What is matter? Mostly empty space.
Things don't fall through other things because they are levitating on an electrostatic field! . . . . When you sit on a chair, you are not really touching it. You see, every atom is surrounded by a shell of electrons. This electron cloud presents a rather negative face to the world. Remember that like charges repel each other. When two atoms approach each other, their electron shells push back at each other, despite the fact that each atom's net charge is 0. This is a very useful feature of nature. It makes our lives a lot easier.From jlab.
Now the question you should be asking is, if atoms push away from each other, why doesn't the entire universe just blow away from itself? The answer is that some, actually most atoms' electron shells are not full. When two atoms come together and have empty spaces in their electron shells, they will share electrons to fill in the spaces in both of their shells.
Hydrogen atom -- Unlike planets revolving around the sun, the electron is not held around the nucleus of the atom by gravity, but rather by electromagnetism.
What we see, what we touch, what we lean upon, chew, swallow, cut, and build, is almost entirely empty space, only partially filled with diffuse electron clouds and relatively tiny atomic nuclei.
Electrons in an atom are said to inhabit areas called atomic orbitals. This area is said to form a probability cloud, space where the electron may be situated. In the helium atom . . . the atomic orbital where the electron may be situated describes a sphere. However, the cloud or atomic orbital that an electron can occupy changes shape depending on the energy of the electron. So some electrons orbit in the shape of a dumbbell designated as p. And the heavier the element, the more electrons there are and the more complicated shapes there are for the orbitals in the atom.Wikipedia.
A simple game of ping pong becomes a metaphor for the world: an empty ball, batted back and forth from surface to surface; the thwock of the ball against the paddle created by the repulsion of electric charges. We are electric illusions, cloudy ghosts of positive and negative charges.
The conclusion that all things are (mostly) empty will sound familiar to casual students of Mahayana philosophy. And the modern theory is not too far from Democritus's.
At least as early as 400 BC, Democritus was teaching and writing that the hidden substance in all physical objects consists of different arrangements of 1) atoms and 2) void. Both atoms and the void were never created, and they will be never ending. . . . The void is infinite and provides the space in which the atoms can pack or scatter differently. The different possible packings and scatterings within the void make up the shifting outlines and bulk of the objects that we feel, see, eat, hear, smell, and taste. We sense hot and cold, but hot and cold have not real existence. For hot and cold are simply sensations produced in us by the different packings and scatterings of the atoms in the void that compose the object that we sense as being "hot" or "cold."Wikipedia.