Comments about "Pauli exclusion principle" in Wikipedia

This document contains comments about the article "Pauli exclusion principle" in Wikipedia
In the last paragraph I explain my own opinion.

Contents

Reflection

Introduction

The article starts with the following sentence.
The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.
Why mention simultaneous? At no other place in this document the word simultaneous is mentioned.
In the case of electrons in atoms, the Pauli exclusion principle can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers: n, the principal quantum number, l , the azimuthal quantum number, ml, the magnetic quantum number, and ms, the spin quantum number.
Okay.
For example, if two electrons reside in the same orbital, then their n, l, and ml values are the same, therefore their ms must be different, and thus the electrons must have opposite half-integer spin projections of 1/2 and -1/2.
Such a sentence requires much more detail, based on experiments. These experiments should demonstrate the different rules which apply for different elementary particles.
When the spin projections must be 1/2 and -1/2 both electrons in some sense are entangled. This is at no place mentioned in this document.
Particles with an integer spin, or bosons, are not subject to the Pauli exclusion principle: any number of identical bosons can occupy the same quantum state, as with, for instance, photons produced by a laser or atoms in a Bose–Einstein condensate.
For particles with integer spin apparently different rules apply. More detail is required specific their relation with the four quantum numbers : n, l, ml and ms.

The fact that photons are not subject to the Pauli exclusion principle seems completely logical, because two photons can occupy the same physical position. In fact: many, all coming from different directions, which in some sense should all interfer with each other

1. Overview

The Pauli exclusion principle describes the behavior of all fermions (particles with "half-integer spin"), while bosons (particles with "integer spin") are subject to other principles.
The question to answer is how a certain principle can describe the fysical behaviour of elementary particles.
Fermions include elementary particles such as quarks, electrons and neutrinos. Additionally, baryons such as protons and neutrons (subatomic particles composed from three quarks) and some atoms (such as helium-3) are fermions, and are therefore described by the Pauli exclusion principle as well.
Same remark.
Bosons include the photon, the Cooper pairs which are responsible for superconductivity, and the W and Z bosons. (Fermions take their name from the Fermi–Dirac statistical distribution that they obey, and bosons from their Bose–Einstein distribution.)
That photons are excluded makes sense because two photons can occupy the same space.

2 History

In 1922, Niels Bohr updated his model of the atom by assuming that certain numbers of electrons (for example 2, 8 and 18) corresponded to stable "closed shells".
That is an important fysical fact and amplifies why certain elements are more stable than others.

3. Connection to quantum state symmetry

3.1 Advanced quantum theory

4. Applications

4.1 Atoms

The Pauli exclusion principle helps explain a wide variety of physical phenomena.
I have my doubts if the Pauli principle can really explain physical facts. The importance of the Bohr Model should not be underestimated.
One particularly important consequence of the principle is the elaborate electron shell structure of atoms and the way atoms share electrons, explaining the variety of chemical elements and their chemical combinations.
All of that is true, but the relation with the Pauli Exclusion principle is not clear.
An example is the neutral helium atom, which has two bound electrons, both of which can occupy the lowest-energy (1s) states by acquiring opposite spin; as spin is part of the quantum state of the electron, the two electrons are in different quantum states and do not violate the Pauli principle.
The fact that they don't violate the Pauli principle but are in accordance does not validate the Pauli principle.
The chemical properties of an element largely depend on the number of electrons in the outermost shell; atoms with different numbers of occupied electron shells but the same number of electrons in the outermost shell have similar properties, which gives rise to the periodic table of the elements.
Which also does not validate the Pauli Principle.

4.2 Solid state properties

Many mechanical, electrical, magnetic, optical and chemical properties of solids are the direct consequence of Pauli exclusion.
More detail should be supplied

4.3 Stability of matter

The stability of each electron state in an atom is described by the quantum theory of the atom, which shows that close approach of an electron to the nucleus necessarily increases the electron's kinetic energy, an application of the uncertainty principle of Heisenberg.
The stability of each electron state in an atom is a complex issue, specific in relation to kinetic energy of the electrons involved.
The stability of these electrons have nothing to do with the uncertainty principle.
The uncertainty principle bassicly reflects human limitations to measure distances and cannot be used to explain physical processes.
However, stability of large systems with many electrons and many nucleons is a different question, and requires the Pauli exclusion principle.
I doubt that the stability it self requires the exclusion principle implying that two electrons cannot be at the same place.
It has been shown that the Pauli exclusion principle is responsible for the fact that ordinary bulk matter is stable and occupies volume.
Same comment as above.
This suggestion was first made in 1931 by Paul Ehrenfest, who pointed out that the electrons of each atom cannot all fall into the lowest-energy orbital and must occupy successively larger shells. Atoms, therefore, occupy a volume and cannot be squeezed too closely together.
This model of an atom i.e. different shells is very clever. However the relation with the Pauli exclusion principle is not clear.

4.3.1 Stability of matter (old as of 6 march 2017)

The stability of the electrons in an atom itself is unrelated to the exclusion principle, but is described by the quantum theory of the atom.
Okay. But requires a deeper explanation.
The underlying idea is that close approach of an electron to the nucleus of the atom necessarily increases its kinetic energy, an application of the uncertainty principle of Heisenberg.
That the speed and energy of an electron closer to the nucleas of atom is higher compared to an electron at larger distance is a physical effect and has nothing to do with the uncertainty principle.
The uncertainty principle bassicly reflects human limitations to measure distances and cannot be used to explain physical processes.
However, stability of large systems with many electrons and many nucleons is a different matter, and requires the Pauli exclusion principle.
I doubt that the stability it self requires the exclusion principle implying that two electrons cannot be at the same place.

4.4 Astrophysics

It is a consequence of general relativity that, in sufficiently intense gravitational fields, matter collapses to form a black hole.
General Relativity is not the cause that matter collapses to form a black hole.
The same physical rules apply when two raindrops merge. They combine, flow togeteher and form a new slightly larger raindrop.
Merging matter behaves the same. The most important issue, for humans, is that a Black Hole does not emit photons. From a physical point of view this is rather unimportant.

As of 13 December 2021, the above sentence seems strange. First of all the formation of a black hole has nothing to do with GR. It must be physical related that first two large stars will merge and than as a consequence a certain threshold will be passed. The resulting star will internally collapse and form a black hole.

Astronomy provides a spectacular demonstration of the effect of the Pauli principle, in the form of white dwarf and neutron stars. In both bodies, the atomic structure is disrupted by extreme pressure, but the stars are held in hydrostatic equilibrium by degeneracy pressure, also known as Fermi pressure.
This seems that the overal explanation is the Fermi Pressure, which is much more a fysical explanation than the Pauli Principle

5. See also

Following is a list with "Comments in Wikipedia" about related subjects

Reflection 1 - The pauli exclusion principle.

Under standing physics implies to understand the difference why all most identical processes are identical.
One important question is what makes the difference between all the elements. Now adays we know the reason: this are the electrons, protons and neutrons which are the building blocks of each atom. To get a better view what it is study this url: https://en.wikipedia.org/wiki/Periodic_table Which shows the Mendeleev Table. In paragraph 4 History you can read:
Prompted by Bohr, Wolfgang Pauli took up the problem of electron configurations in 1923. Pauli extended Bohr's scheme to use four quantum numbers, and formulated his exclusion principle which stated that no two electrons could have the same four quantum numbers. This explained the lengths of the periods in the periodic table (2, 8, 18, and 32), which corresponded to the number of electrons that each shell could occupy.
That is all. The length follows this rule 2*n^2 with n=1 gives 2, with n=2 gives 8, with n=3 gives 18 and with n=4 gives 18. The text does not explain why this is true.

Interesting reading is the Aufbau principle: https://en.wikipedia.org/wiki/Aufbau_principle which claims:
If double occupation does occur, the Pauli exclusion principle requires that electrons that occupy the same orbital must have different spins (+1/2 and -1/2).
To verify this physical behaviour you have to perform certain experiments, which demonstrate what this spinning physical means.
The maximum number of electrons in a subshell (s, p, d, or f) is equal to 2(2l + 1) where l = 0, 1, 2, 3... Thus these subshells can have a maximum of 2, 6, 10, and 14 electrons respectively. In the ground state,
That is true. What the physical implications are, specific related to energy, is not mentioned.

Reflection 2 - stability in Astrophysics

This is a reflection as a responds on what is written in: 4.4 Astrophysics
In the previous version of this site as of 6 September 2020 the same was called: 4.4 Astrophysics and the Pauli principle, which raises the question why this name change.

The overall stability of individual stars, star clusters and galaxies is a fysical fact. Part of the explanation lies in the fact that the creation of stars takes millions of years and that this whole process evolves in a rather regular pattern.
Considering the solar system in general, including our galaxy and all galaxies, the evolution of each evolves in a rather controlled way and at each instant can be considered as stable. The state of each, can be described by Newton's Law implying that, more or less, the evolution of each solar system evolves the same. The same can be said for all galaxies. The overall conclusion is that the evolution of all stars and all galaxies is a stable process and as far I understand has nothing to do with the Pauli exclusion principle.
A different picture exits if two stars or two galaxies collide or merge. In the case when two stars collide or merge the internal stability is not the issue and a very complex process. Generally speaking when two galaxies merge the overall process is a rather continuous process and is a function to the overall movement and influence of each star, and as long as no collisions occur, can be described by Newton's Law.

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Created: 6 March 2017
Modified: 6 September 2020
Modified: 23 December 2021

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