[zmgehlke]

I appreciate the reply!

Yes, if you put little R^4 balls around points of the line, you can still untangle it. It's basically still a line. (They might have to be really little balls, but the definitions all use neighborhoods for defining the legality of knot moves, so you can't "shrink" the knot out of existence.)

My actual thought was slightly more complicated, in that particles dont need to necessarily not be a point all the time, since a sphere you're slicing with a plane can appear as a point -- see sibling comment for what inspired the idea.

[danbruc]

Final thought for tonight. It is certainly an extremely weak argument because it is root in intuition from our macroscopic world, but based on this it makes sense that elementary particles have to be points. At least for me it is somewhat hard to imagine how something could be spatially extended and elementary, i.e. not subdividable. If it has a length, an area, or a volume, I should be able to break it into pieces. This of course immediately conflicts with string theory with which I am sympathetic, sometimes more, sometimes less. But as said, it is an extremely weak argument rooted in a world many orders of magnitudes from where I want to apply it.