The Particulate Nature of Subatomic Matter: an n-Tiered model
Aran David Stubbs of the Inframatter Research Center
Summary
This focuses on the particle side of the wave/particle duality, since Schrödinger has done a satisfactory job of covering the wave side. It treats the “fundamental” particles (leptons, photons, and quarks) as structures and examines their content: an intermediate structure described as proto-matter, each of which is comprised of additional structures described as either mezzo-matter or infra-matter, with the mezzo-matter a structure comprised of infra-matter. It includes an explanation of color and charge as special instances of angular momentum at the mezzo-matter layer. It describes the differences among the flavors of quarks in terms of the orbital dynamics involved for the mezzo-matter within their various proto-matter structures, with up and down quarks involving just s & p orbits of mezzo-matter, strange and charm adding d orbits, bottom (or beauty) adding f orbits, top (or truth) adding g orbits, and postulates higher states with additional orbits. This model has an alternate set of assumptions that differ from the standard model, particularly those involving bound tachyons. See also our article on gravity.
Matter
While much has been made of the wave nature of matter, the particulate nature is also important. Between them Planck and Einstein demonstrated the particulate nature of the photon. The particulate nature of atoms was never seriously questioned. The constituents of atoms also have particle properties: mass, velocity, momentum (both linear and angular), and a finite volume.
The simplest of the constituents of atoms are the
electrons. These have rest mass of about
.
Their velocities vary from a tiny fraction of light to very near that of light,
depending on local conditions. From Compton’s work, they have an effective
radius of about 386 femtometers. Both the rest mass-energy and the effective radius
have been measured to many significant figures. Atoms also contain nuclei.
These have been analyzed more thoroughly in our article on nuclear
structure.
In addition to the atoms, matter consists of various sub-atomic particles. These include the photon, the neutrinos, other leptons, various mesons, and baryons. The quark theory adequately explains the structures of the mesons and the baryons. Except for minor points of contention it will be assumed to be essentially correct. The quark theory treats quarks as fundamental building blocks and does not explain why 12 of them are required.
Proto-Matter
An alternative has layers of structure: each of the “fundamental” particles being structures containing proto-matter trapping pairs of gravitons. The gravitons are trapped when the length of the proto-matter from the gravitons perspective exceeds the circumference of the orbit. Except at low velocities (below 7c) a good approximation of the length from a tachyons perspective of a tardyon near it is vL0/c, where L0 is the rest length.
From our analysis of the neutrino
and the photon, each of which contain a pair of gravitons and some
proto-photons, it was found the angular momentum of the proto-photon in an ns
orbit was n small units of angular momentum, where 1 small unit is 
.
The electron has 6 immediate constituents, each with
particulate properties: a charged proto-lepton, 3 proto-photons, and 2 gravitons.
The proto-lepton has 3 small units of angular momentum. Each of the electrons
constituents is moving briskly, with the proto-photons moving at the speed of
light, the proto-lepton 12/13 of the speed of light, and the gravitons much
faster than light. The proto-lepton has positive real rest mass, the
proto-photons have essentially zero rest mass, and the gravitons (which are
low-energy tachyons) have imaginary negative rest mass. The proto-matter each
has a radius of not more than 
(see
gravitons paper above), while the radius of the graviton is small (circa
diameter).
From our perspective, only the proto-lepton is apparent, since its charge is
the most noticeable property of the electron as a whole. It has a rest energy
of 5/53 that of the electron overall, about 48.2 KeV.
Similarly, the photon has 6 constituents: 4 proto-photons and 2 gravitons. Again, the proto-photons are moving at the speed of light and the gravitons faster. Each of the constituents has a diameter as above. Since energy varies directly as n, a form for finding the energy per equivalent piece was needed. This gives P*, the energy equivalent piece count. For the electron and the photon, P* is 12. EK/P* gives the 1s kinetic energy of a piece (in this context, a bit of proto-matter). If only s orbits are involved, P* is always an integer. See below for an analysis of P* for non-s orbits.
It was possible to find the constituents of the photon and from there the other sub-atomic particles, by taking a force/energy balance on the constituents. For the photon, the proto-photons have essentially zero rest mass and the gravitons have imaginary rest mass, so all the effective mass is kinetic energy. A simple balance determined the gravitational attraction just balances the centripetal force outward for each proto-photon. In theory a photon-like structure can be built with any number of proto-photons, although only structures with 2 gravitons look viable. For constituents with a non-zero rest mass, a color or charge is necessary to bring a balance. Then the gravitational attraction is countered by the sum of the centripetal effect, a color on color repulsion, and a charge on charge repulsion. In most cases the repulsion is autologous: based on a single particle in orbit with charge or color effects pulling outwards against gravitational compression. In the case of charge, these effects are the result of the proto-photons. For color a similar proto-matter entity, the proto-gluon, causes the pull outward. Note – this is a pull, by the proto-bosons, not a push.
Since the energy and force equations are continuous, we need to look to the
angular momentum to find a quantization. It was possible to generalize a
formula to calculate the velocity needed to produce m units of extra angular
momentum for a proto-lepton (or other proto-matter with rest energy) in a ns
orbit where 
,
and 
,
of 
.
This often has 
as
rationals, rather than integers. The photon has zero angular momentum (with 2
wavicles each in the 1s, 2s, and 3s sub-shells), but the neutrino does have
angular momentum. Assuming the simplest case, the Electron-Neutrino has 4
wavicles: 2 gravitons in the 1s orbitals and a proto-photon in a 2s & a 3s orbital.
From the Planck equations, with a 6 piece photon, as above, the 1s pieces have
1/12th the energy each. This gives an angular momentum of 1 unit of This
angular momentum is only the structural portion, the proto-lepton has angular
momentum as well (from its constituent’s orbits), but it is a constant for all
the negatively charged leptons. The sum of the two is typically given as 6
small units, so the proto-lepton contributes either 5 (if its angular momentum
adds to the structural amount), or 7 if they are aligned oppositely (which
seems likelier – and will be used hereafter for calculations).
A solution assuming the muon differs from the electron solely by the orbits the
proto-matter occupies implies a half-life typical of strong interactions:
.
The actual half-life (
)
indicates a weak decay mode, involving changes in the proto-matter itself. While
a proto-lepton is present in each, they are not the same thing.
It is possible to calculate various balance points, where the proto-lepton has m extra units of angular momentum. The obvious balance point for the muon has the proto-lepton in a 3s orbit moving 24/25c (so 9.36 MeV “rest” energy, giving a fourth unit of angular momentum) paired to a 3s proto-photon. Alternately and more likely, the muon could have its 3s proto-lepton travelling 15/17c (with 18.0 MeV “rest” energy), giving 2 extra units of angular momentum paired to a 4s proto-photon (making -6 units total for the muon). This likelier solution is used in calculations below, although both were examined. Similarly the tauon could have its proto-lepton in a 4s orbit moving 40/41c (hence 132.17 MeV “rest” energy) for a fifth unit of angular momentum , but many other solutions are possible. Overall, only wavicles where the forces balance and angular momentum is conserved and quantized would be observed.
In order to generate the required angular momentum, the charged proto-lepton in the electron would have a rest energy of 48.207445 KeV (in a 2s orbit balanced by a proto-photon), which is 5/53 the total energy of the electron. This can be balanced by an electron-neutrino with a 2s proto-photon partly offsetting the angular momentum of a 3s proto-photon (plus, as always, a pair of 1s gravitons). There are many possible neutrino states that could match the Muon and Tauon. See also the Neutrino for an analysis of the possible states that wavicle can enter.
In all 3 cases of charged leptons, besides the proto-photon paired to the proto-lepton, there are also a pair of proto-photons in the other available s orbital which have 0 net angular momentum. Additional charged leptons are possible, some with 3 or more units of structural angular momentum.
Mezzo-Matter and Infra-Matter
As the proto-lepton has “rest” energy, it follows that it is a structure comprised of moving pieces. These pieces will be called Mezzo-matter if they have additional structure or Infra-matter if they are final. All tachyons (including the graviton) are final, that is they have no additional structure. Some of the constituents contribute to the charge of a proto-matter structure, while others contribute to the “color” in the nuclear sense. Additional pieces have energy other than the quantizations derived for charge and color. The infra-matter adds the trivial amount of energy present in the proto-photons and proto-gluons, and the substantial energy in the various kinds of mezzo-matter. The amount of energy depends on scale, with the relatively large proto-photon and proton-gluon (c 10-36 m) having very little (< 10-20 eV), and the relatively small mezzo matter (c 10-60 to 10-64 m) having proportionately more.
2 obvious solutions for distributing the energy of the proto-matter between the charge portions and non-charge portions were examined: there can be color (or chroma) bits and/or there may be bits that add neither charge nor color. Starting from the simpler assumption, the color or chroma bits may either cause net color or add to white. Since 6 states have been identified with the colors, the easiest mapping treats the chroma bits as occupying p orbitals in quarks. The charge bits are in s orbitals with their angular momentum perpendicular to whatever angular momentum comes from the color. The only case where only 2 or 4 orbits are occupied by color tachyons occur when there is a pair of color tardyons above them, typically in the 4g orbits (the next solution divisible by 6). No stable cases were found for 1 or 5 tachyons, as the angular momentum varies between maximum radius and minimum with no reinforcement. If when a p orbital is occupied, there are always 3 tachyons among the 6 orbits, 2 stable solutions can be produced: their angular momentum can be distributed 60 degrees apart or 120 degrees apart. Cases where the 3 are clumped produce reinforcement, where the outer pair adds to a vector that complements the vector of angular momentum of the central vector – hitting a combined maximum where the central vector is minimal and a minimum where the central vector is maximum, which produces a constant angular momentum. Cases where they are 120 degrees apart have the angular momentum add to zero, or white. Higher l orbits are also possible, giving rise to strangeness, charm, etc. Since most of these don’t have reinforcement (which is peculiar to the p and similar orbits), cases with net amounts appear unlikely. The g and j orbits can also cause reinforcement, which will be termed “hue”. The 18 g vectors can be viewed as 3 sets of 6 each with the content of a set being 60 degrees apart, and each set 20 degrees away from each of the other 2. While 7 colors arise from the p orbits (including white) 343 hues arise from the g orbits, and over 16000 from j.
Additionally, the infra-matter must have some energy to be bound together to form proto-matter. That means that neither the proto-photons nor the photons themselves are luxons: they have rest energy, making them tardyons. They are very quick moving tardyons, but still travel somewhat less than the speed of light. Measuring the speed of extremely low energy photons would give a ceiling on the rest energy of the proto-photon. Alternately, measuring the exact moment a glitch occurs in the rhythm of Pulsars in widely different frequencies could be used. From the existing data on photons, the rest energy should be less than 10-20 eV. This looks to be a luxon/tachyon pair in the 1s orbits where the tachyon has a tiny bit of energy at the infra-matter radius, producing a bit of net angular momentum. Like the proto-gluon, the proto-photon has trivial angular momentum in the direction of the relevant vector (here along the z axis), causing it to weakly cling to structures with angular momentum in the opposite direction. The angular momentum of a tachyon is large compared to the angular momentum of a luxon in a similar orbit. Based on the energy and velocity of each, the angular momentum of the luxon is trivial.
It should be noted that in addition to the standard orbits a 0s case is possible, where a small structure is embedded at the center of a large structure – such as a stationary electron containing a nucleus. These are at best transitory, since any contact with the larger structure from outside is likely to disturb it. In this case s may not be the right name, since the s orbits come in pairs (1 with positive angular momentum in the charge or z direction, and 1 with negative), and this is a solitary situation (with 0 angular momentum).
As charge on the electron is 3 times that on a down
quark, a solution with the proto-lepton having 3 tachyon constituents, adding
to -7 small units of angular momentum is plausible. As the amount of angular
momentum for an ns infra-matter tachyon is independent of n (being linear
dependent only on the radius of the orbit), this can be accomplished by
addition or subtraction. The easiest addition has a 1s pair, a 2s pair, and a
3s pair each comprised of a tachyon and a tardyon. Ignoring the structure of
the charge bit, this gives an average 1s energy equivalent for the charge bit
of 4.0172871(4) KeV. Some of this can be rest energy within the tardyon charge
bit; the rest is divided up evenly between the kinetic energy of the 2 types of
bits. From the reported angular momentum, an exact velocity can also be
calculated: with 
,
L=7* ħ/36c, and trivial rest energy the velocity is 
for
1s. Velocity is proportionately slower for the higher tachyon orbits (
).
This gives a minimum diameter of 
for
the charge luxon bits of Inframatter, and a rest energy of 
for
the charge tachyon bits.
A more complex analysis is possible treating the non-tachyonic charge bits as structures. The charge structure resembles the proto-photon with a 1s sub-shell containing an infra-tachyon and an infra-photon. The orbital diameter is dependent on the frequency of the binding tachyon: in the infra-photon case this is a graviton, in the charge structure case it is a charge tachyon. This implies frequency locking, where the frequency of the infra-photon either matches or is a rational fraction of the frequency of the binding tachyon. In this context binding means the tachyon in an orbit tangent to the infra-photon at a single point, in contrast to the infra-tachyon which is tangent to the infra-photon throughout its orbit. Frequency locking occurs where the infra-photon is adjacent to the binding tachyon just as the binding tachyon passes the structure it is part of. In the simplest case, the infra-photon and the binding tachyon have a 1:1 ratio of their frequencies, passing at the point of tangency each orbit. Since the tachyons nearly have a constant frequency, the size of the infra-photons orbit remains nearly constant. When the infra-photon is part of an intermediate structure (a charge particle for instant), the frequency locking becomes tied to the velocity of the larger structure, whose orbital radius is the fraction of the corresponding infra-matter structure equivalent to its velocity as a fraction of light. That is, a charge particle with a velocity .7c occupies an orbit within the proto-matter .7 times the radius of the infra-photon within the proto-photon.
As the Muon has so much more energy than an electron, a structure with 6 chroma bits in the 1p orbits makes sense: with 3 being tachyons and 3 luxons, where the color adds to white (Pcolor*~4.746). That leaves the charge bits as 1s, 2s, 3s, 4s, and 5s orbits, or a Pcharge* of 20. Using these P*s as exact, gives an E/Pcolor* of 3.772 MeV for a 1s orbit equivalent. A more refined analysis showed a best fit if the rest energy of the color structure was about 5.86 Mev, with the other .107 Mev evenly split between the Kinetic energy of the 2 types. Without an exact angular momentum, the velocity, minimum diameter, and rest energy can’t be calculated. A rough estimate gives a velocity about 30 times that of the charge tachyon under equivalent conditions.
|
The eccentricity of the various orbits was earlier calculated for electrons, but applies here also: |
|
At this point a review of the possible geometries is required. The orbits other than s are perpendicular to the s orbits and have a minimum diameter of the relevant s orbits diameter. This puts the center of the ellipse at the center of the overall structure, rather than a vertex at the center of mass. The resultant ellipsoid can bind to other structures most strongly where the 2 orbits cross, but can also bind anywhere else on the s or p orbit. With single ellipsoid solutions, all the proto-matter is in orbits around a common center. Solutions are also possible with 2 or more ellipsoids touching. Only neutral structures can have exactly 2 ellipsoids. These can be a quark and an anti-quark, a diquark and a quark, or a pair of diquarks. Single ellipsoid structures are smaller than multiple-ellipsoid for a given energy. No single ellipsoid solutions were examined for the proton (as they would be < 1.5 fm in diameter), but both single ellipsoid and multiple ellipsoid solutions were examined for the mesons.
For charged structures, the charge related proto-photons orbit the clump of ellipsoids, forming a photon-like shell. This has the absolute value of 3z proto-photons for a structure with charge of z. If structures with net color larger than a single ellipsoid were to form, there would be a gluon-like structure with multiple proto-gluons orbiting (proportionate to the net color present). As is, the proto-gluon orbits at the surface of the individual ellipsoids with net color (either a quark or a diquark). As with neutral structures, charged structures can be comprised of 1, 3, 4, or more total spheres (but not 2). Starting with the 5 ellipsoid structures, it is necessary to examine the arrangement of the ellipsoids in 3 dimensions (with a tetrahedron of the 4 inner ellipsoids possible). Charged structures with mixed charge types can also have proto-photons at the surface of individual ellipsoids, besides the overall photon-like shell. A deuteron, for instance, with a z=1 has 3 proto-photons orbiting the 4 ellipsoid clump, but 2 of the individual ellipsoids also have a proto-photon circling in their basic structure (1 of the diquarks and the down quark). In this context proto-photon count appears to be conserved, with the total number of proto-photons present in a structure equal to the count if the structure were broken into constituent ellipsoids. In the deuteron case, each diquark would have 1 when independent as would the down quark, while the up quark would have 2. Then there are 5 proto-photons total when taken separately; and 5 when combined.
Like the proto-photon, the proto-gluon has only trivial rest energy (about 12.4 times as much as the proto-photon), and trivial angular momentum. While the proto-photon has angular momentum in the z direction (that is aligned to charge), the proto-gluon has its angular momentum in the xy plain in one of the 6 color directions. To achieve this, the proto-gluon has infra-photons in 1s, 2s, 3s, 4s, and 1p orbits, with 7 tachyons and 7 luxons. The 3 tachyons in the p orbits have their angular momentum distributed 60 degrees apart, so they have net angular momentum in the central direction of a constant (though small) amount.
The quarks can have their z angular momentum aligned or opposite. In the case of the diquark, the 2 proto-quarks are normally both in 2s orbits, with their structural angular momentum opposite, but in some cases both have angular momentum in the same direction, with one in the 2s orbit and the other in the 3s. The charge related angular momentum remains aligned based on charge. For proto-quarks this is L=-7/3 for the down, strange, and beauty (or bottom), and +14/3 for the up, charm, and top (or truth). Where a quark is matched to its corresponding anti-quark, the charge related angular momentum always cancels out, but the structure related need not. If the quark is bound to an anti-quark of another type, it is often difficult to locate the matching solution with L=0 (although so far not impossible). It often required assuming at least 1 quark contained its proto-quark in a higher-energy orbit: 3s or above.
For simplicity it was assumed the structures with the least absolute angular momentum were best. This usually means high rest-energy proto-matter in low s orbits, except the gravitons have to be 1s – since they are tachyons and have huge angular momentum even there. Similarly, it was assumed the solution with the smallest overall radius for an energy/angular momentum combination was best.
Baryons have 3 plausible structures under this theory: a trio of monoquarks, a monoquark plus a diquark, and a single tri-quark. Multiple attempts were made to try to force various baryons into the 3 monoquark model, and none fit (not even the delta). Some less well studied baryons may eventually be found to match this case. The negrons (or dark matter particles) look like good matches to the single sphere with 3 proto-quark case. This leaves the diquark (a sphere with 2 proto-quarks sharing a common center) plus a monoquark as the most likely case for the baryons.
The content of the nucleus (described in detail elsewhere) includes monoquarks and diquarks. Each independent monoquark consists of a proto-quark, 4 gravitons (2 in s orbits, 2 in p), plus 1 or 2 proto-photons (depending on charge), and a proto-gluon (since the quark has net color). Each independent diquark is a structure of 2 proto-quarks, 4 gravitons, plus 0 to 4 proto-photons, and a proto-gluon. When 2 or more quarks and/or diquarks are congealed into a nucleus, the proto-photons may be promoted to surround the whole structure. If the structure had net color, the proto-gluons would also be promoted. So the nucleus as a whole also has 1 or more photon-like structures consisting of proto-photons and gravitons. The outermost photon-like structure has 3z proto-photons and at least 2 gravitons, where z is the overall charge on the nucleus. The other proto-photons beyond 3z remain with their quarks and diquarks (especially those interior to the nucleus). Again each of the proto-photons, proto-quarks, proto-gluons, and the gravitons have effective mass, velocity, momentum, and occupy a small volume. Like the atom, the proton is mostly empty space. Unlike the atom – which has a dense nucleus – the proton resembles 2 soap bubbles clinging to each other embedded in a larger soap bubble.
Proto-quarks and proto-diquarks have net color: presumably 2 average units (as in the double blue below), in the 1p set of mezzo orbits. Each of these have a slew of s charge bits, with all the s orbits filled before the corresponding p, and 1 more pair (1p with 4s for instance). In this sense, corresponding is a 3:1 ratio, so the 3s orbit binds the 1p, and the 6s binds the 2p. Similar ratios occur for the higher l orbits, so the 10s binds the 2d. What form this binding takes is unclear. Reinforcement occurs only when the vectors of angular momentum are separated by 60 degrees, where the outer pair has a vector sum equal to the central vector on average. The outer pair has minimum L where the central vector is at its maximum, while the outer pair has maximum L where the central vector is minimal. This gives a constant L for the proto-quark as a whole. When l≠3m+1, this mutual reinforcement does not occur. 3 possible color schemes arise when l=1. Nuclei with a color scheme of red and anti-red would not fuse with either of the other color schemes, nor would blue/anti-blue fuse with green/anti-green. When l=4, as in the truth quark, 343 “colors” are possible (7 choices for each of the 3 sets, independently: no vector, or a vector θ+60m°, where θ which defines a “set” is 0, -20˚ or +20˚, and m is any integer).
Several possible structures can be envisioned for the Proton. The best plausible solution encountered for the proton has an 18 MeV proto-up containing 6 1p color bits, plus 8 charge bits among the 1s through 4s orbits. The matching 36 MeV proto-down has 6 2p and 6 1p color bits, and 14 charge bits among the 1s through 7s orbits. The diquark has 4 gravitons, a proto-up, a proto-down, and a proto-gluon. The up quark has 4 gravitons (a 1s pair and a 1p pair), a proto-up, and a proto-gluon. The proto-gluon has infra-photons in the 1s through 4s orbits, and 1p orbits, with the 1p in the 60 degree configuration giving net color. See the table of structures for more detail.
Radius varies inversely with the amount of Kinetic energy with small changes to the structure of the proto-matter. When there is a significant change to the ratio of up rest energy to diquark rest energy, the balance point often shifts away from the minimum diameter, here at 1.681 fm. Similar solutions can be generated for the Neutron (also with an up/down diquark), and the Deltas (with an up/up in 2 cases (++ and +), or a down/down diquark in the other 2 (0 and -)). It is likely similar solutions can be generated for the other light baryons.
A plausible proto-strange (1p, 2p, and 3p color bits, 2d with d-mezzo bits, and 1s through 11s charge bits: 50 bits total, the Tin case) would have a rest energy of about 270 MeV. Similarly the proto-charm with 1p through 5p color bits, 2d and 3d d-mezzo bits, and 1s through 16s charge bits would be 520 MeV (the Lead case). A heavier charm with the first f (3f) would be around 2100 MeV. Beauty has either 3.6 or 10.4 GeV, Truth 17 or 38 GeV, etc.. Solutions with multiple ellipsoids require similar size pieces to bind (a ratio of diameters for BCC types less than 2.414214:1). KE is inversely proportionate to diameter, and low L solutions occur when KE is similar in size to rest energy.
Without a reported energy, the best clue to the
lowest energy Negron is the angular momentum. With a structure containing 2
gravitons in 1s orbits, 2 proto-downs in 2s orbits, and a proto-up in a 3s
orbit, L=6 small units (spin = ½) means m=3 (where, as above, 
).
Then a=12, b=15, V (for the proto-up) is 12/15th c, meaning the KE
of the proto-up is 2/3rd its “rest” energy of 18 MeV. With a P* of
9, the overall KE is 3 times the 3s KE, so 36 MeV. The combined energy of this
Negron is twice the “rest” energy of the proto-down plus 3 times the “rest”
energy of the proto-up or 126 MeV (assuming all the current versions of the
various proto-matter structures). The lowest energy gamma it could be expected
to absorb is around 4 MeV. As it is by definition stable, and is unaffected by
color or charge, it will be a little hard to spot. The expected concentration
ρ is f(1/T) (that is, concentration is inversely related to local
Temperature), which is equivalent to the ideal gas law.
As a first approximation, all the proto-matter is equidistant from the center of the structure, but looking more closely the structure looks more like an onion skin. There are several thin layers in contact. The innermost layer is the graviton pair. For spherical cases, these are always in the 1s orbits. This is adjacent to the next layer, which is sometimes the only other layer. When there are 3 or more layers the intermediate layer is pulled inward by the gravitons, and outward by the outer layer. Layer is a transient condition here: the proto-photons are adjacent to the gravitons except when they are passing the proto-electrons. This passing to the outside is the cause of the tugging that balances the inward tug of the gravitons.
At the relevant infra-matter scale (
),
a 1s Graviton would have 
(assuming the loosest conditions for
frequency matching), the color bit has 
,
the charge bit has 
,
and the infra-photon would have about 
.
The majority opinion indicates the graviton never gets to that small of orbit,
bottoming out above 
or
v ~7.071c. The exact point at which a graviton is able to escape the orbiting
proto-matter will need to be determined experimentally.
Force Balances
Thus far the solution space has been under specified. An input of total energy was used to find solutions for the various known particles. In nature energy is a resultant, rather than an input. The actual solution is dependent on the force balance, as well as the energy of the infra-matter and the total angular momentum.
A force balance on the proto-electron can be done using a variety of assumptions, many of which were tried. The best fit assumed the pull on the proto-electron by the proto-photons is proportional to the energy of the proto-photons, and the relative likelihood of the proto-photon passing the proto-electron in their respective orbits. With the proto-electron travelling 12/13 c and the proto-photon travelling effectively c, the proto-photon completes 13 circuits in the time the proto-electron completes 12. The 2 anti-parallel proto-photons pass the proto-electron 25 times in this interval, while the parallel proto-photon passes the proto-electron once. This produced a diameter for the proto-electron .8586 times that of the proto-photon or about 4.006*10-36 m.
From the work on quantizing gravity, a force balance
was found where the rest energy of the proto-matter is about zero. When 
.
That is, as the rest energy approaches zero, the gravitational force
approximates the centripetal effect which is always twice the Kinetic energy
over the radius. This solution covers the photon and neutrinos. Any
structures with significant non zero proto-matter rest energy requires a more
complex balance. In general,
.
EK1 is the Kinetic energy of the graviton, EK2 is the Kinetic
energy of the particle it is attracting, and E0 the relevant particle’s
rest energy. Since the graviton follows a form of the Planck equation, 
or
.
Rearranging, 
.
d
(the distance between the centers of the 2 wavicles) varies with velocity
within the proto-matter structure: d=VLp/c√12. For
proto-photons (where V is about c), the residue is about
. This residue
may also be from the charge, the color, or the structure having contact with
another structure. In many cases, all 3 effects are present – which makes
calculation somewhat difficult. The overall equation may result in a GUT, with additional work: solving the attraction for the other 3 tachyons in
parallel to that of the graviton, where d is much less.
Another loose end: the rest energy of the graviton
and its corresponding base frequency. A simplifying assumption would have the
graviton tugging the Inframatter every orbit, so the frequency of each would
match. This leads to an Lv of the diameter of the overall
structure, where we need the circumference. Instead, the graviton can have a
period that is an integer fraction of the Inframatter luxon (1/4 for example:
so the graviton tugs the proto-matter every fourth time the graviton orbits). Since
the proto-matter also contains tachyons, the graviton is repulsed continuously.
The s Inframatter luxons have orbits 
in
circumference, or about 
.
At c, this gives a time of 
seconds
per cycle, or equivalently a frequency of 
cycles
per second. From this frequency, the graviton would have a rest energy of 
or
3/7 that of the charge tachyons. Taking Ž (the letter ‘thorn’)
as the ratio of frequencies between the luxon and the graviton, the rest energy
is Ž times this energy. Within the electron, this means the gravitons are
moving at Ž *
.
Ž is assumed to be a small integer slightly larger than pi, 4 perhaps, but may
be a simple rational (7/2, 10/3, etc.). As the frequency of the graviton
slowly rises with energy: 
,
where energy varies inversely with velocity: 
(with
the same error term), the orbital size of the Inframatter bits would shrink to
match the increased frequency. When the graviton is down to 71c (energy about 
*Ž),
the difference is 0.01% with the proto-photons infra-matter orbits shrinking to
a radius of 
.
At very slow speeds (slow for tachyons, that is), the shrinkage becomes
significant.
From the perspective of the tachyon, the neighboring
tardyon or luxon occupies an angle θ which is nearly constant for any
radius. This is equivalent to saying
.
(Where lambda sub O is the orbital wavelength or n times lambda – the real
wavelength). As above, V is not quite proportionate to r, but the error at the
relevant velocities is small. Similarly, from the perspective of the tardyon
or luxon, the tachyon fills an angle φ, also nearly constant with changing
radius. These angles are a portion of the circumference of the orbit. To trap
a tachyon, θ ≥ 2π, but φ can be quite small (even less
than the angular width of the tardyon or luxon). It is only in the φ
portion of the cycle at which the tachyon tugs inward at the tardyon or luxon.
Structures Spreadsheet with analysis Main Page of Website
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