Posted: Oct 09, 2011 8:30 am
Teuton wrote:
Teuton wrote:
0D objects and 1D objects exist only in the abstract realm of mathematics. Concrete physical objects are (at least) 3D objects.

This means that if there are atoms in the literal sense of the term, i.e. truly fundamental particles, then they must be simple, partless (componentless/constituentless) 3D atoms. Of course, many ask how it is possible for a 3D object to be spatially partless when any (nonzero) volume of space can be partitioned into smaller (nonzero) subvolumes. This is a good question and the only good answer might come from the theory called loop quantum gravity, according to which there are indivisible atoms of space that cannot be partitioned into any smaller subvolumes.

"According to loop quantum gravity, space is made of discrete atoms each of which carries a very tiny unit of volume. … One consequence of this is that there is a smallest possible volume. This minimum volume is miniscule – about 1099 of them would fit into a thimble. If you tried to halve a region of this volume, the result would not be two regions each with half that volume. Instead, the process would create two new regions which together would have more volume than you started with. We describe this by saying that the attempt to measure a unit of volume smaller than the minimal size alters the geometry of the space in a way that allows more volume to be created."

(Smolin, Lee. Three Roads to Quantum Gravity. New York: Basic Books, 2001. p. 106)

So, if a fundamental 3D particle occupies exactly one space-atom, then one can consistently and intelligibly say that it lacks spatial parts.
(It might be the case that the particle-atoms are ontologically reducible to the space-atoms so that the latter would be the fundamental physical objects.)

If there are no 3/4-dimensional particle-atoms or space/spacetime-atoms, then matter or space/spacetime is "gunky", i.e. then it is infinitely divisible and every part of it has proper parts ad infinitum. (This means that "gunky" stuff isn't ultimately composed of simple point-sized objects, which lack proper parts.)

Unfortunately, LQG is not yet in a state where we can talk about fundamental particles "occupying space-atoms". It is not yet known/agreed how to put matter into the LQG picture.