Sunday, June 2, 2013

Spin, Angular Momentum, Shells, and Orbitals in the mnp Model - Edited

Abstract - short

Suggestions for why quantum numbers exist, why electrons follow the rules, and why 1/2 spin particles must be rotated 720 degrees return to the same condition are offered based on the mnp Model, which uses three tiny entities and three interactions operating only at very short distances to explain particles, fields, forces, and the measurement of space and time. A new interpretation of quantum mechanics' Ψ function is offered, perhaps to be called the “mass distribution interpretation” or the “coil surface interpretation.”

Abstract - long

The fixed increments of angular momentum for spin and orbital angular momentum are seen as arising from the mnp Model of electrons as quantized sextets of loops of charge material with an essentially fixed length which coil, in an essentially fixed size with an even number of coils and an odd number of twists. Shells are seen as arising from the uncoiling of one pair of coils per shell number, reducing the number of coils in the electron. Orbital angular momentum is seen arising from reversed coil pairs, which can occur only when enough coil pairs have been straightened to relax the coiled loops.

The mnp Model is based on the premise that all entities making up matter and fields travel at c, the speed of light. This blog post aspired to add a second number, h, as the charge angular momentum of two coils in an electron or positron. After peerless review, the magnitude of h remains an experimental value for the mnp Model.

This document attempts to address one of the minor challenges proposed with the Hauser Criteria of Theoretical Success. “After you account for the quantization of the basic charge, how do you explain or incorporate quantum mechanics, for example, the electron shells.” Note that quantum mechanics is considered a minor challenge for a theory of everything.

The development of the mnp Model has so far been qualitative, directed to understanding the experimental results of physics that must be explained and developing consistent ways to explain those phenomena. The author does hope to avoid chasing ever more complex phenomena with ever increasing mathematical complexity and ever increasing hidden dimensions.

Table of Contents

Deep Background

For those encountering the mnp Model for the first time through this “explanation” of intrinsic spin, quantum angular momentum, and electron orbitals: The mnp Model sees electro-magnetic effects arising from a tendency of the basic entities to align on their axis, which is perpendicular to travel for m's, parallel to travel for n's, and opposite travel for p's. Gravity arises in even stranger fashion from the tendency of the basic entities to align in travel direction (since the basic entities travel BOTH WAYS in recruited gravitational field.) The mass of quarks, the extra mass called glue in quark triplets, the energy held by electron shells, and the basis of the photons of electro-magnetism is all made of the very same basic entity m's. The m's are recruited by loops of charge material, also based on Travel Alignment.

The three basic, tiny entities in the mnp Model are seen as moving at c. The charge material entities, n and p, can form single lines of each type n and p. These filaments formed into quantized loops in the early universe.based on the attraction of Travel Direction plus Axis Direction effects with the tiny entities kept apart by the Separation effect. Since Travel and Axis Direction effects “look forward” somewhat, the filaments tend to coil tightly but also respond to outside influence easily since single filaments are flexible. Many n and p entities remain unattached as single entities and are available for recruitment as fields.

What's an Electron?

Filament loops of n's can form six-strands which coil to form electrons. The six-strand loop has a relatively fixed length and is relatively rigid along its length and is flexible perpendicular to its length but not nearly as flexible as single filaments, As with single filaments, a six-strand loop coils at a relatively fixed radius based on the three effects and the tendency of the Travel and Axis Direction effects to favor looking forward, so that once a turn is started it is self-reinforcing, resisted only by the Separation effect. Since the six-strand is relatively stiff along its length, as a single loop uncoiled the six filaments will “turn over” in one complete traverse of the loop. Since the electron is a physical object and present in real space, the loop must be continuous at any given time and with each of the six filament loops the same length, the simplest loop would be a folded figure eight. (-: Invoking Noether's Theorem for loop and strand conservation would be premature :-) To bend that loop into a smaller area, even numbers of twists will be needed, adding two coils with each pair of twists.

Intuition check: Imagine a long stiff rope spliced to itself. Flaking it down to a smaller dimension will require two opposing twists. The demonstration may be confounded by the twisted nature of most physical rope, which makes twisting one way easier than the other, but the thought experiment remains useful.

An electron will always have an odd number of twists and an even number of loops, based on the longitudinal stiffness and the quantized length of the six loops.

Free electrons are seen in the mnp Model as normally tiny spheroids, though in the presence of fields may spread quite far. Free electrons are coiled naturally, as tight as they can be. A free electron, in the absence of fields, has a maximum number of coils, never more.

Spin is seen arising in the mnp Model from the coiling of the loops that form leptons. Note the contrast to the standard assumption that spin is fundamental.

Orbit is not a useful concept in the mnp Model, which does not see electrons as orbiting at all. The coiled loops form a shell, with the filaments in the coils moving at c. The loops need to “relax” in some fashion to form shells and are seen as recruiting m's to follow the n's moving in the coils, with more m's the larger the coil diameter. These m's form photons (fhotons in mnp parlance) when a shell shrinks. Perturbations to a coil or coils propagates along the six-strand, usually at c. Perturbations may also influence neighboring coils “sideways” faster than the entities traveling along the coil would.

Notice one effect of the mnp Model of the electron: there is no “to big to fail” or “too fast to fail” since the electron is not traveling as a particle at ever higher speeds in larger shells, but just stretching its coiled net further. An electron in a large shell may respond to perturbations more slowly than an electron in a smaller shell when those perturbations travel across the coils while any perturbations along the coils will take the same amount of time to propagate. The mnp Model sees no reasonable limits on electron shell size.

Mass Surface: Leptons are seen as having their mass at their “surface” because of the coiling across the logical surface, which varies as the basic entities within the coiled loops move. Since the coil locations vary and since the coils do not necessarily lay flat with each other and since coils locations move in response to fields and perturbations, the surface is approximate and diffuse, so the concept of “expectation value” remains useful. Cloud is a good term for electrons.

Spin Direction

Viewed from outside, the coils in an electron all travel in one direction, either clockwise or counter-clockwise. Two is an invariant scalar in the universe for the number of directions the coils in a surface can be rotating. The direction of the coils determines the direction of the Spin of the fermion, and that Spin is the same looked at from any direction outside the particle. so it appears to be a fundamental property. The Spin sign explanation is easy. Further, Spin is a constant property of the fermion, though electron shells can be turned inside out to reverse the coil direction and hence the Spin. So particles paired by Spin maintain their “hidden sub-structure” independent of what frames they are measured in. Why the magnitude of the spin is constant is the interesting question that will be raised again after a discussion of angular momentum.

Planck Constant - the Search for Meaning

This document attempts to address an origin for h in leptons. The Planck constant also shows up so significantly in the wavelengths of light and is only partially a matter of light being produced by electron shells contracting. A post long gestating will address this issue (partially); the mechanisms must be somewhat different than the lepton basis discussed here relating to the “tightest” curvature of the coils. The origin of h for photons will be based on the strength and distances of the Separation effect that keeps the basic entities apart as well as the presence of Travel Direction and Axis Alignment Effects. Later.

The author initially hoped that a simple check for a coil to have h/2 angular momentum could proceed as follows: Classical angular momentum is m(r vector cross velocity vector). If each coil has a radius r, there are n coils in a free electron, the mass of the electron is Me, v is known to be c since all basic entities in the mnp Model are moving at c. So the angular momentum of a coil is h/2 which equals (me/n)rc. Mass per coil is .511meV/n or Me(=9.11x10-31 kg)/n, angular momentum of one coil is h/2 and. Unknowns are n and r, n = mc/h times r and. r = n(h/2Mec). In the limit, if n is one and a single loop (the theoretical largest the electron could be), the radius is 2.42e-12 meters.

What would the radius of a loop carrying angular momentum of h/2 be? Using the classical formula with much more effrontery than art may not be a terrible idea, given that the basic entities all travel at c but see space as an orthogonal tabula rasa in the mnp Model. The effective radius would be 2.42E-012 meters. What does THAT mean? 1/21 of the Bohr radius is not a reasonable size for the entire loop that makes up the electron. The mnp Model just crashed and burned if the electron is incapable of expanding into a 1s shell.

A different interpretation of that radius of curvature is called for. Instead of a physical radius, that number is a radius of curvature representing how much the coils must UNCOIL from their natural tight configuration in order to remain a loop in the electron. Start with

nec0 number of electron coils in a free electron
rec0 Radius of electron coils in a free electron
lec total length of the coils in an electron = 2pi nec0 rec0
me electron mass

mass per smallest coil is me / nec0

Geometry: To uncoil (by 2 coils) to the next largest “size” of electron requires that the new coil radius be nec0 / (nec0 - 2) of rec0. For large n, this is close to rec0 + (2 / n) rec0.

So a n=1 shell has one fewer pair of coils, and a n=2 shell has two fewer pairs of coils. What if a pair of coils were to be reversed in direction? In the n=2 case, there would be enough flexibility in the length of all coils for a single pair to be reversed. In the n=1 case, the shortening of length of the total strand would cause the electron to pop back to a free electron state with the reversed coils then being flipped to align with the majority. This reversal of coiling direction is not a brute force uncoiling followed by coiling the other direction, but is just a pair of 180 degree twists in the strand in the opposite direction to the expected twists,

Sub-Shells with Orbital Angular Momentum

P shells now aid in understanding Orbital numbers l and in understanding h. With l=1, the orbital momentum of the electron (x^2+y^2) is seen as h. So the author suggests the angular momentum in the two reversed coils is h or h times a constant, so that approximately 2 rec0 nec0 m c = h or rec0 = h/(2nec0mc) and nec0 = h/(2rec0mc). Note that this is not quite a classical angular momentum, but represents the effort required to get those two coils rotating the opposite direction and does not include the lengthening of the coils due to Coulomb potential. So h is not useful as a magnitude yet, but the units make sense.

How to explain projected orbital magnetic numbers ml? The two reversed coils appear, at any given instant, on one side of the electron. If a measurement is made, the test will force the axis of those coils to be either perpendicular to the z axis (ml=0) or parallel or anti-parallel to the z axis (ml = -1 or +1). The projected orbital momentum ml is ħ. Yet more numbers to visit later.

The taking of a measurement definitely forces a shell to make a choice. If, as mnp hopes to show, other shells with the same shape will be repelled by the choice of the first to be measured, the other similar sub-shells will be making a choice as well. Obviously electrons try to fill the sub-shells rather than collapsing if they happen to run into each other, as indicated by the stability and persistence of atoms in the universe.

D shells offer more degrees of freedom. In shells n=3 and greater, two pairs of counter-rotating coils can exist and the result will be a D-shell electron. A test at a given time can find the axis of both coil pairs perpendicular to the z axis (ml=0, one pair with axis perpendicular and one parallel or anti-parallel for ml=+-1 or both pairs with axis parallel or anti-parallel for ml=+-2. Two possible configurations exist: both counter-rotating coil pairs adjacent or the pairs separated, which would indicate that two types of D shells would exist (unless more are possible with different spacing of the counter rotating coil pairs.) Experiment indicates that 5 D shells can coexist, that different configurations of the counter-rotating coils do not lead to “different enough” shell shapes for more than 5 D shells to co-exist. The subsequent discussion of volume and cross sectional areas occupied by the sub-shells in Why the Pauli Exclusion Principle Works is relevant here.

F shells have three pairs of counter-rotating coils. There are seven possibilities for 3 coil pairs: all axes parallel or anti-parallel to the z axis for +-3, two axes parallel or anti-parallel and one perpendicular for +-2, one parallel and two perpendicular for +-1, or all perpendicular for 0. There are three possible configurations: all counter-rotating coils adjacent, two together and one pair separate, and all three pairs separated. Presumably this would lead to at least three expected shell shapes, unless the relative distance between separated pairs leads to even more variations.

In this picture, the test for orbital momentum in P shells and above DOES make the electron choose. The counter-rotating coils are forces to make a stand either parallel or perpendicular to the choosing field. Current tests do not distinguish any information about 45 degrees or halfway. Those steeped in modern physics might say that such tests are impossible, though by now the reader can tell the author is a skeptic.

Digression on Shell Area:

Naive counting of unwound coils suggests 2p shells have a ”surface area” similar to 1s, 3d similar to 1s or maybe 9/8 of 1s, 4f to 1s, 3p to 2s, 4p similar to 3s, … A table of “unwound coil pairs” for various sub-shells is an approximation of how “relaxed” the electron shell “surface” is: The number of “coil pairs straightened”

s p d f g
1
2 1
3 2 1
4 3 2 1
5 4 3 2 1

How shell area corresponds to shell energy is not entirely clear, since 2p shells definitely have more energy than 1s shells. Yet, with much more area, 2s shells have only 1/4 more energy than 1s shells and electrons can be bumped from 2s to 3s without a lot of energy or difficulty.

Hund's Rules

Since Hund's Rules on the ground state of electrons in an atom fold in electro-static issues as well as spin, the comments here are incomplete since they address only spin and coil direction issues. Electrons in neighboring shells will interfere less if they coil the same direction and have matching spin, since the approaching sides of the shells will have opposite coil rotations that do not interfere with each other, though the electro-static attraction from the nucleus will be the primary impetus for the first "bus seat" rule. If two "adjacent" shells are occupied by single electrons with opposite spin, the coil direction of the neighboring surfaces will match and so will interfere, with one shell probably turning inside out as it aligns with the other, then repelling to occupy separate shells (second rule). When unoccupied sub-shells exist, electrons paired by opposite coil direction and spin in a sub-shell would be expected to separate, with one turning inside out to match the coil direction and spin of its temporary partner, then to separate to occupy the available sub-shell (third rule). With shells more than half full, pairs of electrons with opposite coiling direction and hence opposite spins will interfere less with each other and with neighbors, so the electrons will form pairs when the electro-static forces from the nucleus are low (third rule).

Coulomb potential (static electric fields) are seen in the mnp Model as p entities traveling toward negative charges or away from positive charges, n entities away from negative charges and toward positive charges, and the m entities that form magnetic fields tending to be polarized toward or away from the static charge by Axis Alignment with the n's and p's and tending to travel more perpendicular to radial lines to the charge. This radial travel of the m entities is parallel to the coils of an electron in an s shell, so are available for easy recruitment by the electron's coils.

Photons and the Energy in Shells

The stranded loop that forms the charge structure of an electron will attract additional m entities by Travel Alignment to move parallel to the strand when the curvature of the strand is not too small (when the coils are large enough). That additional mass is traveling along with the coiled charge material in electron shells is traveling by the Travel Direction effect only. It is NOT polarized, since it is constantly changing direction and cannot align by the Axis Alignment effect with the charge material. Or maybe the m entities are polarized form the point of view of the charge material strand, but the net effect of each coil of m's worth is zero so it does not affect moments or angular momentums. In any case, the recruited m's cannot “cause” or create any angular effects themselves since they are caused to turn in the coils only by the longitudinal strength of the charge material loops. That additional mass IS the excitation energy of the shell, which help with the Coulomb forces to keep the the electron coil loops expanded in the shell. The additional mass will be given up as a polarized unit, a photon, if the electron reverts to being a free electron Obviously, since the excitation energy of the electron shell is so much less than the mass of the strand, the m entities that make up the additional energy are not as closely packed longitudinally as the strand itself. The m entities are emitted as a single photon, so the recruited m filaments must form sparse filaments and be close enough to each other to interact by Travel Alignment and Axis Alignment. Gray text is deprecated as of 2013-06-09 in favor of picturing the coils not flat to the “shell” but approximately perpendicular to the expectation surface. See Could Twists Themselves Lead to Spin and Angular Orbital Momentum here and the 2013-06-11 blog post The Twist Variation in the mnp Model for more discussion.

The mnp Model is not quite ready to describe what happens when a fhoton comes into an electron shell. The fhoton may be captured by the shell or not based on quantums of energy. Presumably, in the mnp Model, the fhoton would spend a tiny bit of time to establish whether it “fits” and the electron shell will accept it. If not, since experiment shows that light not absorbed by an electron shell usually passes on through, the fhoton's induced fields lead it back to the original path if it fails to be captured. The answer is also related to the one-photon experiments of modern electro-magnetism, which the mnp Model can not quite explain unless the energy, called in the Model the fhoton, is easily guided by its self induced mechanical and electric fields.

In addition to being "clouds," electron shells and all other entities in the mnp Model are capable of passing through each other. Nothing is a hard shell or impervious, so for example tunneling is feasible, especially if there is an attraction on the loop on the other side once it gets through. A portion of a strand-loop can receive influence in part of itself, and the influence will take time for that influence to average out over the loop.

The energy retained by an electron shell will become important in the next two sections, on Quantum Numbers and Why the Pauli Exclusion Principle works.

Quantum Numbers

Spin offers two choices, based on coil directions either clockwise or counter-clockwise as viewed from outside the closed 3-d shape, which leads to negative or positive spin. The coil orientation is uniform around the shell so there is no “choice” involved when spin is measured, though fields and measurements can cause an electron to turn inside out and so reverse spin.

The following discussion concerns shell shapes. Since two coil directions are possible, all the numbers need to be doubled to determine the number of electrons allowed in that shell or sub-shell. Remember that the mnp Model sees the free electron as tiny, essentially spherical, formed by a coiling strand of six quantized loops.

Spherical, S (Sharp) Shells

For spherical shells, there are no counter-rotating coil pairs, so there can be no sub-shells other than the “sphere” with of course electrons coiling/spinning in opposite directions. There is no choice for the electron to make under measurement, it has an orbital angular momentum of 0.

P (Primary) Shells

For P shells the shell projected angular momentum makes sense if the counter rotation of the differing coils is parallel to z or perpendicular (and on one side or the other). The measurement forces the coils to “choose” an orientation in the potential/field. The possibilities are: coil axis parallel to the measuring z axis or anti-parallel (for -1 or +1 angular momentum projected around the z axis, don't ask me which is which), or perpendicular (0 angular momentum projected onto the z axis)

For a d shell, the momentum can be 2 pairs atop z axis for -2 or +2 angular momentum, on the other side for +2 or -2, both on the side for 0, or one on the side and one on top or bottom for -1 or +1.

Quanta - Why the Pauli Exclusion Principle Works

One of the axioms of Elementary Particle Theory is the Pauli Exclusion Principle, that no two leptons can occupy the same quantum numbers at the reasonably same location. The author's education has not progressed far enough into Quantum Field Theory to know if this exclusion is derived from a more basic set of principles, but the conceit of the mnp Model is to attempt to answer “Why?” from the three basic entities and three basic effects of the mnp Model.

Why do electrons behave quantized, and not occupy shells with the same quantum numbers? The answer comes in two parts. The first half of the answer is “what happens when two electrons with the same spin/coil direction interfere with each other.” When an electron in a shell shares that shell with an electron of the opposite coil direction hence opposite spin, the coils are moving in opposite directions. The shells of course do not exactly overlap and are not stationary, but the two electrons have their own recruited m entities that make up the shell energy, each set traveling with the coils of one electron. Since the directions of travel for each electron are essentially opposite, the interference is very small. Neither electron will be recruiting m's from the other electron, so neither will collapse to a free state or a lower shell because the supporting m's have been removed.

When electrons in shells get too parallel, as when two electrons try to share 1s and have the same coil direction and spin, the energy (m basic entities) guided/recruited/trapped by the coils of one is attracted to the coils of the other. And perhaps vice versa. The electron that attracts more might jump to a higher shell, the electron that loses energy will jump to a lower shell or become a free electron. Depending on whether more energy basic entities are available in the surrounding region or not, the result may be an excited electron and an electron in the original shell or an excited electron and an electron in a lower shell or an excited electron perhaps reverting to the original shell and a free electron. Note: where energy appears, the author is reluctant to use a confusing term, even energy potential or field potential, to refer to the free basic entities that exist wherever “space” exists and which are recruited for form gravitational, electrical, magnetic, and electro-magnetic fields that (mostly) superimpose except when a type of field becomes strong enough to dominate.

The photon comes out as a single photon since the m entities leave the coils almost organized. This experimental observation, that multiple smaller photons do not result from shell contraction, suggests that the strand makes the change starting at one location on the coils. So when the surfaces of two electrons are too parallel and the coil directions of both go the same direction, exclusion occurs.

So if the electrons have matching spin and are orthogonal enough (the Ψ function has spherical harmonics that are orthogonal in three dimensions at every given time), they will not interfere with each other.

Spin + and - states are possible for otherwise matching electrons because the coil direction is opposite, so that the coils are moving independently, mostly opposite in direction, and do not interfere much with each other.

So orthogonal Ψ's is a sufficient condition for electrons to not interfere. Is it necessary? Apparently, in the experimentally encountered shells, they are. Why? For s shells, it is clear (to me) that no two electrons with the same coil direction occupy the same sphere, that they will encounter each other over a large area of coils. For more complicated sub-shells, the author can only sketch investigations into how much surface area and how much volume is involved in the expectation values for the shells. If a shell has enough volume and enough cross sectional area at any given radius for the l(l+1)/2 shapes to not interfere but pretty much fills the surface of some logical concentric sphere with radius between 0 and the Bohr radius for that shell, then that many shells at that quantum number can co-exist. The known elements seem to follow the l(l+1) rule.

When a shell of a certain shape cannot fit with the m other shells of that shape, then overlap will lead to one interfering or stealing the energy holding the other out in the shell and one will revert to a free electron. The shells will try to NOT interfere if there is enough volume. Other electrons in a sub-shell do not insist that our electron of interest take a stand in the quantum mechanics measurement sense, only that the shell is orthogonal ENOUGH to not interfere

Absent geometric investigation, the author is reluctant to extrapolate beyond shells that have been measured or created and insist that electrons in g, h, or higher orbitals follow the Pauli Exclusion Principle that works so well for the known elements.

Spin Revisited

Spin is apparently the same magnitude for all leptons independent of the magnitude of charge. The best guess is that spin is a “physical” property based on the motion of the strand rather than an “electrical” property based on the charge material in the strand. In the mnp Model of quarks, the charge material is some number f of filament loops of one type and 6-f filament loops of the other type, for a charge of +-1/3 or +-2/3 or a neutral that is either rare, primordial, or one form of neutrino. The filaments are stranded, all moving the same direction. Modern physics considers the spins to be 1/2, even though work to measure spin in quarks proceeds.

Spin is apparently the same magnitude for all leptons independent of mass. The best guess is that the rotating fields caused by the intrinsic spin are not affected by the fellow traveling mass of m entities (glue, shell excitation energy, ...) because those entities are being recruited and guided by the charge structure strand anyway. In return, only influence from a measuring field that reaches the charge structure strand will change the course of the lepton during a measurement. (Effective Mass of quarks may confound this.)

The best mnp explanation of Spin currently starts with primordial coils, curved as tight as possible, as if on a cylinder or as coils extruded steadily. In order to even FORM a spheroid, those coils must relax a little. If the filament length is an exact multiple of a minimum coil length, the coils of the loop would need to relax by one coil, also to make an odd number of twists and an even number of coils so that the loops will be continuous and “real.” That one coil worth of relaxation, spread over all the coils, is all that would be available for influence or measurement by a Stern-Gerlach experiment, so spin of -1/2 or +1/2 and projected spin could be +-1/2 ħ. That one coil relaxation allows the strand to cause rotating fields in space and respond to non-homogenous magnetic fields.

In the mnp Model, those fields probably meet Bohm's description of rotating spin fields, but are caused by extra m entities that attempt to line up with the rotating coils by Axis Alignment, the basis of electro-magnetic effects, but by Travel Alignment to be more parallel to the electron surface, each entity moving in a line but the aggregate effect somewhat as whirlwinds. In the unlikely development that the m entities are slightly polarized by Axis Alignment, then quarks might have spin slightly different than 1/2 and the universe might have slight preferences for negative or positive in some cases. The author considers this unlikely. Any fellow traveling entities would tend to open the coils a little more, just as the shell energy opens up the coils of an electron in a shell, but not as effectively or to as large a diameter.

Magnetic Moment

Spin comes from coiling of the electron on the entirety of the surface, so magnetic momentz about the center of the particle will be due to spin projected by the upper half of the electron and the reverse spin projected by the lower half of the electron, though experiments such as the Stein-Gerlach are measuring anomalous spin and seeing just the “top” half. Magnetic moment due to orbital angular momentum will have a factor of 1, since that momentum is from one or more singular locations on the shell rather than the entire shell. (Speculation)

Why 720 Degree Rotations Are Needed to Return to the Same Condition - A Digression

Follow a point around the coiled loops, twisting to the other side of the strand/coil at every completed coil except for the first. Remember that the basic loop figure, a once folded figure eight with two loops, has only one 180 degree twist. By the time the point has traversed the entire loop, it will be back where it started. But it will be on the other side of the strand since there were an odd number of twists in the strand. So the point must make another complete traversal of the loop to get back where it started, on the same side of the strand it started on. The author suggests this is the WHY of 720 degree revolutions described by the spinors for spin 1/2 particles.

Interpretations

The image of an electron presented here is compatible with but supplements the Ψ description of an electron in quantum mechanics. The Born interpretation that Ψ represents probability density is incomplete. The Copenhagen interpretation that the electron is not really anywhere until it is measured is incomplete. The agnostic position, that we cannot say, is also incomplete. In the mnp Model, the electron's coils exist in three-space and are conserved through time, though LEP experiments or encounters with a proton may rearrange the filaments making up the coils. The electron's coils influence and are influenced over space very close to those coils but not by anything at a distance exceeding approximately a coil diameter.

So going back to the beginning of Griffiths Quantum Mechanics p2-5, if one measures a particle at C, “Where was the particle just before … the measurement.” The realist position, it was at C, is approximately right but wrong since the entities in the coil are moving at c and the coils could be changing location in space at some speed less than c. If an experimenter had been able to measure just before, that measurement might have located “the particle” at a distance exceeding c/delta time, but that would be an expected artifact of the measurements which may “catch” the electron anywhere within its mass distribution. Certain interactions, for example of the strong force or the strong force and the weak force, might see implied “spooky interaction at a distance” if part of a quark is interacting at one location and another part is interacting at another and measurements of the after effects of those interactions are taken close to simultaneously.

The orthodox position, the particle had no location, it wasn't really anywhere, fits with the mnp Model in a philosophical sense. The mnp Model suggests the particle WAS really spread over a diffuse “where” related to the Ψ function and enough of it was close to C before the measurement that the measurement placed it at C. The Quantum Hall Effect and Fractional Hall Effect results seem to be more in keeping with a “real but spread” interpretation similar to mnp's.

The agnostic position, “disproved” by Bell in 1964, that one has no way of saying where the particle was before measurement, is also partially true. Again, in the mnp Model we can say that part of the electron was at C but that its mass was spread and that, had we been able to do another measurement just before, we might have caught the electron at some other point in its distribution of mass.

In an atom, Ψ and the expectation value of the shell gives an approximation of the distribution of the electron. A moving free electron may be spread over something like its deBroglie wavelength. An electron moving near c may be spread over something like its Compton wavelength (but that repeats the previous sentence).

We might call the mnp interpretation of the Ψ function the “surface interpretation” or the “coil-surface interpretation” or the “mass spread interpretation” if the “mnp interpretation” or the “hyper-realist interpretation” are considered too narrow and non-descriptive.

Using Ψ to predict or guess how the mass of the electron is spread may be possible, but it does not provide enough information to know that spread. Some guidelines might include
  • The coils will be continuous
  • There are no points on a particle; from any given plane if there is not part of the particle or coils on one side, the first encounter as the plane sweeps toward the particle will be with a coil or a flatter section of strand, never with a true or sharp point. (-: To be blunt.:-)
  • The probability distribution function will have no true zeroes and no true discontinuities.
  • We might expect more coils in a region where the probability density is higher.
  • We might expect fewer coils in a region where the probability density is going down quickly in two dimensions.
  • Coils will tend to have their axis parallel to the axis of lowest probability density change at any given point.
  • Coils might be absent from a region even though the expectation value is non zero in that area or even if the expectation value is greater than 1/nec0.

Extrapolations:

The deBroglie wavelength of an electron may represent the electron's spread in the presence of moderate fields. The deBroglie wavelength has a limit at low speeds - it cannot go to infinity for loops, which have mass and finite, though perhaps large, dimension.

At high speeds, the Compton wavelength of a particle, which is the wavelength of a photon equal to the rest mass of the particle, may represent the lower limit of electron spread along the direction of travel.

We should be modest about our expectations - knowing a day's temperature at a given time is not really possible from an accurate function of average hourly temperature over the year, even when supplemented by an accurate function of average yearly temperature variation.

The author suspects that the Ψ function and Dirac's four vector model may even be about the best we can do in modeling an electron. The author does have the temerity to suggest that the normalization functions of the Dirac formulation will change if the mnp concept of resting mass as diminished by movement compared to the classical understanding of rest mass is accepted.

Put another way, the author has as little hope of codifying the coil surface interpretation of Quantum Mechanics as he does of finding truth in econometric time series of stock movement, though at the end of the day the various indices have their values and their usefulness.

Speculations About Other Probability Distribution Functions

Other probability distribution functions may eventually be created. Could we determine the probability of encountering SOME of the particle in a region? When the wave packet represents parts, how do we calculate and interpret probabilities that a region will contain SOME of the particle - if the total volume is such that a it could not ALL be contained in the rest of the region, then the probability goes to 1 but we don't expect that except for large partitions. Probably something from statistical mechanics?? Still will not get very close to 1 anywhere.

We might try to ask
  • What is the probability density of entity directions in a particle? or
  • What is the probability density of the coil axes in a particle? or
  • What is the probability density of the changes in coil axes in a particle? or
  • Can we normalize to “the probability of finding one coil” or
  • Can we state “the expectation value for coils is _” or
  • Can we state “the expectation for finding basic entities of the particle in a given region is _”
Again, the Ψ function and Dirac four vector Model seem to be proving very useful, thank you very much.

Electrons, Modern Experiments, and Modern Theory

Since we don't usually measure parts of an electron except in the Fractional Hall Quantum Effect experiments, the distinction between expectation values for measuring the electron and expectation values for “how much of the electron is here” are currently of only theoretical interest. Semi-conductor, Cooper Pair, and tunneling experiments and developments will not be affected. The electron is seen as a strong stranded loop in the mnp Model, so it will remain a single entity that cannot be broken with chemical processes. It can in fact participate in a cloud and slip through crevasses and be part of Cooper pairs or Bose-Einstein spin 1 composites, but the loop will always be available to a “measurement” as an electron unless changed by the Weak force.

Electron Shells and Crossing the Nucleus

Conventional Ψ functions in polar coordinates for electrons in P shells and above show 0 values for Ψ at the origin and in planes running thought the origin. That obviously is incompatible with an electron seen as a continuous six-strand loop. Comments of the form “the electron can't visit the nucleus” for higher level shells are frequently heard and seen. The author makes the following suggestions:

The coiled loop crosses over somewhere between the lobes, so the Ψ does not really go to zero at a spatial boundary but at a moving, cannot be located exactly, theoretical boundary. Quantum mechanics is not very concerned about phase anyway, so why not just accept that there is a fuzzy imaginary boundary that is not present in real space. The formulae usually assume the nucleus is a point source to make the polar coordinate development easy. The nucleus certainly is not a point. The author also points out that, in the mnp Model, electro-static fields cannot even be created by points!

Ψ functions for paired particles might separate, but not those of single particles. The author suggests that electrons in P shells and above may cross the nucleus, but that S shell electrons are very unlikely to have entirely crossed the nucleus and be all on one side. Some fields and forces may lead to an S shell electron being briefly on one side of a nucleus, but the author would expect that to usually lead to the electron becoming free. If a matching S shell electron of matching spin is present, one of the two may turn inside out by going through the nucleus from two sides to have opposite spin.

Problems With the mnp Electron and Quark Model

The mnp Model of the electron and other elementary particles is not without difficulties. Spin is not entirely settled. The explanations for the cause of spin and for the equal spin of all leptons does not yet satisfy the author.

If mere relaxation of a single (unbalanced coil or twist) allows Spin to be measured, why does further relaxation of coil pairs for electron shells not add to spin. Is it the unbalanced twisting rather than the extra coil? Or is it the twist itself, unbalanced by any opposing twists, that leads to spin.

Quarks

Why does the spin of quarks seem to match that of electrons? Quarks are more massive, and their charges differ.

For the more massive leptons, one suggestion for the equivalence of the basic spin for all leptons is that it is a function ONLY of the charge structure material, that the additional glue filaments which are easily reoriented in axis perpendicular to travel do NOT enter into angular momentum. If quarks, with mixed charge structure material, have the same inherent spin as electrons and positrons with single charge material, then mixtures of Axis in the strand-coil structure do not affect spin and only Travel Alignment affects spin.

The author suggests this is not a completely satisfying explanation by itself. Quarks are hypothesized to have different coil radii. The loops are all the same length, there will be an even number of coils and an odd number of twists in all sizes, but guaranteeing that there is exactly one coil worth of relaxation in all coil sizes requires a little more information. The measurement/experiment may find only one coil worth of available angular momentum distributed over the spheroid as “spin.” Maybe the maximum error is less than 1 / nspheroid if almost one extra coil of angular momentum is spread over all. Again, not convincing.

Muons

Muon ("who ordered that") spin also presents puzzles in the mnp Model, which sees them as 6 loops of negative material plus 6 loops of negative and 6 loops of positive, providing the material to break up into two electrons and a positron if the loops recombine just right. This model of excitation makes the rare decay to 2e- e+ possible without having that decay product depend on having adequate "broken electrons and positrons" in the form of n loops and p loops from which leptons can be recruited. Variation in decay percentages would have been seen in different experiments in the presence of different byproducts if the muons are only six loops of negative charge material with extra energy or a loopy configuration.

Unfortunately, the 18 loop model of excitation would seems to lead to spin 3/2 if the charge material loops determine spin and orbital angular momentum. Having one strand of six twist in opposite directions seems a little far-fetched.

Could Twists Themselves Lead to Spin and Angular Orbital Momentum - 2013-06-02

Could the twists themselves be the contributor of spin and angular orbital momentum. or the unbalanced or reversed twists, rather than the coils? Possibly.

In P shells and above, could the reversed twists be separated so that multiple coils would be “reversed?” Maybe, but would probably need to have one lobe all one spin even if it is reversed from the other lobe. This does provide another means to turn an electron inside out, turning part inside out then turning the other part back by untwisting. This is perhaps a more efficient way to reverse electron spin than spreading entirely over another shell or inverting over the nucleus. It also supplies a mechanism for the formation of lobes - the turning point going in and coming out are twists in the opposite direction. Quite possible.

The excitation states argue, somehow, that the unbalanced twists in the strand lead to Spin and orbital angular momentum without reference to how much charge material is present. If a twist in one direction is always accompanied by coiling in one direction, the discussion of the quantization of orbital angular momentum remains intact.

An advantage of the twist model is that coil size, coil expansion, coil length details, and fellow travelers all have no effect. The three remaining questions are how a single twist leads to spin all over the lepton, how excited states with extra filament loops create the same spin and orbital angular momentum, and what the magnitude of h means for two 180 degree twists of the structural charge material strand. To be continued...

Deferred and Rejected Ideas

The development of the mnp Model of the electron has gone though many iterations and adjustments over the last three months. A few of those rejected developments are included here as examples of what seems not to work.

#0 - n^2 Straightening Per Shell?

Might 2s shells have 4 pairs uncoiled (4 times the area of the shell??) The energy held by the second shell is not so much greater than in the first. If three extra straightened coil pairs are available for p shells, how do they, the electron, and experimenters decide which is which for orbital angular momentum? And in shell 3, how would 8 different straightened coils keep track of which was d and which was p? Rejected.

#2 - Entire Strand Loop is the Spin Angular Momentum

What if the radius of coils is so small that the entire mass times c times radius IS the spin angular momentum? A quick calculation of mrv as angular momentum and getting 2.42e-11m or less than the initial Bohr radius, rules this out. Rejected.

#3 - Uncoiling Effort is the Momentum

If most of the effort of the coils is spent in coiling, it is only the UNcoiling a little to form a sphere rather than just be coils that leads to spin (and angular momentum). because only that available influence will affect and be affected by fields. Just as “availability” may lead to quarks also having exactly spin 1/2. This has been incorporated in Number One.

#4 - Difference in Total Coil Length for Single Filament Loops and for Stranded Six Filament Loops Exactly Equals One Loop for All Strand Combinations

The quantized loop is based on the length of single coiled loops in the early dense universe, and the coils formed by 6 strands are different. Muons and quarks have different coil diameter. So having an excess loop h/2 moving around on the sphere to be measured seems unlikely. Discussed with Spin Revisited earlier. Highly Unlikely.

#5 - Spin of Quarks

If Spin is an electro-magnetic property, it would differ for the quarks. This led to an early proposal that the net spin projection of a nucleon is ħ/2, but that up quarks have a spin of h/3 and down quarks h/6. In a neutron, one of the down quarks has spin opposite the others for a total of. Oops. Better make sure that's tested! Probably is! The durable neutron is seen in Weak and Strong Join as One Phenomenon in the mnp Model as being one up with spin opposite to the two down quarks.

Protons - down is the binding quark, so spin 2/3+2/3+1/3 for opposite spin but opposite charge. Yikes. A bad idea taken too far. Rejected.

#6 - Spin of Muons

Why do muons have spin 1/2 when they are, in the mnp Model, made up of 6 n loops plus an equal number of n and p loops (either 6n+3p+3n or the preferred 6n+6p+6n)?

Muons have spin 1/2 which suggests that they may merely be “excitations” of 6 strand coils rather than the 18 coils suggested heretofore. How that excitation shows in structure is not clear, though if the twist per coil is 1/2 in the normal state, then twists of 3/2 per coil at least follows a linear relationship that we might expect from spin increments. Though how the extra twists qualify as excitation rather than spin directly … Or if there is enough m-filaments to cause larger coils in a balanced manner (that it, the filaments cause the coils to be larger and the larger coils allow the filaments to stay with the coils … This may be a better model of excitation, since it may match/be similar to what happens with electron shells. If decay were just giving up the extra filaments, as with electrons, we would not expect great structural changes but just an electron and some energy. ? Definitely inconclusive.

#7 - Can Logic Help?

Faced with ugly choices, the author has found that listing the possibilities can aid understanding, idea creation, and decision. 2013-06-02: In this case, the idea that unbalanced twists of the strand itself leads to momentum emerged as a strong candidate.
  • Electrons have been tested and seem, at the scales we can measure, to be homogenous and point like. And light.
  • Muons have been tested and found to be as homogenous and point like as electrons. They can "orbit" a nucleus, albeit closer due to increased mass.
  • Neutrons have been tested and (presumably) show a spin of +-1/2.
  • Could the mnp electro-magnetic intrinsic spin model be wrong? (Completely)
  • Could the mnp quark model be wrong? Do p loops in quarks rotate counter to the n loops, so net charge effect is 6/6 of an elementary charge? No, then the effective charge would be -1. REJECTED.
  • Could the mnp muon model be wrong? Is 12 or 18 loops of charge material too much, with net 6 negative loops for 6/6 negative charge?
  • Do Muon's p loops rotate counter to the n loops, and that rotation have a physical effect of lowering the spin and angular momentum, while in quarks n and p loops rotate the same direction and physically contribute to spin? (No, in that image muons would have an effective charge of -2 or -3. The opposing images of loops sometimes traveling together (quarks) and sometimes traveling opposite (muons) seems ugly. The propagation of influence and adaptation to changes and fields does not work well with filaments traveling in opposite directions. Movement in a strand in both directions does not "move" as mnp sees movement, momentum, and the Lorentz transforms that are an integral part of movement in the mnp Model. REJECTED.
  • Is the mnp Model of Travel alignment effect stronger than Axis Alignment as assumed the last six months, wrong?
  • Is the quark assumption of projected spin ħ/2 wrong? Since the spin of quarks has probably not been tested thoroughly, and since experiment rules and logic and simplicity take second place in the development of the mnp Model, this is not quite answered. But the alternatives are ugly.

2013-06-02: The twist model seems more attractive with every addition to this list of conundrums.

#8 - Dirac Four Vector Description of the Electron

Dirac must have been onto something with his 4 vector approach to the electron, after the Pauli 2x2 matrices and Schroedinger's unitary Ψ function. Translating the useful or interesting details into understanding from the mnp point of view will take time (and education.) At least, as with quantum mechanics, the spheroid must be closed in all 3 spatial directions and consistent in time.

For the Future.

#9 - Speculation on Left-Handed Preference

Could coiling lead to left-handed preference? Could counter-clockwise spin, with the angular momentum inward, be lower energy and clockwise spin with angular momentum out? Given that handedness and the sign of angular momentum is a convention rather than an absolute, the idea that angular momentum of the coiling could be preferred or lower energy is seen as simplistic. Since neutrons have two down and one up, with the two down having one coil direction and Spin and the one up having the opposite coil direction and Spin, a slight preference could be maintained for the life of the neutron. The proton has two up, connected by a down, with the two up having one coil direction and Spin sign and the down the opposite coil direction and Spin sign. Not Ready for Prime Time.

Conclusion

Explanations for the emergence of Spin, Orbital Angular Momentum, and the Planck Constant in the mnp Model have been presented. The two preferred candidates have useful similarities and offer an explanation for the quantum behavior of Orbital Angular Momentum and electron shells. Spin clearly exists, and the coiled twisted nature of the electron in the mnp Model explains the 720 degree symmetry of rotation for 1/2 spin particles. The Number One proposal (momentum is from relaxed and reversed coils) has interesting hints and interesting challenges. The Number Two proposal, that Spin and Orbital Angular momentum both derive from unbalanced twists in the strand forming the charge structure of the particle, is not as well developed. Investigating Dirac's mathematical description of the electron is the most promising third direction. Translating (after understanding intuitively) the electron four vector concepts into mnp terms is the author's goal.

The author has been assured on numerous occasions that “No one is thinking like this.” Yet enough interesting results seem to be emerging to suggest a future in looking for 't Hooft's only possible disproof of Bell's Theorem: “substructure.”

- fini -

Appendix A - Musings

The Planck constant may be a constant in the limit at low energy states. At high n values, the author is prepared to accept experimental results showing the angular momentum change rising gradually. But since the number of coils is very high, we may never measure the difference. The ratio would be on the order of nec/nec0. Of course, if such a change were detected, it would provide a clue as to the magnitude of nec0

When the filament lengths are described as relatively fixed, this means that slight variations may occur in entity spacing, but due to the three effects involved, the spacing will quickly average out. This might be thought of as slight elastic deformation of the filaments. Whether that will complicate calculations or just fall out of the interactions of the basic entities is not clear. Likewise, a coil may not be EXACTLY a certain size; there will be little variations as it overlaps or leads into the “next” coil that precesses around the “surface” of the particle, and temporary variations as the coil responds to fields, influences, and anomalies. Since a given coil is not identifiable, we would speak more of variations in curvature and axis. In fact, the ability to vary is essential so that the electron can absorb influences.

Why Explanation?

Hints that quantum mechanics DOES have explanations are exciting and have potential. EmH comments that physicists mostly just accept relativity and quantum mechanics as is, rather than worrying about why.

EmH also notes that the author is making things complicated. But knowing why something occurs may almost always be more complicated than just knowing what occurs.

Math itself is not causative, but the need for closure (spherical harmonics) IS causative. Geometry alone is not causative in the mnp Model, but geometry plus the nature and effects of the basic entities is (we hope).

Rules and Math

“Exclusion” and equal distribution across degrees of freedom are useful principles in quantum mechanics, thermodynamics, and statistical mechanics but the author prefers to look at each claim on a case by case basis

Why in quantum mechanics each distinguishable configuration would be equally probable is a mystery to me. Statistical mechanics' suggestion that energy is distributed equally across all degrees of freedom feels analogous but probably easier to understand. Of course the multiple universe theorists would see that as analogous directly - the possibilities of existence is evenly spread over the degrees of freedom for that enumerated existence

That said, the Legendre polynomials make sense, and with the potential depending only on radius, the separation of variables in spherical coordinates is magical. Likewise the general separation of independent variables or functions, as when two independent portions of a sum or difference equal a constant, both must BE constant

Quantizing of filament loops may well have happened early with great density and SINGLE loops forming a coiled cylinders, then tight balls. Proto electrons and positrons, 1/6 the modern size, may have been created at times of great density.

Philosophy

Variation is necessary so that electrons find their “stable” configurations for any given conditions/energy level/potentials. Conceptually similar to evolution - variation to find temporary stability. Playing dice is essential to the stability of the universe and its constituents

For the brain steeped in real world experience, it is difficult to imagine that uncoiling just two coils allows the electron to expand 10^6 times, while coiling just two coils the opposite way out of millions of coils leads to measurable momentum and an ability to fold into two lobes. This counter-intuitive small change leads to big effect is conceptually similar to movement in the mnp Model, where the stationary particle gives up some of its coil rotation to move perpendicular to the coil (which slows down internally) to speed up externally. (-: There's potential in this idea. Note the symmetrical -: and :- for parenthetical remarks attempting to be humorous. :-)

Complex numbers allow neatly for a coil's “go away from this location and come back” even though in the mnp Model that “going away” is within orthogonal three space and time. So the complex Ψ functions that must be squared and integrated to create real probabilities may be fairly direct cognates of coil behavior.

Complications Waiting to Happen

The mnp Model does seem to "make things complicated" as quoted below. The Planck constant has been investigated here in the context of electron shells. Another investigation will be needed for the mnp Model to explain the inverse relation between photon energy and wavelength using the three basic entities and three basic effects in the mnp Model. Hint: Light is seen as both particle (spelled fhoton in the mnp Model to avoid confusion with the two modern photons) and electro-magnetic wave, and the energy (m entities) in the fhoton is dense but has volume based on the Separation Effect, with the transverse diameter going up with energy, so the transverse area goes up as the square of the energy and the length parallel to travel goes down as the inverse of the energy.

Appendix B - Fun


Sayings

Oh, to know enough physics to be able to understand it all.
Oh, to not know so much physics that I know this endeavor to explain is impossible.

Humor

If one makes enough predictions and couches them as possibilities, one need never be wrong. - EmH

What's the matter? Indeed! I've been wrestling with that for years.

“It is difficult to play against Einstein’s theory” --on his first loss to Fischer - Mikhail Tal

It was Aron Nimzovich who said, of chess, “Why must I lose to this idiot?” Reportedly to Saemisch. Or maybe not, since Saemisch was a respected player. The story I had heard years ago had Alekhine tipping over a chessboard with the same comment.

Perl's of wisdom - This seems to be a write only blog.

Poincare thought his New Mechanics should not be introduced to undergraduates. I also feel the mnp Model is not ready for undergraduates either. Thinking alike does not make me a great mind.

deBroglie travel and wavelength may be more fundamental than any frequency of light (that is, the gravity of the situation may be more important than the charge or the spark)

This new spin on “angular momentum” for electron shells and electrons may be a turning point.

What's the sound of a physics/quantum theory entering the infinite bit bucket? Planck.

Appendix C - Superseded Ideas

2013-04-28: The l(l+1) formula for sub-shells was attractive as a spherical symmetry. Numbers 2, 6, 12, 20 are all close to regular polyhedra, but then the numbers become 30 42 56 72 …

2013/02/10: Electrons could have a lightweight charge structure, with more mass as m-filaments. Electrons themselves may have a charge structure that makes up much less of the mass even of the electron so that there are many m-filaments even in an electron" The author had been resisting this idea, since larger quarks seem to attract more glue, and the electron, positron, and small quarks are relatively lightweight. Also, the coils in free electrons and positrons are quite tight and would seem not to support m's as fellow travelers.

2013/02/13: Think about how long it takes to even out changes or influence in an electron shell consisting of coils traveling at the speed of light but overlapping significantly. To be continued.

2013/02/13: Attempts to determine, in the structural mnp Model that hopes to explain “everything”, why the units of h are kgm^2/s. Could this be momentum integrated over length. Or force integrated over time?

2013/02/09: Surely the 2pi denominator for h to ħ is NOT actually a 6 (for 6 strands). Since we are taking spherical projections in some cases and working with coils of basic entities traveling at c in most others, 2pi makes sense.

Appendix D - Author's Notes

More diagrams would aid understanding. The author is currently handicapped by a lack of didactic opportunities, which could help identify what needs better or different explanation.

2013-04-26: A turning point: Instead of approaching coils in the electron by logically building from the ring up, modeling could start with a loop and investigate twisting it and seeing how much coverage or what radius it would achieve. That led to questions about even numbers of twists vs. odd numbers (1 twist for 2 coils, 3 for 4 coils). Asking if that additional coil could be related to ħ proved useful as well.

The new Could Twists Themselves Lead to Spin and Angular Orbital Momentum - 2013-06-02 may lead to a quick update of this post.

Edited 2013-06-11: Very minor changes. Shell quantization arguments noted as deprecated.
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