NET FORCES IN QCD Back to the Contents

   Some properties of the Strong Nuclear Force

This page sums up all arguments that are important when thinking about quarks and gluons in nucleons. Used is the model of a particle absorbing Higgs field to gain mass, and an antiparticle within its time border emitting to the Higgs field. The time border is defined in (6.1), (6.2) and (6.3) in paragraph The calculation of the time border at page 2 of THE EXPANSION OF THE UNIVERSE.

This view is based on the storylines NEKG page 3, 4 and 5 and FB TIME DIRECTION page 3. You can skip these preceding pages and read them later as long as you take (6.1) for granted as well as the remarks made above about Higgs absorption and emission.

The first six paragraphs of this page, up to and including “And now for the chances”, are fundamental to this site. The other paragraphs you can read later.

In “Four quarks in the shell” knowledge of renormalization theory is necessary at the level of the book of Feynman, “QED - The strange theory of light and matter”. Or Scientific American of June 1980, Gerard 't Hooft, “Gauge theories of the forces between elementary particles”.

A little knowledge about quaternions would be nice. Especially the remarks all over the place about the structure of the vacuum, are based on the view introduced at page 2 of QG, Quaternion Gravitation, where this structure is introduced. Keep special attention to the quaternion parts and (try to) skip the colorshift remarks. Colorshift is a concept that is abandoned now. The quaternion approach of strong force colors is worked out in the storyline QQD.

The proton
A quark can couple to a gluon. The gluon couples with a quark or another gluon. But quarks do not couple to each other. The proton is the only hadron, the only quark-system, which is stable and can stand on its own in the vacuum. The typical endurance of one color-reaction, like the path of a gluon from one quark to another quark, plus two couplings, one at both ends, is about 10^-23 seconds. Call this length of time a cycle of time, or just a cycle.

From observations. The strong force between nucleon centers at distance r in fm:
< 0.7 Repulsive
> 0.7 Attractive between spin aligned nucleons
0.840 Proton diameter from muonium hydrogen 2S-2P orbitals
0.87 Proton diameter from CERN collisions
0.9 Attraction at maximum
> 0.9 Attraction drops exponentially
1.7 Nuclear and Coulomb force equal strength
2 - 2.5 Coulomb force only significant force between protons

Muonium is a proton orbited by a muon.
Let’s guess both proton diameters are correct: 0.87 at high energies and 0.840 for normal circumstances.

A) So this scheme gives the observed force between nucleons, with a repulsion within 0.7 fm.

B) QCD theory for two quarks in the baryon says that, from the maximum force at about 0.9 fm mutual distance the strong force drops to the inside proportional to the distance, to zero force at zero distance.

Is the property of repulsion within 0.7 fm to be transferred to the constituting quarks? Or, in other words, do quarks repel each other within about 0.7 fm mutual distance? As an extra force added to the proportional-to-distance dependence of QCD?

And then there is the force between gluons.
C1) Does the force between gluons have a dependence from distance?
C2) As in A? That is, repulsion within 0.7 fm?
C3) Or as in B, a dependence proportional to distance?
C4) Or is there no force law working, gluons just couple and before coupling they don't influence each other's paths?

How does a state like the 3 quarks of an antibaryon, know they are white? What is white? What is color? Is it a shape? Do quarks have a spatial shape that fits to a closed circle only when white? And if the quarks not yet form such a circle they keep on reacting? This kind of questions I asked myself until I stuck on quaternions.

A new approach to color is offered in the QQD storyline, Quantum Quaternion Dynamics, using QUATERNIONS instead of colors. We still can talk about colors and depict them as colors, but they are quaternions then.

In QUATERNION GRAVITATION page 2 is proposed to construct the vacuum as a grid from gluons at a distance of about 10^-20 ŕ -21 m (about 10^-5 fm or a little smaller). That would not be possible if the gluons would repel each other as in A. Then the grid would have a density of about 0.7 fm, which is insufficient. So in this site is chosen for A to hold for nucleons, they repel within 0.7 fm. B is chosen for quarks, within 0.9 fm (and thus within 0.7 fm too) the force is proportional to distance and is zero at zero distance.

And C3 would fit the best for gluons. We believe in the gluon table where the double colors of the gluons are replaced by single colors that react just as the single colors of quarks do: within 0.9 fm proportional to distance.

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.

Two gluons colliding then is the picture of two rings colliding, isn't it? When they don't collide head on, they will not do so in any frame - not precisely - mind we took the gluon to move at lightspeed. Then when they try to pass right through each other, the rings touch at intersection points. The ring areas that coincide at the intersection points don't react with each other at those points since their mutual distance is zero. When the center of one gluon enters the ring of the other THEN reaction chance is at maximum.

Meson exchange
In the nucleus the protons and neutrons are supposed to exchange mesons. Imagine one quark to go from a proton to a neutron and a second quark of same color to go from the neutron to the proton along the same route at the same time. Along the route they form an accidental meson. If the proton-to-neutron quark just goes from the proton to the neutron, then the neutron-to-proton quark, in order to follow identical route, has to do so in backward time direction. It converts itself from a quark into an antiquark and remain so during backward time evolving flight, side by side with the proton-to-neutron quark, and when arrived in the proton it turns itself back from antiquark to quark again. This sounds illegal, but as long as the meson is virtual, it is completely in line with usual manners in QED renormalization. There they do this kind of things all the time, see page 2 of this storyline.

The meson exchange can cover larger distances than the quark exchange between neighboring baryons as described below.

Page 2 of THE EXPANSION OF THE UNIVERSE is about particles that absorb mass from the Higgs field and antiparticles, within their time border, that emit mass to the Higgs field. At paragraph The calculation of the time border and the next paragraph of that page and in page 4 of NET FORCE IN QED is worked out that when a particle and its antiparticle approach each other within their time borders, the Higgs field absorption of one particle cancels the Higgs field emission of the other and the particle-antiparticle pair forms a massless composite.

This gives an adapted model for meson exchange. QCD says, analogue to QED, that inside each quark, according to QCD renormalization theory, there is a superposition of a horde of color-anticolor pairs, shielding the “naked” color of the quark. In QED the electron's field is diminished by the electron positron pairs, so the core needs to be stronger to yield same outside field. In QCD the color pairs tend to increase the color field, so the core must have smaller strength to yield same color field to the outside. Color strength is proportional to the distance to the center of the core. At zero distance there is no color force, no color core anymore at all. The picture of the quark then is that of a color shell of diameter 0.9 fm. To the outside the force drops exponentially with distance, to the inside proportional to distance, in the center zero force.

Let us assume the virtual color-anticolor pairs in the shield of a quark can be gluon pairs as well as quark-antiquark pairs.

Let's regard one such quark-antiquark pair out of the infinite number of pairs. At what mutual distance the quark and antiquark are created? As long as the distance isn't zero, they will attract each other. When mutual distance is 10^-19 m (= 10^-4 fm) or smaller at the Earth surface, according to EXPANSION OF THE UNIVERSE, page 2, paragraph The calculation of the time border, they are within their time borders and merge to a massless meson that gains lightspeed and leaves the antibaryon. If the quark and antiquark have opposite color - the standard way quark-antiquark pairs appear - then the colors cancel each other out. This resembles the white gluon then. If energy is available it will be a real white gluon, otherwise it will remain virtual.

This model invites to construct the gluon color ring from its composing two quarks spinning around each other in a circle perpendicular to the direction of motion of the gluon. Mind time is standing still on the gluon, so the rotation is frozen in time. The color spheres of the two constituting quarks Lorentz contract to two rings, both perpendicular to the gluon's direction of motion. These two rings are about 0.9 fm diameter, while their centers are only about 10^-4 fm apart. The gluon color ring in fact consists of two nearly coinciding quark color rings.

The two quarks of a massless pair force each other to follow same path, because when they separate they have to gain mass, and for that the energy is not available. So there is no need for spin alignment for the pair to cohere. This is similar to page 4 of NET FORCE IN QED. The quarks naturally appear with opposite spin, with a sum of zero spin.

Gluon average speed
Suppose the proton diameter equals the average distance between two quarks in the proton. The usual picture when considering two particles is to see them as points and a third particle going from the first to the second travels the distance between the points. However, when a gluon color meets a quark color it looks rather like a ring of 0.9 fm diameter meeting a sphere of same diameter. In the model of a gluon as a quark-antiquark pair massless coinciding, the gluon arises where the quark pair arises. The chance for that, the chance for gluon emission or absorption, is strongest there where the color field is strongest: somewhere at the 0.9 fm sphere of strongest color around the quark.

An emitted gluon ring thus emerges around a point somewhere at the 0.9 fm diameter sphere of the quark's color. When the ring has intersection points with the sphere, at the intersection points there is an enhanced chance for immediate re-absorption. When the gluon meets another gluon the intersection points of the two rings are points of enhanced chance for coupling. Mind 3 gluons merge easier than two, see page 7 of this storyline.

When the gluon ring comes to existence in the quark of a baryon, with its 0.9 fm diameter it in fact spans the entire baryon. If the ring of the gluon is positioned in a right way, this allows for immediate coupling to another quark - no need to travel the distance between the quarks. Only the coupling time - if existing - make it differ from an infinite fast reaction.

Therefore the next presentation of the calculation of the gluon's average speed probably does no right to the real situation in baryons.

The gluon covers the diameter of the proton in between 0.87 / c = 0.29 and 0.840 / c = 0.28 * 10^-23 seconds, leaving about 0.7 * 10^-23 seconds for the two couplings, if one starts from 10^-23 seconds strong force reaction time. So take for one coupling between 0.3 and 0.4 * 10^-23 seconds.

If the typical time for a strong force reaction is 10^-23 s the gluon should cover a distance of 3 * 10^8 m/s * 10^-23 s = 3 * 10^-15 m = 3 fm. The gluon only reaches about 0.84 or 0.87 fm. The gluon from baryon to baryon, doesn’t have time to complete its typical reaction time OR it spends 1/3 of its time traveling and 2/3 of its time coupling.

Maybe it is better to regard the distance at which the strong force is at maximum, about 0.9 fm that is: 0.9 fm / c = ( 0.9 / 3 ) * 10^( -15 -8) = 0.3 * 10^-23 s. Only a tiny little bit better.

IF gluons couples every cycle and IF it travels at lightspeed and IF the gluon is taken to travel the proton's diameter, the gluon average speed is only 1/3 of the speed of light or about 1 fm per cycle. But as said, this does not account for the ring-and-sphere picture of the gluon and the quark.

The strong force attraction makes the nucleons to approach each other until repulsion takes over, at about 0.7 fm that is. Therefore often is assumed that the nucleons do overlap a little in the nucleus. The reach of the strong force is 1.7 fm at maximum, that is about 2 proton diameters. So nucleons only react strong with their nearest neighbor and a tiny little bit (exponential decrease with distance) with the neighbor of that neighbor behind it. One can estimate that a nucleon somewhere in the middle of a not too small nucleus attracts about 12 nucleons directly neighboring plus some residual influence on about 30 nucleons in a shell around those 12 neighbors.

Quark mass
We know little about quark masses. Regard the 3 quarks in a proton. The mass of a quark might be larger than the mass of the proton and then being reduced by the mass defect when the 3 quarks clump together (A). The mass of a quark might be smaller than 1/3 of the mass of the proton and then being enlarged by its high average speed in the proton and special relativity (B). The character of the so-called color confinement is unknown, therefore we cannot judge which argument holds, the larger quark mass or the smaller quark mass. See also page 2 of NEKG.

When you calculate the mass of a nucleus by the number of protons times the mass of the proton plus the number of neutrons times the mass of the neutron, you always get too large a number. The difference between the calculated mass and the observed mass is called the mass defect.
Mass defect exists, the resulting nuclei (and eventual other particles like neutrons, electrons and photons) in nuclear fission as well as fusion, have masses and kinetic energies that fit in with the existence of mass defect.

In the theory of gravitation at page 3, 4 and 5 of NEKG, mass that causes gravitation is proportional to the number of Higgs absorptions per second, the number of couplings per second with absorption from the Higgs field. All quark-gluon couplings are like that. In gluon-gluon couplings there is no mass involved and hence no Higgs absorption and thus no gravitation.

So the number of quark-gluon couplings per second is reduced a little to yield the observed mass defect. In the theory of gravitation presented in this site, with every Higgs absorption disappears a vacuum marble, causing the act of gravity. The mass caused by absorption from the Higgs field according to accepted renormalization theory (which you can call the Higgs mass) is identical to the mass of inertia, impulse and kinetic energy of the particles (which one could call the e=mc mass). It is the same concept.

In (A) the three heavy quarks in a proton have a mass defect. So according to NEKG their number of quark-gluon couplings per second is reduced. And in the same line of reasoning it is in the mass defect of nuclei when protons and neutrons clump together.

In (B) quarks are light and have high speed, causing extra mass according to special relativity. Arguing in the same line then is that when protons and neutrons clump together, a small reduction in quark average speed is sufficient to yield the observed mass defect.

From quaternions is the conjecture that the absorption from the Higgs field equals a multiplication by 1 (QG, page 2, Filling in the vacuum marbles). On its turn multiplication by 1 equals one step forward in time (QQD, page 4 and 5). In our observable world there is no step forward in time without absorption from the Higgs field, and there is no absorption from the Higgs field without one step forward in time, that is the conjecture. Gluon-gluon reactions have no absorptions from the Higgs field and thus are not registered in our frame of reference, the frame of quarks and electrons. Gluon-gluon reactions take place outside the spacetime grid to which all events are attached. Well, maybe not outside, but not inside either. The gluon-gluon reaction doesn't do a step forward in time. So the gluon-gluon reaction time is unimportant. In our frame gluon-gluon reactions take no time at all. In gluon-gluon couplings there is no mass involved and hence no Higgs absorption and thus no gravitation and no time.

Four quarks in the shell
This yields a new view on the color interaction itself, between the quarks in a baryon or antibaryon. We go back to the superposition of innumerable quark-antiquark pairs, shielding the “naked” color of the quark. The color coupling constant is about 1. Therefore 4 quarks appearing in 2 quark antiquark pairs, all within their time borders, all seeing each other, count with same importance as 2 quark antiquark pairs superposed to each other at same mutual distance. (The superposed two quark pairs don't see each other, don't react with each other.)       (a)

We just suppose the 4 quarks to appear within their time borders, at the Earth surface within 10^-19 m or 10^-4 fm, (EXPANSION OF THE UNIVERSE, page 2, paragraph The calculation of the time border). Quarks have maximum attraction at about 0.9 fm, so the 4 quarks hardly attract each other. They don't form pairs under strong force attraction.

Emerging pairs always consist of a quark and an antiquark with opposite taste, color and spin. Electric charge already is “in” the taste, e.g. when the taste is u then electric charge is +2/3 times the electron charge. When the taste is d then the electric charge is -1/3. When the tastes are opposite, the electric charges are so too.

Impulses don't have to be opposite. If one quark from the pair has a small impulse and the other quark has a large impulse in a different direction, when massless coinciding the impulse sum determines the direction and the energy of the resulting lightspeed gluon. It is the direction of the frame of reference in which the quarks do have opposite impulse.

All 4 quarks appear within their time borders. We assume the two pairs to emerge simultaneous within a length of time of 10^-23 sec. A, B, C and D are quarks, A B is one pair, C D is the other pair.
A    C
B    D
The double pair forms 2 gluons (2 times 2 quarks massless coinciding) which can be done in 3 ways: AB CD, AD BC and AC BD (denoted as “II” column pairs, “X” crosswise pairs and “=” row pairs).

A and B have opposite spin and so do C and D. Suppose A and C have spin +1/2. When combining II or when combining X, the double pair can form two spin 0 gluons: quark spins +1/2 -1/2 = 0. In II the two spin 0 gluons necessarily are colorless. But in X they might form a pair of colored spin 0 gluons.       (b)
In fact, as will be described just below, in 18 from 25 cases the two gluons in X have color and in 7 cases they are white-white or black-black.

Colorless and tasteless spin 0 gluon pairs - if formed - will be absorbed by the vacuum, enlarging the vacuum with their volumes, see page 3, 4 and 5 of NEKG and page 2 of QG. There is vacuum everywhere, so this will be set into action immediately.
The gluons don't react with the vacuum gluons at the place they are, mutual distance being too small. Instead they react with the ring of gluons at a distance of 0.9 fm mainly. Somewhere on the ring it presses itself between the other vacuum particles.
The energy of the spin 0 gluon is converted into a tiny parcel of space. The ground state real quark - I mean the real quark in which shield all this is taking place - cannot afford to loose this energy. So, if this takes place, immediately thereafter the vacuum re-emits the spin 0 gluon pairs.

When combining = the 4 quarks form two spin 1 gluons:
quark spins +1/2 +1/2 = +1 and -1/2 -1/2 = -1.       (c)

A single gluon emerging consists of two quarks massless coinciding. The two quarks have opposite spin and color, yielding sole white spin 0 gluons. White gluons don't glue. So 4 quarks making up 2 gluons is the only possibility for colored spin 1 gluons to appear.

The single gluons see the core of the quark in which shield they are emerging, since they shield the core by amplifying its strength. This “seeing” goes by means of gluons and we assume it are spin 1 gluons. Then every gluon swaps the spin. Then spin 1 gluons might be formed. This cost (at least) one cycle of time, which is enough for the constituting quarks to move 3 fm apart. At the Earth surface this is large enough to move far out of the reach of each others time borders. So here on Earth sole emerging quark pairs will not form single spin 1 gluons at a reasonable rate.

And what about the colors? Let's go into quaternions. And use the gluon table. Regard the 2 pairs again. Each pair consists of a color and an anticolor. For each pair that emerges, there are 4 possibilities: and and . (And the fourth pair? Is it ?) The result per pair is to be taken as the “application” of both colors one after the other. One has to multiply the colors with each other and in quaternions multiplication order makes a difference. So which order is to be taken? Set e.g.:
A     C  
B =    and D =

= i * -i = = j * -j = 1 = , so AB as well as CD will form a white gluon. Multiplication order is not important. But how for the other combinations?

= i * -j = -k =
= -j * i = k =
= j * -i = k =
= -i * j = -k =
= i * j = k =
= j * i = -k =
= -i * -j = k =
= -j * -i = -k =

We didn't need to worry. It are all combinations of i and j - with or without a minus sign in front - and the multiplication always will yield k, one with a minus sign in front and the other without. All possible arrangements and orders of the quarks of color i and j (with or without a minus sign in front) yield the gluon pair k -k. Two different pairs of color-anticolor that appear, always yield two times the third possible color-anticolor pair.
What if the two pairs of quarks are the same?

A     C     = i * i = -1 = = i * -i = 1 =
B =    and D =   = -i * -i = -1 = = -i * i = 1 =

The particle and antiparticle in a pair that emerges in the shell cancel each other out. When do colors cancel each other? + = i + -i = 0, the colors and anticolors happen to add up to zero. But in quaternions we don't add colors, we multiply them. Then = i * -i = 1 and indeed 1 is the neutral element with respect to multiplication. Similar for j and k. But black and white multiply to = 1* -1 = -1. Therefore we take = -1 * -1 = 1 = and = 1 * 1 = 1 = to be the colorless color pairs that appear in the shell, instead of . See also QG page 2 paragraph Filling in the vacuum marbles.
So when AB and CD is the same pair of colors the result is a superposition of the black pair and the white pair.

A few other reactions:
A     C     = i * 1 = i = = i * -1 = -i =
B =    and D = or   = -i * 1 = -i = = -i * -1 = i =

= 1 * 1 = 1 = = 1 * -1 = -1 = = -1 * -1 = 1 =
= 1 * 1 = 1 = = 1 * -1 = -1 = = -1 * -1 = 1 =

As you see, the pair doesn't occur.

And last but not least there is taste. In the 1st generation there are two tastes available for hadrons: u and d. There u has always +2/3 electron charge, d has always -1/3, anti-u = u has -2/3 and anti-d = d has +1/3 electric charge. As to speak, charge is “in” the taste. There are 4 possible u and d distributions for the quark pairs AB and CD that emerge in the shell. Keep in mind we assigned spin +1/2 to A and C, and spin -1/2 to B and D.
A C   u u   d d   u d   d u  
B D   u u   d d   u d   d u        (d)

In the first, and similar in the second pair of pairs, II-pairs as well as = are possible, there the tastes cancel out. But X would form charged gluons and that are no gluons. Moreover, X are particle-particle pairs or antiparticle-antiparticle pairs, in which massless coinciding is not possible.        (e)

In the third and fourth pair of pairs situation is even worse: only II can form gluons (colorless spin 0 gluons only) and X and = would yield charged gluons.

The = pairs in the 1st and 2nd scheme are the only possibility to form colored spin 1 gluons, the gluons that mediate the strong force.

Mark the = pairs in the 3rd and 4th scheme are interesting: they form pairs of spin 1 particles of unit charge and the particles can have color but may be white or black too. IF u and d have different mass - and I think they have, at least because of the difference in electric charge - THEN the Higgs field absorption of the one do not cancel the Higgs field emission of the other precisely. The quarks cannot coincide massless, the particle will have some remnant mass. The quarks are within their time borders; they will not separate because the presence within the time border gives some mass reduction. Separation means the quarks have to be supplied by their complete mass; that thus might be huge. We know little about the quark mass, see paragraph Quark mass. Admit, the particle has some resemblance to the W+ W- particle. But well, why W has mass 80385 MeV while the meson consisting of the same quarks then, has mass 140 MeV? So this is not that easy.

Finally one of the colored spin 1 gluons formed from the 4 quarks in the shell, can be absorbed by the real quark in which shield all this is happening, changing its real color. The other color then can be reabsorbed too (yielding no change at all) OR escape to another real quark. This can happen in mesons as well as in baryons.
Also possible is that both gluons leave the real quark where they are born, each of them going to a different quark - in baryons only, baryons have 3 quarks. The mother quark then doesn't change color, but the other two do.

And now for the chances
The 4 quarks in the shell emerge in 2 particle-antiparticle pairs, one pair is AB and the other is CD. From (a) there is a chance of 1 out of 2 for emerging 4 quarks all seeing each other within their time borders.       (chance 1 = 1/2)
And a chance of 1 out of 2 for the pairs just to superpose, despite they appear at precisely the same spots.       (chance 2 = 1/2)

A C   u u   d d   u d   d u  
B D   u u   d d   u d   d u        (d)

The best way to proceed now is to start with the taste. We are in chance 1. When written down as in (d) there is a chance of 1 out of 2 for the first or second pair-of-pairs to form.       (chance 3 = 1/2)
And there is a chance of 1 out of 2 for the third or fourth pair-of-pairs to be formed, yielding colorless spin 0 gluon pairs only.       (chance 4 = 1/2)
(For convenience we assumed the u is as likely to appear as d, which might be wrong)

When in chance 3 (1st and 2nd pair-of-pairs in d), there is a chance of 1 out of 2 for II-pairs, yielding sole colorless spin 0 gluons.       (chance 5 = 1/2)
And a chance of 1 out of 2 for =pairs to be formed.       (chance 6 = 1/2)
And no chance for X-pairs to be formed.

We now shift to spin and color. Set A at spin +1/2 and B at spin -1/2. When in chance 6, there is a chance of 1 out of 2 for C spin +1/2 and D spin -1/2.       (chance 7 = 1/2)
And a chance of 1 out of 2 for C spin -1/2 and D spin +1/2.       (chance 8 = 1/2)

As long as we have no reason to assume otherwise, we assign an equal chance to the 5 possible color-anticolor pairs to emerge. In the scheme at the right we see 25 possible combinations, 18 have color and glue, and 7 are white-white or black-black pairs from which the gluons don't glue.
18/7 = 2.57, 7/18 = 0.39, 25/18 = 1.39, 18/25 = 0.72, 25/7 = 3.57, 7/25 = 0.28.
In chance 7 there is a chance of 18 out of 25 for a pair of colored spin 1 gluons, the particles that make up the strong force.       (chance 9 = 18/25)
When in chance 8, there is a chance of 7 out of 25 for a pair of colorless spin 1 gluons (black-black or white-white).       (chance 10 = 7/25)

When 4 quarks in 2 pairs emerge within their time borders, the chance for two colored spin 1 gluons (two opposite colored spin 1 gluons) is:
Chance 1 x chance 3 x chance 6 x chance 7 x chance 9
= 1/2 * 1/2 * 1/2 * 1/2 * 18/25 = 18/400 = 0.045 or about 5 percent.

This percentage is making up the entire strong force. For spin 1 colored gluons, what we interpreted so far as one reaction in one cycle of time, up until now taken as 10^-23 s, must be about 1/0.045 = 22 reactions, 22 cycles of time - from which only one of them is yielding colored spin 1 gluons. One strong force cycle of time then must be rather 0.5 * 10^-24 s. In that time a light speed gluon covers only 0.15 fm.

Quark exchange
Can a quark go anywhere? In case of the antibaryon, 3 quarks in an antibaryon, that is in 3 quite nearby points A, B and C can go to 3 other quite nearby points D, E and F along all possible paths this can happen - but always the 3 quarks must remain in close proximity, within 10^-15 meters. In groundstate this necessarily forms a kind of bundle through spacetime made of innumerable paths superposing. For a proton this can be any length, and any length of time, since the proton is stable. So yes, a quark can go anywhere, as long as its companions do agree to follow (nearly) the same path.

Consider 2 neighboring antibaryons in a nucleus of several antiprotons and antineutrons. Suppose the 2 yellow quarks happened to be identical except for their location (same energy and impulse, both anti-u-quarks and spin +1/2, by example). Then there is a superposition of “the yellow quark going from C to F and the yellow quark going from I to L” with “the yellow quarks going from C to L and from I to F”. The start-states and end-states are the same so both possibilities superpose. Although the latter with a smaller contribution due to distance-reduction, since path C-L is a little longer than C-F and I-F is a little longer than I-L.

Mind the 2 antibaryons are supposed to overlap a little. Regard the table in paragraph “The proton”. Regard the choices we made for A, B and C. When the 2 yellow quarks are neighboring in the overlap area, they are too near to each other and the force between them is too weak. They will recede until force is strong enough. The quarks have aligned spin and indeed will attract each other. Then I imagine they will spin around each other a number of times and when finally let each other go, they are that dizzy that neither of them will have the slightest idea whether they are in their own antibaryon or in the neighbor, and so these possibilities superpose.

The two antiquarks under consideration are of same color only 1/3 of the time, due to gluon exchange in the antibaryon. They have same spin half of the time. Compared to strong reaction time, they do not change taste. Let's guess their impulse-energy range is identical in half the time. Finally, when circling around each other and happen to end up in their own antibaryon, there is no exchange. In only half of the cases there actually is an interchange. So only in 1/3 * 1/2 * 1/2 * 1/2 = 1/24 of the time our two antiquarks do really interchange.

All possible disturbances count with equal importance
When the straight line segment connecting start state point to end state point is included, color disturbances are closed paths in spacetime. Obviously that straight line segment cannot exceed about 1 fm in space and 1 cycle in time.

For every gluon that appears, the coupling constant of the color interaction appears as a factor in the wavefunction. For every gluon that appears and disappears again the coupling constant appears twice. The coupling-constant of the color-interaction is about one and therefore the repetitive occurrence of the color constant as a factor hardly diminishes the amplitude of the wavefunction.

Suppose, a particle sets out from a certain point in an unknown direction. Nothing disturbs the particle, its impulse remains a constant. The amplitude of its wavefunction is reciprocal to the traveled distance because the surface of the sphere of all points where the particle can be after a certain time, increases with the square of the distance. We accept this to hold for quarks and gluons too. But the gluons emitted by a baryon (3-quark system) often return to that baryon to conserve white end state there. Nowhere color may be left exposed. If colors travel closed paths and when the colors approach their origin again, the wavefunction’s amplitude will increase and finally precisely cancel out the initial decreasing.

So all possible disturbances count with equal importance; almost equal. There are 2 exceptions to this rule: glueballs and neighboring baryons.

In this site each of the superposed reactions is taking place in its own world, having a reality experience of its own and taking the time and space it needs for completion. It experiences itself as the only disturbance taking place at that moment on that place. It doesn’t see the other possibilities, the other disturbances. Despite its status as superposed virtual reaction, every disturbance happens in a complete world that obeys all known laws of nature, like the conservation law of energy, impulse, etc.

A glueball just leaves the baryon and the amplitude of its wavefunction is reciprocal to the traveled distance. They cost a lot of energy to form, we assume, so their abundance, rate of occurrence, is low. The glueball’s high energy gives a lot of possible, existable particle assemblages with identical overall properties guaranteed by the conservation laws. E.g. the possibility the gluon splits in 3 gluons (step 1). Three gluons merge easier than two, see page 7 of this storyline. Each of the three gluons decays in a quark-antiquark pair (step 2), that rejoin crosswise (step 3) and then the gluons rejoin again to the single gluon (step 4). It all are massless universes, in a sense that there is no net Higgs field absorption and thus no gravitation and no time. The superposed gluon universes take no time - that is, not from our time.

Every moment the world splits in as many worlds as there are possibilities for the glueball assemblage to evolve to, to be something. That can be just the same glueball or one of the other possibilities. Assemblages that are unstable decay as soon as possible, in doing so preventing an eventual turning back to the original glueball assemblage. This holds as an observation and you find yourself back in one of them, not seeing the other possibilities no more. The universes then do not rejoin to one universe. In every universe there is another you, eventually evolving differently from now on. This is the decay model of this site in the mind of page 2 of EXPERIMENTS ON THE COLLAPSE OF THE WAVEFUNCTION.

Neighboring baryons
Can photons observe the baryon and terminate a chain of color reactions? The idea is: the photon observes a quark (it is absorbed or emitted by a quark in the nucleon) and then the nucleon to which the quark belongs must have settled its color condition at white, despite the fact that the photon only sees the quark's electric charge and not its color.

In the nucleon there are two kinds of electric charge: the u-quark with +2/3 and the d-quark with -1/3 unit of electric charge. In the proton p = uud there are (2 + 2 + 1) / 3 = 5/3 charges present, in the neutron n = udd, there are only (2 + 1 + 1) / 3 = 4/3. The neutron offers 1/3 charge less than the proton to couple with the photon, that is 20 % cross section less for photons to hit the neutron. So per second the neutron is hit 20 % less than the proton, there is 20 % more time between two subsequent incoming photons. If color reach is restricted by photon observation, the color reach of the neutron is expected to be 20 % larger than the reach of the proton.

(Maybe “neutronium” - matter made from 2 or more neutrons - exists inside the nucleus. There is no net electromagnetic force working on the neutronium to propel it outside or just outside the nucleus. There are only color forces keeping it within.)

The minimal typical electromagnetic reaction time is about 10^-20 seconds. A single source (particle) cannot create photons at a higher pace. So one can have an observation of a baryon by a photon (e.g. from another baryon), then 10^-20 seconds spare time and then the next photon comes in. In 10^-20 seconds a lightspeed gluon covers 3 x 10^8 m/s * 10^-20 s = 3 x 10^-12 meter. This is back and forth since the gluon path is closed. So when restricted by photon observations the reach of the gluon would be about 10^-12 meter: 1000 times farther than the actual reach of the gluon is.

In one proton plus one neutron are present (2/3 + 2/3 + 1/3) + (2/3 + 1/3 + 1/3) = 5/3 + 4/3 = 9/3 = 3 units of electric charge. So to restrict color range by photon observation one needs 10^-12 / (3 x 10^-15) = about 400 or 300 times more nucleons to create the photons needed than there are present.

It obviously doesn’t work like this.

The light speed - Planck constant conjecture
Finally I want to end with a conjecture. The habits in renormalization theory are described by Feynman as “immoral”. However, the backward evolving of time has been justified using the view of this site (see e.g. experiment 2 (page 2 of EXPERIMENTS ON THE COLLAPSE OF THE WAVEFUNCTION) in which superpositions are universes on their own, plus the theories of gravitation (NEKG page 3) and backward time gravitation (page 1 of EXPANSION OF THE UNIVERSE). This leaves only the FTL-behavior (Faster Than Light) of the virtual particles as immoral.

What is the difference between the universes in the superposition and our universe? I guess its mass, its local gravitational field strength, its local number of Higgs field absorptions per cubic meter. If low mass universes like those superposed in QED and QCD renormalization have in fact infinite upper velocity - that's how we calculate with them! - and thus infinite lightspeed, and ours has c = 3 x 10^8 m/s, then lightspeed may be higher for lighter universes, approaching infinite lightspeed in a zero mass universe. All relativistic effects would vanish in low mass universes.
But dependence of lightspeed from local gravitational field strength means light would speed up when further away from the sun and this is not observed in delay times in the covering of Jupiter's moons by Jupiter.

Another conjecture. Keep the fine structure constant at constant, in doing so keeping the atom sizes at constant. Allow c to approach infinity while h approaches zero in such a way that the product hc remains at constant.
alpha = (1 / 4 epsilon ) ( e / h-bar c ) = e / (2 hc epsilon)
Also the energy of the photon, E = hc / wavelength, doesn't change then.
I wonder how QED and QCD renormalization would behave when this is performed. When c approaches to infinity and h approaches to zero one gets a Newtonian universe. How a Newtonian renormalization would be? It reminds me to “Mr Tompkins in Wonderland”. Did George Gamow considered this kind of arguments, then gave up and finally made a wonderful story about it?

Scientific American june 1980, Gerard 't Hooft, Gauge theories of the forces between elementary particles, for the model used in Four quarks in the shell.

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Read the

Read the

The fourth axis
1 ------- -1
is not shown.



First row are quark pairs AB,
first column are quark pairs CD,
in the table the resulting gluon pairs.
means a superposition of

THE SEA OF POSSIBILITIES: THE DIRECTION OF TIME  1  2  3  4  5  6  7  8  9  10  11  12  13  14
NET FORCE IN QED  1  2  3  4  5
NET FORCE  1  2  3  4  5
QUANTUM QUATERNION DYNAMICS  1  2  3  4  5  6  7  8  9  10
NET FORCES IN QCD  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16
QUATERNION GRAVITATION  1  2  3  4  5  6  7
SPECIAL RELATIVITY  1  2  3  4  5  6  7  8  9  10  11  12
DIMENSIONS  1  2  3  4  5  6  7
TIMETRAVEL  1  2  3  4  5  6  7  8
EXISTENCE  1  2  3  4  5  6  7
CROPCIRCLES BY ELECTRIC AND MAGNETIC FIELDS  1  2  3  4  5  6  7  8  9  10  11  12  13  14
ADDITIONS  1  2  3  4  5  6  7  8  9
MATH  1  2  3
EVOLUTION  1  2  3