One of the most far-reaching consequences of spin was articulated by the Austrian physicist Wolfgang Pauli in 1925. Pauli was tuned in to the work of Goudsmit and Uhlenbeck and many experimenters, so he was ready to take a major quantum leap even before all of the symmetric/anti-symmetric mathematics was worked out. Based on the anti-symmetric wave function requirement for two fermions in a quantum system, Pauli concluded that no two identical fermions could ever occupy exactly the same quantum state.
We need to be clear here. This so-called Pauli exclusion principle only applies to fermions, and it only applies to identical fermions. Bosons are all exempt from this principle, as are a combination of two different kinds of fermion (e.g., and electron plus a proton).
DEFINITION
The Pauli exclusion principle states that no two electrons within an atom can share the exact same set of four quantum numbers.
Electrons, of course, are fermions, and were still the primary object of interest for Pauli and the rest of the quantum mechanics. But there are other interesting fermions out there, too, which are subject to the exclusion principle.
Protons and neutrons, for example, are both spin 1⁄2 particles as well. As you no doubt recall, protons and neutrons make up the nucleus of every atom. Even though the nucleus is incredibly tiny, the Pauli exclusion principle forces all the protons in any given nucleus to find different quantum states. The same applies for all the neutrons. This ultimately leads to the size and density of the nucleus. It also tells us a lot about other aspects of nuclear structure. For example, most nuclei happen to have more neutrons than protons. In extreme cases, the Pauli exclusion principle tells us that the outer parts of nuclei will be only made of neutrons, and this has been verified by experiment.
On a larger scale, astronomers now believe that the aftermath of exploding stars (supernovae) is an object made almost entirely out of neutrons. We call such objects “neutron stars,” even though they are very different from the sort of stars we are familiar with. Since neutrons can’t occupy the same quantum state, they have to pile up into higher and higher energy states, which also have more angular momentum and extend farther in space. If we have any chance of understanding the structure and characteristics of these exotic objects, the Pauli exclusion principle will play a major role in the explanation.
WOLFGANG PAULI
Wolfgang Pauli was born in Vienna in 1900, the year that Lord Kelvin predicted “there is nothing new to be discovered in physics.” Fortunately Pauli chose not to heed this prognosis, and went on to discover lots of new things. Some of these even earned him the 1945 Nobel Prize in physics.
By the time he had finished high school, Pauli had become a self-taught expert on Einstein’s theory of general relativity. His grasp of this subject was so renowned that at the age of 20 he was asked to write a review article that is said to have weighed several pounds. His genius was matched by his hard work; so much that Max Born once said to Einstein, “the little chap is not only clever, but industrious as well.”
Though he earned his fame for working out the implications of particle spin, Pauli was initially quite hostile to the notion. He was so dismissive to Ralph Kronig, who is credited with first toying with the concept, that Kronig opted to never publish his idea. Before finally embracing quantum spin, Pauli would call it “a new Copenhagen heresy.”
In later life, Pauli became fascinated by psychology, and he developed a close friendship with Carl Jung, the founder of analytical psychology. There is therefore a fitting irony in the fact that Pauli was described by one of his students as the “conscience of theoretical physics.”
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