Why Can’t Two Electrons Share the Same State? The Pauli Exclusion Principle Explained

Why is a table solid? Why does the periodic table have rows of 2, 8, 18 and 32? Why doesn’t a dead star simply collapse to a point? The answers trace back to one rule, stated by Wolfgang Pauli in 1925: no two electrons in an atom can be in the same quantum state at the same time. Our Exclusor tee is that rule given a bouncer’s job. This post explains what the rule says, why it holds, and what it does not mean.

What does the Pauli exclusion principle say?

Britannica’s definition is a good starting point: the principle is the “assertion that no two electrons in an atom can be at the same time in the same state or configuration,” proposed in 1925 by Pauli “to account for the observed patterns of light emission from atoms,” and later generalised to a whole class of particles (Britannica^[1]). For electrons in an atom, an equivalent statement is that no two electrons can share all four quantum numbers: the shell n, the orbital shape ℓ, the orientation mℓ, and the spin projection ms.

Pauli received the 1945 Nobel Prize in Physics “for the discovery of the Exclusion Principle, also called the Pauli Principle” (NobelPrize.org^[2]).

Which particles obey it?

Particles that obey the rule are called fermions; particles that do not are bosons. Electrons, protons, neutrons, muons and neutrinos are fermions. Photons are bosons. Fermions have half-integer spin (½, 3⁄2, …); bosons have whole-number spin (0, 1, 2, …) (Britannica^[1]; Quanta^[3]).

Why can’t two fermions be in the same state?

The deepest answer is about identity. Two electrons are not merely similar; they are indistinguishable even in principle. In the Feynman Lectures, Richard Feynman shows what follows: if you swap two identical particles, the quantum amplitude can only be multiplied by +1 or −1, because swapping twice must bring you back to where you started. Particles whose amplitudes add with the plus sign are Bose particles; those that combine with the minus sign are Fermi particles (Feynman Lectures III-4^[4]).

Now try putting two Fermi particles into exactly the same state, including spin. The amplitude is “direct minus exchanged,” and when both states are identical those two terms are equal, so the total is zero. As Feynman puts it, “it just isn’t possible at all for two Fermi particles—such as two electrons—to get into exactly the same state” (Feynman Lectures^[4]). The exclusion principle is not an extra law bolted on. It is what the minus sign does.

Why do half-integer spins go with the minus sign?

That link is the spin–statistics theorem. Quanta Magazine’s Charlie Wood explains that Markus Fierz proved in 1939 that the two properties are consequences of the mathematical structure of quantum theory, and that his adviser Pauli published a refined proof the following year (Quanta^[3]). Pauli’s 1940 paper, “The Connection Between Spin and Statistics,” is still cited in our product sources. Feynman famously admitted he could not give an elementary explanation of why the two go together, calling it “one of the few places in physics where there is a rule which can be stated very simply, but for which no one has found a simple and easy explanation” (Feynman Lectures^[4]).

What is spin, and how do we know electrons have two states?

Pauli’s 1925 rule needed a fourth quantum number with exactly two values, which he described as a “two-valuedness not describable classically,” as the Perimeter Institute’s centenary article recounts (Perimeter Institute^[5]). That two-valued property became electron spin.

Spin quantisation had already shown up dramatically in the lab. In the Stern–Gerlach experiment (1922), a beam of silver atoms passed through a non-uniform magnetic field split into two separate beams instead of smearing out (Britannica^[6]). Our sticker Bifurcor is that experiment: two lanes, no middle lane. Spin-½ has another odd feature. Rotate an electron by 360° and its wavefunction picks up a minus sign; it takes 720° to return to the start (Quanta^[3]). That is Revolvix’s whole personality.

How does the exclusion principle build the periodic table?

Each atomic orbital can hold two electrons, one of each spin. Once it is full, the next electron must go into a different orbital, usually higher in energy. The Perimeter Institute notes that the shell capacities 2, 8, 18, 32 (the series 2n²) were known to be important for chemistry before anyone knew why, and that the exclusion principle explained them (Perimeter Institute^[5]).

Feynman walks through what would happen if electrons were bosons instead: every atom would be “a little round ball with all the electrons sitting near the nucleus, nothing directional and nothing complicated.” Because electrons are fermions, lithium’s third electron must sit farther out and is easier to remove, which is the beginning of chemistry (Feynman Lectures^[4]). Neon, with all of its n = 2 states filled (1s² 2s² 2p⁶), is the full house that Exclusor guards.

Why is matter solid?

Atoms are mostly empty space, so why don’t they pass through each other? Part of the answer is electrostatic repulsion, but the exclusion principle is essential. Feynman: “the stability of matter on a large scale is really a consequence of the Fermi particle nature of the electrons” (Feynman Lectures^[4]). Squeeze two atoms together and their electrons would have to share states they cannot share, so they are pushed into higher-energy states instead. That costs energy, and resisting the squeeze is what we feel as solidity.

Is the exclusion principle a force?

No. There is no extra force law in the equations. The effect comes from which states are allowed, not from a push between particles. Feynman calls the result an “apparent force” on spins, much stronger than the tiny magnetic interaction between electrons (Feynman Lectures^[4]). Our house wording is simple: exclusion is not a force; it is a rule about allowed states.

How does Pauli exclusion hold up dead stars?

When a star like the Sun runs out of fuel, its core contracts into a white dwarf. What stops further collapse is electron degeneracy pressure: electrons crammed into a small volume must occupy ever-higher momentum states, because the low ones are already full (Britannica^[7]). Neutron stars are held up in a similar way by neutrons, together with nuclear forces, as the Perimeter Institute piece explains (Perimeter Institute^[5]).

That pressure has a limit. Above about 1.4 solar masses (for a carbon–oxygen white dwarf), electron degeneracy cannot win. Subrahmanyan Chandrasekhar shared the 1983 Nobel Prize in Physics “for his theoretical studies of the physical processes of importance to the structure and evolution of the stars” (NobelPrize.org^[8]). The history of that limit has more names in it than Chandrasekhar’s, as we explain in Who Really Discovered It? Our Chandrasekhar sticker carries the number.

What about bosons? Do they like to share?

Yes, and dramatically. Feynman shows that identical bosons are more likely to enter a state that is already occupied (Feynman Lectures^[4]). The statistics are named after Satyendra Nath Bose, whose 1924 derivation of Planck’s radiation law was extended by Einstein (Britannica^[9]); see our Bose sticker. At very low temperatures, bosonic atoms can pile into a single quantum state, a Bose–Einstein condensate. The 2001 Nobel Prize went to Eric Cornell, Wolfgang Ketterle and Carl Wieman “for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms” (NobelPrize.org^[10]). We follow that thread in What Happens at Absolute Zero?

Common misconceptions

• “Only one electron in the universe can have spin up.” No. The rule applies to states within one system, such as one atom. Two electrons in different orbitals can have the same spin.
• “Electrons can’t be in the same place.” The two electrons in a filled 1s orbital overlap completely in space; they differ in spin. The rule is about the whole state, not position alone (Feynman Lectures^[4]).
• “Pauli explained everything in 1925.” Pauli stated the rule for electrons in atoms. The explanation through the spin–statistics theorem came later, from Fierz (1939) and Pauli (1940) (Quanta^[3]).

Key terms in plain English

• Quantum state: the full specification of a particle in a system: for an electron in an atom, its orbital and its spin together.
• Fermion: a particle with half-integer spin that obeys the exclusion principle. Electrons, protons and neutrons are fermions (Britannica^[1]).
• Boson: a particle with whole-number spin. Any number of identical bosons can share a state, and they are more likely to join one that is already occupied (Feynman Lectures^[4]).
• Spin: an intrinsic angular momentum with no exact classical picture. For an electron, measurements along any axis give one of two values.
• Degeneracy pressure: the resistance to compression that arises because fermions packed together must occupy higher-momentum states. It holds up white dwarfs and, with nuclear forces, neutron stars (Perimeter Institute^[5]).

Why does chemistry depend on spin?

Because two electrons can share a region of space only if their spins are opposite, the exclusion principle shapes how atoms bond. Feynman explains that the strongest chemical binding comes from two electrons of opposite spin sitting between two nuclei, and that there is no stronger binding because the exclusion principle allows no more than two electrons there (Feynman Lectures^[4]). He also notes the role the principle is believed to play, acting through free electrons, in the alignment of spins in ferromagnetic materials, the reason iron can be a magnet. From the shape of the periodic table to the bonds in your body to the fridge magnet, it is the same minus sign at work.

The bottom line

The exclusion principle is not a force and not an extra law. It is what happens when identical particles combine with a minus sign. That one sign gives atoms their shells, chemistry its variety, solids their solidity and white dwarfs their ceiling. Exclusor’s job description fits on a door: one per state, no exceptions, spin checked at the entrance.

FAQ

Who discovered the Pauli exclusion principle?

Wolfgang Pauli, in 1925, to explain atomic spectra (Britannica^[1]). He won the 1945 Nobel Prize for it (NobelPrize.org^[2]).

Do protons and neutrons obey the exclusion principle?

Yes. Both are fermions. Feynman uses it to explain why a proton and neutron can bind into a deuteron while two protons cannot form a stable “helium-2” nucleus (Feynman Lectures^[4]). See What Holds the Nucleus Together?

Why do electrons pair up with opposite spins?

Because an orbital offers exactly two distinct spin states. Fill both, and the orbital is full (Britannica^[1]).

Can the exclusion principle be broken?

No violation has been observed. It follows from the spin–statistics theorem in standard quantum field theory (Quanta^[3]).

Explore the rule in pixels: Exclusor, Bifurcor and the Allowed Values Only sticker sheet, or the whole Quantum collection.

References

1. Encyclopaedia Britannica, “Pauli exclusion principle”. https://www.britannica.com/science/Pauli-exclusion-principle
2. NobelPrize.org, Wolfgang Pauli, Physics 1945, facts. https://www.nobelprize.org/prizes/physics/1945/pauli/facts/
3. Charlie Wood, “Matter vs. Force: Why There Are Exactly Two Types of Particles,” Quanta Magazine (2025). https://www.quantamagazine.org/matter-vs-force-why-there-are-exactly-two-types-of-particles-20250623/
4. Feynman Lectures on Physics, Vol. III, Ch. 4: Identical Particles. https://www.feynmanlectures.caltech.edu/III_04.html
5. Perimeter Institute, “The Pauli Exclusion Principle, 100 Years Later”. https://perimeterinstitute.ca/news/pauli-exclusion-principle-100-years-later
6. Encyclopaedia Britannica, “Stern-Gerlach experiment”. https://www.britannica.com/science/Stern-Gerlach-experiment
7. Encyclopaedia Britannica, “White dwarf star”. https://www.britannica.com/science/white-dwarf-star
8. NobelPrize.org, Subrahmanyan Chandrasekhar, Physics 1983, facts. https://www.nobelprize.org/prizes/physics/1983/chandrasekhar/facts/
9. Encyclopaedia Britannica, “Satyendra Nath Bose”. https://www.britannica.com/biography/Satyendra-Nath-Bose
10. NobelPrize.org, The Nobel Prize in Physics 2001 (Bose–Einstein condensation). https://www.nobelprize.org/prizes/physics/2001/summary/

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.