Re: Why is there a limit on the structure of matter?

This is an excellent example of a simple question that has no definitive answer within known science. In fact, it is not even clear that it can ever truly be answered in principle. For the game plan of physical science for the last several centuries has been to observe nature as carefully as we can, and then to try to relate all these observations into some coherent logical scheme that is much simpler than just the unorganized observations themselves.

But there is always the possibility, whenever we go completely outside of the realm of current observations -- eg, very very small or very very large -- that some totally unexpected phenomena will emerge. In fact, it is astonishing how frequently we are surprised when we look in some region -- large, small, high-energy, ultra-cold, super-fast, etc. -- that we have never looked at before. That is why scientists are always trying to push the limits of observation beyond what has been done, because the historical record is that we are often amazed rather than bored by what turns up.

On the small side, observations today go down to something like 10^-17 meters, roughly 1/100-th the size of a proton, or a bit less. Current theories, called relativistic quantum field theories, which suppose that the truly fundamental particles (electrons, quarks, and so on) are actually dimensionless points, do work fairly well in this 10^-17 m size regime. (Lately some theories suppose the fundamental objects are tiny strings or higher-dimensional membranes.) But this success, even were it far more comprehensive that it is now, would still not rule out deeper layers of yet-unobservable structure.

In the large, we can see out until just shortly (about 300,000 lt years) after the Big Bang; which is roughly 13 billion light years in all directions. In fact, the very geometry of space and time is not yet settled on larger scales, although much recent evidence suggests that spacetime is actually infinite.

More fundamentally, we do not know for sure the number of dimensions of the stage on which physics is played. The four (three spatial, one temporal) of Einstein's Special Relativity Theory we know more or less for sure. But popular candidates for the "ultimate" theory nowadays typically have several additional dimensions that are so tightly curled up as to be completely unobservable with current technology. It has also been argued that "inflation" cosmological models allow multiple universes, each possibly expanding independently from its own initial singularity. Such universes would presumably be embedded in some larger space. While we know very little that is definite of such possibilities now, probably no one can say either that we may not make much further progress reasonably soon.

The ultimate dream of theory is to predict all observable facts about the universe starting from just a minimal set of fundamental laws, so that the entire structure of the cosmos would be derived really by pure mathematical logic from first principles (Weinberg 1994). Most physicists probably hope and believe we can go much much farther towards this dream than we have progressed so far. However, there is a theorem of mathematical logic, due to Kurt Gödel (1931), which appears to say that no finite set of laws or axioms can tell us all the truths of physics. So any hope of a complete solution from first principles may be forlorn as well.

I have included a few references that may give you some feeling for the state of our current ignorance.

REFERENCES:

Ernest Nagel and James R. Newman 1983 "Godel's Proof", New York Univ Pr.

Weinberg, Steven 1994 "Dreams of a Final Theory", Vintage Books.

Guth, Alan H. and Lightman, Alan P. 1998 "The Inflationary Universe", Perseus.

Martin J. Rees 1998 "Before the Beginning : Our Universe and Others", Helix Books