Quantum uncertainty and wave-particle duality are big features of quantum physics. But without Pauli's rule, our Universe wouldn't exist.
Take a look around you at everything on Earth. If you were to investigate what any object is made out of, you could subdivide it into progressively smaller and smaller chunks. All living creatures are made up of cells, which in turn are composed of a complex array of molecules, which themselves are stitched together out of atoms. Atoms themselves can be broken down further: into atomic nuclei and electrons. And finally, atomic nuclei can be further decomposed into their constituent fundamental particles: quarks and gluons. At an elementary level, these are the constituent components of all matter on Earth and, for that matter, all the normal matter we know of in the Universe.
But how do these relatively simple component particles come to make up everything that we see, know, and interact with, here on Earth and in the Universe beyond our world? Even the simplest of complex structures, the atoms, which are composed of atomic nuclei and electrons, come in less than 100 stable or quasi-stable varieties. How is it that such a simple set of “building blocks” gives rise to the enormous diversity of molecules, objects, creatures and everything else we find?
The atomic orbitals in their ground state (top left), along with the next-lowest energy states as you progress rightward and then down. These fundamental configurations govern how atoms behave and exert inter-atomic forces.
When most of us think of quantum mechanics, we think of the bizarre and counterintuitive features of our Universe on the smallest scales. We think about Heisenberg uncertainty, and the fact that it’s impossible to simultaneously know pairs of physical properties (like position and momentum, energy and time, or angular momentum in two perpendicular directions) beyond a limited mutual precision.
We think about the wave-particle nature of matter, and how even single particles (like electrons or photons) can behave as though they interfere with themselves. And we often think about Schrödinger’s cat, and how quantum systems can exist in a combination of multiple possible outcomes simultaneously, only to reduce to one specific outcome when we make a critical, decisive measurement.
In a traditional Schrodinger’s cat experiment, you do not know whether the outcome of a quantum decay has occurred, leading to the cat’s demise or not. Inside the box, the cat will be either alive or dead, depending on whether a radioactive particle decayed or not. If it were a true quantum system, the cat would be neither alive nor dead, but in a superposition of both states until observed. However, you can never observe the cat to be simultaneously both dead and alive.
Most of us barely give a second thought to the Pauli Exclusion Principle, which simply states that no two identical fermions can occupy the same exact quantum state in the same system.
Big deal, right?
Actually, it’s not only a big deal; it’s the biggest deal of all. When Niels Bohr first put out his model of the atom, it was simple but extremely effective. By viewing the electrons as planet-like entities that orbited the nucleus, but only at explicit energy levels that were governed by straightforward mathematical rules, his model reproduced the coarse structure of matter. As electrons transitioned between the energy levels, they emitted or absorbed photons, which in turn described the spectrum of each individual element.
But Bohr’s model was just that: a model that successfully described what was seen. What it didn’t do was explain why this set of rules would exist at all, or provide a set of axioms that allowed such rules to be derived.
Electron transitions in the hydrogen atom, along with the wavelengths of the resultant photons, showcase the effect of binding energy and the relationship between the electron and the proton in quantum physics. The Bohr model of the atom provides the coarse (or rough, or gross) structure of the energy levels, but this already was insufficient to describe the fine and hyperfine structure, which had been seen decades prior.
That’s where the Pauli Exclusion Principle comes in. Simply by demanding that no two identical fermions in the same quantum system occupy the same quantum state, this complex structure emerges: for the behavior of electrons within atoms, as well as for all other composite systems containing multiple identical fermions.
If it weren’t for the Pauli Exclusion Principle, the matter we have in our Universe would behave in an extraordinarily different fashion. The electrons, you see, are examples of fermions. Every electron is fundamentally identical to every other electron in the Universe, with the same charge, mass, lepton number, lepton family number, and intrinsic angular momentum (or spin).
If there were no Pauli Exclusion Principle, there would be no limit to the number of electrons that could fill the ground (lowest-energy) state of an atom. Over time, and at cool enough temperatures, that’s the state that every single electron in the Universe would eventually sink to. The lowest energy orbital — the 1s orbital in each atom — would be the only orbital to contain electrons, and it would contain all of the electrons inherent to every atom.
Wolfgang Pauli’s quantum rule makes existence possible
Reviewed by Explore With Us
on
April 26, 2023
Rating: 5
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