The OP presupposes an utterly impossible entity. It would have ended rather abruptly had it's author noticed this fatal flaw. — creativesoul
As apokrisis has said, the ball effectively vibrates, as its internal molecules move about (Unless the experiment takes place at absolute zero), so it 'pushes' itself, if nothing else does so first. No need even for QM, just Brownian motion is enough to explain it. — Pattern-chaser
The symmetry of the initial conditions is already broken in the sense that there is both a probabilistic process and the barrier preventing it breaking through until a threshold is accidentally breached. — apokrisis
So the context has to be changed in order for the ball not to fall? eliminating each classical cause is the sisyphean task? — JupiterJess
But still, Norton's dome is also its own interesting debate. I'm just saying don't keep mixing the two things up. — apokrisis
For this thought too I would very much appreciate comments. — andrewk
Hmmm... Sounds eerily similar to Zeno. — creativesoul
IE, so even if we specified a starting time for the ball rolling, that's still an incomplete description - we need a start time and a direction. — fdrake
It is an inertial frame. And I’m not claiming that there is no accelerating force. I argue that the necessary force ought to be considered generic rather than particular. The environment did it. Accidents happen because they can’t be suppressed. — apokrisis
We can compare, side by side, two experiments where the infinitesimal limit is being approached, one using an hemispherical dome, say, and the other one using Norton's dome. — Pierre-Normand
In the first case, under successive iterations of the experiment where the ball is placed (or sent) with an ever narrowing error spread towards the apex, and where the apex is materially shaped ever more closely to an ideal hemispherical shape, the time being spent by the ball in the neighborhood of the apex will tend towards infinity. — Pierre-Normand
My OP illustrated one form of such a cut-off - the principle of indifference. If instead of having to count every tiniest, most infintesimal, fluctuation or contribution, we simply arrive at the generic point of not being able to suppress such contributions, then this is just such an internalist mechanism. The crucial property is not a sensitivity to the infinitesimal, but simply a loss of an ability to care about everything smaller in any particular sense. — apokrisis
Specifically it's that no force (0 vector) is applied as an initial condition while the ball is at the apex that leaves room for the indeterminism. — fdrake
See the point. Perhaps I'm too poorly attuned to physics to see much of a distinction between a time symmetry and a radial one. — fdrake
It is an inertial frame. And I’m not claiming that there is no accelerating force. I argue that the necessary force ought to be considered generic rather than particular. The environment did it. Accidents happen because they can’t be suppressed. — apokrisis
Doesn't really matter what point I'm making for the purposes of the discussion, seeing as it's moved on. — fdrake
The major difference between the two in my reading is that the problem is 'set up' to be radially symmetric and so we're primed to think of the problem as of a single dimension (the radial parameter), but the time symmetry falls out of the equations and is surprising.
What is surprising? The indeterminism is uprising, but the time symmetry is expected since the laws of motion are time-symmetrical. — Pierre-Normand
So your claim that "the environment" is an acting agent, is nonsense without some principles whereby "the environment" can be conceived as an acting, unified whole. — Metaphysician Undercover
I think we meant different things by indeterminism. In the paper's sense of 'a single past can be followed by many futures', the translational time symmetry of the non-zero solution is what facilitates that conclusion. If the ball decides to fall in a given direction, its behaviour is determined at every point on that path by the equations of motion (after redefining t-T=0). — fdrake
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