First collisions at the LHC with unprecedented Energy! (Ask a particle physisicist)

[Sappho]

That's not an easy question. I'll try to do the following - present several different aspects of it separately in the hopes of providing a clearer picture.

Maybe the cleanest approach is via Emmy Noether's theorem on conserved quantities. It states that any continuous symmetry in the laws of nature gives rise to a conserved physical quantity, and that vice versa this quantity determines how to perform the symmetry operation.

The relevant case for us is that the laws of nature do not seem to change over time, at least to a very good approximation. This means that formally moving back and forth in time is a symmetry of the laws of nature, just as rotation is a symmetry of a sphere. Noether's theorem states that there should be a conserved quantity associated with this symmetry. We call this quantity "Energy". The theorem makes sure that Energy is not lost over time and therefore Energy appears to us as if it were a substance flowing through space - if it is not lost in total, the reduction of energy in one place must correspond to the increase of energy elsewhere, in the case of the known laws of nature, neighboring patches of space (continuity equation). This creates the notion of a flow. Vice versa, by the same theorem, knowing the Energy of every configuration of particles and forces is sufficient to know what happens as time progresses, to know the dynamics.

Thank you. Although it's hard for me to read this kind of things in english, I think I understand it.

If you don't mind, I have another question, but this is probably an easier one: 
When I think about it myself, it seems reasonable that every elementairy particle is one-dimensional, since only a point is not divisible.
Yet in other sources I read that it must be presented as a function of where it will appear, and those functions can even collide(?) (Bose-Einstein condensate).
Are they both correct, or is my reasoning as usual incorrect?