You Have Never Touched Anything

You press a finger against glass and feel a surface. There is no surface.

Atoms have no edge. An electron cloud is a probability distribution, not a shell, so there is nothing there for two surfaces to meet along. What actually stops your finger is the Pauli exclusion principle: as the electron clouds of your skin and the glass overlap, the electrons are forced into higher energy states, and the energy climbs so steeply that the push feels like a wall instead of a spring. The push is electromagnetic. How absolutely it refuses to let you through is Pauli.

And no, there is no gap. The clouds do overlap and interact — that overlap is the push. Nothing you feel is fake: the fingerprint, the grip, the pain when you hit a wall are all exactly what a force field feels like when it is stiff enough. "Solid" was the only illusion in the room.

Without the Pauli exclusion principle, matter would not hold its shape at all. Dyson and Lenard proved that in 1967.

Sources:
https://www.wtamu.edu/~cbaird/sq/2013/04/16/do-atoms-ever-actually-touch-each-other/
https://van.physics.illinois.edu/ask/listing/64449
https://www.chemistryworld.com/opinion/why-is-matter-stable/4013146.article
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/16%3A_The_Properties_of_Gases/16.06%3A_The_Repulsive_Term_in_the_Lennard-Jones_Potential
https://en.wikibooks.org/wiki/Molecular_Simulation/The_Lennard-Jones_Potential
https://opentextbc.ca/universityphysicsv3openstax/chapter/bonding-in-crystalline-solids/
https://doi.org/10.1063/1.1705209
https://ncatlab.org/nlab/show/stability+of+matter