3027: Exclusion Principle

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Exclusion Principle

Title text: Fermions are weird about each other in a standoffish way. Integer-spin particles are weird about each other in a 'stand uncomfortably close while talking' kind of way.

Explanation

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This comic is about the four fundamental forces of physics: gravity, electromagnetism, the strong force, and the weak force. In typical xkcd fashion, Randall also adds a joke entry.

Transcript

[Inside panel:]

Fundamental Forces

1. Gravity
2. Electromagnetism
3. The Weak Interaction
4. The Strong Interaction
5. Electrons are weird about each other

[Caption below list:]

Big news: Physicists have finally given up on trying to explain about the "exchange interaction" and agreed to just make the exclusion principle a force.

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Discussion

It should be noted, that amusingly, since the quantum gravity has yet to be full explained thanks to the fact that gravity affects, and that for all we know, Exclusion Principle may be just as valid, if not more so, to be on the list as Gravity (even though Exclusion Principle should not, generally, be on this list.) -- LilithRose (talk) 06:48, 21 December 2024 (please sign your comments with ~~~~)

I'm in agreement. "Fundamental Forces" aren't an unalterable fact about the physical universe - they are scientists' best explanation for the unalterable facts about the physical universe until we find a better one. As a result there could be an underlying reason for the exclusion principle being just as fundamental to the universe as electromagnetism - we just don't know it yet. Kev (talk) 12:39, 22 December 2024 (UTC)

Just to be clear, there *is* an underlying reason for the exclusion principle being just as fundamental to the universe as electromagnetism, and physicists know what it is. The only thing is the exclusion principle isn't a fundamental *force*, it's a different kind of fundamental thing.

In short, the exclusion principle necessarily arises as a property of certain particles in any system that includes quantum mechanics. If I had to try to give a rough outline of the reason why, I'd say it's something like this:

Suppose you construct an equation describing a quantum system with two particles that are in different positions but are otherwise identical. In many standard examples, this equation would look like the sort of wave equation you get in many problems that use the Schrodinger equation, where the square of the equation represents the probability of the two particles being observed in a particular state.

Now suppose those particles swap positions. What happens to the equation? Well, since the particles are identical, the observed probabilities must be the same; if there was an observable difference from merely swapping their positions, then the particles wouldn't be identical.

However, since the probabilities are the *square* of the equation, that actually leaves two possible solutions for what the equation could be, for exactly the same reason that the square root of 4 has the two possible solutions of 2 and -2. Similarly, the equation of the swapped particles can either be exactly the same as for the unswapped position *or* it could be negated. Which version you get depends on the properties of the particle itself. Particles where the swapped equation stays the same are called bosons. Particles where the swapped equation negates are called fermions.

This negation is what causes the exclusion principle (and indeed, the behaviors unique to fermions more generally), because it means certain combinations of fermions will subtract rather than add amplitude to the final wave function, decreasing the probability of those states occurring, and in some cases even fully zeroing out the amplitude, resulting in a zero probability of certain states happening at all.

For example, the most familiar case of this effect is how two electrons cannot be in precisely the same state in an atom. To see why that's true, suppose that really did happen. By the logic earlier, swapping those electrons must change the sign of the equation describing them, since this is true of all fermions. However, since the two electrons are in precisely the same state after the swap (note that not even their positions changed, unlike the earlier case discussed), it must also be the case that the resulting equation is exactly the same. The only solution for the conditions y=-x and also y=x is if x=y=0, meaning the probability of this happening is zero.

By contrast, that above logic doesn't apply to bosons, because swapping them doesn't need to negate their wave function, so there can be some probability of two or more bosons being in completely identical states, even including identical positions.

If you'd like a more detailed or precise explanation, most intro to quantum mecahnics textbooks have a chapter on the exclusion principle. Gertuviti (talk) 10:39, 23 December 2024 (UTC)

I would say the negation is caused by the underlying physical fact that causes the exclusion principle. The particles don't know about the equations, do they? 😏 Torzsmokus (talk) 06:54, 24 December 2024 (UTC)

Polymagnetic topologies as "color" charge, strong vs weak, etc?

I'm increasingly under the impression that these forces & principles, are each an expression of complex electromagnetic interactions? I've never quite understood why they're viewed as separate forces, instead of distinct-but-related expressions of a single type of force across complex topologies.

Particularly, I'm unclear why quark\gluon "color" interactions are seen as anything other than topologically-asymmetric fields interlocking; it just looks like the behavior of polymagnet fields, to me. (By the way, I'm glad there's now a common term, "polymagnetic", for the patterned fields that I'm sure many of us assembled while playing with tiny neodymium magnets & wire, as kids! Arranging multiple cores for a smaller, denser field, & observing that the patterns could interlock, felt like major 'Aha!' moments for me, at the time.)

I was so frustrated by my own feeling of "this complex thing I know very little about, really seems to have a very basic underlying principle that's being widely misconstrued", that I've petitioned a mindless bot to hear my case. (You'd have to scroll at least about halfway down, to get to any prompts even slightly interesting.) I'm probably wasting everyone's time with this, but it has been bothering me, more & more for decades, & my reading so far hasn't lessened that.

Why is everyone so insistent that these 'other' forces aren't magnetism? Seems like quite literally everything is magnetism, to me. Besides a formal education in the matter, what the heck am I missing, here?

ProphetZarquon (talk) 15:38, 21 December 2024 (UTC)

I don't know what you mean by "complex topologies." Which topology? The reason we know the strong and weak interactions are not the electromagnetic interaction is that they have completely different gauge symmetries, among other reasons. The electromagnetic interaction has local symmetry group U(1), and the strong interaction has SU(3). Behaviorally-speaking, they are completely different in almost every respect, affecting different sets of particles, having different strengths, having different potentials, different ranges, carried by different fields, etc. Just as an example, an electron doesn't interact via the strong force at all.

It is likely that at extremely high energies, the electromagnetic, weak, and strong interactions are all unified. A theory describing this hypothetical union is called a grand unified theory or GUT, and detecting this experimentally is a major objective of modern physics. The unified "electroweak" interaction has already been observed at lower energies. But that doesn't mean the weak interaction is "just magnetism" or that electromagnetism is "just weak." They are both a consequence of a broken symmetry. The fully symmetric grand unified field would not resemble any one of the interactions that we see at lower energies but would be a symmetric combination of all of them. EebstertheGreat (talk) 16:38, 21 December 2024 (UTC)

I may be out of date but wasn't the electro-weak force unified about 40 years ago? What's changed? (If I had to guess somebodies changed the meaning of "unified" and its relationship to symmetry breaking at low energy?)162.158.159.120 00:51, 25 December 2024 (UTC)

I absolutely won't claim any kind of knowledge, but Richard Behiel's video series on quantum mechanics, culminating in his 3-hour video on electromagnetism as a gauge theory is INCREDIBLE and absolutely explained a lot to me172.71.191.51 23:24, 22 December 2024 (UTC)Bumpf

Actually explaining the Pauli Principle

"Electrons don't like to be in the same 'spot'" is plain wrong. "Same quantum number set" is the buzzword - remember, two electrons fit in the s orbital, one spin up, one spin down. "Spin-statistics theorem" is a good place to start to ponder about the why. 162.158.95.145 09:40, 22 December 2024 (UTC)

Way too complicated, please change the universe so that "same spot" is good enough Kev (talk) 12:35, 22 December 2024 (UTC)

Do we need a category for quantum spin?

I'm seeing well over a dozen comics closely involved with spin in search. 172.69.33.237 20:18, 23 December 2024 (UTC)

Can there be more than one article in any given quantum spin category? 162.158.74.24 20:38, 23 December 2024 (UTC)

Only if they're on different wiki pages. 172.70.211.83 21:06, 23 December 2024 (UTC)

Probably. I sometimes wonder if Randall is riffing off of how bad Wikipedia's article on Spin (physics) is. For a good time, see https://en.wikipedia.org/wiki/Spin_(physics)#Higher_spins 172.68.23.91 21:11, 23 December 2024 (UTC)