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?
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.locationandparticule.speedwould 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 avolatilevariable.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.