sethoflagos Posted October 2 Posted October 2 On 8/9/2024 at 11:49 PM, joigus said: Degeneracy pressure is not electrostatic repulsion, and gravitation has nothing to do with gluons and other ephimeral QCD states going back and forth between nucleons, which is what makes nucleons stick together by QCD. It's a very different animal. Then which of the remaining fundamental forces manifest as degeneracy pressure, and what, if any, is the force carrying particle? Sorry, I did try to export this quote into a new topic, but I couldn't find the right button.
Genady Posted October 2 Posted October 2 Quote Degenerate matter is usually modelled as an ideal Fermi gas, an ensemble of non-interacting fermions. In a quantum mechanical description, particles limited to a finite volume may take only a discrete set of energies, called quantum states. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state. At lowest total energy (when the thermal energy of the particles is negligible), all the lowest energy quantum states are filled. This state is referred to as full degeneracy. ... Adding particles or reducing the volume forces the particles into higher-energy quantum states. In this situation, a compression force is required and is made manifest as a resisting pressure. (https://en.wikipedia.org/wiki/Degenerate_matter)
MigL Posted October 2 Posted October 2 (edited) Degeneracy pressure is not a 'force', but the result of two quantum mechanical principles. The Pauli Exclusion Principle, which says each Fermion is allowed only one quantum state, and must obey Fermi-Dirac statistics, as Genady mentions above. They cannot be 'stacked-up' in the same state as bosons, which obey Bose-Einstein statistics. The other is the Heisenberg Uncertainty Principle. If you put a box around an electron, and keep shrinking the box, its position is determined more and more accurately. Eventually you reach a point where its position is determined so accurately that its momentum could be so great as to exceed c ; a physical impossibility. Nature gets around this problem by forcing electrons to merge with protons, to form neutrons. As the neutron is 2000 more massive than an electron, it is capable of exceeding the electrons momentum by 2000 times before running into the velocity being equal to c problem. This is evidwnt in type 1A supernova where a white dwarf star takes enough material from a companion star, that electron degeneracy can no longer support it against gravity, and it collapses to a neutron star, which is supported by the much greater neutron degeneracy pressure. This is the analysiss Subraihmanyan Chandrasekhar performed in 1930, during his boat trip to England, to study under Sir A Eddington ( who ridiculed his work ), and which today we call the Chandrasekhar Limit for electron degeneracy of white dwarf stars ) about 1.4 solar masses ). Edited October 2 by MigL 5
joigus Posted October 2 Posted October 2 (edited) 4 hours ago, sethoflagos said: Then which of the remaining fundamental forces manifest as degeneracy pressure, and what, if any, is the force carrying particle? Sorry, I did try to export this quote into a new topic, but I couldn't find the right button. Sorry. @MigL beat me to the punch, although I had read your comment. I was pre-configuring the answer in my mind as something like "degeneracy pressure is more of a statistical consequence (of general principles of quantum mechanics) rather than an actual interaction". (Something like that.) But MigL's answer is actually much better. Edited October 2 by joigus minor addition
sethoflagos Posted October 2 Author Posted October 2 (edited) 2 hours ago, MigL said: Eventually you reach a point where its position is determined so accurately that its momentum could be so great as to exceed c ; a physical impossibility. This seems to suggest that maybe admittance of a particle in a 'forbidden' quantum state into an already occupied space is impossible as it would require a superluminal value of momentum to achieve the necessary energy density? This picture at least has the virtues of a) the energy of repulsion is derived from the particle's own KE and b) the force carrier for momentum transfer can be whatever is appropriate for that class of particle eg. virtual photons for electrons etc. I'm pretty comfortable with the old derivation of degeneracy pressure in the classic Fermi paper attached where eqns. 7, 8, 9 pretty well form my understanding of ideal gas heat capacity and entropy at low temperatures. As far as my old day job necessitated anyway. Clearly there's a bridge somewhere that I need to find... 1 hour ago, joigus said: "degeneracy pressure is more of a statistical consequence (of general principles of quantum mechanics) rather than an actual interaction" I'm in no position to question this. But it seems to be an observation rather than an explanation. Fermi Quantisation of MIG.pdf Edited October 2 by sethoflagos Inappropropriate spelling
MigL Posted October 2 Posted October 2 2 minutes ago, sethoflagos said: maybe admittance of a particle in a 'forbidden' quantum state into an already occupied space is impossible as it would require a superluminal value of momentum That is one way of rationalizing it. I'll stick with my 3rd year class in Statistical Thermodynamics, where we derived Fermi-Dirac distributions for quantum particles with half-integer spin ( Fermions ), and Bose-Einstein distributions for quantum particles with integer spin ( bosons ). These distributions dictate how such particles can and cannot act.
Mordred Posted October 2 Posted October 2 (edited) 12 minutes ago, sethoflagos said: This seems to suggest that maybe admittance of a particle in a 'forbidden' quantum state into an already occupied space is impossible as it would require a superluminal value of momentum to achieve the necessary energy density? This picture at least has the virtues of a) the energy of repulsion is derived from the particle's own KE and b) the force carrier for momentum transfer can be whatever is appropropriate for that class of particle eg. virtual photons for electrons etc. I'm pretty comfortable with the old derivation of degeneracy pressure in the classic Fermi paper attached where eqns. 7, 8, 9 pretty well form my understanding of ideal gas heat capacity and entropy at low temperatures. As far as my old day job necessitated anyway. Clearly there's a bridge somewhere that I need to find... I'm in no position to question this. But it seems to be an observation rather than an explanation. Fermi Quantisation of MIG.pdf 90.16 kB · 2 downloads Well that link you included specifies a Fermi-Dirac gas. This specific to fermion fields. The equations in the paper are applying the Fermi-Dirac statistics. For Bosons the statistics is the Einstein-Boltzmann statistics. For mixed stated one uses the Maxwell-Boltzmann statistics. These statistics directly apply the Pauli-Exclusion principle already mentioned in this thread. Another link that may help. Matter takes up space so matter is comprised of fermions and not bosons. Cross posted with Migl Edited October 2 by Mordred
Genady Posted October 2 Posted October 2 13 minutes ago, Mordred said: Einstein-Boltzmann statistics You meant to say rather Bose-Einstein statistics, I believe.
MigL Posted October 2 Posted October 2 (edited) Probably a typo 🙂, but L Boltzmann passed away in 1906, well before the advent of QM and its particles' behavior. Maxwell-Boltzmann distributions apply to ideal gases where particles don't display quantum behavior. Bose-Einstein statistics apply to quantum particles with integer spin ( Bosons ). Bose–Einstein statistics - Wikipedia ( so many names and terms to remember ☹️ ) Edited October 2 by MigL
sethoflagos Posted October 2 Author Posted October 2 22 minutes ago, Mordred said: Well that link you included specifies a Fermi-Dirac gas. Isn't this a fair approximation of a low density ideal gas? 10 minutes ago, MigL said: Maxwell-Boltzmann distributions apply to ideal gases where particles don't display quantum behavior. They do at low enough temperatures. TdS = d (CvT) is a tough ODE to solve as you approach absolute zero if Cv doesn't disappear in tandem. 44 minutes ago, MigL said: I'll stick with my 3rd year class in Statistical Thermodynamics, where we derived Fermi-Dirac distributions for quantum particles with half-integer spin ( Fermions ), and Bose-Einstein distributions for quantum particles with integer spin ( bosons ). These distributions dictate how such particles can and cannot act. I'd still expect them to act in accordance with Newton's 1st Law. In essence, that's all I'm trying to reconcile.
Mordred Posted October 2 Posted October 2 (edited) 1 hour ago, Genady said: You meant to say rather Bose-Einstein statistics, I believe. Yes thanks lol must have gotten distracted. 1 hour ago, sethoflagos said: Isn't this a fair approximation of a low density ideal gas? Fermi-Dirac is often used for low density gas in particular the Fermi level (Fermi-energy) however it's not limited to a low density gas. Other factors included being Fermi temperature and Fermi velocity. See here for details https://en.m.wikipedia.org/wiki/Fermi_energy Edited October 2 by Mordred 1
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