Below is a really hard problem which seems to be on the intersection of math and physics, so I'm posting this to both math and physics stack exchange. I thought of it when reading a knot theory book.
Below in the picture, you see the projection of an unknot (a basic looped string in space).
The red dot marks an infinite line going into your screen perpendicularly. Assume that we know the line weaves through the "inside" of the loop rather than the outside.
Now imagine the dot starts expanding uniformly as a cylinder outwards. Prove/disprove that eventually, the unknot shown above will unravel into a circular band that hugs/wraps around the cylinder. Will this happen in any generalized context?
Assume the cylinder has infinite mass and no friction. Assume the unknot is comprised of an idealized string (e.g. no friction, no mass, no volume, infinite ability to twist, no stretching, infinite strength etc.) Assume that there is no other forces that I didn't mention.
Note that I don't even know if this is true, but it seems highly intuitive that when you pull hard enough, any frictionless loop will unravel. (provided that it's not doubly looped around the cylinder)