You've probably heard that the atoms that make up your body and all other normal matter in the Universe are mostly empty space. That's actually true - yet we seem solid.
Solid enough the elements in our atoms can't just pass through the empty spaces of other atoms, and vice versa.
It all has to do with the electrons that orbit the nucleus of an atom. Drawings of atoms show electrons buzzing around a nucleus in a nice neat pattern, but that's not the case at all - they sort of swarm all around it in more of a cloud configuration.
In order to pass through another atom, the electrons of the first atom would have to exist - however briefly - in the same atomic space as the electrons of the second atom. And, put simply, this is impossible.
As first formulated by Austrian physicist Wolfgang Pauli in 1925, no two electrons in an atom can simultaneously be in the same state and configuration. That is, you can't have two electrons occupying the same space doing the same job. They're a bit like the Highlander - there can only be one.
This is what makes solid objects solid, and keeps them from passing through each other. But does that mean we can never really touch anything? Well, not so fast.
This is sometimes explained in quantum mechanics as a repulsive force between the two fermions, and the popular science interpretation is that this keeps atoms from touching other atoms. But the way the word "force" is used to describe these interactions doesn't translate to the way the word is used in the world at large.
In face, according to a 2003 paper in the American Journal of Physics (published here in full on arXiv), "force" is a poor analogy that has the potential to be misinterpreted by new students. (We still don't have a better one though.)
According to Philip Moriarty, a professor of physics at the University of Nottingham, "contact" does exist on the atomic level - it's the point at which the attractive Van der Waals force balances the repulsive Pauli repulsion. But that's not necessarily the same thing as "touch."
"You can't extend what the normal person thinks about touching down to the quantum level, so you have to come up with another definition," he said. "The analogy entirely breaks down."
So you don't have a post-Crisis Superman-style force field either. Soz.