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Pauli exclusion principle for kids7/28/2023 Let's assume our fermions are at first so energetic that a swarm of them doesn't collapse, and at first let's assume a low density. I am NOT an astronomer so I've no idea of the exact numbers in the following diagram, which is to be taken with a grain of salt given that I heavily mix classical (GR) ideas with quantum interactions. Lastly let's look at the core of a body made up of charged fermions. You can simply think of the crushing force and the particle dynamics in the presence of this force and ignore everything else: interactions between the particles fade into the background. I have heard (I don't have direct experience of this) that in certain kinds of explosive analysis, especially the worthwhile analysis of the evolution of a nuclear explosion in a weapon, you can just assume that everything is a gas, with negligible error. ![]() The Fermi gas in a container model applies when all other forces (electromagnetic, for example, that help arrange solids into crystals and so forth) are very small relative to outside forces crushing the solid. The difference is that, owing to the Pauli exclusion, the force needed to keep particles in their dynamic confined state in a given volume is MUCH bigger for fermions than for bosons. If you confine light in a perfect resonant cavity, there is a backthrusting force and it varies inversely with the resonant cavity's volume. Or, if you like, in a D'Alembertian mindset, there is a backthrusting force but it is an inertial force arising from thinking of the problem from an accelerated frame.Īctually the ideas work equally well for bosons as for fermions. The particles are in motion and the crushing force from the outside is continually changing their state of motion, by Newton II, and thus keeping them confined. Actually, when the crushing force gets really big, this everyday viewpoint breaks down: the problem is more one of dynamics. I and civil engineers tend to think of squashing a block of iron as a problem in statics, so we tend to think that if we are crushing something seemingly "static", there must be a balancing force thrusting back. They are in motion and by Newton II they need force to keep them confined. So I kind of forget that the particles in them are in a dynamic state. I think where I trip up here is that my everyday experience of solids is, well, they are solid! Sometimes like you I feel the need for a Pauli "force". It is the force shaping the infinite potential well that imparts the impulse needed to rebound them back into the well. Likewise, the particles in the Fermi gas in the infinite square well are in the quantum mechanical equivalent of motion. Whatever force holds the walls and piston in place is the force that imparts the impulse to them to rebound them back into container. When the molecules in the ideal gas are in flight between the walls, there is no force on them. What is the fundamental force involved when you try to squash fermions together? It's whatever is confining fermions! You need to think of an ideal gas. I am writing to clarify the especial things that gave rise to my own personal misconceptions, so likely not everybody is going to benefit from this answer. I'd like to add a different take on essentially the same as Anna's answer. Note: does this apply to degenerate pressure too (which was explained to me as $\Delta p$ increasing because $\Delta x$ became smaller because the particles are confined to a smaller space (Heisenberg u.p.), as is what happens when stars collapse)? So my question is: is Pauli-repulsion a phenomenon that has also not yet been explained in terms of any of the three other forces that we know of? As I have read so far, this seems like a "force" that is completely separate from the other well known forces like the strong, electroweak and gravitational interaction (even though the graviton hasn't been observed so far). ![]() Instead, you get a a repulsive force as a consequence of the Pauli exclusion principle. ![]() Yet if you compress them really strongly, the electromagnetic interaction will no longer be the main force pushing them apart to balance the force that pushes them towards each other. (Credit: CK-12 Foundation Source: CK-12 Foundation License: CC BY-NC 3.You can have two electrons that experience each other's force by the exchange of photons (i.e. An arrow pointing upward represents one spin direction, while an arrow pointing downward represents the other spin direction. \): In an orbital filling diagram, a square represents an orbital, while arrows represent electrons.
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