## 2.6 Principles of the messenger particle model of quantino theory

### 2.6.1 Motivation

Up to this point, only cases were considered in which point charges move approximately uniformly. But where forces occur, there are also accelerations. An important special case of an accelerated electrical charge is a charge that oscillates at a certain point, i. e. moves back and forth in sinusoidal form, but rests in average. We know from classical electrodynamics that oscillating charges emit electromagnetic waves. In these waves, the strength of the electric and magnetic force changes periodically on a test charge that is somewhere in the wave's area of influence. So if a charge is forced to vibrate, it simultaneously starts to radiate a wave. The time that passes until this wave reaches the test charge can be measured.It is a very well known fact that the time difference $\Delta t$ between the start of the vibration and the recording of the change in force always corresponds exactly to the distance divided by $c$; provided this experiment is performed in a vacuum or a sufficiently thin gas. This shows that the force is not transferred infinitely fast from source to target. Force formulae, such as the Newtonian law of gravity, the Coulomb law and especially the equation (2.2.1.4) hide this circumstance, as they do not depend on time. What this fact shows us is that force is physically real regardless of the sources. The exact nature of this source-independent existence is the subject of various models and ideas.

One of these ideas is based on the assumption, that the surrounding space is not empty, but filled with a substance called "luminiferous ether". The propagation of force-fluctuations is explained here by propagation of "sound-waves" within this ether. This model has clear weaknesses. On the one hand, it remains unclear how force of a resting charge is transferred to another resting charge. But what weighs more heavily is the fact that ether gas must consist of particles, which by itself have position and speed. As a result, there is some kind of reference frame in which this gas essentially rests, such as air at the surface of the earth in windless conditions. For two electric charges which are in rest to each other, but moving within the ether itself, the speed of light should be different than for two charges which rest to the ether. However, this is demonstrably not the case, because the speed of light does not seem to depend on any absolute speed.

Another historically relevant idea - the corpuscular theory - assumes that force sources emit particles, which then transfer the actual force upon arrival at the recipient. The particles in this model always have emission velocity $c$ plus the velocity of the source. Relativity is therefore no problem. However, the speed of light should vary when transmitter and receiver have a relative speed to each other. But this is not the case either. The speed of light does not depend on the relative speed between transmitter and receiver, nor on the speed of the entire system of transmitter and receiver in relation to any resting frame of reference.

The special theory of relativity is known to be the preferred model of physics for the mathematical description of this paradoxical fact. The two problems described above have been solved here, but at a high price, because the special theory of relativity is counter-intuitive and leads to hidden paradoxes. For example, in the special theory of relativity, a contradictory result is obtained by looking at two objects that move away from a common point in the opposite direction and turn back after a certain time. At some time they meet again where they started. If the Lorentz transform is used, this completely symmetrical thought experiment yields the result, that from the point of view of each object the other object has lost less time. But this is a contradiction, as long as one does not assume that every object has its own reality, as in Hugh Everett's Many-Worlds theory.

But back to the question what is force in the quantino theory. It assumes, in order to explain the finiteness of the propagation speed of force, that electrical charges emit messenger particles called quantinos. This corresponds to the aforementioned corpuscular theory. However, it has been shown that corpuscular theory has the problem of not being able to explain why the force propagation velocity is independent of the differential velocity between transmitter and receiver. In order to solve this problem, quantino theory goes a completely new way, which in this form has never been thought through before and which does not correspond to any of the previously mentioned alternatives. The quantino theory assumes namely that the messenger particles are not sent at a fixed but a random speed, and that the recipients have a property that ensures that messenger particles that are faster than $c$ in the recipient's reference frame do not interact. This additional assumption ensures that

- the principle of relativity always applies and
- at the same time the maximum force propagation velocity is a constant which does not depend on the differential velocity.

### 2.6.2 The Quantino mechanism

In contrast to the relativity theories, quantino theory is not based on the basic idea of a not further explained, axiomatically given four-dimensional space-time, but on the assumption that all forces are conveyed by a messenger particle - the quantino. These messenger particles are emitted from point-shaped sources and form fields in their entirety. When these fields move through the three-dimensional space with universal time, they create the effects usually described in physics by the four-dimensional space-time. So one could say that quantino theory describes how four-dimensional space-time is created at all.The messenger particles are called quantinos. They always have a well-defined location and speed. Once emitted, these quantinos always move in a straight line and at a constant speed through the space. They do not interact with other quantinos, nor can they be distracted, influenced or even destroyed. They therefore exist eternally and continue to penetrate into the previously empty, three-dimensional space around them.

- Figure 2.6.2.1: Charge, which is emitting negative quantinos.

- Figure 2.6.2.2: Charge, which is emitting positive quantinos.

The sources that emit these quantinos are called negative and positive unit charges. They have like quantinos always a well-defined location and a well defined speed. Furthermore, unit charges have a very small but non-zero volume, which is the same for all unit charges. Unit charges of both signs can exist simultaneously at the same place and penetrate each other, since they interact only indirectly via the quantinos. The illustrations 2.6.2.1 and 2.6.2.2 show a negative unit charge (left, shown in red) and a positive unit charge (right, shown in blue) and the quantinos emitted by them.

It should be mentioned that the unit charges of quantino theory are not electrons or positrons, because these posses masses and other properties. In quantino theory, unit charges only have a universally constant amount of electrical charge and nothing else, especially neither gravitational nor inertial mass. Furthermore, electrical charge in quantino theory only means that the object is a quantino source. About an electrical force is not yet said anything at this stage.

- Figure 2.6.2.3: The emission velocities w of the quantinos could be Maxwell-Boltzmann distributed. Only a small part of the quantinos is emitted slower than with the speed of light c.

It is also very important to emphasize that quantinos can also be emitted at velocities well above the so-called speed of light. Even unit charges themselves can move relative to each other and to the reference frame at any speed.

However, the sources or unit charges do not only emit quantinos, they can also interact with them if they come close enough. The interaction can be completely described with a few simple rules:

- A quantino changes the speed of a unit charge in an interaction in the direction of movement of the quantino when the sign of quantino and charge is the same but contrary to each other when the sign is different.
- A unit charge also interacts with quantinos that it has emitted itself.
- The strength of the effect of a quantino is proportional to the square of the relative speed between quantino and unit charge.
- A quantino only interacts with a unit charge if it is within the effective range of this unit charge for long enough.
- The interaction is binary, i. e. it occurs either once and then completely or not at all.

It should be noted that a model has been described here. The processes that actually take place in nature could be similar, but in the details different and especially more complex.

### 2.6.3 The electric force

A look at the rules of section 2.6.2 shows that unit charges repel each other if they have the same signs but attract if the signs are different.- Figure 2.6.3.1: Repulsion of two positive unit charges. It are only shown quantinos in the drawing plane.

- Figure 2.6.3.2: Attraction between a positive and a negative unit charge. It are only shown quantinos in the drawing plane.

As can be seen, the repulsion does not seem to be entirely regular or symmetrical. The reason for this is that unit charges can never be completely at rest, since they emit randomly quantinos and interact with these themselves in accordance with Rule 2. The location and speed of a unit charge is therefore constantly changing, even if there are no other charges in the near vicinity. On average, this randomness disappears over the time and deterministic physical laws arise.

With increasing quantino numbers, the influence of randomness becomes smaller and smaller. If the charges do not move too fast relative to each other and the distance is not too small, the Coulomb's law applies in good approximation. Figure 2.6.3.2 shows that two charges with different polarities attract each other, because charges and quantinos have different signs and therefore cause a change in velocity against the quantino direction of motion.

All other forces, at least gravity and magnetic force, seem to be derivable from the electric force. From the point of view of quantino theory, it therefore makes sense to speak in general terms of the

**EMG force**, even if only the coulomb force has been made plausible up to this point. Its effect is to change the velocity of charges. The higher the force, the greater the speed change per unit of time. It is obvious that the strength of the force is determined by the number of quantinos present per volume of space, as well as their direction of movement and speed.

### 2.6.4 The special principle of relativity

In quantino theory, the special principle of relativity is fully satisfied. Figure 2.6.4.1 shows a moving charge which is emitting quantinos. It is noticeable that the velocities of the quantinos are distributed according to a fixed probability distribution, but that the speed of the source is still added additionally.- Figure 2.6.4.1: The special principle of relativity: It is not possible to tell whether the charge or the observer is moving.

### 2.6.5 Inertia

A quantino is completely independent of the source charge after it has been emitted. This means that a change in the speed of the unit charge after the quantino has been sent out can no longer affect the quantino. This has far-reaching consequences and ultimately leads to the effect known as inertia and thus to the "lex prima", Newton's first law. It states that a body remains in a state of rest or uniform motion as long as it is not forced to change its speed by forces acting on it.- Figure 2.6.5.1: A unit charge rests until it is suddenly accelerated due to external circumstances. The quantino field compression in acceleration direction causes the inertia effect.

For a constant acceleration of a unit charge it is therefore necessary to let a force act and to maintain it. In quantino theory, an external force can only be caused by the presence of other charges. If this external force disappears, the acceleration as well as the counter-acceleration disappears. That a unit charge is accelerated without an external force is not possible because the counter-acceleration would immediately prevent this. This stabilizing effect thus leads to the fact that matter does not suddenly change the speed without reason.

In classical physics the inertia is related to the mass, not to the electrical charge, because this is usually zero. However, neutral materia can be assumed as superposition of two opposite charge-quantities, which neutralize each other. However, under certain conditions, subtle residual interactions remain. Gravity is one of them. The mechanism shown above is therefore not only present at electric charges, but also at objects with mass. It is important to remember that quantinos in the quantino theory are not only the force carriers of electric force, but also the force carriers of magnetic force and gravity.

Another remarkable effect at this point is that the acceleration of a unit charge obviously leads to a deformation of the quantino density field. Figure 2.6.5.1 shows clearly how the field, which was completely radially symmetrical until to the start of acceleration, is compressed in the direction of acceleration and thinned out on the opposite side. After the end of acceleration, the field begins to normalize, whereby the disturbance that has occurred moves away from the unit charge. This phenomen is an electromagnetic wave. As will soon become clear, this deformation spreads between all uniformly moving unit charges exactly at the speed of light. The relative speed does not matter by this.

There is one more point that should be mentioned: It can be namely stated exactly whether the unit charge has been accelerated or the observer. If the charge is accelerated, this leads to a real deformation of the field generated by the charge. In contrast, the field remains completely radially symmetrical when the observer accelerates. Reference systems accelerated to each other are therefore not equivalent. However, a co-accelerated observer at the front of charge would not be able to tell whether all forces in total have disappeared or if the system is only accelerated by external forces. Because of the relationship between electric force and gravity, this also applies to gravity. Albert Einstein called this effect the "strong equivalence principle" and used it as a starting point for the general theory of relativity.

### 2.6.6 The physics of force propagation

In quantino theory, forces are conveyed by tiny messenger particles which are moving through space. These quantinos have a speed, thus a force cannot be transmitted instantaneously from one charge to another. Figure 2.6.6.1 shows how a negative quantino moves towards a positive unit charge at 25% of the speed of light. As can be seen, when the Quantino and the unit charge come into contact, there is an interaction which accelerates the unit charge against the direction of movement of the quantino. This is in accordance with Rule 1 of Section 2.6.2. The green flash-up of the unit charge indicates the time of interaction.- Figure 2.6.6.1: The quantino speed is 25% of the speed of light. The Quantino is not able to penetrate deeply, because soon a comparatively weak interaction occurs.

- Figure 2.6.6.2: The quantino speed is 50% of the speed of light. The quantino penetrates to the middle where a medium-strong interaction occurs.

- Figure 2.6.6.3: The quantino moves at the speed of light. The quantino only interacts shortly before leaving of the unit charge. The effect is very strong.

- Figure 2.6.6.4: The quantino moves slightly faster than the speed of light. The quantino does not interact at all, as it penetrates the unit charge too quickly.

### 2.6.7 The relativity of force

This section is intended to clarify why the electrical force has the elliptical form of equation (2.2.1.4). Figure 2.6.7.1 shows a resting charge which is emitting quantinos. To the left a second resting charge is shown, which acts as a receiver or "observer". For this receiver charge, some of the quantinos are too fast because, as explained in Section 2.6.6, they simply do not stay for long enough in the observers sphere of influence. Other quantinos, however, have enough time because their relative speed is low enough to produce an effect. In order to make both types of quantinos distinguishable, the too fast ones are shown*red*and the others

*green*.

- Figure 2.6.7.1: Quantinos that are too fast are shown in red, but those that are capable to interact are green.

- Figure 2.6.7.2: The electric field from the perspective of a resting charge.

If we draw now at each point in the space an arrow whose length is proportional to the strength of the acceleration which a

*resting*positive charge at this place would experience and which points in the respective direction of acceleration, so we get an image as it is shown in Figure A. The arrow points to the direction of acceleration. The result is the so-called electric field, whereby in Figure 2.6.7.2 it was assumed that the field generating charge is positive. For a negative charge, all arrows rotate once by 180°.

- Figure 2.6.7.3: A charge moving at 80% of the speed of light. Quantinos which are too fast are shown in red, these, which are able to interact, green.

- Figure 2.6.7.4: The resulting electric field.

A detailed analysis shows that the electric field also weakens on the right-hand side. The reason becomes clear when we take a closer look at the animation of Figure 2.6.7.3 in the second half. We can see that the charge moving to the right perceives many quantinos coming from the "wrong direction", although they are moving away from their source charge. However, since the receiver charge is moving even faster, it seems as if these quantinos are moving towards their source charge. Their acceleration effect is thus completely reversed, i. e. an attraction becomes a repulsion and vice versa.

However, because there are also quantinos that are moving away faster from the source charge than the receiver charge, there is as well a force effect in the normal direction. The two opposite forces partially compensate each other. In sum, the acceleration effect is reduced compared to the Coulomb force. The resulting electrical field is shown in Figure 2.6.7.4. We can see that the electric field for moving charges is elliptically deformed.

- Figure 2.6.7.5: The force is different for a moving source or receiver. If the angle between speed direction and connecting line is 0°, the force is weakened. For 90°, the force is strengthened.

The electrical force therefore depends not only on the relative speed between source and receiver, but also on the angle between connecting axis and speed. Figure 2.6.7.5 shows how the force is deformed as a function of the angle.

Mathematically, this relation is described by the relatively simple formula (2.2.1.4), which because of its central role is given here once again:

Formula (2.2.1.4) is very simple in structure and represents a non-conservative central force. This does not apply to force formula (2.1.1.8), which follows from Maxwell's equations. In fact, equation (2.2.1.4) emerges from equation (2.1.1.8) by setting $\vec{u} \to \vec{u}-\vec{v}$ and $\vec{v} \to 0$, then multiplying by the Lorentz factor $\gamma(\vec{u}-\vec{v})$ and finally performing a Taylor series approximation. The resulting formula (2.2.1.4) is completely symmetrical. This means that a charge always experiences a force which, conversely, is the same as the force it generates itself. This ensures that the conservation of inertia applies to Formula (2.2.1.4). It can also be shown that the conservation laws of angular momentum and energy are fulfilled. However, this does not apply to formula (2.1.1.8), which follows from Maxwell's equations, since the factor $\zeta_M$ in formula (2.2.1.4) depends only on the speed $\vec{u}$ of the source. The resulting paradoxes are the root of the fundamental problems of modern physics.

The fact that it is apparently possible to trace back all three basic forces of classical physics to the same central force (2.2.1.4), demands to explain why this force is transferred from the source to the target at all and why its form and strength depends on the relative speed. As has just been shown, the quantino mechanism provides a plausible answer.

### 2.6.8 Quantino waves

It is now time to go one step further and investigate oscillating charges. I was already noted in Section 2.6.5 that the quantino field of an accelerated charge is compressed in the direction of acceleration and thinned out in the opposite direction. A back and forth swinging charge is also constantly accelerated, however in periodically changing directions. The compression and thinning out of the quantino field are therefore alternating on one side and on the other. Figure 2.6.8.1 shows the near field of such an oscillating charge.- Figure 2.6.8.1: An oscillating charge and the quantino field generated by it

*freeze image*. The fact that there is actually a wave propagation, one can only sense when the animation is running. This is due to the fact that a considerable part of the wave is contained in the quantino velocity distribution.

As shown in section Force propagation, such quantinos have the maximal effect, that are moving in the receiver charge's rest frame at the speed of light . The reason for this was Rule 3, according to which the differential velocity between receiver charge and quantino has a quadratic effect on the acceleration generated at the receiver charge. Thus, if we filter out all quantinos in animation 2.6.8.1 that produce little or no effect and increase the number of quantinos sent out per time unit to improve the contrast, so we get animation 2.6.8.2. In animation 2.6.8.2 the wave is now clearly visible.

- Figure 2.6.8.2: Only quantinos are shown here which would have a notable effect on a resting receiver charge.

### 2.6.9 The constant propagation velocity of EMG waves

In the previous section was shown that the oscillation of a charge causes density fluctuations in the surrounding quantino field, which propagate wave-like in all directions. The phase velocities of these waves have very different values, whereby the speed of light does not play a particular role. This particular role it gets only because of the fact that waves, which move relative to a receiver charge at the speed of light, cause a maximal effect and waves moving at a speed faster than the speed of light cannot interact at all.Which wave component has just light speed from the perspective of a moving receiver charge depends only on the relative speed between quantinos and receiver charge. If the speed of the receiver charge changes, another wave component with a different phase velocity becomes relevant. This filter or fade-out effect causes the receiver charge to appear as if the density fluctuation waves of the quantinos always would propagate at a constant speed.

This effect can be recognized even better by looking at two equally strong charges of reverse polarity, which initially rest at the same place and then perform a single opposed swinging movement for a short moment. Figure 2.6.9.1 shows the resulting quantino wave on the left-hand side, whereby only the wave component which has a maximum effect on the receiver charge (top, grey) is shown.

- Figure 2.6.9.1: The quantino field of an oscillating dipole from the viewpoint of a stationary receiver (left) and the resulting electric field (right).

Since Quantinos are force carriers, the receiver charge is accelerated when the wavefronts arrive. This means that if it is positively charged, it is first attracted and then pressed away. Effectively it carries out a single vibration. The time that passes between the oscillation of the dipole (the source) and the oscillation of the receiver charge corresponds to the distance divided by the speed of light.

At the right side of animation 2.6.9.1 the corresponding electric field of the quantino wave is shown. It results from the effects of all waves, including those that move at different phase velocities. As can be seen, the change in electric field strength propagates essentially also in the form of a ring. The radius of the ring thereby increases with the speed of light.

It is important to point out two things here. First of all, this is not yet the field of a Hertzian dipole. Secondly, the direction of the electric field strength does not always show in the direction of movement of the quantinos, as one might think at first glance. Instead, the electric field strength is only the average effect of the fluxes of all quantinos. And of course these can go in different directions at the same time. This is especially the rule for the superimposed fields of more than one charge.

- Figure 2.6.9.2: The quantino field of an oscillating dipole from the viewpoint of a moving receiver (left) and the resulting electric field (right).

It is important to emphasize that nothing has changed in respect of physics. The source and the wave itself are exactly the same in both cases. The waves' effect, however, depends on the perspective of the receiver, whereby it appears to have a completely different shape in different reference frames. And although some important aspects known for light and electromagnetic waves are still missing, the simple model of light described here can be used to explain all test experiments of the special theory of relativity (Except one. See below). This can be justified by the fact that in quantino theory the both axioms of the special theory of relativity, namely the constancy of the speed of light, as well as the validity of the special principle of relativity, are fulfilled. Unfortunately, however, it is not the case that quantino theory and special theory of relativity are equivalent. However, in order to be able to decide between the two theories, new experiments specifically adapted to the differences are needed.

It shall not be concealed that one test experiment, namely the Hafele-Keating experiment, cannot be directly explained by the quantino theory. Quantino theory and special theory of relativity differ in the so-called relativity of simultaneity. The special theory of relativity presumes that a light pulse is a localized event. Quantino theory, on the other hand, assumes that a pulse of light exists simultaneously at many different speeds and that the receiver prefers to perceive the component which, from its point of view, has the speed of light. Therefore, an event that takes place for an observer at the same time is also simultaneous for each other observer. In the special theory of relativity, this cannot apply due to the locality of the light pulse, as Einstein has shown. This eventually leads to the so-called twin paradox. In quantino theory, on the other hand, there is no twin paradox and the time shifts disappear abruptly after the two reference systems rest again. However, this does not mean that time measurements must deliver the same result everywhere! In particular, it can be assumed in quantino theory that a time measurement under the influence of forces will produce different results. Time is not what we read on the watch. A clock measures the speed with which atomic processes run. However, the speed of such processes is determined by force effects, which are also relative in quantino theory. The Hafele-Keating experiment is therefore not a good test experiment to decide between quantino theory and special theory of relativity.