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I have been reading about the exclusion principle a little bit, but I have some questions about it.

How does the information about the state of electrons get "passed around" so that other electrons in similar state can not have that same state? Is there some kind've information carrier?

Is there some unique force created by a set of quantum numbers for a fermion so that, the force then prevents another fermion with the same set of quantum numbers from being permitted? How do electrons know the states of other electrons to determine if their state is allowed?

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Sometimes people say that the Pauli exclusion principle says that "two electrons can't be in the same state." This is not correct. It's not as though each particle has its own "state" that it keeps to itself. It's actually much deeper: the electron field itself has one state it's in (that's the whole point of quantum field theory) and crucially there are simply no states of the electron field corresponding to two electrons with the same spin, position, etc. There is nothing for it to "know," it's just what the quantum electron field is.

Fermionic fields are different from bosonic fields. A boson field also has a single state it's in, but the difference between a bosonic field and a fermionic field is simply that the boson field does have states that correspond to boson particles with the same position, spin, etc. Bosonic fields have way more states than fermionic fields.

(Actually, going a bit further, EVERY field together is really in a single universal state, but that's not really so important for the question at hand.)

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    $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – ACuriousMind May 13 at 9:57
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    $\begingroup$ Nitpick: That bosons have "way more" states than fermions is certainly "intuitively true", but it's not really true, is it? Both the fermionic and the bosonic Fock spaces should have the same cardinality - that of separable Hilbert spaces. $\endgroup$ – ACuriousMind May 13 at 10:02
  • $\begingroup$ Is there a known or relatively easy to verify bijective map between fermionic and bosonic states? $\endgroup$ – lurscher May 14 at 21:05
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Looking for this kind of intuitive understanding of quantum mechanics is one of the things that makes QM hard to learn. You are thinking about how classical particles and waves behave, and are comparing that to quantum behavior. You look for similarities and they make sense because classical physics makes sense. But then the differences do not make sense.

It may be better to think of how quantum mechanical entities behave, and get used to the fact that they are not like classical entities. That is, rather than think about how an electron or photon is kind of like a particle and kind of like a wave, think about the new and different thing electron or photon is. What are its properties?

There are still profound conceptual difficulties. You have to accept that the universe behaves not just in ways that are different from what you expect, but contradict what you expect.

Suppose you had only ever heard of particles. You understand they have a mass, position, and velocity. They have a trajectory. Now someone introduces you to waves. They are different from particles. They don't have a point like position. They extend over a region, perhaps with fuzzy indefinite boundaries. They move, and yet don't have a trajectory. And yet they are something like particles. They carry energy and momentum. And yet they are different. They pass right through each other without bouncing off. It would be very confusing to think of a wave as some sort of particle. It makes more sense when you get used to what a wave is.

Here is a post that explains a photon is neither a particle nor a wave. How can a red light photon be different from a blue light photon? It shows how your intuition can be somewhat helpful and somewhat can get in the way. It turns out that electrons behave like this too, though classically we are more inclined to think of light as waves and electrons as particles.

Here is a link that begins to get at your question. Does the collapse of the wave function happen immediately everywhere? It gets more into how an electron is not like a particle nor a wave. A spread out electron can pass through two slits and interfere with itself on the other side. But then it can hit a single atom. It is very reasonable to wonder how information gets passed around. And yet this is not the right question to ask. There is no answer.

Historically, quantum mechanics addressed this with two sets of rules. One set of rules uses the Schrödinger equation to tell you how the electron's wave function changes with time. This tells you how the electron moves like a wave. These rules apply so long as the electron is not disturbed.

Then the electron gets disturbed, or "measured". Say it hits an atom. The wave function "collapses" to a new state. We don't see what happens during the collapse. We only see that we get a new state and we can describe how it changes with the Schrödinger equation. We can't predict what the new state will be from the old state. There may be a number of possible new states. We can predict probabilities of arriving at each one. Quantum mechanics has no mechanism that shows how information is passed around and no definite answers ahead of time to where it goes. This is called the Copenhagen interpretation of quantum mechanics.

This is something of a messy theory. It was accepted because it fit experiment very well. But it has problems. It isn't very clear exactly what a "measurement" is. It requires two sets of rules to describe what goes on, where one set would be more reasonable. It isn't deterministic.

Quantum mechanics is about a century old. Sometimes it takes a century or two to work out the kinks of a theory, and this is certainly true of quantum mechanics. About 50 years ago, the Everett or "Many Worlds" interpretation was proposed. It is now beginning to get acceptance. Here are a couple links that explain it. Parallel worlds probably exist. Here's why. And What is the Many Worlds interpretation? The jury is still out on this, but it is getting serious attention now.

The Many Worlds interpretation makes exactly the same experimentally testable predictions as the Copenhagen interpretation. But it eliminates the two sets of rules and questions of what a measurement is. It says the universe is deterministic. Where the Copenhagen interpretation says various outcomes might happen, the Many Worlds says all of the possible outcomes do happen every time. When they do, the universe splits into different worlds that can't talk to each other. The wave function doesn't collapse. The randomness comes in because we are split into many different versions of ourselves, and each version is only aware of one world.

This still doesn't provide a satisfactory, intuitive answer to your question. The wave function is all the information about a system that exists. Information gets passed around as described by the Schrödinger equation. Even though there may be two electrons, there is only one wave function that describes everything in all the many worlds. Two electrons never evolve so they have the same state because the Schrödinger equation doesn't permit it. This link explains why not. What causes Pauli's Exclusion Principle?

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    $\begingroup$ I don't see the benefit of discussing Copenhagen vs Many Worlds here. IMHO, that's rather tangential to the question about Pauli exclusion. $\endgroup$ – PM 2Ring May 12 at 13:55
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    $\begingroup$ @PM2Ring - The OP is asking how information is passed around. In Copenhagen, there is a collapse. There is no way to say how information moves around. In MW, information in the wave function continues to flow according to the Scrodinger equation. $\endgroup$ – mmesser314 May 12 at 19:20
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    $\begingroup$ @DescheleSchilder Hidden variable theories have always been preferred by people, and it took considerably more effort to disprove them than would be warranted if it just didn't sound like such a great way to get rid of the "quantum weirdness". Hidden variables sound far more intuitive to humans, whose brains are created to model the world of throwing rocks; but do the experiments, and you get the wrong answers - or the number of hidden variables explodes. The fact that we don't have a good hidden variable theory doesn't come from people not trying. $\endgroup$ – Luaan May 13 at 11:49
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    $\begingroup$ @DescheleSchilder No, hidden variables (at least local ones - bound to single 'particles') contradict experimental results. There exist third interpretation besides Copenhagen and MW - pilot wave; all three give identical results and are mostly philosophical thing :) $\endgroup$ – Arvo May 13 at 14:24
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    $\begingroup$ @DescheleSchilder "Nonlocal" sounds tame; it is not. Local means in this context, among other things, "bounded by the speed of light", and if you break that, you have acausal madness. But somehow blocked from allowing conventional information to be acausal. $\endgroup$ – Yakk May 14 at 19:41
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The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously

Let us talk simple, rock bottom quantum mechanics, not the high language of quantum field theory, which in any case is founded on rock bottom quantum mechanics.

By rock bottom I mean the postulates and the axiomatic postulated elementary particles, as in the standard model.

An important postulate is the wave function, a solution of a differential quantum mechanical equation that describes specific quantum numbers for each energy level of the solution in a potential. Lets take the simple hydrogen wavefunctions. There are three quantum numbers for each energy level, $n, l, m$. The Pauli exclusion fits the experimental observation that there are only single electrons at a single set of $n, l, m$. This makes sense in multi-electron atoms, as if there were no such limit, all electrons of the atom would hover in the lowest energy state, making chemistry impossible. (Even if a different law held, limiting the number in the same energy level chemistry would be different than the one we have.)

In a complex case of more than one atom the potential will not be that simple as to get analytic wavefunctions, but the principle of energy levels as the solution and quantum numbers assigned uniquely to each energy level again holds, thus the simple illustration with the single atoms holds.

If the energy levels are almost a continuum, as they are in the band theory of solids, there is no difficulty in fulfilling the Pauli principle and a large number of electrons.

You ask:

How does the information about the state of electrons get "passed around" so that other electrons in similar state can not have that same state? Is there some kind've information carrier?

The information is built in the wavefunction quantum numbers, no matter how complex the wavefunction is.

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Information does not get "passed around" because it is not even a material thing, it only exists for us and in our imagination which makes us believe that some relative positions of some objects in space have some meaning. But for the nature itself information is just not a thing.

Various particles of matter just keep on moving and interacting with each other until they happen to exchange their energy and more or less temporarily get into one of the locally stable states. How exactly they do the interactions deep down inside - I don't know, and I guess it is not even possible to know for sure, but today we have a way to estimate the shape of the stable regions of space and probabilities of going into ones or the others under various conditions.

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The fact that the two electrons in a given state have one spin up and the other down suggests that the exclusion of others is a result of magnetic dipole interactions.

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    $\begingroup$ All fermions obey Pauli exclusion. That includes neutrinos, which are oblivious to electromagnetism. $\endgroup$ – PM 2Ring May 12 at 14:24
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    $\begingroup$ Ferromagnetism is a direct counterexample to this. Unpaired electrons on adjacent atoms (adjacent in the directions perpendicular to the spin axis) would prefer to have antiparallel spins if the dipole interaction were the dominant factor. However, antiparallel spins lead to symmetric spatial wavefunctions, which end up having a larger electrostatic interaction, which in turn is enough to overpower the dipole interaction. The net result is that parallel spins are energetically favorable (at least over short distances), in direct contrast with the "preference" of the dipole interaction. $\endgroup$ – J. Murray May 12 at 14:43
  • $\begingroup$ +1 The magnetic dipole is primary and the spin is a manifestation of the interaction with an external magnetic field. physics.stackexchange.com/questions/631584/… $\endgroup$ – HolgerFiedler May 13 at 5:27

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