the example, you need to argue that in reality things are never quite so finely balanced, and that we can thus assume what geometers call "general position". (https://en.wikipedia.org/wiki/General_position https://en.wikipedia.org/wiki/General_position)
- kobeya 9y agoThe ball is never moving at any time ever.