More (Non and Partial) Progress on Electromagnetism in the mnp Model

Edited: 2022-03-05 to include classical B and F on diagrams. Added Figure 3 - Gradient Anti-Parallel to Electron Movement, Axis Tensor Perpendicular for reference. Title adjusted - partial progress.

Edited: 2022-03-06 to note that in a moving particle, finding matching points on matching coils with opposite z components in the coil is easy, but given velocity v the z components and hence the x and y components of the basic entity travel are NOT opposite.

(Non and Partial) Progress

This post is a further investigation of particle response to magnetic fields started in Post 48 - Toward a Unified Charge Information Field Model as part of the mnp Model approach to the (massive) topic of electromagnetism. That post has been lightly edited to note that it and this post are a work in progress; not all the “proofs” are satisfying. This material has grown so that inserting it back into Post 48 would be difficult.

Given ∃xperiment and the universe’s ∃xistence, the fundamental finding that coils perpendicular to the Charge Information Tensor Field (called Axis Tensor here and akin to the traditional Vector Potential) do not respond to the Field except for nuances related to mediator travel that lead to creation of attractive electrostatic fields and to electron shell repulsion by the nucleus is deemed a solid part of the mnp Model. A single field, the Axis Tensor Field, is still seen as the origin of all electromagnetic exchange.

Electromagnetism - a Symmetries/Commutation Relation Approach

Here is an approach to picturing and describing moving particle response to Axis Tensor Fields that attempts to use symmetries in the particle, the coils, and the basic entities in those coils. Using travel of the mediators as part of the picture of gradient of the Axis Tensor Field is being avoided here. At the end of February, 2022, the symmetries/Commutation Relation Approach is not very satisfying let alone complete. The exercise may prove useful as an education in “Thinking in the”mnp" Model." It may prove useful in limiting the degrees of freedom in the Model.

For example, thinking about moving particles in an Axial Tensor Field has lead to the thought that velocity v is a part of all the basic entity travel in the coils of a particle, that coil orientations close to perpendicular to the direction of motion become very rare, and that this “Darwinian” selection of coil orientations may lead more of less directly to particle shortening in the direction of movement. This picture feels relativistic; the coils do their normal stuff, just slower by 1/γ and velocity v is tacked on uniformly as if the laws of physics DO apply in all inertial frames. Or not. To be continued…

Principles of Particle Response

Some principles or guidelines for (the author’s use in) thinking about electromagnetism in the mnp Model.

• Entity behavior in the Field:
• The Axis Tensor causes redirection by the Axis Alignment property of the basic n (or p) entities attempt to align their Axis, opposite the direction of travel for n’s and along the direction of travel for p’s.
• The redirection is only perpendicular to the path of the basic entity/entities.
• The gradient only indicates direction of (increasing) Axis Tensor, but is useful for finding “matching” coils and positions on the coil.
• Increases from one side to the other of a particle may lead to turning caused by the Axis Tensor. To be determined.
• For electrons, the particles shown here in all drawings, if the Axis Tensor Field would guide the axis of the entity into the coil, the effect is permitted since the travel direction would be moved out. Mathematically expressed, if Axis Tensor projected onto the radius from center to entity on coil is negative, effects are possible. ?? as (?) Entities in coils, with axis cross Axis Tensor _ away _ from coil can be affected. Here, if the radius on the coil is toward the Axis Tensor, there will be no effect. ??? Need coil direction. ???


• Particle Geometries:
• Given velocity v is along the z axis
• The moving particle is therefore an ellipsoid compressed in the z direction.
• The particle is rotationally symmetric about a line through the center in the v direction. Call that the centerline.
• The particle is mirror across the plane through the center perpendicular to the v direction. Coil rotations are mirrored as if the coil have been slid across the (representational) surface of the ellipsoid.


• Symmetries:
• Start with a point (a) on a coil (A) at a position in the particle. There will be a (huge) number of coils at the same relative orientation to the centerline.
• For any plane containing the centerline, there will be a matching coil and point across that plane.
• For any plane containing the centerline and perpendicular to the first chosen plane, there will be two more coils and points in symmetry.
• Across the equatorial plane, there will be 4 more points and coils in symmetry, but the direction of motion v will cause a z offset to the basic entity travel in the coils. The “moving in coil” directions will mirror, but the z offset will add. Alternate expression: Since the basic entities in the coils are oriented “off coil plane” in moving particles, the basic entity orientation is NOT mirror symmetric in the plane perpendicular to the velocity.
• Other planes cut through the center parallel to a chosen plane through the centerline will cut an ellipsoid of coil orientations, which may be useful but the only matches on density of states will be across the equatorial plane and the center plane perpendicular to the logically cutting plane.
• Other planes cut through the center at skewed angles will cut an ellipsoid of coil orientations which may be useful, but there is no guarantee that the density of states of coil orientations or basic entity presence will be symmetric.
• Further, there will be a (regular but not determined) distribution of coil orientations and corresponding points on an ellipsoid in any chosen plane perpendicular to the gradient, so the corresponding positions in coils to (a) given coil will be continuously distributed, though that distribution may not be exactly linear or identical.
• A certain limited amount of “representation” may be used in the discussion. The author hopes to minimize “representation” and describe the assumptions and reasons when needed.


• Drawings:
• Axis convention: Velocity is parallel to the z axis.
• Coil orientations and points are symmetric about the x axis and the y axis.
• The y’ axis will be in the opposite direction from the gradient. Any y’z plane will be a plane of symmetry.
• All drawings here will be of electrons, with Axis by Franklin’s convention opposite the direction of travel. Electrons are assumed to be spherical(ish) shells or (tiny) spherical(ish) free electrons.

The goal of all this exercise is to show that 1) the off-gradient component of the Axis Tensor does not affect the speed of a (moving) particle but only redirects the particle and 2) if the particle is moving perpendicular to both Axis Tensor and gradient, there is no resultant. An intermediate step is recognizing the symmetries, analogous to looking for commutation relations. Proving a cross product relationship is left for the future.

The symmetries are not exact. Due to the huge numbers of coils and basic entities in the particle and the speed of the basic entities in coils (c) and the tiny time taken for basic entities to traverse one loop and the macroscopic lack of lateral movement, the particle symmetries can be considered exact for the pictures here. Note that for now the coils are assumed to always have correspondents for the planes of symmetry. “Exactly” 90 degrees or “exactly” parallel can be ignored for now as having a vanishingly small density of states, but may be revisited later.

The figures show coil orientations at the “front” of the particle above the coil orientations at the “back” of the particle below. The figures show an equivalent particle with opposite spin on the right, in case the argument for balance needs the opposite spin as well.

Hopes for the “symmetries” (commutation relation) approach are collected here:

• Find corresponding positions/basic entities so that an “integration of resultants” is not needed.
• If coil symmetry itself must be used, we hope not to need to assume that the coil itself sees a uniform Axis Tensor.
• Avoid a foray into argument from statistical physics and finding balance in opposite spins. Hopefully, this is NOT necessary for fields with constant gradient. Thus:
• Avoid using the right hand images at all.
• Perhaps avoid needing to find matching points at other than symmetry positions in coils of symmetrically matching orientations and positions.
• Integrating around a coil or over all coils is avoidable.
• Integrating around an ellipse of distributions of coil orientations or positions on the coils of that ellipsoidal distribution is avoidable.
• Develop the author’s and the diagrams visualization of the effect of Axis Tensor on the particles. The simulation of coil orientations and entity positions and net effects will benefit from this visualization. And this discussion may benefit from the calculations. A work in progress.

Both Gradient and Axis Tensor Perpendicular to Velocity

Figure 1 - Gradient, Axis Tensor, and Velocity All Perpendicular

This diagram shows the Axis Tensor in the xy plane at 45 degrees clockwise from the y axis, pointed away from the viewer. The gradient is in the xy plane at -45 degrees from the y axis. (“Without loss of generality.”) Axis Tensor is perpendicular to velocity. Missing from the diagram is a little halo around the end of the dark arrows, indicating the limits of effect which must be perpendicular to the movement of the entities. Actually a half halo would be appropriate, indicating it cannot coil more tightly.

So, in this isometric, the plane of uniform Axis Tensor parallel to the point of view so shows as a vertical line with the plane projecting directly out of the screen/paper. (a) (a m) (a u) and (a m u) are in a plane of equal Axis Tensor perpendicular to the gradient. Each of those points has a corresponding point across the coil in the plane of uniform Axis Tensor. They are in coils of mirrored orientation in the xy plane (front to back in the upward moving particle) and the vertical plane that includes the gradient. Within a single coil, there is another point on the plane of constant gradient opposite (a), shown as (a o) on the diagram. It is in a line symmetrical position in the coil (across the projection of the gradient onto the plane of the coil) but not similar orientations to the Axis Tensor. On the other side of the z axis (mirrored in the plane x=y) are four corresponding points (b) (b m) (b u) and (b m u), which each see the same higher Axis Tensor as much above the Axis Tensor through the center of the particle as (a) and company see an Axis Tensor below the center/average. The author hopes to not need that “symmetry.”

The classical B comes from a line source to the right, with (+) current moving along x=y so at the origin B is up in the z direction and F is expected to be 0.

Want to show: in a plane of equal Axis tensor, the net change in basic entity direction is 0 perpendicular to the velocity. Even better, the change in basic entity direction is 0.

Half of each coil will be unable to respond to the Axis Tensor. Some of the points in the diagram cannot be affected by the Axis Tensor, since that would require the impossible tightening of the coils. Points (a m u) (x m u) and (a m) and (x m) and (a o) cannot be affected. So in this diagram, of the a series, only (a) and (a u) are candidates for balancing effect as are (x) and (x u):

This proof/argument appears to depend on the effect at supplementary angles being the same. This proof/argument gets easier if the velocity component of EACH basic entity is the same, in the direction of the overall velocity. So for now, assume that the true orientation of EACH basic entity n in the coil has a v component separate from coil motion. By ∃xistence/∃xperiment. For now.

In the figure, (a u) is mirrored in the horizontal plane though the center and matches the (a) familiar from earlier figures. The z component of figment movement in the coil is the same, the x and y components are opposite. The v component offset from the coil is the same. The angles to the Axis Tensor are supplementary. So the Axis Tensor influence on the two will be the same, toward a line x=y in a horizontal plane, but the x and y components will be opposite for no net effect on the particle. The effect on the z component will not balance, since (a u) is being directed down and (a) is being directed down. So the only net non-symmetry is the z component of the offset. Using a statistical physics argument with density of states overtones, there will be as many (x) and (x u) pairs at that Axis Tensor value in the coils that supply the (a) and (a u) pairs, with z components down. The Axis Tensor will tend to redirect those up, hopefully balancing the effect on the z component of n entity motion. A second attempted argument: Since any redirection of that z component must be in that z component direction and the constituents of the particle are already moving at c and cannot be accelerated or decelerated, therefore all other changes will cancel when the Axis Tensor is perpendicular to travel and the gradient is perpendicular to velocity, there will be no effect to redirect velocity. This pairing exists for all basic entities and coil directions in the moving particle. (QED) Sorta.

The “no effect on the z component of the velocity” part of the argument still seems to be a bit of a stretch.

Gradient Anti-Parallel to Velocity, Axis Tensor Perpendicular

(Edit 2022-03-05) The initial post had Axis Tensor anti-parallel to velocity and gradient perpendicular to both here. That did not succeed completely. Subsequent investigation of the gradient anti-parallel to the velocity and the Axis Field perpendicular to the velocity toward -x and so still perpendicular to the gradient, initially intended to follow, was more successful.

In the following diagram, we want to show that the resultant (F) is in the y direction, that there is no resultant parallel to the gradient and velocity.

Figure 2 - Gradient Anti-Parallel to Electron Movement, Axis Tensor Perpendicular

Here the classical B is generated by a line source running +x to -x below the diagram. At the origin, B is in the positive y direction, so F is in the +x direction.

Horizontal planes cut through the particle see uniform Axis Tensors, so (a) (a m) (b) and (b m) AND (a mirrored) (y) (x) and (x m) see the same Axis Tensor direction and magnitude. (a) (b) (a mirrored) and (y) cannot respond, (a m) (b m) (x) and (x m) can respond by redirecting away from the coil. (a m) and (b m) have the same angle to the Axis Tensor, with the same y and x components and opposite z components. They will balance in the z direction. All points on all coils will have a corresponding point on a coil at the same Axis Tensor so no resultant in the z direction is expected. (x) and (b m) have a supplementary angle to the Axis Tensor, with opposite z, y, and x coordinates. The y coordinates of resultant will cancel. The x component of (b m) will increase, the x component of (x) will increase as the coil at that point traveling in the -x direction attempts to open. For all points on all coils that can respond, a corresponding point on a symmetrical coil exists. QED. Sorta. Actually not too bad! (2022-03-06) That proof only works if we ignore the z component due to velocity v. Further investigation of response of the entities as part of the coil are needed.

Note that (a m) and (x m) show on the same coil only because the B and D coils are shown as exactly perpendicular, that actually (a m) would have a corresponding point on another coil also nearly perpendicular to the xz plane so the proof holds. Exactly perpendicular has such a low (essentially 0) density of states that we are ignoring it for now.

Note that investigation of whether partial response is possible or useful remains. Note that "useful" means "shows results consistent with ∃xperiment," which of course looks to some like tailoring the Models.

Gradient Perpendicular to Velocity, Axis Tensor Anti-Parallel

Next, consider the gradient perpendicular to the velocity and the Axis Field anti-parallel to the velocity, so still perpendicular to the gradient. Want to show that the resultant is in the direction of increasing gradient, that there is no resultant perpendicular to the gradient and no resultant parallel to the velocity.

Figure 3 - Gradient Perpendicular to v, Axis Tensor Anti-Parallel to v

Here limitations on which points are affected by the Axis Tensor apply. Pairs (a o) (a u o) and (a m o) (a m u o) are affected, the (a) and (x) series are not in this drawing. Points (a o) and (a u o) make then same angle to the Axis Tensor, with opposite x' and y' and the same z component. The x' components of the resultants match, showing no net resultant in the x' direction. Each affected point on each coil has an equivalent point on a coil mirrored in the y'z plane, so the resultant has no x' component. (1/3 QED) Change to basic entity direction must be perpendicular to the basic entity direction and will be in a vertical plane including the entity travel direction vector. This model of interaction ignores coil orientation and neighboring basic entities, which may also present limiting effects. In this simple model, it appears that the z component of the resultant for (a o) and (a u o) are both increased. It appears the y' components cancel, so this simple Model of interaction with entities in coils needs to be revised. Point (a o) might be usefully paired with (a m o) since they make supplementary angles to the Axis Tensor with opposite x' y' and z' components (except that v increases both z components), so a simple search for canceling/commutation does not appear promising here either. If the resultant must be perpendicular to the coil (due to effects from nearby entities in the coil) then having a velocity component perpendicular to coil motion may provide means for that perpendicular effect to occur and might actually allow a resultant proportional to that component perpendicular to the coil. More thought required.

From the first post: These (a o) and (a u o) pairs are chosen because they have point symmetry in the plane perpendicular to the Axis Tensor in x’ and y’ and match z, so that their x’ and y’ components of movement are opposite and their z components match. The pairs make the same angle with the Axis Tensor, with opposite x’ and y’ components and resultants. The z resultant will be greater by an equal amount for (a o) and (a u o). For corresponding points and coils on the other side of the particle, the effects will be similarly balanced but stronger, causing the electron to move from higher to lower gradient (and accelerate) Clearly this does not happen in ∃xperiment, so something is wrong with the argument. A naive approach to electrostatic fields (like attracts and electrons in shells are attracted to the nucleus) did not work before, so the author needs to think about this more. A lot more.

Here the classical B is caused by a line current to the right, with (+) current flowing down, so B is in the x=y direction and F would be in the -y=x direction.

If the Axis Tensor were upward, similar geometries would exist but the (a) and (x) series would be affected and the (...o) series would not.

Translating Back to Magnetic Fields and Forces

The gradient is higher to the right, so the source of the Axial Tensor Field is a vertical current to the right, flowing down the wire. The electrons are moving up, representing a current down.

To repeat, the result I’m getting is wrong.

Possible adjustments or change in approach for now:

• Just do calculations and simulations, with various reasonable Axis Alignment assumptions, and see what happens. Maybe I have made a mistake in logic or geometry.
• Coils with a z component may behave differently and prevent direct redirection of coils in the z direction. Nature can be arbitrary, as the discoverers of the muon found. Still, it will be consistent.
• Examine small differences in Axis Tensor Field caused by the response of the “near part” of the particle.
• Look at what experiment tells us happens and figure out a way to make the basic entities or coils or collections of coils behave that way. (Next to last choice!) We want the response to be proportional to velocity v, to be perpendicular to v, and to be in the -y’ direction. Not too much to ask.
• Of course, there is the “give up” option. After years of “triumphs” of mechanism, that would be hard. What triumphs, you ask? Mechanisms for shell repulsion, electrostatic opposites attract, universe expansion, slowing universe expansion, ultra high speed cosmic particles, the durability of protons and certain few quark triplets, why quark “strings” get stronger and bigger, explanation of the Higgs particle, two step electron shell preferred expansion and contraction, spin, the one third charges in quarks. Leaving only most of physics to be explained.

Possible adjustments to effects on entities in coils:

• The movement of the particle is (anti) parallel to the Axis Tensor. Still, we want the effect proportional to particle speed.
• Consider going back to the change in orientation of the v component as perpendicular to the coil, so it gives the Axis Tensor something to grab onto.
• Consider allowing only effects perpendicular to the coil. Careful to not undo some of the electron shell and electrostatic Axis Field generation effects.
• Compare to the electrostatic case, which should see no effect. The only difference (other than γ correction) is the addition of a component of v perhaps perpendicular to the coil. Or a component of the entity Axis opposite v to attract to the Axis Tensor and … Note here that if v is zero, we have seen (a o) and (a u o) exactly opposite effects if the pesky z would go away.
• Does coming from a region of higher gradient toward smaller make for different effect than from smaller to greater?
• Will partial effect occur rather than nothing in a not-allowed situation? Different for Axis Tensor than a single figment leaving a coil? Might be easier to investigate numerically.
• Might “changing the whole coil orientation” be a better mode or model for influence on particles?

The Work Not Shown

If this had been successful, then investigating skewed Axis Tensor Fields and then skewed gradient would have been appropriate. One diagram is shown here for reference.

Skewed Axis Tensor Field

Drafts of a skewed Axis Tensor Field approach follow, with limited success.

Figure 4 - Axis Tensor Skewed from v, Perpendicular to Gradient

To align with the gradient and Axis Tensor, rotate x and y 45 degrees to create y’ parallel to the gradient and x’ axes perpendicular to v and the gradient. y’ is hidden by the gradient and x’ is hidden by v and z in the isometric drawing.

The magnetic field is generated by a (+) current moving up in a wire to the right of the diagram, the classical B is in the -x' direction, the (+) velocity v+ is down, and the expected resultant F in the -x',y' direction

If the Axis Tensor is perpendicular to the gradient but NOT to the velocity, the four points mentioned still see equal Axis Tensors, but that tensor is skewed. Here, the Axis Tensor points up and back in the isometric. So the arrows are seen bigger in the up and down direction since they are in a plane sloped perpendicular to the viewer.

The x=-y component of the two movements is the same, the z components are the same perpendicular to the plane parallel to the now skewed Axis Tensor, but the x=y component differ. A better corresponding coil to A and position (a) is across the ellipsoidal distribution in the chosen plane, using the Axis Tensor as the dividing line. A view, from -y’ toward y’, centered on the particle and cut on the (a) equal Axis Tensor plane, which locates (a e) across the ellipse. Note the avoidance of the term “section” or “cross section.”. In the following figure, the fuzzy gray ellipse represents coil locations on the approximate surface of the particle. Coil Ae may NOT have the same density of states as coil A so the balances can NOT be investigated about the skewed Axis Tensor. Sigh.

Figure 5 - Cut View of Particle in Iso-Axis Tensor Plane for Skewed Axis Tensor

For now, this effort requires more thought and “unconscious time.” Experimentation with computational modeling is appropriate. Fortunately, resorting to computation is not seen as the last resort of scoundrels in modern physics.

Onward.