Tuesday, June 11, 2013

Mechanism for Spin and Orbital Angular Momentum
Revisited Using the Twist Variation in the mnp Model

Introduction

This document builds on the 2013-06-02 post on Spin, Angular Momentum, Shells, and Orbitals and does not repeat the background information contained there and in previous posts and the main mnp document (currently somewhat outdated 2012-12-). Certain suggestions in the June 2nd blog are called into question. Qualitative suggestions, including additional reasons to picture particle structure as coils perpendicular to the surface rather than flat on the expectation surface, are presented. Many different ways of trying to understand h and angular momentum in the mnp Model all seem to lead to the conclusion that the basic entities may have a relatively large radius of influence and certainly a relatively large radius of "effective mass."

Table of Contents

Twist Variation of Angular Momentum

The twist variant of spin and orbital angular momentum behaves "properly" for leptons of differing mass and charge and differing coil diameters in the mnp Model of elementary particles. The mnp Model sees, for example, electrons as six quantized loops of "negative charge material" made up of aligned basic n-entities as closely packed longitudinally as the equilibrium between Travel Alignment plus Axis Alignment against Separation "allows." What does angular momentum mean when a six-filament strand twists? The strand may twist many different ways, but to form a closed figure (think of a spheroid) the strand must make an odd number of twists. That odd twist is (for the twist variation to behave "properly") the source of Spin for the particle.

Take a transverse section of the strand, with radius r:
  o   o
     /r
o   +   o

  o   o
The radius r and distance to adjacent filaments r represents the equilibrium distance between filaments based on the Separation effect. The angular momentum is actually in the movement (precession?) of the filaments in the strand around the center of the strand. The entire very long strand, compared to its radius, is rotating and that angular momentum of the rolling cylinder leads (to be explained later and calculated even later) to Spin. Any direction of view from outside the electron will see this rotation projected around the axis or view.

Orbital Angular Momentum

If the spherical shape is twisted 180 degrees, two 180 degree twists are applied to the strand to achieve the resulting multi (in the first case, two) lobed shapes. The 180 degree twists are in opposite directions from the flexible point of view of the center of the strand, but in the same direction when viewed from outside the electron. So from outside we see angular momentum if looking along the axis of the twist, either clockwise or counterclockwise, and no orbital angular momentum if looking across the twist. Projected on a z axis, that should be 0 or +h/2π or -h/2π.

Shell Sizes

The author has had difficulty relinquishing the image of the coils having axis mostly perpendicular to a surface of expectation. The previous blog Spin, Angular Momentum, Shells, and Orbitals in the mnp Model contains explanations of coils unraveled with Coulomb potential and m basic m entities supplying the means to open up the coils. That blog was missing an essential point. The ONLY way for coils flat to the surface to open up is to have fewer coils, since the length of the quantized filament loops is essentially fixed, as is the length of the strand loop.

Coils Perhaps Perpendicular to the Expectation Surface of the Shell?

If the coils of the electron charge structure have an axis parallel to the "surface" of the shell, shell quantization might be explained. Losing a coil might allow the other coils to spread more along the coil axis to a limit, since the longitudinal stiffness of the strand might allow a certain amount of expansion. The argument for relaxation of coils as the six filaments are slightly less tightly coiled in the previous blog Spin, Angular Momentum, Shells, and Orbitals in the mnp Model is useful here, but does not apply in the plane of the coil due to the quantum length of the strand and loops.

Coils perpendicular would not need to twist in alternate directions to lie "flat" on an approximate surface of equal Coulomb potential in the case of S-shells. The energy in the shells would be contained by Axis Alignment (the basis of charge and magnetic effects) rather than Travel Alignment and would not need to stay with the coils themselves but would be bending at much higher radii to merely stay within the shell, tending to follow the axis of the "spring" of the coils. The basic entities that constitute this energy will be approximately aligned in Axis and hence more or less polarized.

Electro-static fields become simpler. Coils perpendicular to the surface will actually send individual entities of the same type more perpendicular to the surface and individual entities of the opposite type more parallel to the surface, independent of which way the coils are rotating.

Additional Support for Coils Perpendicular to the Surface (2013-06-09)

  • Coils need a half twist to flow smoothly due to the longitudinal stiffness of the six filaments, and those twists need to be basically the same direction.
  • By twisting six existing loops, the Model provides a mechanism for quantum loops of charge material to combine, separate, and re-combine.
  • The weak interaction, seen in the mnp Model as the complete exchange or separation of charge material loops between particles, takes time to unravel the entire strand. The length of the loops will be approximately one or two times c * interaction time. The factor of two is present because an untwisting may also untwist the "back" or "other side" of the loops.
  • The strong interaction, seen in the mnp Model as the interrupted and incomplete exchange of charge material loops between quarks, has time for the transfer of filament loops to be interrupted, with no early completion as a weak force interaction since the strands are completely twisted.
  • Since a large number of coils are expected to be present, the difference in Spin Angular Momentum at shell numbers less than thousands is not expected to be apparent for numerical models that rely on all coils to provide angular momentum. (2013-06-10 2110 considered unlikely to be needed)
  • The basic entities in the mnp Model can pass through each other, and strands and loops can pass through each other, but parallel and almost parallel stranded filament loops have a great deal of resistance to passing through, since so many basic entities are involved in aligned filaments.

Much in the mnp Model of static charge fields, moving charge fields, and magnetic fields will need to be revisited, as will response to Coulomb fields. So the author includes coils perpendicular to the "surface" as a definite possibility. To be continued.

Checking the Numbers

Looking at (and for) numbers can be a useful sanity check for a theory. Even determining if a range on numbers could make sense is better than discovering the numbers could never make sense. Discovering that the numbers could never make sense is still better than running with an impossible theory.

So the author will try (again) to examine angular momentum in a mostly classical fashion. Spoiler alert (2013-06-10 1500): if the twist variation does not work, the angular momentum is not a direct effect, but as in the previous blog is a "peeling back" from the normal tight configuration of the strand. As such, no direct justification for h is possible yet .

As a starting point, if total angular momentum h were to be provided by a particle with mass 9.11e-31kg acting as a point or a ring moving at c, the radius of the circle would be:

momentum h = m r c -so-
r = h / mc = 2.424e-12m

This should give some clue that unless the angular momentum effect comes from somewhere else or some non-intuitive configuration, movement of mass alone cannot account for Spin. (2013-06-09) A number of explorations of configuration follow.

Notation:
me = mass of electron
ll = length of the quantized loops
r1 = radius of strand = closest the basic entities want to be in a transverse direction

If the strand, traveling longitudinally at c, makes 1/2 twists per quantized loop,

c/ll = number of half rotations per second
c/2ll = number of rotations per second

Spin Angular Momentum - I (2013-06-04)

The first approach to angular momentum looks at angular momentum of the mass of the electron rotating in the strand (m(r x v)) as centered on the center of the six filaments in the strand. Transverse velocity of the filaments in the strand is

2π r1 c/2ll -or- π r1 c/ll

Transverse angular momenum due to a twist is

mec π r12/ll

Experiment shows that projected angular momentum Sz is ħ/2. The author may have a constant factor wrong, but suggests that the angular momentum in the twist, spread over the entire surface of the electron, is h. The Stern Gerlach experiments measure anomalous angular momentum (from outside the particle) so sees basically the spin of the top half of the particle. Viewed from inside the particle, the effect of spin is twice as much. At least that is the author's current interpretation of one of the differences between introductory quantum mechanics' model of the electron and Dirac's four vector description of the electron.

The details of the first set of calculations for Spin Angular Momentum have been relegated to the Appendix. Twist momentum is proportional to the square of radius r1 and inversely to the length of the loop ll, so twist momentum goes down linearly as the radius goes down since loop length is proportional to radius.

Stop the Presses - Spin Angular Momentum - II (2013-06-09 0530)

But the entities are not necessarily seen in the mnp Model as acting at their center. The r1 distance represents the Separation distance, not the radius of the effect of entity interaction. Since the basic entities are seen as having effects on each other ONLY to some radius reffect, other models of "mass" distribution are possible. The author finds thinking of the entities as a "shell" useful if imprecise. The Separation distance could represent something like the thickness of the "shell." The "mass" would be distributed around the 4πreffect surface. Since mass arises from the existence of the basic entities, their three interactions, and their ability to change the direction and axis of other entities and have their direction changed by other entities, the author prefers to use "mass" in quotes. Inventing another term such as "presence" is the alternative.

The angular momentum of a spherical shell of negligible thickness is

2/3 mass r2(revolutions per second) or
2/3 m1rinfluence2c/2ll

The radius of Separation r1 is much smaller than the radius of influence rinfluence so assuming a center for the entire stand is the center for all 6 loops and assuming all 6 loops rotate around the center of the strand with radius rinfluence will lead to negligible differences in calculations of angular momentum (certainly less than our assumption of spherical shells for each entity!) When all the entities in a strand from the flexible reference frame of the center of the strand are included:

2/3 merinfluence2c/2ll = h so
me = 3 h 2ll/ 2crinfluence2 or
me = 3 h ll/ crinfluence2
ll = mecrinfluence2/3 h

Calculating ll for a range of rinfluence values:
 ll rotations/s imputed speed
rinfluence   
1E-06 1.375E-01 1.091E+09 6.855E+03
1E-07 1.375E-03 1.091E+11 6.855E+04
1E-08 1.375E-05 1.091E+13 6.855E+05
1E-09 1.375E-07 1.091E+15 6.855E+06
1E-10 1.375E-09 1.091E+17 6.855E+07
1E-11 1.375E-11 1.091E+19 6.855E+08
1E-12 1.375E-13 1.091E+21 6.855E+09
1E-13 1.375E-15 1.091E+23 6.855E+10
1E-14 1.375E-17 1.091E+25 6.855E+11
1E-15 1.375E-19 1.091E+27 6.855E+12
1E-16 1.375E-21 1.091E+29 6.855E+13
1E-17 1.375E-23 1.091E+31 6.855E+14
1E-18 1.375E-25 1.091E+33 6.855E+15
1E-19 1.375E-27 1.091E+35 6.855E+16
1E-20 1.375E-29 1.091E+37 6.855E+17
1E-21 1.375E-31 1.091E+39 6.855E+18
1E-22 1.375E-33 1.091E+41 6.855E+19

The rotations per second and imputed speed columns are added for reference. Internally, the entities may behave very differently than the external behavior. They may not be physically rotating within themselves or they may not be limited to c within themselves so that apparent rotation of the basic entities may have outer surfaces appearing to move faster than light.

If the apparent size of quarks were 10-10m, then this table might seem reasonable. Having a lot happening inside an apparent fuzzy sphere surface might be plausible for quarks, perhaps even for neutrons and protons, but not for electrons which the experimentalists still consider points. Certainly if 10-18m is considered the upper limit for quark and electron size and 10-17m the range of the weak force, the 10-10m number is not feasible. The range of the weak force is considered the range of filament contact for quarks, which exchange is completed in weak interactions. The size of protons and neutrons 10-15m to 10-12m is the range of filament movement in the strong force, which is seen in the mnp Model as attempted filament exchange constantly prevented from completing.

Angular Momentum - III (2013-06-09)

The "twist" variant of Spin Angular Momentum still behaves "properly" for different charges in quarks and electrons and positrons. The magnitude appears much too low, though the mechanism of measurement and torque transfer has not been explained. That mechanism needs to rely on Travel Alignment and not Axis Alignment, since the same value for Spin is measured independent of the charge of the particle. So an additional mechanism, in the mnp Model search for why, needs to be found for the magnitudes of h and hence the Spin of the electron.

Repeated coiled loops might be a way to "generate" more apparent momentum. With rinfluence around 10-20m the generation of influence needs to be about 1024 greater. If an effective radius can be 1012 greater, that works. If the effect is linear, as if number of coils would increase the measured angular momentum as a linear factor, 1024 coils might be required.

Angular Momentum - IV (2013-06-09 1900)

The perpendicular coil model may offer a number of numerical and theoretical advantages, in addition to the qualitative advantages listed earlier.
  • Twist will exist everywhere.
  • The magnitude of influence radius, coil radius, and angular momentum promises to be better. Investigated below.
  • Since a large number of coils are expected to be present, the difference in Spin Angular Momentum at shell numbers less than thousands is not expected to be apparent.

So how do the numbers work? Coil radius is expected to be somewhat but not hugely greater than the radius of influence rinfluence. The author suggests

1.5 rinfluence < rcoil < 10 rinfluence
ntwists is the number of half twists (odd)
ntwists = ll/2πrcoil
Try ansatz 2: rcoil = 2 rinfluence
angular momentum = ?1/2? ntwists 2/3 merinfluence2c/2ll
h = (1/2 l=>l / 2πrcoil) 2/3 merinfluence2c/2ll or
h = 1/6 merinfluence2c/(2πrcoil try
h = 1/6 merinfluence2c / (4πrinfluenceinfluence) or
h = 1/6 merinfluencec/(4π)

So if the coiling radius is twice the influence radius,

rinfluence = 24πh/mec

The radius of influence would be, uh, 1.828e-10m. Again, the direct approach is not feasible.

Angular Momentum V (2013-06-10 1600)

Return, finally, to the indirect or difference picture of angular momentum used in the previous blog Spin, Angular Momentum, Shells, and Orbitals in the mnp Model. Try to see the angular momentum as a difference from the "normal" tight coils for the electron. If the entire loop length is suggested by weak interaction decay which takes 1-8 seconds, the loop length will be 3m to 6m. If the loop has, for convenience, a diameter of 1m and a circumference of πm, the angular momentum of an electron mass traveling at c in a radius of .5m would be 1.366e-22. To reduce the angular momentum by h would be subtracting 4.849e-12 from the diameter. This suggests that the strand has in the neighborhood of 2e11 coils, give or take a factor of 4. The coil radius would be about 2.4e-12m, which again is bigger than expected from experimental results. Probably again related to the magnitudes of h, c, and the mass of the electron. This is a coil momentum variation, not a twist variant.

Angular Momentum Needs Extended Radius - Speculation VI (2013-06-10 1950)

The author's recent attempts to understand h all seem to point to needing a radius larger than the elementary particles. This could be shortsightedness. Yet:

Could the radius of influence and the radius of effective mass be MUCH bigger than the radius of coiling or the apparent radius of a free electron? The effects between entities would be minimal until the basic entities are almost coincident. This might allow coiling in small dimensions but "mass" to appear distant so that angular momentum are relatively large and dimensions are small. The twist variations may call for a radius of effective mass somewhat greater than the coil variations, but the difference is relatively minor compared to the leap from coil radius to influence radius.

In a twist variant with large influence radius, momentum of a single twist or half twist goes up as the square of the influence radius but down linearly as the number of coils goes up. To be continued.

Orbital Angular Momentum - Revisited

The theoretical Sx2+Sy2 angular momentum from quantum mechanics might actually be zero, since looking all around the shell as if it were in a cylindrical sensing system, would see as much twisting in the strand going clockwise as counter.

In the perpendicular coil model, the magnitude of the orbital angular momentum may not be important, just the presence of twists in the opposite direction. The difference in projected angular momentum may appear to be reversing the spin of half the shell, though the effort to reverse that spin in two coils is miniscule. Currently, the magnitudes of momentum do seem to the author like a rabbit pulled out of a hat. The quantization related to twists is clear, so further development is warranted.

Conclusion

The twist variant of Spin and Orbital Angular Momentum is attractive in that it "explains" and tracks experimental and some theoretical quantum behavior. All methods of trying to "understand" angular momentum lead to similar "coils too big" results.

The V (fifth) approach attempts to compare h, the angular momentum of removing one coil, from a "tightly coiled natural loop" ignoring closure requirements by estimating loop size based on the time required for weak interaction decays and comparing the angular momentum of the mass of an electron traveling at c in that loop. Hand-waving to be sure; the 2e11 count for coils might be reasonable except that the coil size remains in the neighborhood of 2.5e-12m.

The VI (sixth) speculation suggests that the radius of influence and radius of effective "mass" are large, but the effects of the basic entities on each other are small until those basic entities get very close.

The perpendicular coil model, in which the lepton has a structure of tight coils with the strand twisted essentially one way with half a twist per coil and coil axis essentially parallel to the expectation surface, has a number of advantages over coils with axis perpendicular to the expectation surface. The perpendicular coil model could support either loop or twist momentum if the radius of influence is large.

- fini -

Appendix A - Notes

Yes, this is a new twist on the mnp Model.

One source suggests that a theory per week is about right for a productive theorist. Apparently I'm not usually that productive.

Regarding the Shell Quantization in the June 2 blog Photons and the Energy in Shells: "Theorize in haste, repent at leisure."

The author finds that differentiating the concepts (nouns such as Spin) from actions (verbs, such as spin) by capitalization helps keep what little clarity has been achieved.

Quantum mechanics unmeasurables, such as the magnitude of the spin angular momentum of an electron in any theoretical "measured" xy dimensions, where Sxy = .866ħ, does not seem very useful at this point, nor are the cross sectional diagrams showing spinz. To be continued.

Regarding fast and radical changes in a theory: A principle of what is now called computer science is that if the developers are finding bugs on an hourly or daily basis, there is no point in sending the product to beta testers to find bugs too. Maybe for usability testing, though a product ridden with bugs may not be very usable either. So maybe I should count blessings that few people are looking at the mnp Model now.

Understanding puns is harder than creating them. In like manner, understanding the mnp Model may be harder than creating it. Hats off to the brave readers.

Appendix B - Spin Angular Momentum - I - Details (2013-06-04)

Much of the material from the first investigation of spin angular momentum is included here, with less than optimal proof-reading.

mec π r12/ll = h
mec = hll/π r12
Used later: me = hll/πc r12

Solving for r1 and for ll gives

r1 = sqrt(hll / πmec)
ll = mec 2πr12 / h
mloop = me/6 = mass of one loop

If the transverse separation and the longitudinal separation of the basic entities making up the filament loops are equal, then more equations can be written, but since the mass of a single entity must be introduced, we are not closer to having two equations in two unknowns which would allow calculating the mass of a basic entity, the separation distance r1, and the length of the quantized loop ll.

nl = ll/r1 = number of basic entities in a filament loop
ne = 6 ll/r1 = number of basic entities in an electron
m1 = mer1/6ll = mass of one entity

If the maximum density (that of the energy in fhotons, the particle aspect of classical photons as pictured by the mnp Model) were known, then numerical experiments with the magnitudes of the three interesting numbers could be made. The actual value for maximum density is likely to be between the Planckian density 5.155e96 kg/m3 and theoretical quark star densities 3e18 kg/m3 or neutron star densities up to 5.9e17 kg/m3.

m1 = mer1/6ll
me = 6llm1/r1

substitute for me in "Used Later" in the angular momentum formulas above

me = hll/πc r12
= 6llm1/r1
h/πc r1 = 6m1
m1 = h/6πc r1
r1 = h/6πc m1

m1 = ħ c/π r1
me = 6llm1/r1

So as r1 goes up, the mass of each entity goes down, and the number of entities goes up. The filament loop gets longer, and the angular momentum of the wider separated filament twist goes up.

As a magnitude check, try the Planck density as the density of the filaments:

5.155500x10^96 kg/m^3 yields (with a factor of sqrt(3)/2 for the hexagonal packing transverse to the strand)
r1 = .34901045002666E-043
ll = π mec r12/6ħ

a mass of one entity 1.69e17 and a filament length of 4.7e-73m which is shorter than the radius. LoL The transverse rotation of the strand better not be too fast, or the basic entities may slow their "forward" progress to be making that lateral speed. No worries at twist numbers less than _

So for various theoretical r1 values, what would ll be. If rtransverse = rlongitudinal what would ne and m1 be?

Obviously, this first approach doesn't work.

So five more alternates were looked at, starting at Stop the Presses - Spin Angular Momentum - II
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