Does Neutron Star collapse violate quantum theory?
As part of my Extended Project (a project taken in your last year of school in the uk (17-18 years old)) I have been writing a dissertation on whether Neutron star collapse violates quantum theory. I had a brief understanding before the project that the matter in the neutron star was degenerate (cannot be compacted any further), therefore I wanted to find out whether the fact that neutron stars can collapse further (into black holes) violates the pauli exclusion principle. **In short it doesn't Heisenberg uncertainty allows for a bypass of this degeneracy**
I haven't finished the project, which will become a post on the blog when complete. But here is an exert of the chapter on Pauli exclusion:
“With such a large mass the gravitational crush of the Neutron star on itself is very significant. Before it’s death the star actively fused elements in its core for most of its life (on the main sequence), this was the fusion of hydrogen atoms into helium, creating a lot of energy. This “radiation pressure” caused an outwards push, helping to resist the inwards crush of the star’s gravitational field. Once the star has got to the neutron star phase, its days of nuclear fusion have long gone. Therefore, there must be something else resisting the huge gravitational inwards force. This ends up being entirely described by quantum mechanics. It is quite rare to see the baffling work of quantum mechanics macroscopically, but the neutron star is a rare example of exactly this.
As mentioned in the introduction chapter the space the neutron star occupies is entirely filled with neutrons. But what does filled mean? When talking about the space the neutron star occupies, due to the nature of the matter, it is insufficient to talk just about 3 dimensional space. Due to its quantum nature it is more appropriate to look at the entity in terms of quantum phase space . Phase space represents all the possible states of a dynamic system, in this case the neutron star, with “all states” simplified to just position and momentum . This is aided by the fact that the neutron has no charge. In the case of our neutron star we have to consider not only the 3 spacial dimensions, but also a momentum dimension associated with all the spacial ones. For this reason, the space the neutron star occupies is more accurate described as 6 dimensional quantum phase space. With the six dimensions coming from the 3 spacial and 3 momentum dimensions. In the case of the neutron star phase space is full of neutrons. Thus every spacial position and every possible momentum linked to each position is full of neutrons. This state where phase space is full is called degeneracy, and in this case neutron degeneracy. The reason why neutrons cannot be further compacted is explained by the Pauli exclusion principle.
The Pauli exclusion principle states that no two fermions* can be in the same quantum state . This holds true for neutrons (hadrons), not only fundamental particles such as the electron . Thus, no two neutrons can have the same position, and the same momentum (and any other quantum state).
This can be shown in terms of the wavefunction of the fermions, and in particular the wavefunction of a system comprising two neutrons. The wavefunction of a fermion describes mathematically its position and other such quantum properties ..."
PlanckTime - Amin
If I recall, PBS spacetime does a great video on the topic. Reccomend watching (I'll link it afterwards). But the main point I recall clearly is that the volume of a neutron star actually DECREASES as its mass increases. (Until the radius falls below the Schwarzchild radius (don't trust my spelling there), at which point it becomes a black hole). The reason for this is as mass increases, there is less uncertainty in position, so the uncertainty in momentum increases massively. This effectively "creates" more momentum space that can be occupied. Thus preventing violation of the pauli exclusion principle. Obviously this is a brief overview, potentially wrong, with no maths to back up my claim (though the maths shouldn't be impossible, even for pre-undergraduate level). If I am wrong please do correct. I dont know much about this, and I find it a very interesting topic.
Here is the link to the PBS spacetime video on it. https://youtu.be/xx4562gesw0
"Either this wallpaper goes, or I go"- Oscar Wilde's last words
Yeah as I mention in the post above it's Heisenberg uncertainty which allows for ultimate collapse. The principle states that as the position of the neutron becomes more certain, it's momentum becomes highly undefined- and yes the star expands in "momentum space" but actually shrinks in spacial terms. The maths here isn't incredibly challenging, however as part of my project I'm writing about degeneracy pressure in the star. This pressure arises from all possible wave-functions being defined, and the maths here gets difficult. I'm getting my dad to help me get my head around it lol.
Will be sure to keep this thread posted about my progress, but yeah it's super interesting!
PlanckTime - Amin
Very interesting EPQ planck timers,
The content covered in this project baffles me and all I want to do is immerse myself in the subject. However I have no quibbles that the detail covered will score you the highest mark
Thanks for you post Lit Lewis. I heard you're taking the EP qualification, when you're done it would be very interesting to heard about it!
PlanckTime - Amin