Two Identical Things Can’t Occupy the Same Space fact

An Overly Simplified Explanation of the Pauli Exclusion Principle

The Pauli Exclusion Principle says, two identical fermions (matter particles) can’t occupy the same quantum state. In simple terms, two identical things can’t occupy the same space. This helps to explain why two things can “never touch.”^[1]

This principle generally applies to all particles with a half-integer spin (all fermions, all quarks and leptons). However, it does not apply to particles with an integer spin (bosons). Any number of identical bosons can occupy the same quantum state (although like with fermions with opposite spins their wave-packets overlap, they really aren’t directly touching).^[2]

Let’s see how this Pauli Exclusion Principle works with electrons orbiting an atom first, and then we will see how this same rule applies to quarks and the other quantum particles that make up matter.

TIP: A laser consists of many photons condensed into a single space. Their wave-packets overlap, but they aren’t directly touching. They more over-lapping waves, AKA the more photons, in a single space, the more energy the laser has. Bosons can do that, identical fermions can’t.

TIP: Since atoms are made of quantum particles, it can be helpful to do a quick overview of the standard model of particle physics. See our simple explainer of the standard model here.

Pauli Exclusion in Atoms

In an atom, the Pauli Exclusion Principle says two electrons (types of leptons) with the same charge can’t occupy the same energy state, but two electrons with different charges can. If you think about electrons like tiny magnets, it will help. See the video for a visual.

What are the Pauli Exclusion Principle, Aufbau Principle, and Hunds Rule? This video is simple, the next one by UCBerkely is a little more complete and complex.

Pauli Exclusion and Quantum Numbers

Technically, the Pauli Exclusion Principle says no two electrons orbiting an atom can have the same set of four quantum numbers.

The quantum numbers describe energy state in orbit, orbit direction, magnetic charge, and direction of an electron’s spin.

They are:^[3]

• n (the principal quantum number, the energy state the electron is in).
• ℓ (the orbital angular momentum quantum number, the direction of the orbit).
• mℓ (the magnetic quantum number, the magnetic charge).
• ms (the spin quantum number, the direction of the electron’s spin).

TIP: The concept of Pauli exclusion and quantum numbers applies to elementary particles like quarks, but with a few minor differences. So same basic concept, but a few different proprieties to consider (like “color” for instance).

Pauli Exclusion Only Applies to Matter Particles (Fermions and Leptons with a Half-Integer Spin)

The Pauli Exclusion Principle only applies to particles with a “half-integer spin” (matter particles, which have a 1/2 or -1/2 spin).

Particles with an integer spin (1, -1 or 2, -2), or bosons, are not subject to the Pauli exclusion principle.

This can essentially be simplified to say the principle applies to any particles with mass or anything we consider matter.

Any number of identical bosons can occupy the same quantum state. An example of this is lasers, where many photons are condensed into a single space.

Quantum States and Pauli Exclusion Principle Example.

Pauli Exclusion, Aufbau Principle, and Hund’s Rule – Rule-sets for Electrons

When the above rules are combined with the Aufbau Principle and Hund’s rule, we get all the rule-sets we need to explain the behavior of electrons orbiting atoms. The Aufbau Principle say that Orbitals of the lowest energy are filled first from the bottom up. Hund’s rule says that if there are multiple orbitals of the same energy, each space gets filled before they double up.

Below we explain Pauli Exclusion, which applies to all elementary and composite particles (not just electrons orbiting an atom’s shell), and then we will explain in a bit more detail how the Pauli Exclusion, Aufbau Principle, and Hund’s Rule work together to create the building blocks of elements, the atom.

I suggest watching the next video before moving on.

Pauli Exclusion Principle.

TIP: The exclusion principle is named after it’s discoverer, pioneer of quantum physics and theoretical physicist Wolfgang Pauli.

The Pauli Exclusion Principle in Quantum Particles

The Pauli exclusion principle applies to the elementary particles, and to the composite particles they form.

When speaking of elementary particles, the Pauli Exclusion Principle says two identical fermions (matter particles) can never occupy the same quantum state (same spacetime coordinates, with particles properties like spin, considered). Different types of the same particle and multiple “bosons” (force mediator particles) of the same type can occupy the same quantum state.^[4][5]

In other words, the same kind of quarks or leptons (fermions), with the same spin, mass, charge, etc. can’t be in the same place at the same time (same spacetime coordinates), and instead like-particles change states when they interact, via bosons”.

Arthur Miller’s CERN lecture on Wolfgang Pauli and Carl Jung. This doesn’t have a lot to do with the above, but it is a great video on Wolfgang Pauli as a person and his and Carl Jung’s relationship.

Pauli Exclusion and Boson and Fermion Interaction

Bosons are “force” particles that mediate the forces between fermions. When two fermions interact they don’ touch, rather they effect each other via bosons, and this exchange changes the fermions type.

It’s a lot like a magnet where negative and positive charges attract. Or rather, we are essentially talking about electromagnetic force when we talk about a charge, so it’s almost exactly like a magnet.

This mechanic is why we have all the different fermion types (types of quarks and leptons) and helps explain how each type of fermion fits together with other fermions like a magnetic puzzle to create all the known composite particle that combine to make atoms.

Pauli exclusion principle: How spin works inside proton. This video explains the quantum Antisymmetry Principle (Pauli Exclusion) in more detailed terms.

Pauli Exclusion in Atoms – Technical

Atoms are made out of quantum particles, and the Pauli exclusion principle applies both to the quarks in the atom’s nucleus and protons, and to the electrons orbiting the atom.

In atoms, this Pauli exclusion principle says two electrons with the same state can’t exist in the same orbital and must have opposite half-integer spins, 1/2 and -1/2.

So it is impossible for two electrons to occupy the same space in an atoms shell. This is why we get things like free-radicals and electron sharing between atoms, and why negatively and positively charged electrons bounce around to “holes” in atoms.

The ability of fermions like electrons and quarks to change properties via the forces, and the rules for how they bond together, explain much of how elementary particles interact to form composite particles from quarks, to atoms, to elements.

Solvay Physics Conference 1927. Learn more about Wolfgang Pauli, one of the fathers of quantum physics.

1. This Month in Physics History – January 1925: Wolfgang Pauli announces the exclusion principle
2. Pauli Exclusion Principle
3. Pauli exclusion principle
4. No two identical fermions can have the same quantum state at once?
5. Pauli exclusion principle