100 years of the Pauli principle
How the rules of the quantum world took shape
How old do you have to be to go down in the history of science? Wolfgang Ernst Pauli managed it at the age of 25. In 1925, he published a theory that is still relevant today and represents a central building block for understanding the world around us. Rightly named after him, the Pauli principle is more than just an abstract quantum mechanical rule: it explains real phenomena, from smartphone technology to stellar physics.
The era of the great scientists
Wolfgang Pauli was born in Vienna on 25th April 1900 and became one of the brightest minds in theoretical physics. At just 21, he obtained his doctorate with distinction and pointed out weaknesses in the prevailing atomic (shell) model in his dissertation [1].
Pauli was active at a time when some of the most renowned figures in science were making huge advances. He initially worked as an assistant to Max Born in Göttingen and later spent some time working with Niels Bohr in Copenhagen [1]. Pauli also maintained close scientific exchanges with Werner Heisenberg and Albert Einstein. Einstein and Pauli corresponded for years on the fundamentals of quantum physics – more than 2000 letters have been documented [2].
The scientific world that Pauli entered was on the verge of fundamental upheaval. It was not until 1900, the year Pauli was born, that the German physicist Max Planck published his hypothesis that energy is not infinitely divisible, but is instead portioned into the smallest of units called quanta [3]. Since then, the strange phenomena of quantum mechanics have preoccupied large parts of the scientific community. Einstein also demonstrated this quantification of energy for light in a paper published in 1905, but a profound understanding of these still new effects was lacking.
The structure of atoms also held a number of mysteries. Although Bohr’s shell model from 1913 already described different energy levels (shells) of electrons, it did not provide a satisfactory explanation for the structure of the periodic table, nor for the fact that electrons do not simply all fall together into the most energetically favourable ground state [1].
Three becomes four: a new quantum number with spin
The lack of an explanation for the nature of the elements also bothered Pauli until he finally had the pivotal idea: in February 1925, he postulated a rule according to which only two electrons are allowed per shell, thus formulating an exclusion principle [4]. According to Pauli’s assumption, the electrons in a shell can never have the same physical (quantum) state.
Up to this point, the electrons of an atom were still described by three quantum numbers (principal quantum number, azimuthal quantum number and magnetic quantum number). Pauli quickly added a fourth, which could be used to describe the “ambiguity” of the electron pairs in the shells. If these two states are present, the atomic shell is full and cannot accommodate another electron [3].
Four numbers define matter
Each electron in an atom is defined by four quantum numbers. In very simplified terms, the quantum numbers work as follows:
• Principal quantum number (n): energy level or size of the electron orbital
• Azimuthal quantum number (l): shape of the orbital (spherical s-orbital, dumbbell-shaped p-orbital, etc.)
• Magnetic quantum number (m): spatial orientation of the orbital
• Spin quantum number (s): indicates the intrinsic angular momentum of the electron (spin, denoted as +1/2 or -1/2)
The result of his theory was a completely revised atomic model that explains the different properties of the elements in the periodic table, as well as the previously mysterious fine splitting of energy levels in what is known as the Zeeman effect [11]. Without the Pauli principle, all electrons would fall into the lowest energy orbital, and the diversity of chemical elements would not exist. Chemical reactions driven by the different energy levels of electrons would not occur – and life as we know it could not have come into being.
The Zeeman effect: when observing the spectrum of an element, characteristic spectral lines can be seen. When a magnetic field is applied, these lines split. This can be explained by the fact that the electrons of an atom occupy individual quantum mechanical states and can therefore be distinguished from one another. The magnetic quantum number is responsible for the splitting of the spectral lines. However, the fine splitting of the lines can only be described by the fourth quantum number introduced by Pauli – later called the spin quantum number.
Order in the atom: electrons and bus passengers
Today, the Pauli principle is taught at every university offering natural sciences: two electrons in an atom cannot have the same values for all four quantum numbers [4]. Shortly after Pauli postulated the fourth quantum number in 1925, it was discovered to be the spin (intrinsic angular momentum) of electrons – a property he himself had previously argued against [1]. Within an atomic orbital with space for two electrons, these electrons must therefore have opposite spins.
The Pauli exclusion principle gives rise to the so-called Hund’s rule for electron occupation in an atom, also formulated in 1925 by the German physicist Friedrich Hund. It describes how electrons initially occupy individual orbitals with the same energy. Only when these orbitals are all already occupied by one electron do pairs form in the orbitals with additional electrons. This phenomenon is strikingly similar to the behaviour of people when choosing seats on a bus and is therefore also described as the “bus seat rule”.
Whether it’s an electron in an atom or a person on a bus, both agree on the choice of the next position to be filled. The electrons follow Friedrich Hund’s rule and the Pauli exclusion principle – people are more likely to follow their desire for privacy.
Consequences of the Pauli principle: hard drives and stellar explosions
The significance of the Pauli principle manifests itself in many ways. For example, it gives rise to exchange interaction – a force that stabilises elementary magnets and thus enables ferromagnetic materials such as iron and nickel [5]. Without this quantum effect, there would be no permanent magnets and therefore no hard drives for computers.
In astronomy, the Pauli principle manifests itself in a spectacular way: as a precursor to stellar explosions. When stars with a mass comparable to that of our Sun have used up their nuclear fuel, gravity pulls them together into white dwarfs. The fact that the star does not continue to compress indefinitely is due to what is known as degeneracy pressure – an opposing force that results from the Pauli principle [6]. Instead of compressing further, the electrons in the star accelerate. When they are accelerated to almost the speed of light by the increasing pressure, an explosion in the form of a core collapse supernova eventually occurs once a threshold value (the Chandrasekhar limit) is reached [6, 7].
Less spectacular, but much more useful, is the Pauli principle in technical applications. It explains how semiconductors work in transistors, in which electrons can occupy or leave certain quantum states, thus enabling circuits and information storage – the basis of all computers and smartphones [8].
LEDs and solar cells are also based on the band model of semiconductors, whose theoretical basis is the Pauli principle [9]. LEDs generate light when electrons fall back from the conduction band into the valence band with photon emission. With solar cells, it works the other way round: photons lift electrons from the valence band to the conduction band, creating electron-hole pairs and enabling a flow of current.
We explain an example of state-of-the-art transistors in our ROTH Xplains blog High-performance energy-saving chips
The Pauli effect: the curse of a brilliant mind?
While the Pauli principle explains the world of matter, the Pauli effect is a synonym for chaos. It describes anecdotal evidence that experimental equipment and technology in general failed unusually often in Pauli’s presence [6]. Whether it was the slide projector failing during his lecture or a particle accelerator catching fire in Princeton in 1950, Pauli seemed to attract technical defects as if by magic [10]. His friend and fellow researcher Otto Stern even temporarily banned him from entering the institute for fear of the notorious incidents occurring in Pauli’s presence.
It is impossible to say how much truth there is behind the technological curse of the brilliant scholar. It is clear that Pauli’s work continues to influence science to this day. In 1945, he rightly received the Nobel Prize in Physics [1].
Pauli can be considered to be a key figure for a new era of science. Based on the Pauli effect, Heisenberg formulated the basic principles of quantum mechanics and thus fuelled rapid research in this still new field. Together, the two scientists campaigned for the establishment of the European nuclear research laboratory CERN near Geneva and worked on the idea of a “world formula” – a unified field theory of elementary particles, which remains the goal of science to this day.
Pauli died on 15th December 1958, aged just 58. His work still stands up to scientific progress today. And the next time the centrifuge or printer in the laboratory breaks down, some people may think back to that famous spirit of discovery.
Sources:
[1] https://science.apa.at/power-search/17978254575858792918
[2] https://de.wikipedia.org/wiki/Wolfgang_Pauli
[4] https://schneppat.de/wolfgang-pauli/
[5] https://www.supermagnete.de/magnetismus/Austauschwechselwirkung
[6] https://www.sun.org/de/encyclopedia/degeneracy
[7] https://de.wikipedia.org/wiki/Chandrasekhar-Grenze
[8] https://schneppat.de/pauli-prinzip/
[9] https://www.spektrum.de/lexikon/physik/baendermodell/1213
[11] P. Zeeman: Über einen Einfluss der Magnetisirung auf die Natur des von einer Substanz emittirten Lichtes, Verhandlungen der Physikalischen Gesellschaft zu Berlin, S. 127, 1896. (Die Internetquelle enthält zwischen den Seiten des Artikels irrtümlich weitere Seiten des Bandes.)