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Fermions are spin-1, half of spin points "hyper-spatially" ?


Widdekind
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Fermions (s = 1/2) have a total magnitude, of angular momentum, directed through the three standard spatial dimensions (xyx) of

[math]S^2 = \hbar^2 s\left(s+1\right)[/math]

[math] S = \hbar \sqrt{s\left(s+1\right)} = \hbar \frac{\sqrt{3}}{2}[/math]

Such suggests, that spin-half Fermions have another half-unit of spin, directed through a fourth, "hyper" spatial dimension (w), of the "thickness" of the fabric of space-time. I.e. Fermions are actually four-spatial-dimensional quantum wave-functions, having a total actual magnitude of angular momentum, equal to one unit of [math]\hbar[/math]:

[math]S^2 = \hbar^2 = S_w^2 + S_{xyz}^2 = \hbar^2 \times \left( \left( \frac{1}{2} \right)^2 + \left( \frac{\sqrt{3}}{2} \right)^2 \right)[/math]

By comparable calculation, Bosons (s = 1) have a total angular momentum, directed spatially, of [math]\hbar \sqrt{2}[/math], suggesting that they are actually spin-2 particles, having half of their spin directed hyper-spatially:

[math]S^2 = \hbar^2 = S_w^2 + S_{xyz}^2 = \hbar^2 \times \left( \sqrt{2}^2 + \sqrt{2}^2 \right)[/math]

--------------------

i re-propose, that the three "colors" of quarks actually represent three standard spatial axial orientations of quarks; and that the demand for "color neutrality" is actually a requirement for "tri-axial omni-directionality" of the quark triplets, making up nucleons. Quarks have four charge coupling "slots", which can be activated (+/-), or deactivated (0), said slots representing the coupling, of quarks, into the four spatial-and-hyper-spatial dimensions (xyz+w). For instance, a proton, composed of two up-quarks, and one down quark, could exist in the following detailed "fempto state"

Similarly, a neutron could be composed of:

u = (+,+,0,-)

d = (-,0,0,-)

d = (0,-,0,-)

----------------

n = (0,0,0,-)

For comparison, electrons:

e = (-,-,-,-)

and neutrinos:

ve = (0,0,0,-)

Gluons resemble W+/- in that they carry away charge, i.e. charge coupling constants, from one quark, to another:

W+ = (+,+,+,0)

W- = (-,-,-,0)

g1 = (+,-,0,0)

g2 = (+,0,-,0)

g3 = (0,+,-,0)

g4 = (-,+,0,0)

g5 = (-,0,+,0)

g6 = (0,-,+,0)

From the above, one can clearly comprehend, that those gluons "toggle" quarks, from one axial orientation to another; and do so, in such a way, that their absorption by another of their fellows, also "toggles" them, from the other orientation to the one:

u = (+,+,0,-) ----> (+,0,+,-) + g3

u = (+,0,+,-) ----> (+,+,0,-) - g3

d = (-,0,0,-)

----------------

p = (+,+,+,-)

 

Quarks only couple, by the one-and-only-grand-unified-force, into one, or into two, spatial dimensions... they are observed, macroscopically, from far far away, averaged over long long time spans, to have "fractional" charges, only because, as they spin and tumble and roll around every which way, spatially, they only couple into those directions, on average, one-third (or two-thirds) of the time.

 

By analogy to the common "color" model, quarks can "fake out" and "feint" their fellows, by the emission of "axis - anti-axis" gluons (in the color model, called color-anticolor, e.g. red-antired):

 

g7 = (+/-,0,0,0)

g8 = (0,+/-,0,0)

g9 = (0,0,+/-,0)

 

 

u = (+,+,0,-) ----> (+,+,0,-) + g7 or 8 or 9

u = (+,0,+,-)

d = (-,0,0,-)

----------------

p = (+,+,+,-)

 

such "psyched-you-out" gluons represent quarks beginning to "toggle"... but then "thinking better of it" and reverting back, to the way they were, originally. For complete clarity, the "axial orientation" of up quarks is defined, by the standard spatial axis which lacks a charge coupling; and of down quarks, by the standard spatial axis which actually contains a coupling.

 

Due to the need for constant tri-axial omni-directionality, when one quark begins to "extrude" or "emit" or "emanate" a gluon, carrying away some of its charge(s), to another of its fellows, then the other quark "must must must" absorb the whole entire gluon, head-to-tail, so flipping into a complementary orientation, before the first quark "lets go" of its gluon. If, during that exchange process, one or the other (or both) of the quarks is "kicked" by a hard nuclear interaction, then the "extruder" can be "gripping" the tail of its gluon, while its fellow is "gripping" the head of the same gluon -- when the exchange is suddenly rudely interrupted, prematurely. Such can cause the gluon to "stretch and rip and tear", producing pions:

 

 

uz = (+,+,0,-) ----> (+,0,+,-) + (0,+,-,0) ----> (0,+,0,+) + (0,0,-,-) = !dy + dz

uy = (+,0,+,-)

dx = (-,0,0,-)

----------------

p = (+,+,+,-)

 

The proton partners are "left in the lurch", with two mis-(parallel-)aligned up quarks, and several down (and anti-down) quarks, two of which constitute a pion. Violent processes then sort out the mis-matches.

 

Note, that nucleons are highly "hyper-charged"... unlike charge neutrality of atoms, in the three standard spatial dimension, every quark is equally charged, in the fourth hyper-dimension, such that all nucleons have

 

--- = -1e

 

unit of charge, focused in the hyper-spatial "w" dimension... and the addition of all of an atom's electrons only exacerbates the hyper-charge accumulation, in close confines

 

 

 

--------------------

The fabric of space-time has a hyper-spatial thickness, approximately equal, to the range of the Weak interaction (~10-18m = 0.001 fm), which represents the range at which wave-functions begin to "stack up over each other" through that "thickness" in the hyper-spatial "w" thickness dimension.

 

The three "flavors" of fundamental Fermions represent the three bound states, of Fermions, in the potential well, created by the two parallel hyper-surfaces, of the fabric of space-time ("the wafers of the ice-cream sandwich"). As evidenced by the top quark, that potential well is ~200GeV deep.

 

Since there exists only one single grand-unified force, and since quantum wave-functions of Fermions are attracted into the fabric of space-time by their interaction with its "hyper-potential", such implies that the hyper-surfaces, of the fabric of space-time, are charged. Further, since charged matter, and anti-charged anti-matter, both bind into space-time, with (nearly) identical energies, symmetry suggests, that one hyper-surface is positively charged, and the other negatively. I.e. the fabric of space-time is similar, to a dielectric gel, between the two parallel plates, of a capacitor.

 

Now, those hyper-surfaces are the 3D surfaces, of 4D space (xyz+w)... every point in space (xyz) is bound "out" and "in" by two other points (xyz +/- dw). From known numbers, one can estimate the value of the forces involved:

 

 

Volts = Joules / Coulomb = 200GeV / (1/3e) = 600 GV

 

(three units of charge, one each in x+y+z, is perceived as "one" unit of electron charge; matter only carries a single unit of charge, coupling into the fourth, hyper-spatial, "thickness" dimension, "w")

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Fermions (s = 1/2) have a total magnitude, of angular momentum, directed through the three standard spatial dimensions (xyx) of

[math]S^2 = \hbar^2 s\left(s+1\right)[/math]

[math] S = \hbar \sqrt{s\left(s+1\right)} = \hbar \frac{\sqrt{3}}{2}[/math]

Such suggests, that spin-half Fermions have another half-unit of spin, directed through a fourth, "hyper" spatial dimension (w), of the "thickness" of the fabric of space-time. I.e. Fermions are actually four-spatial-dimensional quantum wave-functions, having a total actual magnitude of angular momentum, equal to one unit of [math]\hbar[/math]:

 

 

How is this "suggested" by the equations?

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How is this "suggested" by the equations?

 

[math]\frac{\sqrt{3}}{2}[/math] commonly occurs, in conjunction, with 30-60-90 right triangles... that number so suggests its orthogonal compliment, [math]\frac{1}{2}[/math]... and a spin of 1/2, orthogonal to the three standard spatial dimensions (xyz), suggests a fourth "hyper-dimension" (w), parsimoniously interpreted, as a "small" dimension, being the "thickness" of the fabric of space-time, i.e. the "thickness of the rubber-sheet of Flatland" in down-dimensioned analogy. Again, i re-propose, that the exact same lines of logic, allow parsimonious interpretation, of rest-mass, as momentum directed through a dimension (w) orthogonal to the three standard spatial dimensions (xyz),

 

E2 = m2 + p2 = pw2 + pxyz2

 

Professor Rudy Rucker (Geometry, Relativity, Fourth Dimension) wrote, that the fabric of space-time, may have a "hyper-thickness" (w), rather than actually really truly having zero thickness, and being infinitesimally thin. Such seems patently implausible -- the fabric of space-time spans billions of light-years in numerous other dimensions, curving around through a higher hyperspatial dimension. A "small" but non-zero thickness certainly seems much more plausible, and parsimoniously explains rest-mass as "hyper-momentum" (momentum directed hyper-dimensionally, "across" the fabric of space-time); non-interger-quantized spin, as the "spatial half" of integer spin values; "color" as axial orientation.

 

 

 

--------------------------------------------------------------------------------------------------------

 

 

 

 

that rest-masses, of the three "flavors", of up-quarks, as functions of the "flavor" number (n=1,2,3), quite closely follow:

 

m = 2 n10

 

Thus, the "fourth flavor", which according to this hyper-spatial hypothesis, is the "first ionized" state, would be predicted to occur, at an energy, of approximately 3000 GeV = 3 TeV. Thus, i would offer, from this hyper-spatial hypothesis, that at energies of order 3 TeV per quark = 10 TeV per nucleon, physicists would witness "magic moments", wherein matter, in ultra-high-energy collisions, "vanished" from the collision chamber, leaving no traces. At such super-high-energies, matter might be "blasted off of the Flatland fabric of space-time", out into hyperspace, "ionized" out of the hyper-spatial potential well, within which all mass-energy, embedded within our fabric of space-time, resides.

 

Conceivably, matter "blasted out into hyperspace" might gradually "rain back down onto the fabric of space-time" elsewhere, perhaps far from the original collision location. If so, then perhaps the centers of cloud-chambers would remain pristine... and then, some moments after the collision, matter might spontaneously "poof (back) into the fabric of space-time", way out at the edges of the cloud-chambers (or something similar).

Edited by Widdekind
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[math]\frac{\sqrt{3}}{2}[/math] commonly occurs, in conjunction, with 30-60-90 right triangles

We're discussing physics, not numerology.

 

 

How do you test your idea? How does this extra-dimensional spin component affect any observation? What are the spin commutation relations?

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Fermions with "hyper-spatial spin" pointing "out" (say) = matter = "pan-cake right-side up on griddle"

 

pointing "in" = anti-matter = "same pan-cake but upside-down on griddle"

 

matter + anti-matter = (+1/2) + (-1/2) = 0 = Boson = photons

 

this simple picture explains anti-matter as the "flip-side" of matter; and explains why when M+AM collide, the result = Bosons w/ no "hyper-spin"

 

Fermions have angular & linear momentum in the hyper-spatial dimension; Bosons have neither angular nor linear momentum in that "w" dimension (from Rudy Rucker's convention)

 

(i've revised my speculation -- i think that there is a common unified "electro-weak-strong" force, for interactions between particles w/in the fabric of space-time... its "currency" = charge...

 

and another force, for interactions between all of those particles, and all of their force-carrying kin... to the fabric of space-time... its "currency" = mass-energy)

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thin thickness of space-time fabric could account for electrons' anomalously large magnetic moments

 

If space is fundamentally 4D = xyz+w, then fundamental forces are 4D. Then, fundamental forces would decrease, over 4D hyper-distances, as 4D field-lines dispersed, over the 3D hyper-surface-areas, of the 4D hyper-spheres, surrounding some force-field-line-generating particle, at a particular point (xyzw) in 4D space.

 

The volume of a 4D hyper-sphere is

 

 

[math]V_4 = \frac{\pi^2}{2} R^4[/math]

 

 

so the 3D hyper-surface-area of such is

 

 

[math]S_3 = \frac{\partial}{\partial R} V_4 = 2 \pi^2 R^3[/math]

 

 

Thus, 4D force-fields would be

 

 

[math]\vec{F}_4 = \frac{G_4 m}{2 \pi^2 R^3}[/math]

 

 

i.e. the particle generates [math]G_4 m[/math] field-lines, which disperse & spread out, over hyper-surface-areas. Now, if the fabric of space-time is 4D, but very thin, in the hyper-dimension "w", then those field-lines could be constrained, to "arch over" and "bend down", from the "hyper-poles" of those hyper-surface-areas, to the "hyper-equator", so as to remain within the thin fabric of space-time. If so, then those [math]G_4 m[/math] field-lines, emerging from some particle, would actually only disperse & spread out, over a radically reduced hyper-surface-area:

 

 

[math]\vec{F}_4 \longrightarrow \frac{G_4 m}{\left( 4 \pi R^2 \right) \times \Delta w} = \frac{G_4}{4 \pi \Delta w} \frac{m}{R^2}[/math]

 

 

So, we can quickly identify

 

 

[math]\frac{G_4}{4 \pi \Delta w} \longrightarrow G_3 = 6.67 \times 10^{-10} N m^2 kg^{-2}[/math]

 

 

However, if field-lines could disperse away into surrounding hyper-space (the "Bulk" of String-Theory), then the number of field-lines captured, within the thin fabric of space-time, would simply decrease "normally" (from 4D hyper-spatial perspective):

 

 

number of field-lines captured = [math]\frac{G_4 m}{2 \pi^2 R^3} \times \left( 4 \pi R^2 \Delta w \right)[/math]

field-lines per perceived standard-spatial surface-area = [math]\frac{G_4 m}{2 \pi^2 R^3} \frac{4 \pi R^2 \Delta w}{4 \pi R^2}[/math]

 

 

which decreases as distance cubed, far faster than any known fundamental force (i.e. gravity, electro-magnetism). Ipso facto, force-field-lines could be constrained, to "compress down" and remain inside the fabric of space-time, unable to disperse away, through higher dimensions, into hyperspace. Et ergo, if electrons actually are full spin-1 particles, then they actually have twice the spin now known, and so would generate twice the magnetic moment... all of whose magnetic field-lines would "twist over", constrained to remain within the fabric of space-time, so that although half of their mechanical angular momentum is "hidden in the hyper-dimension", all of their electro-magnetic moment "twists over" and projects into-and-then-through the fabric of space-time.

 

hyper_spatial_fields.png

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thin thickness of space-time fabric => Higgs potential

If the fabric of space-time is fully 4D, and if a particle is attracted, to every "cell" of the space-time fabric, with a hyper-force...

then if that particle strayed away from the hyper-mid-"plane" (= 3D volume at hyper-planar-center of 4D-but-thin space-time)...

then that particle would be pulled back towards the hyper-mid-"plane"...

by a force proportional to its hyper-displacement [math]\Delta w[/math]...

which would be described by a potential proportional to the square of its hyper-displacement [math]\frac{1}{2} \Delta w^2[/math]...

which describes the quadratic Higgs potential, of the Higgs field (the quanta of which are the Higgs bosons), as described in Riccardo Barbieri's Lectures on the Electro-Weak Interaction...

Proof:

The differential 4D force, of attraction, between our particle (of mass m), and some "cell" of the space-time fabric, is

[math]d \vec{F}_4 = \frac{G_4 m \rho_4 dV_4}{2 \pi^2 R^4} \vec{R} = \frac{G_4 m \rho_4 dV_4}{2 \pi^2 R^4} \begin{bmatrix}{c} x \\ y \\ z \\ w-W \end{bmatrix}[/math]

By spatial symmetry, all of the spatial components (Fxyz) cancel. For, for every four-voxel of 4D space at (say) x, another at -x produces precisely the same magnitude of x-force, but in the opposite direction. Thus, seemingly sensibly, this 4-force never pushes particles spatially, through the fabric of space-time... particles never acquire "sudden impulses of momentum magically". Thus, we only consider the hyper-spatial 4-force component Fw.

[math] F_w = \int dF_w = \left( \frac{G_4 m \rho_4}{2 \pi^2} \right) \int dw dx dy dz \frac{w-W}{\left( x^2 + y^2 + z^2 + \left( w - W \right)^2 \right)^2} [/math]

 

Since the hyper-dimension is orthogonal to all three standard spatial dimensions, and by symmetry of standard space, the triple-standard-spatial integral can be converted, into 3D spherical coordinates:

[math] = \left( \frac{G_4 m}{2 \pi^2} \right) \int dw \int 4 \pi r^2 dr \frac{w-W}{\left( r^2 + \left( w - W \right)^2 \right)^2} [/math]

[math] = \left( \frac{ G_4 m}{ 2 \pi^2 } \right) \left( 4 \pi \right) \left( \int_{W}^{W_{max}} - \int_{W_{min}}^W \right) \left( \int d\chi \frac{\chi^2}{ \left( \chi^2 + 1 \right)^2 } \right) [/math]

 

where one re-scales the standard-spatial-radius coordinate, into units of the hyper-spatial-displacement distance, which requires breaking the hyper-spatial integral into two pieces, according to the sign of the hyper-displacement (w-W). Then, the re-scaled, dimensionless, [math]\chi[/math] integral, by variable substitution [math]\chi \equiv tan(\theta)[/math] simplifies into the integral of [math]\int sin^2(\theta) d\theta = \frac{\pi}{4}[/math].

So,

[math] F_w = \left( \frac{G_4 m}{2 \pi^2} \right) \left( 4 \pi \right) \left( \frac{\pi}{4} \right) \left( \left( W_{max} - W \right) - \left( W - W_{min} \right) \right)[/math]

 

Since space-time is assumedly symmetric, hyper-spatially, Wmin = - Wmax, et ipso facto

[math] F_w = \left( \frac{G_4 m}{2} \right) \left( - 2 W \right) [/math]

[math] \boxed{ F_w = - \left( G_4 m \right) W} [/math]

 

Thus, hyper-displacements, away from the hyper-mid-"plane" of space, would experience restoring forces, proportional to that hyper-displacement, which is equivalent to a quadratic potential, equivalent to the proposed potential, of the Higgs field.

hyper_spatial_Higgs_field.png

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(oops)

 

[math] \boxed{ F_w = - \left( G_4 m \rho_4 \right) W} [/math]

 

Note that [math]dm = dV_4 \rho_4 = dV_3 \Delta w rho_4 = dV_3 \left( \Delta w rho_4 \right)[/math], so that the perceived 3D mass-density of space, is the product of the actual 4D hyper-density, and the 4thD hyper-thickness, of the fabric of space-time.

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!

Moderator Note

Discussions involve responding to those who are talking to you in an informative manner. Please make sure this doesn't become a blog-like entry, or some kind of soapbox for your idea. Repeated requests for clarity that go unanswered usually means the thread gets closed and no one wants that.

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hyper-spin commutation relations would basically break down as Sw x Sxyz... the hyper-spin Sw defines particle / antiparticle, and is "pinned" (with want of worthier words)... if anything could flip hyper-spin, 'twould be Weak-bosons, in intense "point blank" Weak interactions (interpreted as when particles start to "stack" hyper-spatially, (partially) occupying the same xyz, but "stacking" in w, so as to be blasted, at "point blank" range, by hyper-high energy interactions)

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Stacking? How do you explain the Pauli exclusion principle, which tells us this stacking does not exist for half-integral spin particles.

 

 

PXP => no two particles, in exactly the same state, in the same space...

 

if there exists a "w", "in-out", hyper-thickness to the fabric of space-time...

 

and if Fermions are full spin-1 Bosons, half of whose spin is directed thru the hyper-dimension "w"...

 

(again, S2 = 1 = Sw2 + Sxyz2 = (1/2)2 + (sqrt(3)/2)2 = 1/4 + " (S=1/2) x (S=1/2 + 1) "...)

 

and if that hyper-spin determines matter / antimatter...

 

Sw = +1/2 = positrons & positron-neutrinos = antimatter

Sw = -1/2 = negatrons & negatron-neutrinos = matter

 

then the extrapolated-PXP would imply, that two positrons, or two negatrons, could not "stack"...

 

but, one neutrino could stack w/ one electron (say)... those are different particles, different particle states, different wave-functions... and Weak-interactions involve neutrinos and electrons, not (to my knowledge) pairs of electrons, although i guess their could be neutral current interactions...

 

i'm simply saying, that the fringes of wave-functions could conceivably begin to "stack" hyper-spatially, in fairly-flat-thin-land analogy similar to checkers, or a pair of burgers on a grill, stacked so that the edge of one was resting on the edge of the other, but not fully doubled up...

 

the Weak-interaction can be interpreted, as regular run-of-the-proverbial-mill, EM interaction... through the hyper-dimension "w", when pairs of particles begin to double-stack hyper-spatially... the "Weak hyper-charge" is regular run-of-the-oft-mentioned-mill electric charge, aiming into the hyper-dimension (whereas "electric charge" couples into the standard spatial dimensions "xyz"). The neutrino has no "electric charge", i.e. its qx = qy = qz = 0... but it has "weak charge", interpretable as qw = -e... so the neutrino is "blind" to standard spatial displacements "xyz"... but when it wanders "into-and-under" or "into-and-over" another wave-function, it suddenly starts interacting intensely, other-wise-normal-electro-magnetically, through the hyper-dimension "w", apparently at "point blank range" ~10-18m = range of Weak-force = thickness "dw" of space-time...

 

so i predict, that because the neutrino possesses some electric charge... neutrinos also generate some magnetic moment... whose magnetic dipole-esque field-lines try to point hyper-spatially through "dw"... but which "arc over" at the "top & bottom" of space-time, and re-direct through the three standard spatial dimensions "xyz"...

 

i predict, that the "Higgs force", between quanta within the fabric of space-time, and space-time itself, is ultimately a grand-unifiable-example, of "the" one-and-only "grand unified force"...

so the reason why neutrinos evidence nearly no "resting" mass-energy... is because they only "see" a short ("dw" long) sliver, of the fabric of space-time... owing to neutrinos only having hyper-spatially-directed charge qw = -e...

neutrinos notice nearly no space-time -- only the vertical "hyper-section" of space-time exactly at their own spatial position "xyz" and only atto-meters thick "dw"...

so they are barely attracted into the fabric of space-time, by the "Higgs force" = "EM force between quanta in space-time to-and-from space-time"...

 

so, on that set of assumptions, i predict that neutrinos generate a magnetic moment, of magnitude, relative to electrons... comparable to the mass of the neutrino, relative to electrons... i.e. ~10-6 x ue

 

again, neutrinos only "know" the one-and-only-grand-unified-force = "EM/W/S forces (thru space-time) between particles (w/in space-time)" = "Higgs force between particles and space-time itself"...

neutrinos only know that force, through the hyper-spatial "thickness" dimension "dw"...

so they have nearly no interaction w/ the fabric of space-time => nearly no mass

because they also have nearly no "one-and-only-force charge" (only qw > 0) => nearly no magnetic moment

(and nearly no interactions w/ other particles either)

 

seemingly, astronomy could answer whether neutrinos possess any magnetic moment > 0...

accordingly to the following powerpoint presentation in pdf, electron-neutrinos can emit W+ bosons, becoming electrons... if so, then perhaps neutrinos can in fact "flip hyper-spin" in intensely energetic interactions

 

http://nucla.physics.ucla.edu/sites/default/files/NeutrinoMagneticMoment_2012Nov8.pdf

the following figure attempts to depict an explanation for the forces at work in the world...

 

EM/W/S forces, through the fabric of space-time, in between pairs of particles w/in the fabric of space-time...

 

and the Higgs force, from those particles, to the fabric of space-time, itself...

 

in analogy, particles are a little like boats...

 

force-carryiers are a little like bottles between boats...

 

and Higgs bosons are a little like anchors from boats to the bottom...

post-11564-0-22933600-1378588623_thumb.png

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PXP says no two particles, in exactly the same state, in the same space, if they are half-integral spin. Bose statistics say that integral spin particles CAN "stack"

 

Checking the literature for a neutrino magnetic moment should be trivial.

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PXP says no two particles, in exactly the same state, in the same space, if they are half-integral spin. Bose statistics say that integral spin particles CAN "stack"

 

Checking the literature for a neutrino magnetic moment should be trivial.

 

in intuiting, that positrons are "hyper-spin up", and negatrons are the same but "hyper-spin down"...

 

so the extrapolation, of the PXP, would be, that whereas electrons can "stack" spatially, if they spin oppositely, so two electrons could stack, if they hyper-spin oppositely, i.e. you could observe matter co-occupying the same space "xyz+w", as its antimatter "inverse-twin"

 

now, if Fermions are actually spin-1 Bosons, half of whose spin points hyper-spatially (Sw = +/- 1/2)...

 

in practice, that difference is equivalent to "rest-mass" vs. "mass-less"...

 

the PXP would, then, derive from the "hyper-spatially directed hyper-momentum (pw2)" and/or "hyper-spatially directed spin (Sw)"...

 

particles whose wave-functions are not "sloshing hyper-out and hyper-in" can stack over each other... but hyper-momentum must impede & impair such stacking...

 

you can have two electrons, in exactly the same states, nano-scopically near each other, through space "xyz", e.g. in metallic crystal lattices...

 

perhaps you can have two "Bosons", in exactly the same states, atto-scopically near each other, through the hyper-spatial "w" thickness dimension ? To wit, when you say you see two photons "in the same space", in simplified notation, the one is at "xyz,w" and the other at "xyz,w+dw"...

 

if so, then this hyper-space hypothesis would predict, that due to the limited thickness "dw" of the fabric of space-time, so the stack-ability of bosons spatially (but at varying hyper-spatial "heights" out-in) would also be limited... photon-photon scattering ?

 

 

 

--------------------------------------------------------------------------------------------------------------------------------

 

perhaps the Weinberg angle, which makes the mass of Z0 > W+/-, reflects the hyper-angle, at which Z0 propagate, both "across" the hyper-thickness of space-time, and also through standard spatial dimensions... whereas W-bosons "bounce back and forth" solely through the thin "thickness" hyper-dimension... the extra momentum-energy of the Z0 would then be greater by

 

[math]m_Z^2 = p_w^2 + p_{xyz}^2 > p_w^2 = m_W^2[/math]

 

according to the Weinberg-Salam equation

 

[math]\frac{m_W}{m_Z} = cos(\theta_W) = \frac{A}{H}[/math]

 

whereas i would suggest, seemingly similarly

 

[math] = \frac{p_w^2}{p_w^2 + p_{xyz}^2}[/math]

 

which is certainly similar (maybe more of a cos2 type of term)

 

 

 

 

 

( i tried to talk about HS here )

wait wait wait

 

electrons & even neutrinos have "hyper-charge", which i'm interpreting, as electric charge, coupling into-and-through the 'thickness" hyper-dimension...

 

i'm interpreting Z0 bosons, as hyper-dimension-ally directed photons, emitted when "hyper-spatially-charged" Fermions start to stack, and blast each other at "point blank range", atto-meters = 100GeV

 

so, hyper-spatial charging => Fermions blast each other at hyper-high energies, if ever the seek to stack...

 

whereas Bosons do not carry "hyper-charge" (the emission/absorption of bosons never affects "hyper-charge")... so, through the "thickness" hyper-dimension, Bosons are as non-interacting, as neutrinos are, through the three standard spatial dimensions...

 

so, perhaps the PXP is "enforced" by Weak-bosons, interpreted as regular normal photons, except propagating through the "thickness" hyper-dimension "w", which blast between hyper-charged Fermions, whenever the seek to start stacking, w/in the thin "thickness" of space-time "dw". Z0 = "in-out" directed but otherwise normal regular photons... the PXP is "enforced" and is the result of, the hyper-charges, of (all) Fermions...

 

so, since "Bosons" are un-hyper-charged, they act like neutrinos, hyper-spatially, so "stacking" as easily, as nearly-non-interacting neutrinos standard spatially

 

 

 

 

"hyper-charge" defines the "B" quantum field, orthogonal to the W3 field... that starts to sound similar, to these simplistic suggestions... the "B0" eigenstate would be a perfectly-hyper-propagating photon... orthogonal to purely-space-propagating photons... the Z0 is a mixture of both, propagating mostly "in-out across" the fabric of space-time, but also propagating spatially to some extent...

 

http://en.wikipedia.org/wiki/Weak_hypercharge

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Bose and Fermi statistics dictate when the Pauli exclusion principle applies. It applies to half-integral spin particles, whose wavefunctions must be antisymmetric. Integral spin has a symmetric wavefunction, and these particles can occupy the same state. No "sloshing" or any other hand-wavy discussion about crystals. Atomic structure is what it is because of this difference. Atoms exist because electrons obey the PXP.

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Electro-Weak-Strong unification ?

 

Only one force, into which quanta couple with charge. Force-carrying Bosons can propagate, either through the standard spatial dimensions "xyz", or through the thin "thickness" hyper-dimension "w"; and, the Bosons can be charge-less, or charged:

 

[math]\bordermatrix{ \; & xyz & w \cr 0 & \gamma & Z^0 \cr q & g & W^{\pm} \cr}[/math]

 

Charge is a four-vector quantity:

 

[math]\tilde{q}=\begin{array}{r} \left( q_x q_y q_z q_w \right) \end{array}[/math]

 

and the four fundamental forms of Fermions are charged, in either zero (neutrinos), one (down-quarks), two (up-quarks), or three (electrons) standard spatial dimensions "xyz"; all have hyper-charge into the hyper-dimension "w"; all are massive, spin-one (S=1), having hyper-spin half (Sw = 1/2):

 

[math]\tilde{\nu}=\begin{array}{r} \left( 0 0 0 - \right) \end{array}[/math]

[math]\tilde{d}=\begin{array}{r} \left( - 0 0 - \right) \end{array}[/math]

[math]\tilde{u}=\begin{array}{r} \left( + + 0 + \right) \end{array}[/math]

[math]\tilde{e}=\begin{array}{r} \left( - - - - \right) \end{array}[/math]

 

Particles can rotate around through the standard spatial dimensions, during their interactions. So, on time average, [math]q_x \leftrightarrow q_y \leftrightarrow q_z[/math], and qualitatively, only the number of spatial-dimensional chargings (0-3) is of qualitative importance, and defines their Classical (scalar) charge

 

[math]q_C = \frac{1}{3}\sum_{xyz}q_i[/math]

 

Charged particles cannot accommodate both types of charge (+/-), loaded within the same particle wave-function, i.e. particle axial charges are either all positive (or neutral), or all negative (or neutral), i.e. particle charge four-vectors are positive-semi-definite, or negative-semi-definite.

 

To lowest order, this universe consists of equal numbers of protons (uud) and electrons (e), and so is both neutrally charged, and also neutrally hyper-charged. Demanding charge (and hyper-charge) neutrality imposes a pair of possibilities upon matter (protons + electrons, or anti-protons + anti-electrons). Whichever one occurred in the Big Bang, humans would come to call the cosmos' constituents "matter", and the other "anti-matter". So, this hyper-space hypothesis, and the Anthropic Principle, can account for so-called matter/antimatter asymmetry.

 

Force-carrying Bosons also can carry charge, in either zero (photons, Z0), one-two (gluons), or three (W+/-) standard spatial dimensions "xyz":

 

[math]\tilde{\gamma}, \tilde{Z^0}=\begin{array}{r} \left( 0 0 0 0 \right) \end{array}[/math]

[math]\tilde{g}^+=\begin{array}{r} \left( + 0 0 0 \right) \end{array}[/math]

[math]\tilde{g}^{++}=\begin{array}{r} \left( + + 0 0 \right) \end{array}[/math]

[math]\tilde{W}^-=\begin{array}{r} \left( - - - 0 \right) \end{array}[/math]

 

When partially-charged particles interact, they either give away none of their spatial-chargings ("hold"), or give away all of their spatial-chargings ("fold / flush"). They cannot give away only some of their spatial-chargings (or else protons could decay into positive pions). Meanwhile, they can receive any missing spatial-charging(s) ("fill"). This hyper-space hypothesis could account, for positive pion decay, [math]\pi^+ \rightarrow \bar{e} + \nu[/math], without invoking the triply-charged W+ Boson, but instead solely single or doubly-charged g+, g++ Gluons:

 

[math]\bar{e}=\begin{array}{r} \left( + + + + \right) \end{array} \; \bar{\nu}=\begin{array}{r} \left( 0 0 0 + \right) \end{array}[/math]

 

[math]\nwarrow \; \; g^{+,++} \; \; \nearrow[/math]

[math]\nearrow \cdots \cdots \cdots \nwarrow[/math]

 

[math]u=\begin{array}{r} \left( + + 0 + \right) \end{array} \; \bar{d}=\begin{array}{r} \left( 0 0 + + \right) \end{array}[/math]

 

Unlike Fermions, force-carrying Bosons can accommodate both types of charge (+/-) within one wave-function; force-carrying Bosons can be charged-and-anticharged:

 

[math]\tilde{g}'=\begin{array}{r} \left( \pm 0 0 0 \right) \end{array}[/math]

[math]\tilde{g}''=\begin{array}{r} \left( \pm \pm 0 0 \right) \end{array}[/math]

[math]\tilde{W}=\begin{array}{r} \left( \pm \pm \pm 0 \right) \end{array}[/math]

 

The last Boson, a hypothetical "double W", has been observed, as the source of supposed Higgs Bosons, [math]W^+ + W^- \rightarrow H^0[/math]. The Strong-force, inside nucleons, is mediated by "double Gluons", carrying a charge and an anti-charge, by which emitting quarks can rotate, inside their nucleon:

 

[math]u=\begin{array}{r} \left( + 0 + + \right) \end{array} \; u=\begin{array}{r} \left( + + 0 + \right) \end{array}[/math]

 

[math]\nwarrow\tilde{g}=\begin{array}{r}\left(0 + - 0\right)\end{array}\nearrow[/math]

[math]\nearrow \cdots \cdots \cdots \cdots \cdots \nwarrow[/math]

 

[math]u=\begin{array}{r} \left( + + 0 + \right) \end{array} \; u=\begin{array}{r} \left( + 0 + + \right) \end{array}[/math]

 

Strong-force "color charge", with its three possible values, and (nearly) nine possible "color / anticolor charged" Gluons, can be explained, instead, as directional chargings of quarks, and double-directional charged / anticharged Gluons:

 

[math]R G B \leftrightarrow x y z[/math]

 

[math]\tilde{g}_{R\bar{R}} \leftrightarrow \begin{array}{r} \left( \pm 0 0 0 \right)\end{array}[/math]

[math]\tilde{g}_{R\bar{Y}} \leftrightarrow \begin{array}{r} \left( + - 0 0 \right)\end{array}[/math]

[math]\tilde{g}_{R\bar{B}} \leftrightarrow \begin{array}{r} \left( + 0 - 0 \right)\end{array}[/math]

[math]\tilde{g}_{Y\bar{R}} \leftrightarrow \begin{array}{r} \left( - + 0 0 \right)\end{array}[/math]

[math]\tilde{g}_{Y\bar{Y}} \leftrightarrow \begin{array}{r} \left( 0 \pm 0 0 \right)\end{array}[/math]

[math]\tilde{g}_{Y\bar{B}} \leftrightarrow \begin{array}{r} \left( 0 + - 0 \right)\end{array}[/math]

[math]\tilde{g}_{B\bar{R}} \leftrightarrow \begin{array}{r} \left( - 0 + 0 \right)\end{array}[/math]

[math]\tilde{g}_{B\bar{Y}} \leftrightarrow \begin{array}{r} \left( 0 - + 0 \right)\end{array}[/math]

[math]\tilde{g}_{B\bar{B}} \leftrightarrow \begin{array}{r} \left( 0 0 \pm 0 \right)\end{array}[/math]

 

[math]\tilde{g}_{i j}^{k} = \delta_i^k - \delta_j^k[/math]

 

to try tensor notation.

 

 

 

 

why do we (nearly) never notice the 4th spatial D ?

Practically, people don't perceive the 4th space-like dimension "w", because people never perceive physical objects "stacking", through "w", at the same 3D space place "xyz". Conversely, people perceive things "stacking", through the 3rd space-like dimension "z", because people perceive things occupying the same 2D space place "xy", e.g. eclipses of one object in front of another as seen on the sky; or needing to know the floor, to deliver mail, to someone working in some city skyscraper, on some specific street-by-street corner. However, since (nearly) nothing ever "stacks", at the same space place "xyz", no additional dimension "w" is perceived, practically. But, at hyper-high energies, in the Weak interactions, sub-atomic particles are starting to "stack" hyper-spatially, occupying the same place "xyz", but displaced through the thin "thickness" hyper-dimension "w".

 

 

 

why Weak alpha (~1/4) is 40x EM alpha ?

If space is fundamentally 4D, and if particles possess charge (and hyper-charge) coupling them into "The Force" through those 4Ds, then the electro-static 4-force presumably possesses hyper-spherical symmetry:
[math]\vec{E}_4 = \frac{q}{2 \pi^2 \epsilon_4 R^3} \hat{R}[/math]
Now, since the space-time fabric is so thin, most of the (hyper-)field lines emerging from some particle, are directed hyper-spatially, to high hyper-polar latitudes, well away from the hyper-mid-3-plane at the hyper-equator. But only field-lines emerging into that hyper-equatorial hyper-mid-3-plane, would then thread into the fabric of space-time. I.e. the vast majority of field-lines would be "lost into hyper-space", which would account for the feebleness of the known EM 3-force:
[math]\alpha\equiv\frac{q_e^2}{4\pi\epsilon_0\hbar c}\approx\frac{1}{140}[/math]
In reduced dimensional "fairly-flat-Thin-land" analogy, a three-dimensionally charged particle, embedded into fairly-flat-Thin-land, would generate field-lines, most of which pointed up, into the air above Thin-land; or down, into the air below Thin-land. Only a few field lines near the exact equator of the particle, would flow forth straight sideways, threading into the thin "thickness" height of space-time.
However, in Weak interactions, particles are starting to slam into each other, so forcefully, that their wave-functions converge and overlap, at intensely short ranges. So, since particles are starting to "stack" hyper-spatially "over and under" each other, they start to perceive all of those hyper-polar (hyper-)field lines. Thus, the Weak-force is far stronger than the EM force, with a coupling coefficient ~40x greater. In reduced dimensional "fairly-flat-Thin-land" analogy, a three-dimensionally charged particle, embedded into fairly-flat-Thin-land, would generate field-lines, most of which pointed up, into the air above Thin-land; or down, into the air below Thin-land. But, if another fairly-flat-Thinlander particle slammed into its side, so forcefully, that it started to "slither under" or "ride up over" the 3D particle, then all of those polar field lines would begin to be perceived, so amplifying the effect of the forceful interaction.
Thus, this hyper-space hypothesis can account for the coupling coefficients, of the EM vs. W interactions (as well as the "running" effects, whereby with increasing energy, the Weinberg angle decreases, since at higher & higher energies, particles would "ride up over" each other more & more).
The following integrals would be worthwhile, for semi-quantitative analyses:
[math]r_{\perp}^2 + z^2 = R^2[/math]
[math]ds = dz \frac{ds}{dz} = dz \sqrt{1 + \left( \frac{dr}{dz} \right)^2} = dz \frac{R}{r}[/math]
[math]S_2 = 4 \pi R^2 = \int_{-R}^R 2 \pi r ds = 2 \pi R^2 \int_{-1}^1 dz' [/math]
[math]S_3 = 2 \pi^2 R^3 = \int_{-R}^R 4 \pi r^2 ds = 4 \pi R^3 \int_{-1}^1 \sqrt{1-z'^2} \; dz' [/math]
Estimating the hyper-angle (from the hyper-equator) which would sweep up ~1/4 of all field lines, results in an angle, closely comparable to the known Weinberg angle.
neutron-stars become proton-stars ?
Neutrons are electrically-neutral spatially ("xyz"), but are negatively hyper-charged ("w"), [math]q_{w,u} + 2 q_{w,d} = -1[/math]. "Normally", particles' wave-functions are much much wider spatially "xyz", than they are "thick" through "w" (a little like pancakes on a griddle). So, "normally", particles cannot rotate, through hyper-polar angles (a little like pancakes trying to flip themselves over). But, inside neutron stars, quarks could conceivably become compressed, spatially ("xyz"), until their spatial sizes were squished as small, as their hyper-spatial "heights" ("w"). Then, such squished quarks could conceivably rotate, through hyper-polar angles (a little like pancakes, compressed into dense spheroidal blobs of batter, beginning to roll around on the griddle). The squished quarks would begin to perceive reality as four symmetric space-like dimensions. And then, their hyper-charges would begin to "bleed over", from the hyper-dimension "w", into standard spatial dimensions "xyz". So, on time average, the ultra-dense neutronium would acquire a net spatial charge,
[math]\tilde{q}_4 = \begin{array}{r}\left( 0 0 0 -1 \right)\end{array} \longrightarrow \frac{1}{4} \times \begin{array}{r}\left( -1 -1 -1 -1\right)\end{array}[/math].
Thus, the compressed neutron-star would become comparable to a (anti-)proton star. Seen "from the side" through space "xyz", the neutronium would seem to acquire a net (negative) charge, on time average, "from nowhere", which would in fact have come from the particles' net negative hyper-charges.
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(1) regarding "sloshing" as a (non-)technical term...

 

there are available visualizers, for finite potential wells' wave-functions in 1D...

if you choose appropriate parameters, then you can produce potential wells w/ three (3) discrete bound states

if you then choose your wave-function, to be a super-position of those three static stationary eigenstates (best by choosing coefficients from Weak-interaction mixing matrices, e.g. Cabibbo-Kobayashi-Maskawa)...

then you see, that the wave-function super-position states "sloshes" side-to-side, with its biggest peak bouncing back-and-forth from well-wall to well-wall

 

i'm suggesting, that the Higgs force-field is what binds mass-energy w/in the fabric of space-time... w/o the Higgs force-field, quanta would drift off the "brane" of space-time, out in to the hyper-dimensional "bulk" beyond...

the Higgs force-field is a 1D quantum well, whose "walls" are the "inner" and "outer" (hyper-)surfaces of the space-time fabric...

quanta embedded w/in the fabric of space-time occupy discrete bound states w/in the well...

and their finite energies, w/in the well, are their rest-mass energies...

 

e.g. an electron is the lowest-lying bound-state, for electrons, w/in the 1D Higgs potential "across" the fabric of space-time, through the thin "thickness" hyper-dimension "w"

muons are the first excited state of the same, and taons the second excited state

 

the Weak-force can be construed, as electro-magnetism, through the thin "thickness" hyper-dimension "w"...

when wave-functions interact intensely, so as to try to occupy the same place in space "xyz", then they start to "stack" through the thin "thickness" hyper-dimension "w"...

and their hyper-charges make them begin blasting each other, w/ hyper-high energy, hyper-dimension directed, photons = Weak bosons

 

when a neutrino emerges from Weak interactions, it exists in a super-position, of neutrino mass states [math]\nu_e = \alpha \nu_1 + \beta \nu_2 + \gamma \nu_3[/math]... the neutrino mass states would be the actual eigenstates of them in the Higgs potential...

But, known neutrinos emerge from Weak interactions, in the "electron" or "muon" or "taon" super-positions, of those eigenstates, w/ coefficients tabulated in the CKM mixing matrix...

those coefficients make the neutrinos "slosh" through the thin "thickness" hyper-dimension "w", bouncing back and forth from wall-to-wall of the 1D ("w") well of the Higgs potential

since, in their intensely energetic interaction, at "point blank range", through the "w" dimension, the neutrinos were blasted by 90GeV Weak bosons, so you'd expect, that conservation of momentum, applied to the hyper-dimension "w", would require conservation of hyper-directed-momentum...

so you'd expect the neutrinos to oscillate "out" and then "in" and then "out" etc. as they recoiled, thru the hyper-dimension, in conservation of hyper-momentum

that picture potentially explains "neutrino oscillations"...

in a Weak-force intensely intimate & energetic interaction, the neutrinos are basically "blasted back to the Higgs'-well-wall" and the "outer" or "inner" hyper-surface of space-time... after which they start "sloshing" side-to-hyper-dimensional-side, through "w", a little like a train car tipping from side-to-side in a rapidly running-away train on tracks

 

 

 

(2) oops on the Strong-Force

 

the Strong-Force affects the E/W force, and gluons carry E/W charge to-and-from quarks...

but the SF is not directly any kind of E/W force... instead, it is the force of "color confinement", interpreted as confining quarks into collections, of omni-directional spatial charge

 

(2A) Mesons

 

[math]\pi^+ = u + \bar{d}[/math]

 

the up-quark is a 2D "flat-land" particle, positively-electrically-charged in 2 standard-spatial dimensions "xy"...

that naturally defines an orthogonal 3rd normal direction, perpendicular to the "xy" plane, i.e. "z"

that naturally would define the up-quark's direction of spin

 

[math]\vec{S}_u = \pm \frac{\hbar}{2} \hat{z}[/math]

 

the anti-down anti-quark is a 1D "line-land" particle, positively-electrically-charged in 1 standard-spatial dimension "z"

which would naturally define the anti-down-anti-quark's direction of spin

 

[math]\vec{S}_{\bar{d}} = \pm \frac{\hbar}{2} \hat{z}[/math]

 

the SF between them both, is a "twisting torquing" force, somewhat similar to magnetic dipoles in magnetic fields...

since (most) mesons are spinless scalars, so evidently the SF makes quarks spin-anti-align

 

[math]V \propto \vec{S}_q \circ \vec{S}_{\bar{q}}[/math]

 

[math]-\vec{F} \propto \nabla V[/math]

 

the interaction-potential is minimized, when their spins point anti-parallel

 

 

(2B) baryons

 

a proton is composed of two 2D ups and a 1D down quark...

 

their axial charges net-sum to (qxqyqz) = (+++) if-and-only-if they all spin in mutually-orthogonal directions [math]\pm \hat{x} \pm \hat{y} \pm \hat{z}[/math]

 

u1 = (++0)

u2 = (+0+)

d = (-00)

------------

p = (+++)

 

so, the SF between a bunch of quarks (or between a bunch of antiquarks) is different, from the SF between opposite-matter-kinds of quarks

 

[math]V \propto \left( \vec{S}_{q_1} \circ \vec{S}_{q_2} \right)^2[/math]

 

[math]V_{p^+} \propto \left( \vec{S}_{u_1} \circ \vec{S}_{u_2} \right)^2+\left( \vec{S}_{u_1} \circ \vec{S}_{d} \right)^2+\left( \vec{S}_{d} \circ \vec{S}_{u_2} \right)^2[/math]

 

the interaction-potential is minimized, when their spins point parallel

 

 

(2C) distance term

 

presumably, the SF interaction also involves inter-particle distance; all now-known natural forces decrease w/ distance as [math]\propto d^{-2}[/math]


oops

 

"the interaction-potential is minimized, when their spins point parallel" [math]\longrightarrow[/math]

 

"the interaction-potential is minimized, when their spins point orthogonal"


requiring quarks to be mutually orthogonal w/in nucleons, cogently accounts for the current conundrum, of nucleon spin, not deriving directly, from constituent quarks:

 

http://en.wikipedia.org/wiki/Proton_spin_crisis

 

this hyper-space hypothesis, predicts that the three quarks' spins are all mutually orthogonal, effectively forming a LH or RH cartesian coordinate basis... so that they all form large angles, to their nucleon's net spin

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  • 2 weeks later...

"Charge Vector" model explains 3-Jet events in Lepton collisions

 

Nicholas Mee, Higgs Force:

 

a head-on collision of an electron and a positron results in their complete annihilation, and from the energy that is released a high-energy quark and a high-energy antiquark are produced... the quark and the antiquark carry colour charges, which means that the colour force operates between them. As they recede from each other, the energy contained in the colour interaction between them is converted into a shower of other quarks and antiquarks. All the quarks and antiquarks rapidly combine, so that their naked colour charges become hidden within colour-neutral particles, and these particles are the ones that are seen in the detector. The event appears in the detector as two narrow jets of particles emitted in opposite directions from the point of the electron–positron impact.
Occasionally, three jets of particles are produced... PETRA produced the first such three-jet event in 1979. The QCD analysis suggests that occasionally either the quark or the antiquark produced in the electron–positron impact emits a gluon just at the moment that it comes into existence. The gluon results in a third jet of particles emanating from the point of the electron– positron impact. By analysing the distribution of all the particles within a jet it is possible to distinguish between a jet that has formed from a quark and one that has formed from a gluon. It might not be possible to isolate a quark or a gluon, pick it up with tweezers and put it in a box, in the same way that an electron can be isolated and studied, but the production of individual quarks and gluons is effectively being seen in these jets.

 

Recall the charge-4-vectors q4 = ( qx qy qz | qw) of electrons & anti-electrons:

 

[math]\tilde{q}_{e^-} = \begin{bmatrix} -1 & -1 & -1 & | -1 \end{bmatrix}[/math]

[math]\tilde{q}_{e^+} = \begin{bmatrix} +1 & +1 & +1 & | +1 \end{bmatrix}[/math]

 

In high-energy head-on collisions, the electrons & anti-electrons could conceivably "break up", a little like a head-on collision, between fighter-jets, at an airshow...

 

the electron is (presumably) spin-backwards (i.e. left-handed) and the anti-electron is (presumably) spin-forwards (i.e. right-handed)...

without loss of generality, the collision occurs in the [math]\hat{x}[/math] direction...

 

then, the internal charge components of the colliding pair of particles, could conceivably combine in directional-pairs, producing a pair of partial-charged quarks, and a gluon (along the collision axis):

 

[math]\longrightarrow[/math]

[math]\begin{bmatrix} \pm & 0 & 0 & | 0 \end{bmatrix} \times \hat{S}_{\hat{x}}[/math]

[math]\begin{bmatrix} 0 & \pm & 0 & | 0 \end{bmatrix}[/math]

[math]\begin{bmatrix} 0 & 0 & \pm & | 0 \end{bmatrix}[/math]

[math]=[/math]

[math]\tilde{g}_{xx}[/math] (spin 1)

[math]\left( d \bar{d} \right) = \pi^0[/math] (spin 0, in [math]y \bar{y} \leftrightarrow[/math] "green-antigreen")

[math]\left( d \bar{d} \right) = \pi^0[/math] (spin 0, in [math]z \bar{z} \leftrightarrow[/math] "blue-antiblue")

 

Conversely, two-jet collisions could conceivably result, from fragmentation, into a pair of particles, e.g.:

 

[math]\longrightarrow[/math]

[math]\begin{bmatrix} \pm & \pm & 0 & | -1 \end{bmatrix}[/math]

[math]\begin{bmatrix} 0 & 0 & \pm & | +1 \end{bmatrix}[/math]

[math]=[/math]

[math]\left( u \bar{u} \right) = \pi^0[/math] (spin 0, in [math]z \bar{z} \leftrightarrow[/math] "blue-antiblue")

[math]\left( d \bar{d} \right) = \pi^0[/math] (spin 0, in [math]z \bar{z} \leftrightarrow[/math] "blue-antiblue")

 

 

 

internal structure of Leptons could unify EW <---> S forces

 

The Classical Electron Radius ~1fm, essentially the same size as normal nucleons. And, in net, the charge-4-vector of a proton q4 = ( +1 +1 +1 | -3) is (spatially-speaking) the same as that of an (anti-)electron, q4 = ( +1 +1 +1 | +1). So, if the Strong force binds the separate charged sub-components (quarks) of nucleons together; then perhaps the Strong force operates inside electrons, too, binding their three separate standard-spatial charge-unit-vectors together...

 

normally, the Strong force-carrier gluons are hidden inside the whole electron, like fuel is hidden inside fighter-jets... only in head-on collisions, does all the internal jet-fuel spray far and wide, becoming apparent to outside observers. In some semi-Classical sense, electrons and protons are the same fempto-meter size; and both are held together internally, by Strong-force carrying gluons... which glue is allot less stressed, inside a single electron, as compared to the combination of quarks comprising protons (note the difference in "w" directed hyper-charge).

 

 

 

spin of quarks could account for Strong-force field "gluon gob"

 

"Bare" quarks have been observed, e.g. ephemeral top quarks, which decay before generating gluons. So, the exact instant that a quark is created in a collider, the quark is created "bare", "born" without any surrounding Strong-force field... indeed, gluons could only then begin to emanate away, at (up to) the speed-of-light... so that some time would be required, for the quark's gluon field to "inflate" around the particle...

 

Now, quarks have (spatial) spin, which, due to quantum uncertainty, always has some non-zero probability, of pointing in directions orthogonal (note -- not anti-parallel, though) to the spin state, because the overlaps < Sx | Sy,z > are non-zero...

 

and, gluons generate rotations, of quarks' spin axes, e.g.

 

[math]d_{red} = d_x = \begin{bmatrix} -1 & 0 & 0 & | -1 \end{bmatrix}[/math]

[math]\longrightarrow \begin{bmatrix} 0 & -1 & 0 & | -1 \end{bmatrix} + \begin{bmatrix} -1 & +1 & 0 & | 0 \end{bmatrix}[/math]

[math] = d_y + \tilde{g}_{x\bar{y}}[/math]

[math] = \left( d_{green} \right) + \tilde{g}_{red-antigreen}[/math]

 

So, since the spin of quarks is constantly rotating them around; and if quark rotation requires gluon emissions; then the spin of quarks would immediately begin emanating a surrounding "cloud" of gluons, as the quark spun itself, into a superposition of spin states.

 

 

 

"bare" electrons briefly resemble neutrinos ?

 

If quarks are "born" "bare", being low-mass (few MeV), lacking a surrounding gluon field... which field, when generated, dramatically increases the mass of the quark (70-350 MeV) in mesons & baryons...

 

then perhaps electrons are "born bare", being low-mass (few eV), lacking a surrounding photon field... which field, when emanated, increases the mass of the electron (half MeV) ?

 

 

 

 

all energy / momentum is EM ?

 

In the presence of (external) EM fields, the generalized Einstein relation is:

 

[math]\left( E - q \Phi \right)^2 - \left( c \vec{p} - q \vec{A} \right)^2 = \left( m c^2\right)^2[/math]

 

Thus, at rest, an electron (say) has an energy equal to

 

[math]E = mc^2 + q \Phi[/math]

 

where q = -e for an electron. So, external scalar potential (Voltage) fields affect the mass-energy of electrons... such suggests, that the rest-mass-energy of electrons could come, from the internal scalar potential field of the electron:

 

[math]m c^2 \equiv q_e \Phi_e \approx \frac{e^2}{4 \pi \epsilon_0 R_e}[/math]

 

assuming that the electron is a spherical ball of uniform charge density. The above equation is that, of the Classical Electron Radius ~1fm. So, if electrons where small balls, about the same size as normal nucleons... then the Voltage their own charge distribution generated, withinside themselves, would give their charge, an electron-rest-mass worth of mass-energy.

 

Such suggests, that the effective rest-mass-energy of (say) electrons, is the simple sum:

 

[math]E = q \left( \Phi_{internal} + \Phi_{external} \right)[/math]

 

Similar logic leads to (in the low-energy limit):

 

[math]c^2 \vec{p} = q \vec{v} \left( \Phi_{internal} + \Phi_{external} \right)[/math]

 

since [math]c^2 \vec{A} \equiv \vec{v} \Phi[/math] for particles. If some force "glued" electrons tightly together, into small balls of nucleon-sized charge... then all energy-momentum, of charged particles, could be construed, and attributed, to external/internal EM forces / interactions (and self-interactions). Indeed, in the absence of external fields, the internal fields of (say) electrons would appear to increase, by the appropriate gamma factor, correctly accounting for the equal increase in the apparent mass, of moving electrons:

 

[math]\Phi_{int} \rightarrow \gamma \Phi_{int}[/math]

[math]E \rightarrow \gamma E[/math]

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Table of Fundamental Fermions

charge (col) vs. Hyper-charge (row)

 

[math]\bordermatrix{ ~ & -1 & -\frac{2}{3} & -\frac{1}{3} & 0 & +\frac{1}{3} & +\frac{2}{3} & +1 \cr

+1 & ~ & \bar{u} & ~ & \bar{\nu} & \bar{d} & ~ & \bar{e} \cr

-1 & e & ~ & d & \nu & ~ & u & ~ \cr}[/math]

 

for Fermions spinning in [math]\langle +\hat{z} \rangle[/math], Fermions' charge-4-vectors are:

 

[math]\bordermatrix{ ~ & \hat{x} & \hat{y} & \langle \hat{z} \rangle & \hat{w} \cr

e & -1 & -1 & \langle -1 \rangle & -1 \cr

d & 0 & 0 & \langle -1 \rangle & -1 \cr

\nu & 0 & 0 & \langle 0 \rangle & -1 \cr

u & +1 & +1 & \langle 0 \rangle & -1 \cr}[/math]

 

et vice versa for anti-Fermions

 

 

 

Selection Rules for Fundamental Fermions:

 

charge of spin axis [math]\left( \hat{z} \right)[/math] cannot oppose hyper-charge of hyper-spin axis [math]\left( \hat{w} \right)[/math]

charges of non-spin axes [math]\left( \hat{x} \hat{y} \right)[/math] cannot oppose charge of spin axis [math]\left( \hat{z} \right)[/math]

charges of non-spin axes [math]\left( \hat{x} \hat{y} \right)[/math] cannot differ (i.e. are indistinguishable, i.e. only the spin axis is "special")

charges of non-spin axes [math]\left( \hat{x} \hat{y} \right)[/math] must be less like hyper-charge of hyper-spin axis [math]\left( \hat{w} \right)[/math], than the charge of spin axis [math]\left( \hat{z} \right)[/math]

 

For Fermions:

 

[math]q_{x,y} \ge q_z \ge q_w[/math]

 

et vice versa for anti-Fermions

 

 

 

Higgs Boson could conceivably convert Fermions from-and-to anti-Fermions (??)

 

Fermions have hyper-spin Sw = -1/2, and anti-Fermions have hyper-spin Sw = +1/2

Higgs Boson has spatial spin Sxyz = 0

Higgs Boson may have hyper-spatial spin Sw = 1

Higgs Boson may hyper-spin-flip Fermions from-and-to anti-Fermions ??

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