I gave a talk yesterday as part of our new seminar series at work. It was based on my FQXi essay. One of the issues I raised was how to describe degenerate matter on a massive scale, specifically white dwarf stars. Normal stars are supported against gravitational collapse by the stellar fusion process. But stellar fusion has stopped in white dwarfs and the accepted explanation for the non-collapse of white dwarf stars is that electron degeneracy pressure couteracts gravitation. Electron degeneracy pressure is a consequence of the Pauli exclusion principle.
One of the points I make in my essay is that, normally, we associate forces with interactions in which some kind of information is exchanged. If we assume this definition of force, how do we draw a free-body diagram for a chunk of white dwarf star? By this definition of forces, there is only an inward one – gravity. This may not seem like a major problem since it is confined to a highly specialized area of research. We don’t encounter white dwarf stars on an everyday basis. But with an increasing amount of research – and even technology – probing the quantum-classical boundary, we will need to address this issue if we expect our descriptions of nature to be self-consistent.
Aside from that issue, however, a colleague of mine in the chemistry department posed an intriguing question: “I still wonder whether the necessary increase in energy that accompanies greater spatial confinement according to the uncertainty principle is an equally valid explanation for the failure of anything to fully collapse. (Albeit one which is not one of the 4 forces.)”
That got me thinking. So, first of all, he wondered why it wasn’t just electromagnetism that prevented a white dwarf from collapsing. The answer to this is that they are known to be so dense that the individual particles are presumably closer than they could have gotten if it was an electrostatic repulsion preventing such a thing, i.e. an electrostatic explanation doesn’t jive with the experimental data. At least that’s been my understanding of the problem. Given that, then, I wondered if perhaps there was a way to get something to be even more dense than degenerate matter without its complete collapse using his criteria – the uncertainty principle. Or, perhaps, this is really what is at the heart of what prevents super-dense bosonic matter from collapsing, e.g. Bose-Einstein condensates, which we know have their own analogue of exclusion that prevents complete collapse. Either way, the example of the white dwarf (or even a neutron star) begs the question: just how close can two fermions get before exclusion prevents them from getting any closer? This is, perhaps, related to the question: how close do two particles (for example, two electrons forming a Cooper pair) have to be before they can be considered a system, particularly considering that electromagnetism has an infinite range?
These are some intriguing questions that I don’t have answers to yet. I’d be curious to know the thoughts of anyone else out there who has, perhaps, more experience in this line of inquiry.