Atoms look empty on the surface, but the space inside them isn’t freely navigable. At the core, two key principles make solid objects impenetrable: electrostatic repulsion and the Pauli exclusion principle, tells this interesting article on Live Science.
Putting it in simple words: electrons in atoms don’t orbit neatly; they form probabilistic “clouds” around the nucleus. These clouds carry negative charge, and when the electron clouds of atoms in your hand approach those in a wall, the like charges repel. It’s like trying to bring two north poles of magnets into contact; they push away.
But electrostatic repulsion isn’t the whole story. Electrons are fermions, which means they obey the Pauli exclusion principle, i.e., they can’t occupy the same quantum state or location at the same time. When your electrons meet the wall’s electrons, that rule kicks in. Even if repulsion were somehow overcome, electrons simply can’t collapse into the same state, making interpenetration impossible.
Quantum mechanics does allow for tunneling, i.e., a non-zero (but absurdly tiny) probability that particles can “pass through” barriers. However, the odds of a human, or even a single electron, tunneling across solid objects on a macroscopic scale are effectively zero, “something like 1 in 10 to the power of 10 to the power of 30,” says Raheem Hashmani, a doctoral student in physics at the University of Wisconsin-Madison.
So, in engineering terms, matter isn’t penetrable because electron field interactions and quantum exclusion rules enforce a barrier. The only loophole, quantum tunneling, is absurdly improbable at our scale.