Since 2003, there have been many reactions to the dome. Some are amused to see that indeterminism arises in so simple an example in Newtonian physics. Others are indifferent. The response that surprised me, however, came from those who had a full grasp of the technical issues, but nonetheless experienced a powerful intuition that the dome somehow lies outside what is proper in Newtonian theory.
Its not necessarily either. ... There are reason(s) why the ball bearing was displaced, and with enough sophistication in the instruments of measure (whatever they may be) these reasons can be revealed and your question answered. — DingoJones
If the net force acting on the ball bearing was zero, why would the ball move? On the other hand, can a ball sit on another ball without moving? Or must it eventually move as a chance event? — Bitter Crank
What's interesting about the dome is that the ball's starting from rest, and, after a finite time, rolling in an arbitrary direction, is a valid solution to Newton's laws of motion. — Pierre-Normand
How so? If the ball has mass, it has inertia. A push is required to set it moving. — apokrisis
I cast my vote for "it fell" rather than "it was pushed". For one thing, all the environmental forces operating on the rock are cumulative, and have been operating for a long time. — Bitter Crank
Could you imagine ceasing to care about the individual pushes and instead accepting that the generic impossibility of eliminating all disturbances is this deep truth? — apokrisis
I am guessing you would resist that alternative view strongly. The question becomes why? With what good justification? — apokrisis
Not so, as I've already explained to Bitter. The shape of the dome is such that, as the ball is getting infinitesimally close to the apex, the second derivatives of its horizontal motion tends towards zero; and hence, also, the horizontal component of the force. — Pierre-Normand
Another way to view it is to imagine the time reversal of the process where the ball is being sent rolling up the dome with just enough speed so that it will end up at rest at the apex, after a finite time. Thereafter -- and this is unmysterious -- it may remain at rest for an arbitrary period of time. If this is a valid solution to Newton's equations, then, so is the time reversal of this process where it remains at rest for some time and then "spontaneously" starts rolling (with an initial instantaneous null acceleration). — Pierre-Normand
I cant think of a reason that it would be impossible. — DingoJones
But now if you time reverse the story, you still only can arrive infinitesimally close to the apex, not actually perched exactly on it. — apokrisis
But that is the easy presumption that is under attack here. Most people probably do find no reason to even question the possibility of being able to eliminate every possible source of perturbation in some physical system. — apokrisis
I told you that I cannot think of a good reason to accept that it is impossible to eliminate all disturbances. Do you have one? — DingoJones
I'm not sure I understand your point. If the particle is perfectly balanced on top of the dome, then there it shall remain until some net force moves it. — LD Saunders
Do you buy his story? — apokrisis
Quantum mechanics — apokrisis
As a way of thinking about what causes the ball to start to roll, the answer becomes we couldn't prevent that because any placement on the apex had to involve infinitesimal error. — apokrisis
That is my view. The ball fell because when it was released by whatever was holding it on the apex, its centre of mass was not exactly above the point of contact with the dome, so it started falling.the answer becomes we couldn't prevent that because any placement on the apex had to involve infinitesimal error. — apokrisis
That is my view. The ball fell because when it was released by whatever was holding it on the apex, its centre of mass was not exactly above the point of contact with the dome, so it started falling. — andrewk
Making the generic cause to be about the impossibility of placing a ball with arbitrary accuracy on an apex is both another way of saying the same thing, but not quite as strong a version as focusing on the impossibility of eliminating triggering fluctuations. — apokrisis
(There may be a emergent law specifying the half-life of a ball's staying poised before starting to fall). — Pierre-Normand
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