Can the Pauli principle be visualized?

[Tsunami]

For years, I've taken the Pauli principle for granted, but now that I've taken a course on Subatomic Physics, I'm mystified again.

The example is given in the course of Neutron Stars. Neutron stars are burning stars that experience an incredible compression, drawing a lot of matter in a very small space. Apparently, under these conditions protons can react and become neutrons, but neutrons cannot react and become protons, because of the Pauli principle - they are simply too close together.

So, what we see here, is how the Pauli principle is behaving like some sort of 'absolute' (?) resistance : you simply can't have two quantum states with the same quantum numbers. So, the Pauli principle acts as some kind of potential energy which becomes ridiculously high at 'zero' distances in the 'quantum phase space'.

This is what I'm trying to achieve here: is it possible to visualize the Pauli principle? Can it be explained as some kind of resistance in a 'quantum space'?

Also, can someone try to explain why the Pauli principle works for protons, but not for neutrons in this example? Thank you.

 

[turbo]

I visualize particles as waves in the quantum vacuum and visualize the PEP not as a force resulting from the nearness of two similar particles, but as a result of the inability of the quantum vacuum to support the existence of these similar waves concurrently. This is more natural IMO than visualizing a repulsive force between two similar particles. To put it anthropomorphically, how can a particle "know" that it is being forced into the same quantum state as a same-spin twin and resist the superposition? It's simpler to imagine that the vacuum has a carrying capacity. Naively, the "carrying capacity" is variable, based on the gravitational potential in which the local vacuum is located.

 

[Tsunami]

Right.

I'm not so sure how I'm supposed to imagine this 'gravitating potential'. Does a 'heavier' particle like the neutron (compared to the neutron) invoke a stronger gravitating potential? And how does this influence the carrying vacuum?

 

[mathman]

This may be an oversimplification. Proton plus electron take up more space than a neutron. Gravity forces the particles in a neutron star to occupy as little room as possible. Add a little more mass and the whole thing becomes a black hole.

 

[masudr]

Some knowledge of the density of states function might also help.