Archive for October, 2023

Oct 27 2023

Pauli Exclusion Principle

With the Pauli exclusion principle, “Only two electrons (with opposite spins) can occupy a given quantum state.” ([1], pg. 798) The magnetic moments being in opposite directions help keep the separation, though it is electric current loops in each electron doing the work.

Ref: https://www.fruechtetheory.com/blog/2022/02/14/spin-drive/

The reason orbitals in an atom or molecule are limited to two electrons has to do with the fact that “σ, τ are any (local) bisections of G”. ([2], pg. 28) In mechanical engineering, σ is the symbol for stress. Likewise, σ is the symbol here for local negative charge stress in the gamma ray field, and we have “The map φ: σ → γ” ([3], pg. 226). Alternatively, there is “the sheaf of germs of local bisections of G.” ([2], pg. 133) Here we have another name for the graviton in “germ”, and a “sheaf” is a member of the h field, when two or more gravitons get combined to do the work.

With the spin of the electron, “the mapping Sσ → aσn Sσ” ([4], pg. 162) provides a matrix theory to the Coulomb field, with “cyclic groups (σi) of orders ni” ([4], pg. 130). This provides additional proof that Coulomb groups are pulsed.

Two other authors call the Pauli exclusion principle a “set of pairs (τ, J)” ([5], pg. 68), with “permutations σ” ([6], pg. 293). J is a charged mass:

https://www.fruechtetheory.com/blog/2023/06/29/vector-bosons-and-other-fleeting-field-particles/,

and in this case we are referring to an electron.

Physicists already knew most of this blog entry before it was entered. What many people do not know is the presence of a gamma ray field, though it is reasonable to know because of the gamma ray telescopes.

[1] Tipler, Paul A., “Physics”, Worth Publishers, Inc., 1976

[2] Mackenzie, Kirill C. H., “General Theory of Lie Groupoids and Lie Algebroids”, c. 2005 Kirill C. H. Mackenzie, London Mathematical Society

[3] Bishop, Richard L. and Crittenden, Richard J., “Geometry of Manifolds”, AMS CHELSEA PUBLISHING, Copyright 1964 held by the American Mathematical Society. Reprinted with corrections by the American Mathematical Society, 2001

[4] Zassenhaus, Hans J., “THE THEORY OF GROUPS”, Dover Publications Inc., 1999 (Originally published by Chelsea Publishing Co., 1958)

[5] Kobayashi, Shoshichi and Nomizu, Katsumi, “Foundations of Differential Geometry Volume I”, John Wiley & Sons, Inc., c. 1963

[6] Kobayashi, Shoshichi and Nomizu, Katsumi, “Foundations of Differential Geometry Volume II”, John Wiley & Sons, Inc., c. 1969

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Oct 16 2023

Atomic and Molecular Electron Arcs

Further to uniting Riemannian geometry, Lie groups, and symmetric spaces with gravity, τ is an atomic or molecular arc, and “τ is a segment” ([1], pg. 168). Also, “τ is minimizing” ([1], pg. 166).

Sometimes τ is called a complete orbital, and we “divide τ into a finite number of arcs, say, τ1, τ2, … , τk” ([1], pg. 191).

Ref: https://www.fruechtetheory.com/blog/2008/06/28/gravity-and-the-uncertainty-principle-2-2/

In an orbital arc the “endomorphisms A1, … , Ak are linearly independent” ([2], pg. 353), and k – 1 in this instance is the number of gravitons absorbed in an arc. “A” is the vector potential, and each time an electron absorbs a graviton in an orbital, its vector potential increases. We know that A1, … , Ak is not pulsed Lie groups in the gamma ray field, because there is no “…” after the Ak. In the same paragraph it talks about a “mapping ξ → Aξ“, therefore in a particle mass, and in groups or manifolds in the open gamma ray field, the gamma rays are blended and surjective.

If a function can be called “the growth of an orbital electron in size and charge”:

https://www.fruechtetheory.com/blog/2022/08/27/concentrated-group-action/ ,

then “γ and f point in opposite directions” ([3], pg.165).

The Φ field is within atomic and molecular orbitals, including the boundary, and Ψ is outside of the orbitals. In an emitting antenna, it is the Ψ field as well, since the electrons are free. “Φ0 is isomorphic to Ψ0 in a natural manner” ([1], pg. 193), because the gamma ray field is normally constant in the area within and around the molecule.

Often in a molecule, or any type of p orbital, the Gaussian curvature, when ¾ through the arc compared to ¼ through the arc, is negative.

In the open gamma ray field “m = dim M and n = dim Δ” ([4], pg. 155), and m – n is the number of singularities in a locality. Stoker terms it “singularity in the coordinate system” ([5], pg. 84). A singularity is when the electric and magnetic fields of a gamma ray cross over the t axis, though when near the axis it could be called a singularity also.

If the polarization factor is greater than 2, as at the surface of the sun or Jupiter, then specific nuclei likely have more mass than on the face of the earth, and electrons in atomic or molecular arcs grow larger. It could be because of these factors the value of Newton’s gravitational constant G = 6.672 x 10-11 (N-m2)/ kg2 stays the same.

[1] Kobayashi, Shoshichi and Nomizu, Katsumi, “Foundations of Differential Geometry Volume I”, John Wiley & Sons, Inc., c. 1963

[2] Kobayashi, Shoshichi and Nomizu, Katsumi, “Foundations of Differential Geometry Volume II”, John Wiley & Sons, Inc., c. 1969

[3] Mackenzie, Kirill C. H., “General Theory of Lie Groupoids and Lie Algebroids”, c. 2005 Kirill C. H. Mackenzie, London Mathematical Society

[4] Boothby, William M., “An Introduction to Differentiable Manifolds and Riemannian Geometry”, Academic Press, 2003

[5] Stoker, James J., “Differential Geometry”, John Wiley & Sons, Inc., c. 1969

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