The Mystery of Matter's Solidness: Why Objects Don't Pass Through Each Other

Scientific Summary

The article explains why matter, although composed of more than 99.999% empty space, is solid and impenetrable thanks to three intertwined quantum and electromagnetic mechanisms. The Pauli exclusion principle forbids two identical electrons from occupying the same quantum state, creating a violent repulsion at very short distances. The electrostatic Coulomb repulsion between negatively charged electron clouds prevents atoms from penetrating each other. Finally, electron degeneracy pressure resists any further compression. Matter is therefore held together by a subtle balance between attraction (nuclei-electrons) and repulsion (Pauli + Coulomb), making solidity an emergent property of the fundamental laws of physics.

Why don't objects pass through each other even though matter is almost entirely empty?

Although an atom is more than 99.999% empty space, matter is solid and impenetrable due to three intertwined quantum and electromagnetic mechanisms. Pauli's exclusion principle forbids two identical electrons from occupying the same quantum state, creating violent repulsion at very short distances. Coulomb electrostatic repulsion between negatively charged electron clouds prevents atoms from penetrating each other. Finally, electron degeneracy pressure resists any further compression. Matter is thus held together by a subtle balance between attraction (nucleus-electrons) and repulsion (Pauli + Coulomb).

The Paradox of Emptiness: An Almost Empty Yet Solid World

If all the empty space inside the atoms making up a human being could be removed, their volume would shrink to that of a grain of dust. Yet, our daily experience confronts us with the opposite reality: matter is solid, impenetrable. We do not pass through the ground, and our hand stops abruptly on the surface of a table. This apparent solidity is one of the most fundamental and counterintuitive phenomena in physics, resulting from the laws of quantum mechanics and electromagnetism.

The answer lies in three key principles: electron exclusion, the wave-like nature of particles, and electromagnetic repulsion forces. An atom is not a compact little ball, but a diffuse structure where particles are never exactly in one place. They rather form areas of probable presence, governed by energy levels and the physical fields that make them interact.

N.B. :
At the atomic scale, matter is more than 99.999% empty space. Atomic nuclei have a radius on the order of \(10^{-15}\) m, while atoms measure about \(10^{-10}\) m.

The Pauli Exclusion Principle: When Nature Imposes Quantum Distances

The first and deepest reason for the solidity of matter was formulated by physicist Wolfgang Pauli (1900-1958) in 1925. The Pauli exclusion principle states that two identical fermions (such as electrons) cannot be in the same quantum state.

In an atom, electrons are organized in layers (orbitals) of defined energies. Each orbital can only accommodate a limited number of electrons with opposite spins. When two atoms approach each other, their electron clouds begin to overlap and the regions of electron presence probability form a quantum barrier without contact.

When two atoms approach, their valence electrons begin to occupy regions of space already associated with the quantum states of the other atom. The Pauli exclusion principle then forbids these identical electrons from sharing the same quantum state. To avoid this forbidden overlap, the system must increase its energy, which manifests as a very intense repulsive force at very short distances.

This repulsion is not, however, dominant at all times. At slightly greater distances, the electrostatic attraction between nuclei and electrons balances this repulsion, creating a stable equilibrium distance. It is this subtle balance between quantum attraction and repulsion that allows matter to remain coherent and solid, while preventing its gravitational collapse.

N.B.:
The "very short distance" corresponds to interatomic separations for which electron clouds begin to strongly overlap, typically less than 0.1 to 0.2 nanometers. The quantum kinetic energy imposed by the Pauli exclusion principle increases abruptly, generating an extremely steep repulsion. At "slightly greater distances", on the order of 0.2 to 0.3 nanometers, the electromagnetic attraction between nuclei and electrons dominates, creating a stable equilibrium distance that ensures the cohesion and solidity of matter.

Electromagnetic Force: Repulsion Between Negative Charges

Even in the absence of the exclusion principle, a major barrier remains. Electrons all carry a negative electric charge. Coulomb's law, established in the 18th century, states that charges of the same sign repel each other with a force inversely proportional to the square of the distance separating them \( F = k \frac{q_1 q_2}{r^2} \).

When two atoms approach, the negatively charged electron clouds interact first. The Coulomb repulsion between these clouds quickly becomes enormous as the distance decreases, preventing the penetration of the positive nuclei. Thus, even if atoms were mostly made of empty space, this "emptiness" is guarded by an extremely effective repulsive electric field. The hardness of a material, such as diamond, is directly related to the strength of chemical bonds and the intensity of this electronic repulsion.

N.B.:
A common analogy is to compare matter to two rapidly rotating fans. Although the space between the blades is empty, it is impossible to pass an object through rotating blades without collision. On a macroscopic scale, the probability of finding a free passage is practically zero. Similarly, even if atoms are essentially empty, electrons are never still. Their quantum clouds extend, fluctuate, and constantly renew. At our scale, this ceaseless activity results in a stable repulsive barrier, preventing material objects from passing through each other.

Wave-Particle Duality and "Degeneracy Pressure"

Quantum mechanics teaches us that particles like electrons also have a wave-like nature. The wavelength associated with an electron (De Broglie wavelength) depends on its momentum. When electrons are confined in a small volume (such as when trying to compress matter), their effective wavelength decreases, which increases their kinetic energy. This increase in energy due to confinement manifests as a pressure, called electron degeneracy pressure.

It is this same pressure that prevents white dwarfs, remnants of stars like the Sun, from collapsing under their own gravity. On our scale, it is an additional component that opposes the compression of matter, contributing to its rigidity. For two objects to pass through each other, one would have to either violate the exclusion principle or compress their electrons to the point of overcoming the degeneracy pressure, which would require densities and energies totally beyond reach under ordinary terrestrial conditions.

Why Do Particles Sometimes Pass Through Matter?

FAQ: Everything about the solidity of matter

Forces and Principles Responsible for the Solidness of Matter
Principle / Force	Scale	Role in Impenetrability	Example / Analogy
Pauli exclusion principle	Quantum (fermions)	Prevents two electrons from occupying the same quantum state, generating a short-range repulsion.	Impossible to stack more than two electrons per atomic orbital.
Electrostatic repulsion (Coulomb)	Atomic / Molecular	Negatively charged electron clouds repel each other with intense force.	Repulsion between two magnets oriented with like poles facing each other.
Electron degeneracy pressure	Quantum / Stellar	Quantum pressure due to electron confinement, which resists compression.	Supports the equilibrium of a white dwarf against gravitational collapse.
Chemical bonds	Molecular / Macroscopic	Organize atoms into rigid structures (crystalline lattices, polymers) that transmit repulsive forces.	Rigid covalent lattice of diamond vs. weak stacking of graphite atoms.

What is Pauli's exclusion principle and how does it contribute to the solidity of matter?

Formulated in 1925 by Wolfgang Pauli, this fundamental quantum principle states that two identical fermions (such as electrons) cannot occupy the same quantum state. In an atom, each orbital can only contain two electrons with opposite spins. When two atoms approach each other, their electron clouds overlap, and the exclusion principle forbids their valence electrons from sharing the same quantum states. To avoid this forbidden situation, the system must increase its energy, manifesting as an intense repulsive force at very short distances, thus contributing to the impenetrability of matter.

What is the role of electrostatic repulsion (Coulomb's law) in solidity?

All electrons carry a negative electric charge. Coulomb's law states that like charges repel each other with a force inversely proportional to the square of the distance between them: F = k·q₁·q₂ / r². When two atoms approach, their negatively charged electron clouds interact first, generating Coulomb repulsion that becomes enormous at short distances. This repulsion prevents positive nuclei from penetrating the neighboring electronic space. The hardness of a material (like diamond) is directly related to the intensity of this electronic repulsion and the strength of chemical bonds.

What is electron degeneracy pressure?

Electron degeneracy pressure is a direct consequence of Pauli's exclusion principle and wave-particle duality. When electrons are confined to a small volume (for example, when trying to compress matter), their effective wavelength decreases, increasing their kinetic energy. This increase manifests as a pressure that resists compression. This same pressure prevents white dwarfs (remnants of stars like the Sun) from collapsing under their own gravity. At our scale, it contributes to the rigidity of matter. To pass through an object, one would need to overcome this pressure, which would require densities and energies inaccessible under normal terrestrial conditions.