The notion of Electron degeneracy pressure, universally accepted by the mainstream scientific community, is:
"Electrons are part of a family of particles known as fermions that follow Pauli's exclusion principle and Fermi–Dirac statistics. In general, for an ensemble of non-interacting fermions, also known as Fermi gas, each particle can be treated independently with a single-fermion energy given by the kinetic term (p2/2m), where p is the momentum and m its mass. The electron degeneracy pressure is given by (ne.v.p) where ne is the number density, and v the mean speed of the degenerate electrons. Essentially, the Fermi–Dirac distribution applies only to a quantum system of non-interacting fermions. In White dwarfs, Electron degeneracy pressure will halt the gravitational collapse of a star if its mass is below the Chandrasekhar limit (1.44 solar masses). A star exceeding this limit and without significant thermally generated pressure will continue to collapse to form either a neutron star or black hole, because the degeneracy pressure provided by the electrons is weaker than the inward pull of gravity."
In kinetic theory of ideal gases, the kinetic pressure is generated through momentum exchange of identical non-interacting particle in elastic collisions. Similarly, the electron degeneracy pressure is assumed to be generated through momentum exchange of free non-interacting electron particles in elastic collisions. At high core densities, when a star begins to cool down, electron degeneracy pressure is assumed to be the only mechanism available to support the inward pull of gravity. In the absence of adequate thermal pressure, gravity will accelerate heavy ions radially inwards and to counter this inward acceleration, the high-speed electrons will be required to push these ions radially upwards, by their degeneracy pressure, that is by exchanging their momentum through elastic collisions with these ions.
Actually however, due to their electrostatic interactions high energy free electrons cannot exchange their momentum with positive ions, through elastic collisions. That means the electron degeneracy pressure can be produced only if we assume the electrons, protons, and positive ions to be non-interacting. Since the 'electron degeneracy pressure' is the crucial fundamental concept in all Stellar Core Collapse Models, that lead to the formation of Black Holes, it implies that the electrons, protons, and positive ions are always assumed to be non-interacting in such models.
Hence, the popular notion of electron degeneracy pressure is founded on the faulty assumption of non-interacting electrons and protons and there is no physical mechanism to support this notion.
Therefore, I invite learned Astrophysicists and 'Black Hole' believers to logically defend the notion of electron degeneracy pressure and provide a plausible physical mechanism for its development in White Dwarf stars and Solid Iron Stellar Cores.
Article Black Holes are a Mathematical Fantasy, not a Physical Reality
Dear Gurcharn Singh Sandhu
What do you believe happens when electron meets a proton (or a heavy ion)?
They are attracted by electrostatics but, they do not annihilate. This means that an electron cannot destroy a proton (or a heavy ion) in any known interaction, therefore exchange of momenta, in such collisions, gives the needed radial pressure.
JES
Dear Stellan Gustafsson ,
It is an extremely simple matter that an electron can never never experience an elastic collision with a proton. For an elastic collision the colliding particles must be non-interacting.
Dear Gurcharn Singh Sandhu
The proton is a complex ensemble of sub-atomic particles, they have certainly plus and minus charges. The total charge is positive but, the proton must also have negatively charged surfaces. The exact interaction is unknown but to say that there cannot be an elastic collision is to go too far, according to my opinion.
JES
Dear Stellan Gustafsson ,
There are NO negatively charged surfaces on the proton. As per the very definition of elastic collisions, there can be NO elastic collisions between an electron and a proton.
Dear Gurcharn Singh Sandhu
You don't know if there is negative surfaces on the proton (nobody knows).
There is a proverb saying "never say never"
JES
Dear Gurcharn,
“…Actually however, due to their electrostatic interactions high energy free electrons cannot exchange their momentum with positive ions, through elastic collisions. That means the electron degeneracy pressure can be produced only if we assume the electrons, protons, and positive ions to be non-interacting.…..”
The 'electron degeneracy pressure' doesn’t appear because of some electrostatic interactions, at least as that is known now. That is because of the Pauli's exclusion principle.
That is another thing, that the Pauli's exclusion principle is introduced in QM as some mystic phenomenon, which is some mystic “purely QM effect”, and which by some mystic way forces, say, electrons on the s-orbits in atoms to be as a system of only two electrons with oppositely directed spins.
However that indeed happens in Matter, from what for normal humans seems as rationally follows that besides 4 officially known fundamental Nature forces there exist also an once more fundamental Nature force, that really prohibits for other electrons to have the same energy as the two ones on this quantum energy level.
And the 'electron degeneracy pressure' in models of exotic cosmological objects means that some object with extreme gravity transforms into some extremely large quantum system, where electrons quite densely fill all possible energy levels, and such object cannot so to be compacted more.
Because of the mystics above, this premise is mystic as well, including, first of all, that if the Pauli's exclusion principle relates to some force, then, because of all known forces have limited strengths, the premise above is seem as questionable suggestion that this force’s strength is infinite.
When it isn’t infinite, than the corresponding models of the cosmological exotics really have some limitations.
So a rational discussion of this problem is possible only after the problem “what is Pauli's exclusion principle”? will be solved.
More see https://www.researchgate.net/publication/342600304_The_informational_physical_model_some_fundamental_problems_in_physics DOI: 10.13140/RG.2.2.12325.734.
Cheers
Dear Gurcharn Singh Sandhu
I have made some considerations.
Let us say that the action between electrons and protons is completely elastic, i.e., they interact only through an "approximately" electrostatic action. In this case the electrons moves around the protons at a certain medium distance. The interaction, which is attractive, will then produce an equilibrium in temperature (energy). This means that the degenerate electrons, which increase there temperature (energy), with increasing gravitational pressure, will impose an increased temperature on the protons. Such an increase of temperature will increase the radial pressure and eventually produce an equilibrium with the gravitational force.
So a completely elastic interaction is sufficient to produce an equilibrium!
JES
The Pauli's exclusion principle is invoked specifically to impart energy, that is velocity and momentum to the degenerate or free electrons. The electron momentum is necessary for producing pressure but not sufficient. As in kinetic theory of gases, there must be a physical mechanism of exchanging momentum between constituent particles through elastic collisions to develop pressure. Pauli's exclusion principle by itself only provides velocity to the electrons, it does not generate pressure.
Energy per unit volume of a high energy electron beam does not constitute pressure until the high energy electrons rebound from some surface or other particles through elastic collisions. You may try the derivation of kinetic pressure from first principles as per the kinetic theory of gases.
Yes, dimensions of pressure (Force per unit volume) and the energy density (energy per unit volume) are the same.
Dear Prof. Gurcharn Singh Sandhu ,
In the monograph by L. Landau and E. Lifschitz, Statistical Physics part I, Pergamon, 1980, pp. 329; there is a chapter on neutron starts and electron degeneracy at very high density.
They point out two mechanisms for equilibrium states of such massive Fermi bodies as neutron spheres. One is electrons and nuclei and the other is a neutron gas were the electrons have been captured by protons. They emphasize that the state of a neutron gas is thermodynamic favourable.
Dear Dr. Gurcharn Singh Sandhu
The whole question is in theory, role of electron, the complexity proton/neutron compartment "Hardon' and the rest of an atom itself, such as quantum field, and other commination, but over all atom is unknow due to mechanical perception.
But one thing is for sure is clear, atoms are smallest complete unit of the universe. there is no indication of any thing smaller than atom with characteristic behavior, i.e. electron is electron when it is inside of an atom, not outside. there is no evidence of any part of an atom outside of an atom to be recognized, and that is including proton/neutron, baryon, meson...etc. thus. white Dwarfs and Solid Iron Stellar Cores is just postulation and only a theory. it is the same with black hole, wormhole, curvature of space and so forth.
Our universe with over 100 billons of galaxies is well organized entity, cannot work mechanically due to the Big Bang theory. bright sun, dimed sun must have quantum mechanics foundation explanation.
Deleted research item The research item mentioned here has been deleted
The article below is the best way how language of universe is working.
Article How the Language of the Universe Works
regards
Dear P. Contreras,
In the electron capture process, when an electron hits a proton it gets captured by the proton to produce a neutron. It is therefore, quite obvious that during the development of 'electron degeneracy pressure' when a high speed electron collides with a proton it may get captured in the proton through an inelastic collision but the electron can never rebound back from the target proton through an elastic collision. Hence in a high density stellar core, the electrons, in the form of Fermi gas, can never produce the so-called 'electron degeneracy pressure' to stop the gravitational inward acceleration of the protons and positive ions.
Unfortunately, the notions of 'electron degeneracy pressure' and 'neutron degeneracy pressure' have been invoked to support high density stellar cores against gravitational collapse since no other mechanism is available in Astrophysics to provide "Hydrostatic Equilibrium" in such stellar cores under self-gravitation. Further, since adequate mathematical support has been provided to justify the notion of 'electron degeneracy pressure' the need for a physical mechanism to support and validate this notion has never been highlighted. The mathematical support too has been provided by assuming all electrons, protons and ions to be non-interacting.
Just imagine, in Astrophysics a large ball of cold, inert solid iron, of about one solar mass, is thought to be in "Hydrostatic Equilibrium" under self-gravitation, entirely through the action of 'electron degeneracy pressure'!
We must take an atom as a smallest complete intelligent unit of universe that it carrying information. That is including Hadron, Electron and Space of atom.
Atoms are not mechanical element to function mechanically.
regards
Thank you very much for your excellent and detailed explanation about the electron capture in neutron starts Dear Prof. Gurcharn Singh Sandhu.
I come from the field of normal metals solid-state theoretical physics, hereby it is hard for me to think about a noninteracting gas of electrons since interacting fermions describe the normal state of most metals at sufficiently low temperatures, but it could be that the so very high density makes those particles to undergo a phase transition to another physical state with "Hydrostatic Equilibrium" under self-gravitation?.
This field of quasars and neutron stars is very interesting. To study the metallic states of elements like Hydrogen or Iron that have different numbers of electrons at so high-density rho and pressure P.
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