Net Forces, QCD, Gravitation

Updated November 2023

Originally this page had to be conclusive, merging the results of my search for a net force, between electric charges first and then between color charges too. Since then new storylines has come to existence. Newton Einstein Gravitation, where space turns out not to be curved, while Einstein's equations still remain completely valid. QQD, where nuclear colors are replaced by quaternion units and color theory is rather SU(2) than SU(3). Quaternion Gravitation, where so much has found its place.

This page now is a mixture of its original goal since 2007 (net force of electric charges) and 2008 (net force of color force) and what the entire of it finally has become, since 2011 (gravitation) and 2012 (quaternions) up until now.

Net Forces

When in a group of colors they repel or attract each other, such a color collective might yield a color net force. Page 1 of this storyline NET FORCE gives a mechanism how a neutral collective of real electric charges contracts and causes an attractive force on electric charges outside the collective. A likewise force should act between the virtual electric charges in every single contributing Feynman diagram, that's page 2 of this storyline. And so a likewise force should also act between the virtual colors in every single contributing Feynman diagram. The storyline NET FORCES IN QCD (removed now, remaining only page 9 at the end of storyline QCD) was originally set up in order to find an attracting remnant force between quarks and gluons that can be identified with gravitation. The last paragraph of this page is the original contents of the first try as it was written somewhere in 2008, quite unfinished as it is.

My search for a net force comprising gravitation has come to a halt. I found a mechanism for gravitation that is quite different. The vacuum consists of solid marbles, static not-contracting not-expanding marbles. Every time a coupling between real particles takes place, a vacuum marble, a Higgs field particle, is absorbed. This is the mass absorption from the Higgs field. A marble disappears out of the vacuum marble sea, leaving behind a hole. The surrounding field of marbles sinks into the hole while dragging along with it all particles in it and all light rays traversing it, standing-still particles as well as moving particles. The vacuum always starts out as flat space, Minkowski space, not curved. Then disappearing vacuum marbles curve spacetime, and the subsequent act of gravitation curves it back. This is worked out best in page 5 of NEWTON EINSTEIN GRAVITATION. In The Spin Consideration at page 3 of QUATERNION GRAVITATION, the Higgs field is proposed as a short-living intermediate state between the gravitational vacuum marble sea and matter, a result that is adopted since. Gravitation is a kind of streaming of vacuum marbles, a liquid Bose condensate, excluding other forms to contribute. A lot is told in the storyline NEG (NEWTON EINSTEIN GRAVITATION) especially page 3, 4 and 5.

The newest contribution to the theory ()

At page 2 of the storyline QUATERNION GRAVITATION the vacuum marbles are identified with gluon pairs. A quark or gluon is always immersed in the vacuum marble sea, a sea of color.

Diverting from this straight line are gluNons, see page 7 of QCD. A gluon pair can be called a glu2on, a gluNon state with n=2. If gluon pairs can, then larger color collectives will do too, is the message. Mind the coupling constant of the color force is about 1, there is no reduction of the Feynman diagram contribution when the number of colors grows. Color collectives are white gluNon states, white states of N bound (not merging) gluons. White gluNons are called glueNballs. They should add to the superposition. Mind the color constant is approximately 1. All diagrams, simple as well as complicated, do count with same weight. Only energy can be a restriction in superposing contributions. To represent the vacuum marbles of gravitation the color collectives should not contract nor expand.

In the storyline QQD, Quantum Quaternion Dynamics, color is replaced by quaternion units. The calculation rules of quaternions making up colors are completed now and without contradictions. The mapping of QQD on SU(3) is missing, but there is argued SU(2) is a better candidate for the color force, the strong nuclear force. The most complete argument is at page 9 of QQD, about quaternion units as product of Pauli matrices.

The backward time evolving version of my theory of gravitation starts at page 1 of the storyline THE EXPANSION OF THE UNIVERSE (grey buttons). In page 1 and 2 of that storyline is shown the backward evolving version leads to assume the existence of backward time evolving dark galaxies causing the acceleration of the expansion of the universe (usually attributed to Dark Energy, mind the capitals). At page 2 of the storyline THE EXPANSION OF THE UNIVERSE, paragraph Massless coinciding, the backward time evolving version of my theory of gravitation leads to a way to construct the photon from an electron and a positron that are massless coinciding. At page 5 of NET FORCE IN QED is worked out how the lepton Higgs field is constructed from spin 0 photons.

At page 4 of QUATERNION GRAVITATION is argued the electron is the black quark, the antiparticle. And the positron turns out to be the white quark, the particle. Initially I thought Electrons don't feel the strong force, they cannot absorb gluons from the vacuum sea, so they need a Higgs field of their own. But at The color of the photon at page 5 of NET FORCE IN QED is worked out how electrons and positrons can be assigned a colorless color.

Four quarks in the shell at page 5 of NET FORCE IN QCD shows a similar way to construct the gluon from a quark and its antiquark, massless coinciding. (In fact construct two gluons from two such pairs of quark and antiquark, hence four quarks in the shell). This yields the possibility to construct spacetime and the hadron Higgs field from spin 1 gluon pairs, that are white in only one direction, the direction of time. In The Spin Consideration at page 3 of QUATERNION GRAVITATION is shown a gluon pair has spin 2 in the vacuum (1 + 1 = 2) and spin 0 (1 - 1 = 0) in the short-living intermediate state that in fact is the (hadronic) Higgs field. For the time axis being the direction of white color, see page 2 of QUATERNION GRAVITATION and also the speculations up to number (5.4) at page 5 of QQD.

Finally at page 5 of QUATERNION GRAVITATION is proposed the neutrinophotons as Higgs field for the 1rst generation *), the spin 0 photons as Higgs field of the 2nd generation and the gluon pair Higgs field for the 3rd generation.

*) For neutrinophotons see paragraph Neutrinophotons at page 4 of QUATERNION GRAVITATION.

Within each others time border particles cancel each others Higgs field absorption and emission and can be massless. The time border depends on the involved gravitational field strengths, see (21), (22) and (23) at paragraph The calculation of the time border at page 2 of THE EXPANSION OF THE UNIVERSE. E.g. by coincide we mean: for electrons and positrons at the Earth surface, within a distance of about 10^-20 m, which is near to the highest resolution the vacuum marbles can support, as calculated in the pop-up frame radius of the Higgs boson.

In paragraph Dark Mechanics at page 2 of QUATERNION GRAVITATION is taken the E = mc mass-energy of antiparticles to count as negative. So maybe energy is not such a restricting factor to color collectives after all.

One of the first tasks now is to investigate color collectives in quaternions, maybe page 8 of QQD will lead to something. As always I wonder if I can make it, with so little mathematical skills at my disposal. Formulas have never been my strongest point. (Well, I didn't work at it for years - april 2022)

Is the search for any net force quite over now? At page 5 of NEG I say: A mechanism how the rearrangement of vacuum marbles actually works, is still missing. Shortly before this remark, in the sentence starting with As long as the box is closed, in principle something strange happens, I suggest that the rearrangement of vacuum marbles takes place as one single quantum jump and does not need any extra mechanism. Just after the rearrangement remark I note as a second suggestion that the theory of Erik Verlinde might come to the rescue, or the simulations of Renate Loll. Or E8 x E8, if applicable at all if there is no space behind the space. The hole should be filled by a force, see page 5 of NEWTON EINSTEIN GRAVITATION (NEG). Is that a net force acting between the gluons surrounding the hole? The actual theory of gravitation then might be a combination of the mechanism from page 3 of NEG and pages 1 and 2 from ELECTRIC NET FORCE IN REAL MATTER that follows my own old ideas. Or the mentioned persons should contribute another mechanism with the use of quaternion units as colors. No, the search for a net force between vacuum particles is not over, although I don't think it will be me completing it.

In strong gravitation fields sole vacuum marbles - maybe even patches - may tear of, or boil from the vacuum marble grid, in doing so forming a kind of tiny universes superposed to ours.


QCD is a complete, full theory. They say we know all necessary computation rules with which in principle one can calculate all color properties, all properties of the strong force. But the color coupling constant is about one, therefore complicated contributions count as valid as the simple ones. The involved Feynman diagrams diverge. Up until now no one can actually calculate this.

QCD renormalization calculates from 3 quarks in white start state onto those 3 quarks in white end state along all possible ways the reaction might have taken place. It is a big brother copy of QED. Experimentally sole quarks cannot be separated and open color does not exist. Therefore there is no point in calculating from the start state of one quark color to its end state.

There must be a different QCD renormalization for mesons too.

This includes automatically all reactions shown in page 3 of the storyline QCD, Two gluons emitted simultaneously.

It also automatically includes all reactions of three gluons emitted simultaneously, and so on.

It includes too all possible splittings and mergers of gluons in between the white start state and the white end state of the 3 quarks of the baryon. One gluon exploding in 1,000,000 gluons does contribute.

Provided there is point to the gluNon concept, all possible gluNon states should be automatically included too in QCD renormalization. The gluNon states with higher N and non-zero orbital impulse momentum will be polarized in difficult ways. One has to incorporate all possible polarizations.

Is energy a restricting factor? I mean, when a whole universe of gluons and quarks forms a contributing superposition, larger in total energy than our whole visible universe all together - it feels as if this won’t work. Energy must be a constraining factor. Contributions with zero or sufficiently zero net mass absorption (sufficiently equal mass absorption and emission) can be allowed. Also contributions are valid with net mass absorption from the Higgs field that cancel out quite other contributions of net mass emission. In paragraph Do large numbers of N count? at page 7 of storyline QCD, is assumed in (nearly) ground state possibilities of higher N don’t count.

In Color confinement at page 8 of QCD, is proposed that for the 3 quarks in the baryon, the large reduction of states in the course of returning to white end state, causes a force keeping the colors within. It says: The strength of the interaction is inversely proportional to the remaining number of worlds in interference. It starts from the assumption of the overwhelming urge to maintain white state, isn't it? Page 8 needs revision. The process itself should automatically be incorporated in QCD.

Can 1 color (1 quark) emit 2 gluons simultaneously? In different directions? If not, then per cycle of 10^-23 seconds there only are 0, 1, 2 or 3 gluons allowed to be emitted simultaneously by the 3 quarks in the baryon. The difficult part then is those gluons splitting in more gluons, forming gluNon states.

Why 2 baryons, like a proton and a neutron, don’t merge into one white 6-quark system? I guess it is energetically favorable to split up. But to calculate this is something different.

Is a net force in color collectives automatically included in QCD renormalization? Posing the question is admitting the quest for a net force is not quite over.


In the QQD storyline the gluon colors of QCD are replaced by quaternion units. QQD is meant to have same renormalization procedure as QCD, but has different outcome than QCD renormalization. No, I haven't undertaken an effort to estimate, that is far beyond my capabilities and skills. Meant is there is QED (still valid), QCD (replaced) and QQD (strong force colors as quaternion units). And QQD is SU(2), while QCD is SU(3).

The storyline TONE gives a summary of most of my findings so far in fundamental physics. A TONE page is recognizable by the table

at the top of the page. You can always start via the uppermost part of the CONTENTS, you always find the contents by the black dot Back to the Contents at the end of the name of the first storyline in the navigation part of virtually every page of this website. TONE is also accessible via the small contents at the end of virtually every page, click nr 9 in the Additions storyline.

Suppose the two quarks in a gluon differ in magnitude of their opposite mass absorption from the Higgs field. One would get a net mass absorption from the Higgs field or net mass emission towards the Higgs field and thus massive gluons. The gluon immediately loses its lightspeed status, would gain a lower velocity and an ordinary elapse of time. That allows for an impulse momentum of 0, 1 or 2 of the two quarks orbiting each other. But do the quarks attract each other?

The mechanism of gravitation Dark and bright planets and stars of equal mass at page 2 of EXPANSION OF THE UNIVERSE shows that a planet and an antiplanet of equal mass don't attract nor repel each other. But this are no planets but quarks and this is no gravitation but color force. In chapter The proton at page 4 of QCD is said:

The picture of the gluon now is that of a shell of diameter of about 0.9 fm, moving at lightspeed. The shell Lorentz contracts to a circle, a ring of diameter about 0.9 fm perpendicular to the line of motion, and time is standing still at the gluon. A strange picture.

So when the time border remains quite smaller than 0.9 fm the two quarks are too near to each other and the color force is very near to zero and there hardly is any attraction between the quark and the antiquark. Otherwise, the quarks cannot separate because the canceling out of Higgs field absorpion and emission would cease and then the energy of the full mass would have to be payed for each of them, which is not there.

Or is this assemblage just the meson? Maybe it is the gluon when the quarks are within their respective time borders, and it is the meson when the quarks maintain larger mutual distance.

In paragraph Four quarks in the shell at page 5 of QCD, from Mark the = pairs in the 3rd and 4th scheme are interesting, I tried to suggest the W+ and W- particle consists of 2 quarks within their time borders. This is the only place I tried to investigate W+ W- composition (Z0 yet to be found).

Quarks have color and from the quaternion approach of color (see the QQD storyline) follows then the possibility of white and black quarks. At page 4 of QG (QUATERNION GRAVITATION) is given a very nice estimation how the leptons can be those white and black quarks. Remarkable is the outcome that if one agrees to name red, green and blue quarks (and not anti-quarks) then the electron is black, the electron is an antiparticle.

And why more or less massive gluons cannot consist of three quarks? The 3rd quark has to be matter or antimatter, ending up with 2 matter quarks and 1 antimatter quark, or the other way around. I guess it is impossible to achieve zero net mass absorption from the Higgs field then, so the particle has mass. First there is the rule that quarks have color and antiquarks have anticolor and so you cannot not end with a colorless end state here. But that's oke, gluons have color. But that are lightspeed gluons, not massive ones. Massive particles made of quarks - baryons (3 quarks) and mesons (2 quarks) - have no net color. Second, the spin doesn't come out right for a gluon. You end with a half spin, as in the baryon. Gluons have integer spin, otherwise it are not gluons. Ok, that's an argument. So no, there are no qu3ark states making up a massive gluon-like particle. (Say 3quark states to save you voice in pronouncing.)

And four quarks, will that do? Yes, that will do, see Four quarks in the Shell. That is, that part is about 4 quarks in 2 gluons. Here is meant 4 quarks in 1 massive gluon. And lightspeed gluons, when two lightspeed gluons merge, do you get a lightspeed gluon again, made of 2 quarks and 2 antiquarks? Their mass absorption from the Higgs field still is expected to cancel out. Maybe they are unstable and decay as soon as possible in two ordinary lightspeed gluons again each made of a quark and an antiquark. If not, then spin 0 gluons and spin 2 gluons made of 4 quarks will be possible.

Where do they go? As said, in The Spin Consideration at page 3 of QUATERNION GRAVITATION, the vacuum should consist of spin 2 gluon pairs and the Higgs field is proposed as a short-living spin 0 intermediate state between the gravitational vacuum marble sea and matter.

In constructing TONE I just had to stop somewhere.

An early effort to net force in QCD

The particles 1 and 2 are quarks now and the lines connecting them are gluons. The shown color depicts the color charge of the particle. Both quarks and gluons have color charge.

Despite the two virtual colorcharges appear in each others neighborhood, nearer than a proton diameter, at overlapping time intervals, they don’t see each other since the connecting gluon between them is missing. Particles in superposition without explicitly mentioned any reacting particle between them, don’t see each other, just like the electric charges in the according diagrams of QED. They live in different worlds.

Att: 00000
Rep: 00000
Net: 00000

The next contributing diagram is

There is a law stating:

If the force-mediating particle has an even spin then equal named particles will attract each other and unequal named particles will repel each other.

If the force-mediating particle has an uneven spin then equal named particles will repel each other and unequal named particles will attract each other.

In the second part of the law one recognizes the spin1 photon causing negative charges to repel each other, positive charges to repel each other and an attraction between negative and positive charges.

Att: 20110
Rep: 21001
Net: 0-111-1

Cyan colorcharges repel each other and so do the magenta charges. The magenta and cyan charges attract each other. A previous attempt.