The Strong Nuclear Force 1

Page 4 and 6 of this storyline sum up all arguments that are important when thinking about quarks and gluons in nucleons in this website. 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 (21), (22) and (23) in paragraph The calculation of the time border at page 2 of THE EXPANSION OF THE UNIVERSE.

This view is based on the storylines NEG page 3, 4 and 5 and FB TIME DIRECTION page 3. You can skip these pages and read them later as long as you take (4), (5) and (6) from page 2 of THE EXPANSION OF THE UNIVERSE for granted as well as the remarks made above about Higgs absorption and emission.

Several remarks all over the place about the structure of the vacuum, are based on the view introduced at page 2 of QG, Quaternion Gravitation. A little knowledge about quaternions is necessary. 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.

Table 1. 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.           (2)

A) So this scheme gives the observed force between nucleons, with a repulsion within 0.7 fm.           (3)

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.           (4)

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.           (5)

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 à -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.           (6)

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.           (7)

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.           (8)

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.           (9)

## 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.           (20)

The meson exchange can cover larger distances than the quark exchange between neighboring baryons as described below.           (21)

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 following paragraph at that page, and in page 5 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.           (22)

As can be inferred from the previous paragraph above, 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.           (23)

Let us assume the virtual color-anticolor pairs in the shield of a quark can be gluon pairs as well as quark-antiquark pairs.           (24)

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.           (25)

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.           (26)

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 5 of NET FORCE IN QED. The quarks naturally appear with opposite spin, with a sum of zero spin.           (27)

## 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.           (30)

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.           (31)

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.           (32)

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.           (33)

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.           (34)

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.           (35)

IF gluons couples every cycle and IF it travels at lightspeed and IF the gluon is taken to travel the proton's diameter, then 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.           (36)

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.           (37)

## 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 NEG.           (40)

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 NEG, 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.           (41)

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.           (42)

In (A) the three heavy quarks in a proton have a mass defect. So according to NEG 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.           (43)

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.           (44)

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.           (45)

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.           (46)

That is the conjecture. However, this conjecture does not fit in with (3.71) and the text just above it in paragraph Two gluons of opposite sign do not react at page 3 of QG.

A few other conjectures like this is in paragraph The Light Speed - Planck Constant - conjecture at page 6 of QCD.