I’ve been reading a lot about massive stellar objects, degenerate matter, and how the Pauli exclusion principle works at that scale. One thing I don’t understand is what it means for two particles to occupy the same quantum state, or what a quantum state really is.
My background in computers probably isn’t helping either. When I think of what “state” means, I imagine a class or a structure. It has a spin field, an energy_level field, and whatever else is required by the model. Two such instances would be indistinguishable if all of their properties were equal. Is this in any way relevant to what a quantum state is, or should I completely abandon this idea?
How many properties does it take to describe, for example, an electron? What kind of precision does it take to tell whether the two states are identical?
Is it even possible to explain it in an intuitive manner?
Not a physicist, but I’ve listened to some podcasts. You’re close enough for a hobbyist.
First off, there are 2 types of particles: Bosons and Fermions. Bosons don’t follow the Pauli Exclusion principal. You can cram more and more photons into a tiny space without reasonable limits. There’s an “unreasonable” limit where eventually things break, but that’s not related to Pauli.
Fermions follow Pauli. Electrons are Fermions, and won’t let you cram them too closely together. Electrons bound to an atom settle into energy levels called “shells”. The first shell can hold two electrons, but only if they’re in different quantum states. Since they’re at the same energy level, we’re left with spin. To fit two electrons into the lowest shell (energy level), one has to be spin-up, and the other must be spin-down. As you add more electrons to the atom, they begin to fill higher shells. Some of these shells can hold more than 2 electrons, but the electrons always get added in pairs. There aren’t any shells with an odd-number limit of electrons because you fill the shells with spin-up and spin-down electrons.
Now, what you’re talking about, massive stellar objects, and degenerate matter, is an atom taken to 11. A star is an equilibrium of outward pressure from the fusion reactions, and inward pressure from gravity. Once a star stops fusing elements, there’s nothing to counteract gravity, and the star collapses catastrophically. Giant stars can leave behind a core so heavy that it keeps compressing until if forms a black hole. But if it’s not quite big enough to do that, it will just squeeze all the leftover matter into some weird shit. First, at the surface all the protons and electrons will be squeezed together to form neutrons. I suppose if there are leftover electrons they just kind of swim around on the surface
Underneath all these neutrons are neutrons that are squeezed so close together they’ve been broken apart into raw quarks. Quarks are fermions, but they have 3 different charges (called color) instead of just 2. And their electrical charge is a fraction of an electron charge, either 1/3 or 2/3 a fundamental charge. A neutron is 3 quarks, and a proton is 3 different quarks (and those are all gone at this depth anyway). Once things are broken down into quarks, it’s called degenerate matter. Conditions are so extreme that matter as we know it can’t form. It’s degenerate.
And the rest is just theory. There’s a spaghetti layer, and a lasagna layer, named for the theoretical shape the degenerate matter takes at that pressure. And below that is…I guess the next pasta type would be some kind of hard, solid block of gluten.