Science

I don’t watch YouTube videos with those stupid clickbait thumbnails out of principle, if it was a serious video worth watching they wouldn’t resort to that.

As a total amateur my instinctive response to the "unexpected" result is to validate that apply Newtonian physic is appropriate, and if not, we should look for an explanation at a level where the unexpected phenomenon becomes possible, aka non-Newtonian physics. We know that Newtonian physics works fine until we try to explain things at the atomic or subatomic level, or under extreme gravity, or close to the speed of light. Why not the same at extremely small points on a dome?

The dome used is the same shape as the graph she showed. The closer to zero you get on the graph the more vertical the line "looks", but with enough resolution in the data it becomes clear line is never vertical except at the starting position of zero. When you make a dome based on the same curve the zero point is so small that it falls into the realm of non-Newtonian physics where you run into uncertainty. I can't do the maths myself but I'm going to guess the zero point needs to be subatomic in size for the "unexpected" excitation event to have an impact. If true, and the zero point is too large, the ball is going to remain stationary until an explainable force acts on it.

I'm guessing the ball needs to be a perfect sphere. Does the maths incorrectly neglect the ball?

Edit - I feel like I used non-Newtonian wrong when I should have used quantum or something instead. But hopefully it made sense enough to see my point.

I see some people are having issues with the scenario, but it's not as impossible as it seems. The key is that Newtonian mechanics are in principle time-reversible. If a system got to a state one way, it can get back to the state it was by running it backwards, so to speak. A ball going down an inclined plain with a given kinetic energy could be going up that inclined plain up to the top with that same amount of energy.

The problem with these systems is, it's possible to impel the right amount of force on a mobile so that it goes through a path and then stops. But since there is time reversibility, it should be possible for the mobile to spontaneously start moving from that stopping point and draw the same path.

Other weird similar cases are the so-called space invader (particle going to infinity, and therefore spontaneously appearing in reverse) and some strange n-body problem cases.

What? An object at rest stays at rest unless acted upon by an outside force. If there are no outside forces, there is no reason for it to roll off.

Math is an approximation, when applied to physics. Sometimes the approximation is useful, sometimes it is not useful.

Math, by itself, does not care about physical realities, it just provides a model that may or may not be helpful to approximate reality