Chapter 6. Fermions – Particles with Proper Mass.   

A particle with proper mass has energy also when at rest, in contrast to the photon. Therefore its properties differ in many ways from the properties of the photon, and must be addressed separately.

All particles we relate to in everyday life, except for the photon, have proper mass, meaning that they have mass also when they stay at one location. Normally, we talk about fermions as neutrons, protons and electrons.

Fig. 10 A. A particle at rest, for instance a neutron. The red sphere is the same particle in three different phases of K interaction. At rest, the neutron constitutes a ball-like target for K interaction. The neutron absorbs Ks, retains the Ks for the retention time, and emits theKs randomly in a manner to balance sideways momentum at emission. Thus, any bias in the incoming K flux will transfer a net momentum to the particle.  

Again we must see if it is possible for fermions to travel at constant speed through a dense flux of K particles without any source of energy supply. Evidently we cannot get away with a statement saying that fermions have no forward facing target, or forwards amplitude for K interaction, as we did with the photon. Our mechanism for the gravitation requires that fermions interact with Ks from all directions, also when the fermions are at rest, hence they must have a spherical target at rest. (The amplitude for fermion-K interaction is the same in all directions). This was actually one of the very first properties of Ks which had to be addressed. Gravity required a spherical amplitude at rest, but this made it hard to understand how fermions could move at all. The non-relativistic fix had 3 components:

• Fermions have no permanent energy of their own, they exchange energy with the K flux all the time. 
• To fill fermions with energy, the K - which carries its basic energy quant E_K - has to stay on board for some time. There is a certain retention time of Ks inside fermions. 
• When fermions move through the K flux, they attract more hits from the front than from the rear. A backward emission angle of Ks from fermions could solve this. 

 

Fig. 11. The same particle moving with velocity v. When a fixed, round target moves in a homogenous flux of Ks, it will receive more hits from ahead than from the rear. The particle must emit the Ks slightly backwards to balance incoming and outgoing momentum. The prolonged shape is meant to illustrate how the target size must increase as kinetic energy is added with increased speed. The particle may still be round, but all the added kinetic energy comes as an added sideways target, just like photons add their energy.

Only by obeying the rules in Fig. 11 for how its amplitude for K interaction changes when kinetic energy is added, can a neutron:

• Keep a constant speed through a K flux without needing to get extra energy added. 
• Reach a velocity close to that of light when energy is added. 
• Comply with the laws of the special theory of relativity. 

   Fig. 12. The same particle moving with velocity v approaching the speed of light, c.

• The strong increase in kinetic energy gives a much larger target (amplitude). 
• All the extra target (amplitude) for K interaction must be sideways (here illustrated with a large sideways facing surface). 
• The neutron absorbs much more Ks from ahead than from the rear because it has a forward facing target. 
• More absorption from ahead than from the rear forbids the fermion ever to reach the speed of light. 
• Most Ks are absorbed from the side, and Ks absorbed from the side have a 0 velocity relative to the background. 
• All Ks are accelerated to v in the direction of the fermion’s line of motion 
• After the retention time, Ks are therefore emitted backwards with a velocity greater than –v relative to the fermion. 
• The K emission angle increases again and approaches 90 degrees as v→c. 

 Note that the retention time of Ks inside EPs is again essential. Suppose that the entire energy of a neutron is made up of the sum of energy of Ks temporarily on board:

E_neutron = N_K · E_K = f_K · t_ret · E_K 

• N_K = the number of Ks retained simultaneously. 
• E_K = the energy of 1 K. 
• f_K = the frequency of K interaction with the neutron. 
• t_ret = the retention time of Ks in EPs = the time each K stays inside the neutron lending its energy to the neutron. 

The beauty of this is that it also shows how and why we have conservation of momentum.

Having solved the problem of fermions moving in a dense K flux, immediately another major problem would pop up. With a forwards facing target (amplitude), - how could the fermions travel even close to the speed of light? Did they emit Ks with a backward velocity greater than c relative to their own speed? For a while that was kept as an open possibility, but the red shift in photons suggested that the speed of light, c, was an absolute limitation for the component of speed in any direction relative to the emitting EP. If so, it would be even trickier to move at 0,99c. Considering how fermions add energy as their speed approaches that of light, the relativistic fermions had to be some sort of hybrids between fermions and photons. The only evident solution seemed to be that the fermions have a constant forward facing target (amplitude) for K absorption, while the added kinetic energy only showed up as an increase in their sideways facing target. Since increased speed increases the number of hits on a constant target, one should assume that the forwards amplitude increases with the increase in speed, while the backwards amplitude decreases. To visualise the process, it helps to think both in terms of EPs as targets, and as having a certain amplitude for K interaction.

If we look back at the way we describe gravitation, we see that if gravitation was caused by a minute absorption of some Ks, which were not emitted in a way to conserve the momentum of the matter, then such absorption would halt any body of matter moving through a K flux. Hence the K neutrinos must be emitted with the same amount of energy as regular Ks, and K neutrinos must be emitted in just the same manner as regular Ks.

Let us therefore explore in which manner Ks are absorbed by, retained inside and emitted from fermions, then also counting the K neutrinos at emission. See Fig. 10. To avoid any issues with electric properties at this stage, let us stick to the neutron. We have demonstrated that all Ks interacting with a photon have an average zero momentum in the direction of motion of the photon at absorption, which is possible because the photon has no amplitude facing forwards.

Not so with a fermion - it interacts with Ks also when at “rest”, otherwise we would feel no gravity on Earth. Therefore the fermion at rest must have an amplitude for K interaction more like a ball target. For a fermion to keep constant speed forwards without kinetic energy being added, requires a mechanism that takes care of the energy conservation when the fermion is hit by additional Ks from the front, relative to hits from the back, when it moves. The fermion has part of its amplitude outside the line of motion (facing forwards and backwards), and will for this reason experience more hits from the front than from the rear.

Analogue to the photon, a fermion with velocity v absorbs Ks, and changes the momentum of the Ks to match its own velocity during retention. Contrary to the photon, the neutron emits Ks sideways with a backward component to balance the extra number of incoming Ks from ahead. The absorbed Ks being accelerated to v in the direction of the fermion upon absorption. How must the K emission take place from a moving fermion to secure a net zero sideways momentum effect from emitted Ks? The slightly backward K emission should take place in either a rotating manner, or in pairs with opposite sideways components of velocity. See Fig. 11.

All Ks have momentum p_K and energy E_K = c·p_K, and Ks can also be assigned a mass m_K = E_K/c². When absorbed by a fermion moving at velocity v, the average K will have a certain component of its momentum in the opposite direction of the momentum

p _f = m_f·v

of the fermion. During retention, the K must have a component of its momentum m_K·v parallel to the fermion, while the rest of its momentum is tied up in internal movements inside the structure of the fermion. Hence an average absorbed K has a greater change of its momentum in the direction of the fermion than m_K·v. This is why the K is emitted with a backwards component of its momentum, sufficient to bring balance in the account of incoming and outgoing K momentums. The backward angle of emission becomes steeper as the fermion’s speed is increasing. But we’ll see that we get an interesting relativistic effect when v approaches c, and the angle of emission becomes more sideways again.

Consequence 14:

At rest, a fermion will have an amplitude for K interaction like a ball target, and in motion the fermion therefore interacts with more Ks coming against it than from behind, and hence the backwards component of the momentum of emitted Ks must be larger than mKv relative to the fermion. Relative to the neutral frame of reference, the emission angle must equal the average angle of incoming Ks in a non-relativistic approximation.

When kinetic energy is added to a fermion, the fermion must either increase its probability (A2) for K interaction proportional to the added kinetic energy, or it may retain Ks for longer time in order to add energy in a relativistic manner. Here are 3 different alternative ways to add energy proportional to mc2 for a fermion:

1. The Amplitude (A) may increase by becoming more like a photon, allowing the added extra amplitude only to be sideways. Then the additional amplitude will provide more interaction with Ks, but the additional interaction will be with Ks that at absorption have an average zero momentum in the direction of the velocity vector of the fermion.

2. The amplitude remains the same, only the retention time of the Ks increase, and then the fermion can carry more Ks simultaneously.

3. The amplitude may increase with an increase of the ball-shaped target size.

Alternative 3 would have as a consequence that when the speed of the fermion approaches c, almost the entire K-flux would be from the front, and the average momentum of incoming Ks - at for instance v = 0,99c - would be so much to the negative that it is way past the possibility for energy conservation when the maximum backwards release velocity is –c relative to the fermion.

Provided that this speed limitation is true regarding the relative speed of Ks to the fermion, alternative 3 can be ruled out. Alternative 1 must be the correct description for how the fermion’s amplitude develops in response to increased energy / speed if there is a change in amplitude at all. Option 2 seems to be a possibility for a fermion because it could be in line with the time dilation of the special theory of relativity, where bosons and fermions behave quite differently. For calculating purposes it is not so easy to see the difference between option 1 and 2 until the fermion starts moving. If the fermion cannot gather amplitude along its side, also option 2 will fail to allow for speed close to c, just like option 3. It cannot balance the energy of incoming and outgoing Ks at v = 0.99c, given the limitations in the speed of emitted Ks to be that of light. See Fig. 12.

Consequence 15:

In motion, a fermion will increase its energy proportional to the added kinetic energy by adding sideways facing amplitude for K interaction, hence increasing the overall number of K interactions. The initial spherical target facing forwards remains constant. The greater number of K hits from the front than from the rear is a consequence of the speed of the fermion, and has nothing to do with the increase in amplitude.  

The spherical part of the fermion’s amplitude is probably Ks moving sideways inside the structures of the fermion. For this reason the extra length shown in Fig. 11 may be misguiding, since extra length is not necessary for adapting an extra sideways amplitude, but it illustrates the point of taking more hits from the side.

The quantum transfer of the K seems to be elastic in the sense that the K is absorbed and emitted in the same basic form - except for a few which are transformed to K neutrinos - but K neutrinos are also emitted in the same manner as regular Ks and with the same momentum and energy. The direction for each individual K will change between absorption and emission. But for a particle (fermion) which travels free of influence from forces in a homogeneous K flux, the average incoming (absorbed) vector momentum of Ks must equal the average outgoing (emitted) vector momentum.

As argued earlier, the interaction must take a while (the retention time of Ks). This delay will contribute to limit the number of interactions there may be. It is easy to assume that the K interaction is elastic in the sense that K’s momentum is absorbed and emitted without loss of energy when a new K is emitted in a different direction. We know that some regular Ks are transformed to a state of smaller amplitude for EP interaction. And if our explanation of electromagnetic interaction is fairly correct, then there is a switch of “sign” for some Ks, so a perfect elastic interaction of Ks with fermions would be a hasty conclusion. This process must rather be seen as a complex interaction between EPs and Ks, a process which ends up obeying rather simple rules which we can understand.

How can we know that Ks are sent out again in a direction which relates to the speed and direction of the EP? If it were passed on in exactly the same direction as before the interaction, then no elementary particle could sense any net gravitational force. So Ks must be emitted in a random direction in order to catch directional differences in the K flux. But not totally random - the angle of emission must be such that inertia is taken care of. Emission will be in a sideways direction relative to the fermion, allowing the momentum of the fermion at emission to give back to the fermion a push so it keeps moving against the surplus flux of Ks coming against it.

This is where the ether theories were buried a hundred years ago - one saw no working mechanism for how particles could move in space, if space consisted of anything but emptiness. The model presented here goes around this issue, since it postulates an empty space, which is so empty that it cannot even curve like Einstein said. But the space is filled with Ks, which represents the curvature of space, and Ks fill space with something that may or may not resemble the ether. Just like the vacuum energy of quantum mechanics have been known to fill the empty space, without being thought of as the ether.

Consequence 16:

Fermions absorb Ks like a vector with a momentum, and emit Ks again like a vector in a rotating, sideways direction balancing the backward component with the speed of the fermion, in a way that conserves the momentum of the fermion in a zone of homogeneous K-flux and no acceleration.

Fermions absorb and emit Ks at a very high frequency (of the order 10²³ times per second for a quark). The net gravitational force is a question of the angular distribution of the flux of regular Ks, which corresponds to the vector sum of the flux of regular Ks. The larger the gravitational potential, the larger is the net vector sum of Ks from the background minus the vector sum of regular Ks coming from matter (and the larger is the net vector sum of non-interacting K neutrinos from matter).

Consequence 17:

When a fermion by itself moves away from a massive body, it will loose speed because it has a K flux with larger amplitude for EP interaction coming towards it from ahead than from behind.

The above consequence goes for a fermion which is shot out from a place in a gravity zone, and travels outwards without any outside help. If you place a 1 kg cube inside a space ship, and take it into orbit, the spaceship will provide the energy to bring it into orbit. In the process of moving away from the Earth, the cube will increase its mass in space due to increased K-flux from the side of matter because of the increased distance from the Earth.

The homogeneous nature of the K-flux indicates some K-K scattering. We know that in empty space there are a lot of photons from the cosmic background radiation. This will limit the range of distance travelled for Ks between interactions. But the lack of regular K momentum from the side of an absorbing mass will not fade away with distance because of random scattering, only the lack of momentum carried in one direction will be spread on Ks from various directions, maintaining the same lack in net momentum as if there were no scattering. Hence the net force will still follow  

F = GmM/r² 

as the distance in empty space increases.

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