Good idea. That one failed pretty badly.
Only because roundies couldn't grasp the concept.
No, it's you that can't grasp the fact that a sphere touching a plane is not physically impossible.
Okay then, answer this:
We place our absolutely flat huge table on spherical earth. Where do the balls run?
*Sigh* Won't give up, will you?
Assuming a surface with almost no rolling (or other) friction[nb]If it were
perfectly frictionless, the balls would roll back and forth through the point nearest the center of the Earth and never stop.[/nb] and perfectly spherical balls (hey, it's a thought experiment, right...), the balls would end up at the point closest to the center of the Earth. And, before you trip all over yourself responding "but that's not what we see", remember, it's a thought experiment. A
real snooker table 1) isn't even remotely big enough for this to present itself because, 2) it isn't a perfect plane, 3) the surface is far from frictionless, and 4) the balls aren't perfectly spherical.
I haven't run the numbers, but in an area the size of a regulation snooker table, the difference between a plane and surface of a sphere 8,000 miles in diameter is
minuscule. We're talking about changes on the order of the thickness of a human hair, if that much. Feel free to do the calculations if you want.
[Edit] Add "or other" friction for completeness.
[Edit to add] A back of the envelope calculation gives the change in elevation in the middle of an arc with 6400 km radius and a straight line the length of the diagonal of a 12' X 6' table (slightly larger than a full-size snooker table) is about 8 nanometers. This is about 1/10000 the thickness of a human hair! Munuscule. Someone please check this.