Archive for the 'Quantum Field Theory' Category

Mar 17 2023

Nuclear Ideals

On April 10, 2008, it was put forth that “we would have gravitational energy replenishing Coulomb energy through both the electrons and the nucleus of an atom”, through absorption of gamma rays:

http://www.fruechtetheory.com/blog/2008/04/10/the-nucleus-and-gravitons-2/

It wasn’t until 2022 that mathematics was applied to the process, and of course free nuclei and electrons would be absorbing gravitons as well to produce Coulomb fields.

In Krane’s work, the section on Spin-Orbit Potential starts on page 123. There, in the language of atomic physicists applied to nuclear physics: “total angular momentum j = l + s” ([1], pg. 124). In the same way, in the language of differential geometry, Lie groups, and manifolds, J can be called a nucleus, or “an isometry J of N” ([2], pg. 207). There is a “closed embedded submanifold N ⊂ M” ([3], pg. 165), and “N is closed in M” ([2], pg. 236). In this case N is the space atoms and molecules take up, to the outer reaches of the electron orbitals.

In “its ideal system J = (J, R(f), θ) is uniform” ([3], pg. 170). This infers that each different nuclei has a unique structure, and R(f) is the radius of the nuclear fibration. Since nuclei are normally parts of systems of atoms and molecules, θ refers to the angle of an electron arc, and each nucleus knows when to send spin flip signals for each electron arc for which it is responsible. The structure of nuclei is so complex that “covariant derivatives of J vanish” ([2], pg. 142).

As far as holding nuclear material and groups together, magnetic fields are mostly responsible, and serve as the function of chirality in Coulomb fields. As an example, “inductors correspond to, and characterize, pullback groupoids” ([3], pg. 83), as put out from a charged mass. Also, “(φ,f) is an inductor if φ!! is a diffeomorphism” ([3], pg. 176).

[1] Krane, Kenneth S., “Introductory Nuclear Physics”, c. 1988, John Wiley & Sons, Inc.

[2] 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

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

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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”:

http://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”:

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

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

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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

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Dec 15 2022

Fusion

At Lawrence Livermore Laboratory a fusion reaction was produced using 192 lasers. By a factor of 1.5, more energy was produced than the energy put in by the lasers.
Early in my education at the University of Wisconsin – Madison, we learned of conservation of energy. If a reaction can absorb enough gravitons during a process, then it would appear that conservation of energy is violated, though it was not really violated.

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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 (pi), 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:

http://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:

http://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

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Aug 27 2022

Concentrated Group Action

There is another slightly different view in which the Coulomb field transmits when it comes to nuclei as parts of molecules, and that is by pulsating, concentrated Weyl groups or frames of a small conical angle, toward another nucleus. It is not wholly different from the last blog entry because spherical pulses could also be seen as groups, and for a given charge these concentrated groups are in addition to spherical groups.

When an O2 or N2 binuclear molecule forms, or let us say a benzene molecule, each nucleus senses the other nuclei closest. This is a strong repulsion, so the nuclei may start sending out groups concentrated toward the other nuclei for efficiency, while the electron cloud in between the nuclei offers attraction and keeps the molecule from flying apart. This also changes the Calabi-Yau structures within the nuclei.

For Coulomb attraction, a frame may wrap around another charge. For Coulomb repulsion, there may be partial contact and some backflush. As two close nuclei in a molecule sense each other, there may also be alternating, concentrated, group pulses between the two. This is likened to a synchronization between the nuclei, without the need for backflush. With phonon transmission this is a very fast process and transmits without intercepting electrons in orbitals. When we compare the size of nuclei and electrons to molecular size, there is a lot of empty space filled with gravitons, so this synchronization is reasonable.

In larger nuclei there are more compact spaces and more affine connections between them. For a nucleus we may call these irreducible representations, where the exception is fission, as a “reduced root system in V” ([1], pg. 461). The nuclear charge manufactures springboard groups repeatedly, with oscillations and accordion motion in multiple axes. A stable nucleus in a molecule is an isomorphism, though we must be careful here because as orientations change, there may be slight changes in structure. Particle colliders are excluded from this discussion.

A nucleus consists of involutive automorphisms, the summation adding to the entity’s spin, as it absorbs gravitons for the energy to send out groups or frames. Boothby calls these “inner automorphisms of G” ([2]. Pg. 237). A Weyl chamber is part of atomic mass, while a Weyl group transmits as a packet in the not so compact space of the gamma ray field.

We see that “π is a continuous and open mapping.” ([1], pg. 120]. In certain areas of deep space we may call this Riemannian globally symmetric space I, with perfect sine waves and no circular polarization. “Riemannian globally symmetric spaces of type II” ([1], pg. 516) are due to the bi-invariant structure of the Coulomb field. In both cases there is a “strong orthogonality” ([1], pg. 576) which produces a polarization factor of 2, as used in the blackbody radiation formula and in G = 4hf/3. π may be called a free graviton, since it is one half wavelength long.

As far as the Coulomb field produced by an electron in an atomic or a molecular orbital: “Let N0 be a bounded star-shaped open neighborhood of 0 ϵ g which exp maps diffeomorphically onto an open neighborhood Ne of e in G.” ([1], pg. 552) Let e be the electron, star-shaped be the lobes of orbitals, and exp be the growth of an orbital electron in size and charge. The increase in size of an electron in the orbital enables it to absorb more gravitons at a given time, thus increasing gravitational pull in the second half of the arc.

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

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

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Mar 29 2022

Transmission of the Coulomb Field

The gamma ray field we live in is extremely rich and dense.  For the forms we find in nuclei and assorted particles, there is all the energy needed to drive all physical processes.

A Calabi-Yau shape within a nucleus or particle needs an external energy supply to maintain it. Gravity provides the energy. Here we are talking about force and pressure within a nucleus or particle, with only indirect connection to the outside, or connection at a point, curve, or surface.  There may also be tears joining and reforming.

Occasionally we refer to neutrons, protons, electrons, and nuclei.  A proton can be a hydrogen nucleus, though we list it separately when we talk about free protons, such as in the solar wind, particle colliders, or elsewhere.  Let’s take an Oxygen nucleus for example with the makings of 8 protons and 8 neutrons. Inside the nucleus, at the top, parachutes with baskets attached through ropes, or strings, instead of a parachutist, may cause some gravitons to loop around the insides of the parachutes, or branes, and into the baskets with enough force to hold the parachutes against the highest flux density of gravitons. Then the gravitons would find ways to tunnel through the baskets, pushed from behind.  In the motions of O2 in air, the parachutes may slide around to stay opposite the maximum flux.

This may also help explain weak interaction parity violation, because as an electron forming within a nucleus tries to escape, out the bottom is easier, due to escape out the top involving going through the gaps in the parachutes.  More than 50% would come out downward.

The manifold of the sun’s gamma ray field, the manifold of the earth’s gamma ray field, and likewise with other celestial bodies, provides a combination of symmetric spaces. During the day, at noon let’s say, the vectors of the sun’s manifold are in the opposite direction as the vectors of the earth’s terrestrial manifold. The Coulomb field uses all vectors of all manifolds to propagate, because all vectors, within a distance of 10 meters at least, are frozen in time for phonon transmission.

Let’s say M1 is the earth’s manifold, and M2 is the combination of the earth’s and sun’s manifolds. “…a diffeomorphism F: M1 → M2 of manifolds oriented by Ω1, Ω2, is orientation-preserving if F*Ω2 = λΩ1, where λ > 0 is a C function on M.” ([1] pg. 209) In our example here, λ > 1, and we have neglected the earth’s moon for simplification.

We may call a negative charge a left coset space, and a positive charge a right coset space. Each creates its own homomorphism in the dense gamma ray field, by a diffeomorphism on the electric fields of the gamma rays.  For one thing, there is circular polarization. For another, perpendicular to the greatest flux density of gamma rays the electric fields of the gamma rays may have skewed sine wave lobes, somewhere between a normal sine wave and a sawtooth. The Coulomb field acts tangent to the R vector sphere, and “(∇XY)p depends not on the vector field X but only on its value Xp at p.” ([1] pg. 309]  The way that the Coulomb field transmits radially is by centrifugal force through the gamma ray field.

The inside of an atom may be called a geodesic.  An electron path in an atomic orbital may also be called a geodesic, and “a long geodesic may not be minimal.” ([2] pg. 62)  This is due to the Lorentz force:

http://www.fruechtetheory.com/blog/2010/12/23/electron-orbitals-and-the-lorentz-force/

Gravity is an integral manifold.  Each orbital arc is a line integral absorbing gravitons.  The Coulomb field, on the other hand, is a charge induced diffeomorphism in the gamma ray field. Substantially outside of neutral atoms there is a propensity for positive and negative charges to cancel, though in the near field we have van der Waals forces.

Phonons for the Coulomb interaction are generated inside a charge.  The field created, that acts on another charge, may act on the outside of another charge, possibly only 5% of the diameter deep.  The fields may also act in the interspace, producing backflush to the charges that generate the fields.  Phonons of opposite chirality attract, and of the same chirality repel.

As points meet for the Coulomb force, the acceleration would be periodic, and relates to the vector potential.  A Fourier Series can be applied to the vector potential, with the direction of force being the side of the ‘x’ axis where the sine or cosine function has larger lobes.  Often a geodesic is called piecewise smooth, due to gravitons being separate, though on a classical scale the motion is smooth.

Two electrons can occupy the same atomic orbital if they have opposite half-integer spin projections.  This is the Pauli exclusion principle.  In terms of tensor math, “the subspaces are mutually orthogonal and each is a nontrivial irreducible subspace.” ([1] pg. 242)

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

[2] J. Milnor, based on lecture notes by M. Spivak and R. Wells, Morse Theory, Princeton University Press, 1969

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Feb 14 2022

Spin Drive

Published by under Quantum Field Theory

When an electron enters an atomic orbital, it receives a signal from the nucleus that changes and redefines its internal wavefunctions to a configuration that can accept more than 137 gravitons. It can then grow in diameter, mass, and charge. At the end of an arc, at a spin flip, the electron reduces to 1.3335 x 10-15 diameter and free electron structure. It is likely that another wave function signal comes immediately after the spin flip signal to set unlimited graviton absorption mode again. At the face of the earth, and at many other places in the universe, the gravitational field is very dense, and can carry many signals in the form of field quanta. I prefer to call them massless signals or messengers and give quantum field theorists the leeway to name them. Some names will come from existing tables.

A nucleus would know the number of electrons in orbit and exactly where they are in relation to the nucleus at any given time. An analogy might be a cell phone tower monitoring numerous cell phones in its vicinity.

It is acceptable to name gravitons differently when inside an electron because they can be greatly compressed. Wavelength is shorter and amplitude is normally smaller. In a large nucleus there would be wider variability with these parameters. In either instance, the gravitons are changed and compactified. Wave packets may form, such as with harmonics in music, selecting a few integer wavelengths to fit inside a longer wavelength, with position boundary conditions matching.

As for free electrons, these exchange gravitons as well. It is not two at a time exchange but a one for one exchange. This leaves the electron jiggling and/or pulsating.  Gravitons entering an electron drive the spin, even if they do not pass through. For this we have the example of the metal pump top:

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

Once an electron escapes an orbital, as in metals, it reduces to free electron diameter and internal mode. It is only a free electron that continually produces a fundamental charge of 1.602 x 10-19 C.

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Dec 04 2019

Electric and Magnetic Fields

Jon Rogawski has a cool diagram and calculation using Faraday’s Law on page 979 of his Multivariable Calculus book*. The magnetic field around the straight wire with an alternating current flowing in it produces a voltage in an adjacent looped wire with no conventional energy applied except that from the other wire.

Of course this magnetic field, and likewise for electric fields, must have a pervasive field in which to transmit. One may say it transmits through the air, however Faraday’s law also applies in space.

These E and B fields transmit by turning and bending the E and B fields of the dense gamma rays.

* Rogawski, Jon, “Multivariable Calculus”, W. H. Freeman and Company, c. 2008

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Oct 27 2019

Medical Uses

Took a walk on campus on this beautiful sunny autumn day, and when walking by the Microbial Sciences building it reminded me of possible medical uses for the gamma rays.  For example, using layers of high voltage plates, the gamma rays can be downscattered into lower energy gamma rays or x-rays.  The plates may be stepped down in area as traversing upward, so that specific wavelengths may be focused on smaller areas.

Most of the benefits of the general knowledge that we are in a dense gamma ray field will be found and developed by coming generations.  Nevertheless, the public already knows about the gamma ray field because gamma ray space telescopes have measured it since the 1990’s.  Medical research could be started without the researchers even knowing that it is gravity.

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