You can’t see what sub atomic particles look like because they’re smaller than light itself … well, at least smaller than the wavelength of visible light. But if you hit an atomic nucleus hard, really hard, you can break it apart and see what it’s made of and how those pieces interact. It’s somewhat like trying to figure out how a Swiss watch works by shooting it with a gun.
Over the last century, scientists have done just that. The guns they used are particle accelerators (colliders) and they help us develop what’s known as the Standard Model of particle physics. This Standard Model describes nuclear interactions that mediate the dynamics of the known subatomic particles. Any model has its limits. A desk-top globe is a model of the earth, but it doesn’t show the current weather patterns and you can’t use it to find your way home from the grocery store. It shows one thing well at a macro scale: political or topographic or some other feature. A globe works well because it shows us what the world looks like from a distance. Without it (and without pictures from space), all we can see of the Earth is as far as the horizon.
In the same way, the Standard Model is a representation of the very small, but it also has its limits. It’s good at showing how sub-atomic particles interact, but it doesn’t show what happens with dark energy, dark mater, neutrino oscillations, or gravity (as described by general relativity).
And there may be another problem. The model appears to leak.
If you want more explanation of the standard model in layman’s terms, click here. It’s a great video.
If you want to see what university education might look like a hundred years from now, read Cohesion Lost, a science fiction short story full of suspense, a couple of twists, and a little humor.