May 18 2024

## Emitting Cell Phone, Radio, and Television EM Waves

Let us say there is an imaginary horizontal disk centered on a vertical, unshielded emitting antenna. Cosine waves of various frequencies and amplitudes go out in all directions centered on the disk. As a cosine wave travels away from the disk, it imbues EM waves of the same frequency perpendicular outward in a push and peel process, in pairs, backward, laterally at an acute angle. As the cosine wave comes back toward the disk, there is no push, preventing double signals. Each torus grows continually until it runs out of momentum, and in a complex set of signals there are many interspersed tori.

The amplitude of each cosine signal, as it multiplies, may not be constant throughout the torus, though frequency is. For a given location of a receiving antenna, the amplitude ratios of all the signals are the same.

The H field, just like in electrodynamics, is a magnetic field.

“ h + n(I) = dim H ≤ a(I) = i(I) + n(I), so h ≤ i(I) “      ([1], pg. 233)

“ h “ is centripetal force from a magnetic field, producing a corkscrew, and n(I) is the antenna.

24.10.  THEOREM.  “If n ≡ 0 mod 4, then πn (Rn+1) contains a cyclic group of order 2 whose non-zero element is represented by Tn+2.”   ([2], pg. 130)

The electrons in the antenna produce 4 corkscrews for each signal. Electrons tend to congregate at the outside of the antenna, so it may be 4 electrons to a signal. Outside the antenna they quickly spread. What is meant by augmented index, a(I), is that the cosine waves, as they are emitted, go out in all directions from the antenna.

[1] 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

[2] Steenrod, Norman, “The Topolgy of Fibre Bundles”, Princeton University Press, c. 1951

Mar 19 2024

## Spherical Groups

With spherical groups of opposite charge signs, like emitted by the proton and electron in hydrogen, why would they not annihilate each other at different spots? For one thing they are segmented and pulsed, and spread out, and come out of a charged mass in pairs. These are convex regions, and “A region X open or closed, will be called convex if any two points in X are joined by at least one path which does not leave X.” ([1], pg. 7)

Additionally, “Let X be any open region and its closure.” ([1], pg. 7) It is like the groups have AI, and know how to avoid each other and know how to come back together. In footnote “*” on page 7, attributed to K. Menger, “We may think of X as filled with substance which conducts light along paths, all the space except X being opaque.”

At least in atoms or molecules, at close range, the groups are strong enough to avoid each other, before the polarization factor takes over. As far as hitting a target, the Coulomb field travels at the speed of light squared, and more groups come through fast.

[1] Whitehead, J. H. C., “CONVEX REGIONS IN THE GEOMETRY OF PATHS”, Princeton Press, (Received 15 August 1931)

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.

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

Sep 30 2023

## Michelson-Morley experiment

It has been said that “The electric field travels faster the denser a gravitational field is, though the speed difference may not be discernable.” Also: “What we have is an infinitesimal zigzag pattern, though when we back out to the classical level, it does not matter for any application.”

As it turns out, the speed difference may have been indirectly discerned by the Michelson-Morley experiment in 1887, and the “infinitesimal zigzag pattern” is less for a denser gravitational field.

A picture and description of the Michelson-Morley experiment tells it was mounted on a large block of sandstone, for stability, and floated on an annular trough of mercury for rotation.

The block that the experiment was on, and the sensors and brackets in the forward direction of travel of the whole apparatus, would have helped decompress the gamma rays toward the center of the apparatus, near the forward brackets. The brackets behind would have compressed the gamma rays. What was probably happening was a slow-fast travel of the electromagnetic waves in one direction, and a fast-slow travel in the opposite direction.

ηi is when the center t of a gamma ray moves one way in an alternative direction. ξi is a smooth electric field, and ηi and ξi work together to smear electric fields of the gamma rays into electromagnetic waves of larger dimensions, as a laser, emitted cell phone wave, etc. As a tornado takes up air molecules and expels others, these waves of lower frequency than a graviton take up gravitons they reach. “Assume that ξ is affine” ([1], pg. 377), and “ξ is a (column) vector in Rn” ([2], pg. 269). The gravitons that are expelled can take off in almost any direction. “ξi and ηi are orthogonal” ([3], pg. 315], because they are independent. “t” is not an electric field, it is a singularity.

ξi is caused by the H field, though it is specific to an emitted wave, subject to “the compatibility conditions which ξ and H are obliged to satisfy” ([1], pg. 362), and “ξ is a pure translation” ([4], pg. 193).

In the Michelson-Morley experiment, in the denser gamma ray field the ξ field is more efficient and moves faster, and the wavelength is slightly shorter than average. In the less dense gamma ray field, the wavelength is slightly longer than average.

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

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

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

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

Jul 06 2023

## Polarization Factor

It has been said that the Coulomb field transmits by torsion and centrifugal force:

https://www.fruechtetheory.com/blog/2023/01/29/magnetic-fields-as-effecting-coulomb-groups/

https://www.fruechtetheory.com/blog/2022/03/29/transmission-of-the-coulomb-field/

In the near field of molecules there are van der Waals attractive forces “proportional to 1/r7.“ ([1], pg. 390) This is a fast reduction, in part due to the polarization factor, which is very strong, though not as strong as the Coulomb force of a concentrated charge of mass when another concentrated charge of mass is nearby.

Kobayashi and Nomizu put it this way:

“Theorem 2.2.  Every Riemannian manifold admits a unique metric connection with vanishing torsion.” ([2], pg. 158)

Additionally, there is an “invariant Riemannian metric which is naturally reductive”. ([3], pg. 377)

It has been said before that gauge invariance is local at a given time. When it is referred to as a “unique metric connection”, the instantaneous density of the gravitational field at an area of the surface of any planet is unique.

One reason the potential energy of a point charge is not infinite was given here:

https://www.fruechtetheory.com/blog/2009/03/15/electric-charges/

In real time, the polarization factor is the reason the potential energy of a point charge is not infinite.

[1] Tipler, Paul A. and Llewellyn, Ralph A., “Modern Physics Sixth Edition”, W.H. Freeman and Company, New York, c. 2012

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

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

Jan 29 2023

## Magnetic Fields as Effecting Coulomb Groups

An electric field of an electromagnetic wave does the work to extend the magnetic field of the same wave. What makes the electric field turn around must have something to do with running out of energy to extend the magnetic field further. Griffiths says: “Magnetic forces do no work” ([1], pg. 207), and that is why it is said that transmission of the Coulomb field is “a diffeomorphism on the electric fields of the gamma rays”:

https://www.fruechtetheory.com/blog/2022/03/29/transmission-of-the-coulomb-field/

Magnetic fields can act as guides however, and can help hold together a groupoid in the gamma ray field so it can act transitively. There is “energy stored in the magnetic field” ([1], pg. 317] and “Magnetic forces may alter the direction in which a particle moves, but they cannot speed it up or slow it down.” ([1], pg. 207) It is the same in Coulomb groups, spherical or concentrated, that carry the Coulomb field, – there are electric currents that are altered in direction by magnetic fields. Another example of this is gravitational lensing.

An involution may be a charged particle, or nucleus, with mass, as it absorbs gravitons for the energy to send out Coulomb groups, or it may be a Coulomb group itself in an open field. As a spherical group travels, for example, it takes on new gamma rays and leaves some behind, and the new gamma rays may be called an involution as they become part of the Coulomb group.

When it is said that with Coulomb phonon transmission, the gamma rays are “frozen in time” up to “10 meters at least”:

it is in relation to travel, though they may travel a miniscule amount. It is torsion that transmits the Coulomb field, and the angular velocity, ω, is higher the stronger the field.

In a Cartan decomposition, “g1 = t1 + p1 and g2 = t2 + p2“ ([2], pg.517), p is the peak point of the electric field of a graviton. In a Riemannian globally symmetric space of type I, p follows the peak of a sine wave, and it also follows the peak in a Riemannian globally symmetric space of type II.

[1] Griffiths, David J., “Introduction to Electrodynamics”, Prentice Hall, 1999

[2] Helgason, Sigurdur, “Differential Geometry, Lie Groups, and Symmetric Spaces”, American Mathematical Society, 2012

Jan 17 2023

## Action of the Electric Field

When a molecule is formed, each nucleus senses the one(s) closest by its spherical pulses. Then each nucleus starts sending out alternating concentrated groupoids toward the nearest nuclei in the molecule.

In a Coulomb attraction, the groupoid decides how to bisect by the spin of a target. The two brackets then compress against other gamma rays and subsequentially spring back and squeegee along the backside of the target in what is called a pullback. Past the target, the brackets “re-emerge as action morphisms of Lie algebroids” ([1], pg. 152), and join a spherical group.

The scalar potential has units of J/s, which is energy per time. The electric field has units of N/C, and Force = mass x acceleration per Newton’s second law. The acceleration is less for a larger mass of charge, and there are neutrons in most nuclei which makes the effect greater. The electric field travels faster the denser a gravitational field is, though the speed difference may not be discernable.

We can have “a π-saturated open set” ([1], pg. 97) with “saturated local flow”, though the gravitons will be at various phases on sine waves when an electric field comes through. Thus, in terms of analytic coordinates, “such coordinates do not usually exist for Lie groupoids.” ([1], pg.  pg. 142) What we have is an infinitesimal zigzag pattern, though when we back out to the classical level, it does not matter for any application.

As said earlier, Coulomb repulsion acts on the frontside of another charge. The electric field travels much faster than the charged mass it pushes, in part due to inertia, so likewise, after the push, the brackets join another spherical group behind the target. A nuclear concentrated groupoid may join a spherical groupoid once it passes a target.

In both cases, Coulomb attraction or repulsion, the spherical group from which the brackets came mends itself.

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

Nov 17 2022

## The Coulomb Gauge

There is another name for a free graviton, – it is “the identity isomorphism idEx, here denoted 1x, and the elements 1x, x ϵ M, act as unities for any multiplication in which they can take part” ([1], pg. 4). We see that unlike π, idEx has some degree of circular polarization and/or skewed sine waves. In some writing instances π is the same as idEx and I am not trying to dictate how they should be used.

In the “Coulomb, radiation, or transverse gauge. This is the gauge in which ∇ · A = 0” ([2], pg. 241), we have a classical description. In the tensor sense, we have the forms Χij. The direction we choose for Χ is always transverse to the radial electric field at a chosen point, and the coordinate frame Ui is picked centered on the same point, creating a k-plane. We have that “The forms Χij are the transition forms for the Lie algebroid atlas {Ui, ψi, Θi}” ([1], pg. 206), and Θi varies with the density of the gamma ray field:

https://www.fruechtetheory.com/blog/2022/10/05/the-vector-potential/

Considering the transition form TP/G [1], we may here call G the density of the gravitational field. It is seen that as the density goes up the transition angle Θi decreases for a given charge and distance from the charge.

In Jackson’s problem 6.19 (b), “the original and space-inverted vector potential differ by a gauge transformation” ([2], pg. 291). Though the earth catches some of the sun’s gravitons all the time, the sun’s gravitons during the day are greater at the face of the earth than at night, and inverted, changing the Coulomb gauge.

With the “Lorenz condition (1867), ∇ · A + (1/c2) ẟφ/dt = 0” ([2], pg. 240), it is mathematically shown that the system {Ui, ψi, Θi} acts fast compared to the gradient of A, and
ιX (φ ˄ ψ) = ιX(φ) ˄ ψ + (-1)i φ ˄ ιX(ψ)              ([1], pg. 306)
Also, as small as gravitons are, we may as well call the k-planes “flat connections Θi“ ([1], pg. 206).

Since we have “t the fixed point set of θ” ([3], pg. 401), t is on the center line of a gamma ray, and “g0 = t0 + p0 is a Cartan decomposition of g0“ ([3], pg. 184). In certain situations the center can shift as well, in which case “c0 is the center of t0” ([3], pg. 452) as t0 moves back and forth.

With the polarization factor, it is interesting to call h the vector summation of two gamma ray electric fields. When a gravitational field is yet more compact, h is the summation of more than 2 electric fields, so that “f: MH be a smooth map” ([1], pg. 183), and “Let h be a proper subalgebra of g of maximum dimension” ([3], pg. 160).

Incidentally, the identity isomorphism reminds us of quantum 1:

https://www.fruechtetheory.com/blog/2009/09/16/the-fundamental-quantum-unit/

[1] Mackenzie, Kirill C. H., “General Theory of Lie Groupoids and Lie Algebroids”, c. 2005 Kirill C. H. Mackenzie, London Mathematical Society
[2] Jackson, J. D., “Classical Electrodynamics, Third Edition”, c. 1999 John David Jackson, John Wiley & Sons, Inc
[3] Helgason, Sigurdur, “Differential Geometry, Lie Groups, and Symmetric Spaces”, American Mathematical Society, 2012

Oct 05 2022

## The Vector Potential

In electrodynamics we find that “A quantum-mechanical description of photons necessitates quantization of only the vector potential” ([1], pg. 242), as in the summation of all the manifolds of gravitational fields at a given location. In a more densely packed summation of manifolds, the action of an electric charge will have a lesser rotational effect on the electric fields of the gamma rays than on a less dense field. The power of the rotation is the same in either field however, as long as we are referring to a gravitational field that is not too sparse for electric fields to propagate.

“The definition of B = ∇ x A specifies the curl of A, but it doesn’t say anything about the divergence – we are at liberty to pick that as we see fit, and zero is ordinarily the simplest choice.” ([2], pg. 235) The reason we may pick the divergence as zero is that the manifolds “are frozen in time for phonon transmission”:

https://www.fruechtetheory.com/blog/2022/03/29/transmission-of-the-coulomb-field/

As far as group action, Mackenzie [3] calls these “groupoids”, such as an ellipsoid, a spheroid, or another 3-dimensional shape. The definition of a spheroid I find is that it is like a sphere, but not a perfect sphere, and in the present case we have “oscillations and accordion motion in multiple axes”:

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

On a side note, though related to manifolds of gravitational fields, the Nobel Prize in Physics is being given this year for essentially this:

https://www.fruechtetheory.com/blog/2014/05/30/quantum-entanglement/

[1] Jackson, J. D., “Classical Electrodynamics, Third Edition”, c. 1999 John David Jackson, John Wiley & Sons, Inc
[2] Griffiths, David J., “Introduction to Electrodynamics, Third Edition”, c. 1999, Prentice-Hall, Inc.
[3] Mackenzie, Kirill C. H., “General Theory of Lie Groupoids and Lie Algebroids”, c. 2005 Kirill C. H. Mackenzie, London Mathematical Society

Feb 11 2022

## Isotropic Property of the Coulomb Potential

In the vicinity of where our machines have been, we know that electric current will flow in any designated direction and is not particular to the direction of the highest flux density of gravitons.

For various reasons, we cannot have protons and electrons continuously flipping, – the Stern-Gerlach experiment proves that they do not. There must be internal processes of the proton and electron which produce isotropic electric fields. Some of this was previously addressed in two blog entries:

https://www.fruechtetheory.com/blog/2010/12/09/field-line-curvature/

https://www.fruechtetheory.com/blog/2010/06/15/muonic-states/

It is possible that not all conjugate wave gravitons pass straight through a proton or electron, or that even with a free proton or electron that the gravitons leaving have just entered. Some may make a horseshoe pattern and come out near the same point entered. They may be able to come back out at any angle. As compressed as the gravitons become inside a particle, almost any shape can occur. Gravitational pressure dictates a consistent size of a free proton or electron.

With the flux density coming out of the face of the earth, we seem to have a conundrum with the idea of gravitational pressure, one side having much greater pressure than the other. Why do gravitons not burst out the top, resulting in particle collapse? It also begs the question as to why electrons are perfectly round, and not teardrop shaped:

https://www.fruechtetheory.com/blog/2011/05/28/free-electrons-perfectly-round-3/

Possibly, branes form at the top of an electron and reform in a spin flip.  These branes would be linked inside the particle so that they do not bust out, and may deflect some exiting gravitons at various angles. These branes may also help keep the electron round. Here we are designating “top” as away from the highest flux density of gravitons.

As far as isotropic fields, at this point we must say that it is designed internal to the proton or electron and is of consistent pattern.  The open field starts just outside the particle, so it is maintained that electric and magnetic fields transmit openly by “phase shift and chirality” or “phase shift and parity”.  The Coulomb force is considered instantaneous at reasonable distances:

https://www.fruechtetheory.com/blog/2014/05/30/quantum-entanglement/

It appears as though this is necessary, because then the speed that free gravitons travel at, the speed of light in a vacuum, does not effect the electric and magnetic fields generated.

Next »