Explain Like I'm Five

ELI5: Imagine a ring on a table. They putting some marbles in that ring. They can roll anywhere, right? Well, quantum mechanics makes you put those marbles in a neat little grid. The marble can still ‘roll’ like a piece moves on a chess board: to unoccupied spots around it. If there’s something already in it, though, it won’t be able to move there. Each of those spots is a ‘quantum state.’

(Importantly, the ring on the table typically represents spots in phase space—something that involves both position and momentum—rather than real space)

ELI15: A quantum state is a state that a quantum system can be in. That isn’t very helpful, but you are asking about something very fundamental and thus something very difficult to describe without getting into the math.

It is important to note that a ‘state’ means very little without knowing what ‘system’ it describes. A system is made up of all the interacting particles that pull on each other and is what we are interested in describing.

All of these interactions collectively generate the ‘potential’ at every point in space and time, and knowing this potential allows us to write down the specific Schrödinger equation that we want to solve. This equation will have a limited^1^ number of solutions.

Consider your computer science class-instance again. Each instance of the class represents a state, but there is a larger class called System that has an array-type property that holds the States that solve it. Additionally, you should add another property to the State class: occupation. For bosons, this property is an Int, but for fermions, it is a Bool.^2^ Now, in order for a boson to join the system, it needs to increment the occupation counter on one of the States, but for a fermion to join, it needs to find a State with a False occupation and flip it to True.

Allowing for multiple fermions in the same state would result in a loss of information; nothing changes if a True state is flipped to True. This is thus not allowed, forming the basis of the Pauli exclusion principle.

ELI25: A quantum state is a linear combination of eigenstates for an observable quantum operator—typically the Hamiltonian of a system. Saying that the PEP disallows fermions from entering the same quantum state is a crude way of saying that their combined wavefunction must be antisymmetric:

Ψ(𝛙~1~, 𝛙~2~) = -Ψ(𝛙~2~, 𝛙~1~)

But then if

𝛙~1~ = 𝛙~2~

We get

Ψ(𝛙~1~, 𝛙~2~) = -Ψ(𝛙~1~, 𝛙~2~)

Which means

Ψ = 0

And is thus disallowed

^1^ limited means ‘quantized’ here—not ‘finite’

^2^ notably, you get a different system and thus a different set of States for every particle type. So a clump of neutrons would be unable to ‘exclude’ an electron

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.

So I think where popsci messaging is bad is because they get all mixed up between particles and waves

A superposition isn't a particle, it's a wave. It only has the mass/energy associated with the particle, but it is everywhere it can be all at once

The particle is like... The minimum size the wave can fit into. One photon of light can jump one electron up once energy state, and it has to pick one electron to actually do this

You can channel the wave into a particle long enough to measure it, but to measure any aspect of the wave you have to consume it. Now you've converted the energy from one form into another, so any other information that could have been gained is destroyed

That's my understanding at least, it is very much not digital. There's no either or, it's even more analog than analog

One example would be the electrons in an atom. The shell, subshell, orbital and spin together make up one quantum state.

In a more general sense quantum states are solutions to the Schrödinger equation for a given system.

At the subatomic scale, things are less particule-like and more wave-like.

The most famous visualization of this is the double-slit experiment: there's a source of light, two slits and a wall. There should be two lines right? Nope, you get a wave interference pattern. So which slit did the electron take? Both at the same time, it seems. You can know which path it likely took, but in reality the photon could have taken a detour Taco Bell faster than the speed of light for all we know, as long as the end result doesn't it's physically totally fine.

The crazy part of the experiment is that in order measure which slit the photon actually went through, it would have to interfere with your detector. And because it interacted with your detector, the uncertainty collapses and the whole interference pattern disappears. The measurement causes side effects that affect where it possibly could have gone through. You thus only see paths where it did go through your detector.

The universe seems to prefer the path of least action. All possible paths are evaluated at the same time, including ones that would violate the speed of light. You won't catch the universe doing it, but you can observe that photons and electrons make it places they physically shouldn't be able to, but mathematically, they can and do in the real world. Do they even actually travel any given path? We don't know, we know it went from A to B with no idea where it was in-between or how fast it went.

To circle back to your coding example: the particule is a class with getters, but the getters don't read a property, it makes up the value on the fly. So particule.spin, particule.location and particule.speed would return you the values, but they would be inconsistent. It only materializes on demand when probed, and you can't get two of them at the same time. When you check you only get one possible value it can have, but you check again and it's a different value. In C that would be a volatile variable.

That's why in atoms you end up with a blurry electron cloud. At this scale, it's a wave of probable positions, it's everywhere and nowhere at the same time.

A quantum state is basically that. It's not a defined state, it's an equation of all possible states and how probable it is to be in a given state. The only guarantee you have is that all the state will physically make sense if you measure it, so if you measure the spin of an entangled particule, to stay consistent, the other one will take the opposite state because you can't catch the universe in a lie. But until you observe that state, it's both at the same time.

PBS Space Time is a great channel on YouTube for this.

In very simple terms, it means that something is changing state so impossibly fast ("on a quantum level") that we can't tell what exactly that state is besides at the instant we check it. Exactly is doing a lot of heavy lifting here, because we can have an idea or an area, but not exactly. What that means in turn though is that by checking or measuring that state, we have interacted with it, therefore making the state we measured no longer valid for what it currently is now, or at rest.

Think of it like taking a measure of a water droplet, in the middle of a lake. You can say "there it is, those atoms are in that droplet and theyre this hot". But the drop you measured is constantly mixing with the water around it. Sure, you measured the temperature of those atoms in that droplet, but if you try to measure it again you could get a different result. (It's not a perfect example, but it gets the idea through)

Using your programming model, think of it like reading memory in memory that is shorting out. You can read it once, but there's no guarantee that it will be the same value again next time you read that bit, because it's in constant flux.

If you put a cat into a box, then leave and come back sometime later and you can't see or hear the cat (just the outside of the box), you don't actually know if the cat is still alive or if it died while you were away.

Because of the uncertainty, the cat is considered to be in a quantum state of BOTH dead and alive.

You open the box to observe, and can see it breathing: it's just asleep. It is no longer in a quantum state, as you can be certain that it is alive.