Just in the interest of being Less Wrong™, let’s explore why it’s not true that solidity is an illusion on account of matter (supposedly) being mostly empty space.
The popular aphorism goes that matter is mostly empty space. The reasoning is that matter is made of atoms, which are situated and vibrating some distance apart from each other in space, held in place by physical forces, and within those atoms the distance between the electron shells and the nuclei are extremely far relative to the size of the nuclei. Maybe one would also extend the argument to the space between the electrons in the shells (okay, technically electron shells aren’t actually made of electrons; the electrons don’t exist until you detect them and collapse the wave function), the space between the shells, the space between the protons and neutrons within the nucleus, and the space between the quarks within the protons and neutrons.
But the thing is this: why is it notable how much space there is, when there is no solidity to contrast it with? Electrons aren’t solid, protons aren’t solid, and quarks aren’t solid. They are forcefields of some sort with no clearly defined boundaries. You’re in a forcefield right now—the earth’s gravity. That field extends infinitely in all directions. Similarly, an electron’s electric field extends infinitely, just with faster attenuation and extremely small intensity. The electron itself (when it even exists) is just an excitation within a field. So, all you have is space and fields within it that permeate it everywhere.
Solidity is therefore not a concept that applies to the micro scale. If solidity exists at all, it is merely a mode of material interaction, applying only on a macroscopic scale, by which objects cannot pass through each other. Being understood as such, it makes no sense to say that things are any less solid than they appear to be due to sub-nanoscopic structures, because the solid-vs.-vacuum dichotomy doesn’t exist on that scale. If anything, nuclear physics tells us that, solidity being a purely macroscopic phenomenon, things can only be exactly as solid as they appear and not any less so. And as for the empty space supposedly existing within matter between particles, there is nothing other than empty space, so that idea is meaningless. (You could say only space without forcefields in it is “empty,” but all space is full of fields and forcefields.)