Posted: Oct 08, 2011 2:41 pm
That's a conceptual truth. 0D, 1D, and 2D objects, i.e. points, lines, and surfaces, are geometrically ideal boundaries of physical objects but not physical objects (substances) themselves. They are too "thin", too insubstantial to be physical objects (substances); they aren't bodies (in the most general sense of the word, including nonsolid bodies).
"Elementary particles in the ordinary view of things are point particles. A point can’t have many, many properties. A point is too simple to have properties. However, we know that elementary particles have a lot of properties. They have spin, they have electric charge, they have something called isotopic spin, they have a quantum number called color - it’s not got anything to do with ordinary color - they have generations that they belong to, there are whole catalogs of different kinds of quantum numbers, of different kinds of properties that quarks, electrons, netrinos, or photons have. It sounds unreasonable for a point to have that structure. So the feeling most of us have is that, at some level, if you look deeply enough into things, you‘ll discover that particles aren’t points. That they must have all kinds of internal machinery that gives them these properties."
(Leonard Susskind, interview by George Zarkadakis, April 27, 2009. Feline Quanta Blog. http://felinequanta.blogspot.com/2009/04/interview-with-leonard-susskind.html.)