By Qasim Mahmood Raja
Why is matter stable? We are all well aware that we are made up of atoms, but why are they stable? Why don’t they all just collapse into a compact configuration, like a massive star that collapses due to its strong gravitational pull and turns into a black hole? I bet you’ve never thought about why you haven’t turned into a black hole. But you know what? The time has come, and now we’re going to think about this together.
I know what you’re thinking you’re going to say: electrons repel each other and that’s why they don’t just all come together. Another person might add that we shouldn’t forget about thermal energy. Well, that’s all true, but today I am going to introduce an additional culprit which is quite often ignored, and that’s (drum roll please!) the Pauli Exclusion Principle.
First, a slight review of quantum mechanics. In Quantum mechanics, particles exist in quantum states which have fixed energy. Energy only comes in discrete packets. You can jump from one energy level to the next, say from one joule to 2 joules. The energy of particles doesn’t increase continuously. Also, particles in different quantum states can have the same energy level. Particles are of two types, bosons, and fermions. Particles like electrons and neutrons are fermions, while a photon is a boson. Composite objects like atoms are also fermions as long as they contain an odd number of elementary fermions.
The real culprit is the Pauli Exclusion principle which says that fermions cannot occupy the same quantum state. What instead happens is each progressive electron keeps going to the next energy level. The highest such energy level is called Fermi energy. For ordinary metals, their Fermi energy is much greater than their thermal energy, so in this sense, they are ‘cold’, i.e., the energy contributed by Fermi energy is much greater than the one merely due to temperature.
This quantum-mechanical energy acts analogous to ordinary thermal energy in that it exerts pressure that resists compression by other forces such as gravity, etc. (the more they are confined the harder they fight back).
Now, let’s see what happens in the stars. This is where you truly witness the power of this pressure due to the Pauli exclusion principle which, although it only contributes partially to the stability of ordinary room temperature objects, for stars, it being sufficient enough or not becomes more or less the only factor that determines their stability.
When stars with sufficiently low mass, like our Sun (no offense, sun), exhaust their fuel, the main factor that prevents their collapse is the electronic pressure resulting from the Pauli exclusion principle which keeps it stable. It still collapses into a dwarf star, mind you, but at least it doesn’t turn into a black hole!
However, when stars are more massive than the Chandrasekhar limit, this pressure of electrons is not enough to keep them stable. The star begins to collapse, but something fishy happens during the collapse, protons merge with electrons creating neutrons (also fermions). These neutrons create an even greater (quantum mechanical) pressure which, in stars within the so-called Chandrasekhar mass limit, is enough to prevent them from completely collapsing and voilà, a neutron star is born!
But when stars are too massive, say more than the Tolman-Oppenheimer-Volkoff limit, even this pressure of neutrons is not enough to overcome gravity, and the neutron star collapses, and we get (big drum roll, please!) a black hole.
This is a good counterexample for those who think quantum mechanics applies only at small scales.
Now, you might ponder that this is good
and all, but is this quantum mechanical pressure (termed Pauli pressure) as effective as the good old Coulomb repulsion of electrons? Now, you might remember from your chemistry class that crystals such as the table salt you use are very stable and formed due to the ionic (read charged) nature of their constituents. Essentially, the repulsion of like-charged particles forms the beautiful pattern observed in (ionic) crystals. Could this pressure be due to the Pauli exclusion principle forms crystals? The answer is in the affirmative!
They’re formed when a group of ultra-cold atoms repels each other solely due to the Pauli exclusion principle. They are very fragile and tiny.
Isn’t this amazing? And this is the pic of the experiment.
So, the takeaway here is that it seems this pressure of fermions is quite important to the stability of matter, and also, Pauli crystals are so cool!
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