TLDW
A paper, by philosopher of physics John Norton, describes a scenario in which a ball is placed at the apex of a perfectly smooth and frictionless dome. The paper argues that, according to Newton’s laws, the ball will spontaneously start rolling down the dome at some random time, without any external force acting on it. Norton’s claim suggests that Newtonian mechanics may not a deterministic theory or that there are multiple possible interpretations.
https://sites.pitt.edu/~jdnorton/papers/DomePSA2006.pdf
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.
It’s not spontaneously starting to move from rest. There was a force exerted on it to cause it to stop. That force will cause it to start moving in time-reversal.
The loophole here is that the motion starts so smoothly from rest that there is still no force at the starting point, but that it rather appears simulatneously with the motion
It doesn’t matter how smooth it is. If it came to a stop, there was an outside force.