In classical mechanics it’s quite common to say something is “at rest” and then instantaneously acted upon by a force, so just because something is at rest does

In classical mechanics it’s quite common to say something is “at rest” and then instantaneously acted upon by a force, so just because something is at rest doesn’t mean it will never move. It usually just means dr/dt = 0 in a particular coordinate system. In fact[1] “at rest” doesn’t even mean the thing isn’t moving, accelerating or even that the rate of acceleration isn’t increasing. It just means than an inertial frame exists from which you can conveniently assume that these things aren’t happening, and Newton’s first law tells us that indeed such a frame always exists. I’m not sure I buy the example of the Norton’s Dome though. I get the technical argument from continuity but it seems weak to me. Lots of differential equations (eg the wave equation) have a trivial solution where u(x,t)=0 for all x and t - that doesn’t actually translate to us not knowing whether or not something will move in the real world. As you have said it will fundamentally always move or always not move given a particular set of initial conditions - we may just be lacking enough information to say which of those cases may hold, but that doesn’t make it non-determanistic - just it appears so to us. [1] I got this from Kleppner and Kolenkow, which is an amazing book if you’re interested in Classical Mechanics