dependent change in length is observed and used as magnetostriction or electrostriction.

If a ferromagnetic material, e.g. a nickel rod, is brought into an alternating magnetic field,

then field dependent longitudinal length oscillations are observed. In the same manner

barium titanate or quartz crystal oscillates in the electric field if a high-frequency

alternating voltage is applied.

A practical application forms the production of ultrasound.

In this chapter are, as already announced, the quantum properties of the elementary

particles calculated and in this way is furnished perhaps the most convincing proof for the

existence of potential vortices and for the correctness of the field-theoretical approach

and the theory which is based on it.

A special challenge represents the calculation of the particle mass. This mass stretches

from 207 electron masses of the myon over 1839 of the neutron into the order of

magnitude of 18513 electron masses (Y°). Doing so not only can be tested, if the

calculated values correspond with the measured ones. Also the gaps have to correspond,

i.e. where there doesn't exist a discrete mathematical solution also no particle should exist.

The fig. 7.0 standing on the left page anticipates the result and shows that even this strict

condition is fulfilled! The agreement of the calculated with the measured results is

excellent. If in individual cases small deviations become visible, we always have to bear in

mind that the measurements as a rule are analysed statistically and the results are falsified

if small particles creep in unrecognized. Particle physics nowadays has at its disposal

extremely precise gauges, but even here remaining errors can't be excluded.

Quantum physics is occupied with further taking apart the elementary particles into

hypothetic particles, the quarks, and to sort these according to properties and symmetries.

Seen strictly causal this procedure thus corresponds to the quantum physical approach.

We however have taken the field-theoretical approach, and this excludes the introduction

of hypothetic particles from the start. It should be our goal to derive and to explain the

quantum structure as a field property. Yes, we even want to calculate it, with which we

would have overtaken quantum physics in the scientific competition with one leap!

Strong support our approach has experienced by current experiments, in which matter was

transformed in electromagnetic waves - practically the reversal of the rolling up of waves

to vortices. To do so at the Massachusetts Institute of Technology (David Pritchard and

others) sodium atoms were dematerialized in waves by lattice scattering

*. According to*

Einstein one surely could have blown the whole M.I.T. in the air with the occurring mass

defect; but don't worry, no emission of energy whatsoever has been observed, entirely as

predicted by the vortex theory.

7.1 Elementary vortices

We had derived the electron and the positron as elementary vortices (fig. 4.3). Before we

can go in the calculation, we must gain a clear picture of the possible configurations of

vortices, which for reason of the derived properties are possible. For that we start with the

elementary vortex and afterwards we predict the behaviour of interaction which can be

expected.

Actually only one single particle is really elementary. According to the realizations of the

new theory it is an elementary vortex in the form of a sphere. Its size is determined by the

speed of light and this again by the local field strength; its stability is founded in the

concentration effect of the potential vortex. The whirling takes place everywhere with the

speed of light, even in the vortex centre, where all field lines run together, where the field

increases infinitely and the speed of light goes to zero. This last circumstance owes the

elementary vortex its localization.

We can attribute a charge to this vortex for reason of the field lines which on the outside

run towards infinity and which we can measure (fig. 4.3). This is the smallest indivisible

unit, the elementary charge e. Structure and course of the field lines suggest to understand

and to calculate the elementary vortex as a spherical capacitor. By basing on the classical

radius of the electron re given in fig. 6.3 the capacity according to equation 6.4 is

calculated to be:

(6.4*)

Here the theory of objectivity has provided us the realization that even for a change of the

radius of the electron the capacity remains unchanged constant (6.30), and this entirely

corresponds to our observation.

Between the hull of the elementary vortex, measured at the radius re, and its centre,

respectively also with regard to infinity, there exists according to equation 6.31 the tension

voltage of:

Ue = e/Ce = 511 kV (6.31*)

It as well is constant and independent of the size of the elementary vortex.

Since a different solution is refused, we'll have to assume that all elementary particles

consist of an integer multiple of elementary vortices. For that the amassing, like closely

packed tennis balls, or the overlapping of individual vortices in the form of shells, like in

the case of an onion (phenomenon of transport) can be considered.

The among each other occurring forces of attraction can be traced back to the fact that

every elementary vortex is compressed by the field of its neighbour as a consequence of

the field dependent speed of light. This field as a rule is for the small distances

considerably larger than the field on the outside. Therefore do compound elementary

particles not have the twofold or triple mass, but at once the 207-fold (myon) or the 1836-

fold (proton) mass. After all there is no other explanation for the fact that there don't exist

lighter particles (with a mass less than 207 electron masses)!

a. The electron-positron pair

b. . The e- - e+ pair for a small distance:

138 matter and anti-matter

139

7.2 Matter and anti-matter

For the amassing or overlapping of elementary vortices several cases must be distinguished,

because two inverse forms of formation are possible for the elementary vortex:

the negatively charged electron and the positively charged positron. Whereas in the case

of the electron the vortex produces a component of the electric field which points from the

inside to the outside, has the field in the case of the positron the opposite direction for

reason of a reversed swirl direction.

This statement can be generalized: if we consider the elementary particles from the

outside, then we assign the particles with a swirl direction identical to that of the electron

to the world of matter and call the particles with the opposite swirl direction anti-matter. It

now is strongly recommended, to take colours to hand, in order to optically clarify the

properties of vortices. The electron will be marked as a green sphere and the antiparticle,

the positron, as a red sphere.

If we now look into the world of matter, then appears our world of matter to us "green",

the world of anti-matter however "red". The uniform green colour of all the in our world

existing elementary particles however doesn't exclude that red anti-vortices can exist

hidden in the inside of the green vortices, where we can't discover them. But they must be

completely covered, otherwise a disastrous reaction occurs, the pair annihilation, as a

consequence of the oppositely directed property of the vortices which cancel out.

By means of the pair annihilation a dematerialization can occur, because every

elementary vortex keeps in its inside the same amount of energy with opposite sign and

the fusion of two inverse particles can result in a zero sum of the energy. The best known

example is the annihilation of an electron-positron pair under emission of radiation

discovered by Klemperer in 1934. In the upper representation (fig. 7.2a) the elementary

vortices still are symmetrical, but the outside field lines already are "bent" and linked

together in such a way that, with the exception of the ones in the direction of the axis, no

interaction takes place which can be measured.

The two particles for reason of the different charge approach each other quickly, and the

closer they are, the larger the mutual force of attraction becomes; a vicious circle, which

leads to the asymmetry shown in the lower sketch (fig. 7.2b) and only comes to rest, if

both particles have destroyed themselves mutually.

The electron and the positron had the same amount of, but oppositely directed swirl

activity, so that purely arithmetically seen a zero sum of the rest energy results. But it

should be paid attention to both particles having some kinetic energy on the occasion of

the relative motion to each other and if they rotate around their own axis also rotational

energy. An emission of annihilation radiation occurs, is the explanation of particle

physics.

With the knowledge of the photon (fig. 4.6) we can interpret the annihilation radiation as a

consequence of the phenomenon of transport. The faster and consequently smaller vortex,

for instance the green one, slips into the red one and sees the green inside, which is

compatible for it. Unfortunately it only can remain there, as long as it is smaller, thus is

faster, and therefore it shoots out on the other side again. Now the electromagnetic force

of attraction fully takes effect. It is slowed down and the red vortex correspondingly

accelerates. The process is reversed.

These around each other oscillating vortices, so we had derived, have a characteristic

frequency (colour), are polarizable and are moving forward with the speed of light as a

consequence of the open vortex centre. It therefore concerns the photon.

140 Positronium

Fig. 7.3: Theoretical final state of the positronium

= static -quant (photon).

proof ______________________________________________________________ 141

7.3 Positronium

But before the two elementary vortices, the electron and the positron, are annihilated

under emission of radiation, they will for a short time take a shell-shaped, a bound state, in

which one vortex overlaps the other.

Its formation we can imagine as follows: an electron, flying past a resting positron, is

cached by this for reason of the electromagnetic attraction and spirals on an elliptic path

towards the positron. In doing so its angular velocity increases considerably. It will be

pulled apart to a flat disc for reason of the high centrifugal forces, to eventually lay itself

around the positron as a closed shell.

Now the red positron sees the electron vortex so to speak "from the inside" and doing so it

sees as well red; because the green vortex has a red centre and vice versa! The result is the

in fig. 7.3 given configuration.

The number of field lines, which run from the red border of the positron in the direction of

the centre, is identical to the number, which point towards the green border of the electron.

Here already the same state has been reached as in the centre, which corresponds to the

state at infinity. That means that no field lines point from the green border to the outside;

seen from the outside the particle behaves electrically neutral. It doesn't show any

electromagnetic interaction with its surroundings.

If the particle were long-living, then it undoubtedly would be the lightest elementary

particle besides the electron; but without stabilizing influence from the outside the

positronium can't take the in fig. 7.3 shown state at all. The positron takes up the kinetic

energy which is released if the electron becomes a shell around it. But before the bound

state can arise, which would identify the positronium as an elementary particle, the equal

rights of both vortices comes to light. With the same right, with which the electron wants

to overlap the positron, it itself vice versa could also be overlapped.

If the stabilization of the one or the other state from the outside doesn't occur, then the

stated annihilation under emission of y-quanta is the unavoidable consequence (fig. 4.6).

142 dipol moment

Fig. 7.4: Two electrons with oppositely directed spin

proof 143

7.4 Dipole moment

As electrically charged spheres elementary vortices have a magnetic dipole moment along

their axis of rotation as a consequence of the rotation of their own (fig. 7.4). This is

measurable very precisely and for the most important elementary particles also known

quantitatively. In contrast to the angular momentum the magnetic moment can't be

constant according to the here presented theory. It should slightly change, if we increase

the field strength in the laboratory.

In a particle consisting of several elementary vortices the vortices mutually increase the

local field strength. Therefore we measure at the proton, which consists of three vortices,

not the triple, but only the 2,793-fold of the nuclear magneton which can be expected for

reason of its mass. Also the neutron has instead of the double only the 1,913-fold nuclear

magneton. The deviations therefore are explicable as a consequence of the surrounding

fields.

Prerequisite for this point are two other, still unanswered, key questions of quantum

physics:

XII: Why is measured for the proton approximately the triple of the magnetic dipole

moment which can be expected for reason of the charge?

XIII: Why does the neutron, as an uncharged particle, actually have a magnetic

moment?

These questions can only be brought to a conclusive answer, if we have derived the vortex

structures of the respective particles.

The elementary vortex, as a consequence of the spin along its axis, forms a magnetic north

pole and a south pole. Another possibility to interact with an external field or with other

particles is founded on this property. This shall be studied by means of two electrons.

which form an electron pair.

For reason of the equal charge the two electrons at first will repel each other. If they rotate

of their own they however will mutually contract, which, seen from the outside, is

interpreted as a force of attraction. And in addition will they align their axes of rotation

antiparallelly. While they now rotate in the opposite direction, a magnetic force of

attraction occurs.

As is shown in fig. 7.4, the magnetic dipole field in this way is compensated towards the

outside, as is clarified by the field line (H) with a closed course. Between both electrons a

space free of E-field stretches. If both vortices are a small distance apart they lay

themselves around this space like two half-shells of a sphere. A particle forms which seen

from the outside is magnetically neutral, but it carries the double elementary charge (fig.

7.4b).

The exceptional affinity is always restricted to two vortices of equal charge with an

opposite direction of rotation. Further vortices can't be integrated anymore and are

repelled. This property of vortices covers the quantum condition (Pauli's exclusion

principle) for the spin quantum number perfectly.

144 myon

Fig. 7.5: The mvon and the electric field E(x)

of the three elementary vortices

proof 145

7.5 Myon

We now have discussed all conceivable possibilities, which two elementary vortices can

form: the creation of a pair for like charge and the annihilation under emission of photons

via the formation of the positronium as an intermediate result for unequal charge. Next

another elementary vortex shall be added and all different possibilities and configurations

will be derived, which can be formed by amassing or overlapping.

The positronium can, as said, only take the in fig. 7.3 shown bound structure, if it is

stabilized from the outside. This task now a further electron shall take over. According to

the shell model the innermost elementary vortex an electron (e-), is overlapped by a

positron (e+) and that again overlapped by an electron (e-).

With an in the sum single negative charge, a completely symmetric structure as well as a

half-integer spin this particle will show a behaviour corresponding to a large extent to that

of the electron. Merely the mass will be considerably larger, because every vortex each

time compresses the other two.

It therefore concerns the myon which also is called "heavy electron". The myon

was discovered 1937 in the cosmic radiation (Anderson and others).

In fig. 7.5 are drawn above each other the shell-shaped structure of the myon and the

electric field E(x) of the three elementary vortices.

It is visible that merely in the proximity of the particle the actual course of the field

deviates from and is smaller, than the course which theoretically can be expected for a

single negatively charged body. The difference is marked by a hatching.

We now can tackle the calculation of the myon. For that the following considerations to

begin with are useful:

Mass is an auxiliary term founded in usefulness, which describes the influence of the

electromagnetic field on the speed of light and with that on the spatial extension of the

"point mass".

Without exception the local cosmic field Eo has an effect on a free and unbound

elementary vortex, thus on an individual e- or e+, and determines so its size and its mass.

But as long as we haven't determined this field strength, the calculation of its quantum

properties won't succeed.

Instead the masses of compound particles will be compared to each other, which are so

heavy that the field strength of the neighbouring vortices is predominant over the basic

field E0, so that a neglect of Eo seems to be allowed. The course of the calculation is made

for all elementary particles in the same manner, which is explained hereafter.

146 calculation of the vortex fields

Fig. 7.6: Calculation of the electric field strength E(r) of

the myon from its dependency on radius

proof 147

7.6 Calculation of the vortex fields

The tension voltage of an elementary vortex, like for a spherical capacitor, is determined

by integrating over the electric field strength from the inner radius ri up to the outer radius

ra:

(7.1)

For the electron (ri = 0 und ra = re) we already have carried out the integration and

determined the tension voltage to be 511 kV (equation 6.31 *).

Doing so we further had discovered that it won't change, if the radius r varies. Even for a

shell configuration, in which electrons and positrons alternately overlap, the approach is

valid:

U1 = U2 = U3 = U4 = ... = Un (7.2)

At a certain radius all elementary vortices show the same density of field lines and with

that also the identical field strength, so that we can solve the integral (7.1) for the each

time neighbouring vortex shells and can compare the results:

At the radius r1 with E(r1) = E1 the agreement, according to equation 7.1* (fig. 7.6), is

valid for the innermost and the overlapped vortex shell.

At the radius r2 with E(r2) = E2 the agreement according to equation 7.1** (fig. 7.6) is

valid analogously for the 2nd and 3rd shell.

If still more shells are present, then we can arbitrarily repeat this procedure. For the radius

of each shell we always obtain relation 7.3, which, related to the innermost radius,

provides the following simple expression for the individual radii:

r 2 = 2 * r 1 ; r3 = 3 • r1; ... ; rn = n * r1 (7.4)

From the comparison of the integration results 7.1* and 7.1** follows further that all

elementary vortices produce the same field strength:

E1 = E2 = E3 = ... = En (7.5)

We infer from the transformation table (fig. 6.18, eq. 6.27) that the field strengths E and H

decrease with 1/r. In fig. 7.5 the decrease of the fields with 1/r is shown. Up to the radius

r, the field of the innermost vortex E1 has worn off to the value E31 = - E1 • (r1/r3).

This field is overlapped by E32 = E2 * (r2/r3) as well as the cosmic basic field Eo:

E(r3) = E31+ E32+ E0 = E1 • (r2 - r1)/r3 + Eo (7.6)

The local basic field Eo is not known, but it is very small with regard to the field of the

neighbouring vortex shells, so that a neglect seems to be allowed.

From equation (7.6) in this way follows with the radius relation (7.4):

(7.7)

For the shell-shaped configuration of the myon (fig. 7.5) relation (7.7) indicates, which

field the outside vortex shell is exposed to. From this can already be seen, how much it is

compressed thanks to the field dependent speed of light and how much its mass as a

consequence is increased.

148 calculation of the proton

Structure of the proton p+:

Calculation:

structure consisting of two shells, inner vortices with 2 • E1,

field strength at the outer radius r2:

E ( r 2 ) = 2 * E2 1 = 2 * E 1 ( r 1 / r 2 ) = E1 (7.8)

Comparison of p+ (7.8) with u- (7.7) (ze = number of the elementary

vortices being involved with)

in building up the structure, here each time ze = 3):

Comparison of the radii with E ~ l / r (6.27)

(7.9)

Theory of objectivity (fig. 6.18): m~l/r2 (6.34)

(7.10)

mp/me = 9 * (mu/me) = 9 * 207 = 1863 (7.11)

Measurement value, proton mass: mp = 1836 • me

Resp.:

measurement value myon mass mu = 207 * me

myon calculated value: mp = 204 * me. (error = 1,5% )

Since we, by using this calculation method, for the first time succeeded

in deriving the mass of an elementary particle from that of another

particle, the particle mass isn't a constant of nature anymore!

Fig. 7.7: Calculation of the proton

proof________________________________________________________________ 149

7.7 Calculation of the proton

If we again remember the affinity of two elementary vortices, which rotate with opposite

spin. They align their axis of rotation antiparallel and form a very probable, but not

particularly tight bound pair (fig. 7.4).

If we this time start with a positron pair, then does this pair have a double positive

elementary charge. The two e+ hence exert a particularly big force of attraction on

electrons flying past them. If they have cached one and put it round as a shell, like a coat,

then they will never again give it back! To again remove the electron, a triple positive

charge would be necessary. But such a particle can't exist at all. The new particle

therefore has an absolute stability and a very big mass, because the positron pair is

considerably compressed by its outer shell. The total charge is single positive. With these

properties it actually only can concern the proton. Its structure is shown in fig. 7.7.

We can start from the assumption that both positrons are very close together in the inside

and thus each forms the half of a sphere. For the calculation of the proton mass we then

can assume as an approximation a structure of two shells, in which the inner vortex will

have the double charge and the double field (2 * E1). With equation 7.4 the field strength at

the outer radius r2 is:

E(r2) = 2*E21 = 2*E1*(r1/r2) = E1 (7.8)

If we want to compare the results of the p+ (7.8) and the (7.7), then it should be

considered that the field of the innermost elementary vortex E1 only is equal, if the number

ze of the elementary vortices involved in building up the particle is identical. Here with

each time ze = 3 this is the case. Because of equation 6.27 (E, H ~ 1/r) now also the radii

are comparable:

(7.9)

The mass of a particle first is determined by the number of the elementary vortices ze.

According to the theory of objectivity (fig. 6.18) however also the radius has an influence

on the mass: m ~ 1/r2 (6.34)

This proportionality should be applied to the - comparison.

(7.10)

The calculation provides a nine times bigger mass for the proton with regard to the mass

of the myon. Therefore the mass of the proton related to the mass of the electron is:

mp/me = 9* = 9*207 = 1863 (7.11)

It would be favourable, to start from the with measuring techniques determined value for

the mass of the proton mp/me = 1836 and calculate backwards the related mass of the

myon.

Then we obtain 204 as the calculated value instead of the measurement value =

207.

The reason for the deviation of 1.5 percent is caused by the neglect of the cosmic field Eo

with regard to the field of the neighbouring elementary vortex. This neglect takes very

much less effect for the relatively heavy proton than for the light myon.

The cosmic field therefore will compress the myon more strongly and increase the mass

more strongly as is calculated here, in agreement with the measurement results.

Summarizing: since we, by using this calculation method, for the first time succeeded in

deriving the mass of an elementary particle from that of another particle, the particle

mass isn't a constant of nature anymore!

150 ,,strong interaction"

Fig. 7.8: The proton and the electric field of the three

elementary vortices in x-, y- and z-direction

proof 151

7.8 "Strong interaction"

A central question of nuclear physics concerns the forces which keep the atomic nucleus,

which consists of many neutrons and protons, together and give it its very good stability in

spite of the like positive charge (key question XIV fig. 7.13).

According to today's textbook opinion (course of the field indicated with a in fig. 7.8) the

forces of repulsion between the individual protons increase further as the distance gets

smaller, to obtain immense values within the nucleus. They theoretically had to be

overcome by new and unknown nuclear forces. Therefore physicists assume the

hypothesis of a "strong interaction". But they are mistaken.

The answer to this open question is provided by the course of the field (b) for the proton,

sketched in fig. 7.8. We see that the electric field at first indeed still increases if we

approach the proton, but in the proximity it contrary to all expectations decreases again

until it is zero. With that then also any force of repulsion has vanished! But the course of

the field follows without compulsion from the overlap of the three individual elementary

vortex fields.

The field direction in the z-direction even is reversed! In this topsy-turvy world, in theory,

an electromagnetic force of attraction between two like charged protons can occur. We

conclude:

A strong interaction doesn't exist at all. The usually given values for "range" and

"strength" just represent a misinterpretation. The hatched drawn area marks the difference

which is misinterpreted by quantum physics. The model concept over and above that

answers another mysterious property of the proton. As an electrically charged particle with

a spin it first of all should form a magnetic moment for reason of the rotating charge. But

until now the measurable order of magnitude couldn't be explained.

7.9 Magnetic moment of the proton

If the inner positrons rotate around each other with oppositely pointing spin, then the

magnetic field line is already closed within the particle and no effect in x- or y-direction is

observable from the outside.

As pair they however still can rotate together around the z-axis and they'll do that. The

overlapping electron for reason of its rotation of its own will likewise build up a magnetic

dipole moment along its axis of rotation. It also will align its axis in the z-direction, so that

now all three elementary vortices have one field axis. Being comparable to individually

"elementary magnets" aligned in the same direction they produce a triple magnetic

moment (key question XII fig. 7.13).

If we namely would start with a single positively charged body according to the theory of

quantum mechanics, then we would have expected the value of the nuclear magneton

Einstein one surely could have blown the whole M.I.T. in the air with the occurring mass

defect; but don't worry, no emission of energy whatsoever has been observed, entirely as

predicted by the vortex theory.

7.1 Elementary vortices

We had derived the electron and the positron as elementary vortices (fig. 4.3). Before we

can go in the calculation, we must gain a clear picture of the possible configurations of

vortices, which for reason of the derived properties are possible. For that we start with the

elementary vortex and afterwards we predict the behaviour of interaction which can be

expected.

Actually only one single particle is really elementary. According to the realizations of the

new theory it is an elementary vortex in the form of a sphere. Its size is determined by the

speed of light and this again by the local field strength; its stability is founded in the

concentration effect of the potential vortex. The whirling takes place everywhere with the

speed of light, even in the vortex centre, where all field lines run together, where the field

increases infinitely and the speed of light goes to zero. This last circumstance owes the

elementary vortex its localization.

We can attribute a charge to this vortex for reason of the field lines which on the outside

run towards infinity and which we can measure (fig. 4.3). This is the smallest indivisible

unit, the elementary charge e. Structure and course of the field lines suggest to understand

and to calculate the elementary vortex as a spherical capacitor. By basing on the classical

radius of the electron re given in fig. 6.3 the capacity according to equation 6.4 is

calculated to be:

(6.4*)

Here the theory of objectivity has provided us the realization that even for a change of the

radius of the electron the capacity remains unchanged constant (6.30), and this entirely

corresponds to our observation.

Between the hull of the elementary vortex, measured at the radius re, and its centre,

respectively also with regard to infinity, there exists according to equation 6.31 the tension

voltage of:

Ue = e/Ce = 511 kV (6.31*)

It as well is constant and independent of the size of the elementary vortex.

Since a different solution is refused, we'll have to assume that all elementary particles

consist of an integer multiple of elementary vortices. For that the amassing, like closely

packed tennis balls, or the overlapping of individual vortices in the form of shells, like in

the case of an onion (phenomenon of transport) can be considered.

The among each other occurring forces of attraction can be traced back to the fact that

every elementary vortex is compressed by the field of its neighbour as a consequence of

the field dependent speed of light. This field as a rule is for the small distances

considerably larger than the field on the outside. Therefore do compound elementary

particles not have the twofold or triple mass, but at once the 207-fold (myon) or the 1836-

fold (proton) mass. After all there is no other explanation for the fact that there don't exist

lighter particles (with a mass less than 207 electron masses)!

a. The electron-positron pair

b. . The e- - e+ pair for a small distance:

138 matter and anti-matter

139

7.2 Matter and anti-matter

For the amassing or overlapping of elementary vortices several cases must be distinguished,

because two inverse forms of formation are possible for the elementary vortex:

the negatively charged electron and the positively charged positron. Whereas in the case

of the electron the vortex produces a component of the electric field which points from the

inside to the outside, has the field in the case of the positron the opposite direction for

reason of a reversed swirl direction.

This statement can be generalized: if we consider the elementary particles from the

outside, then we assign the particles with a swirl direction identical to that of the electron

to the world of matter and call the particles with the opposite swirl direction anti-matter. It

now is strongly recommended, to take colours to hand, in order to optically clarify the

properties of vortices. The electron will be marked as a green sphere and the antiparticle,

the positron, as a red sphere.

If we now look into the world of matter, then appears our world of matter to us "green",

the world of anti-matter however "red". The uniform green colour of all the in our world

existing elementary particles however doesn't exclude that red anti-vortices can exist

hidden in the inside of the green vortices, where we can't discover them. But they must be

completely covered, otherwise a disastrous reaction occurs, the pair annihilation, as a

consequence of the oppositely directed property of the vortices which cancel out.

By means of the pair annihilation a dematerialization can occur, because every

elementary vortex keeps in its inside the same amount of energy with opposite sign and

the fusion of two inverse particles can result in a zero sum of the energy. The best known

example is the annihilation of an electron-positron pair under emission of radiation

discovered by Klemperer in 1934. In the upper representation (fig. 7.2a) the elementary

vortices still are symmetrical, but the outside field lines already are "bent" and linked

together in such a way that, with the exception of the ones in the direction of the axis, no

interaction takes place which can be measured.

The two particles for reason of the different charge approach each other quickly, and the

closer they are, the larger the mutual force of attraction becomes; a vicious circle, which

leads to the asymmetry shown in the lower sketch (fig. 7.2b) and only comes to rest, if

both particles have destroyed themselves mutually.

The electron and the positron had the same amount of, but oppositely directed swirl

activity, so that purely arithmetically seen a zero sum of the rest energy results. But it

should be paid attention to both particles having some kinetic energy on the occasion of

the relative motion to each other and if they rotate around their own axis also rotational

energy. An emission of annihilation radiation occurs, is the explanation of particle

physics.

With the knowledge of the photon (fig. 4.6) we can interpret the annihilation radiation as a

consequence of the phenomenon of transport. The faster and consequently smaller vortex,

for instance the green one, slips into the red one and sees the green inside, which is

compatible for it. Unfortunately it only can remain there, as long as it is smaller, thus is

faster, and therefore it shoots out on the other side again. Now the electromagnetic force

of attraction fully takes effect. It is slowed down and the red vortex correspondingly

accelerates. The process is reversed.

These around each other oscillating vortices, so we had derived, have a characteristic

frequency (colour), are polarizable and are moving forward with the speed of light as a

consequence of the open vortex centre. It therefore concerns the photon.

140 Positronium

Fig. 7.3: Theoretical final state of the positronium

= static -quant (photon).

proof ______________________________________________________________ 141

7.3 Positronium

But before the two elementary vortices, the electron and the positron, are annihilated

under emission of radiation, they will for a short time take a shell-shaped, a bound state, in

which one vortex overlaps the other.

Its formation we can imagine as follows: an electron, flying past a resting positron, is

cached by this for reason of the electromagnetic attraction and spirals on an elliptic path

towards the positron. In doing so its angular velocity increases considerably. It will be

pulled apart to a flat disc for reason of the high centrifugal forces, to eventually lay itself

around the positron as a closed shell.

Now the red positron sees the electron vortex so to speak "from the inside" and doing so it

sees as well red; because the green vortex has a red centre and vice versa! The result is the

in fig. 7.3 given configuration.

The number of field lines, which run from the red border of the positron in the direction of

the centre, is identical to the number, which point towards the green border of the electron.

Here already the same state has been reached as in the centre, which corresponds to the

state at infinity. That means that no field lines point from the green border to the outside;

seen from the outside the particle behaves electrically neutral. It doesn't show any

electromagnetic interaction with its surroundings.

If the particle were long-living, then it undoubtedly would be the lightest elementary

particle besides the electron; but without stabilizing influence from the outside the

positronium can't take the in fig. 7.3 shown state at all. The positron takes up the kinetic

energy which is released if the electron becomes a shell around it. But before the bound

state can arise, which would identify the positronium as an elementary particle, the equal

rights of both vortices comes to light. With the same right, with which the electron wants

to overlap the positron, it itself vice versa could also be overlapped.

If the stabilization of the one or the other state from the outside doesn't occur, then the

stated annihilation under emission of y-quanta is the unavoidable consequence (fig. 4.6).

142 dipol moment

Fig. 7.4: Two electrons with oppositely directed spin

proof 143

7.4 Dipole moment

As electrically charged spheres elementary vortices have a magnetic dipole moment along

their axis of rotation as a consequence of the rotation of their own (fig. 7.4). This is

measurable very precisely and for the most important elementary particles also known

quantitatively. In contrast to the angular momentum the magnetic moment can't be

constant according to the here presented theory. It should slightly change, if we increase

the field strength in the laboratory.

In a particle consisting of several elementary vortices the vortices mutually increase the

local field strength. Therefore we measure at the proton, which consists of three vortices,

not the triple, but only the 2,793-fold of the nuclear magneton which can be expected for

reason of its mass. Also the neutron has instead of the double only the 1,913-fold nuclear

magneton. The deviations therefore are explicable as a consequence of the surrounding

fields.

Prerequisite for this point are two other, still unanswered, key questions of quantum

physics:

XII: Why is measured for the proton approximately the triple of the magnetic dipole

moment which can be expected for reason of the charge?

XIII: Why does the neutron, as an uncharged particle, actually have a magnetic

moment?

These questions can only be brought to a conclusive answer, if we have derived the vortex

structures of the respective particles.

The elementary vortex, as a consequence of the spin along its axis, forms a magnetic north

pole and a south pole. Another possibility to interact with an external field or with other

particles is founded on this property. This shall be studied by means of two electrons.

which form an electron pair.

For reason of the equal charge the two electrons at first will repel each other. If they rotate

of their own they however will mutually contract, which, seen from the outside, is

interpreted as a force of attraction. And in addition will they align their axes of rotation

antiparallelly. While they now rotate in the opposite direction, a magnetic force of

attraction occurs.

As is shown in fig. 7.4, the magnetic dipole field in this way is compensated towards the

outside, as is clarified by the field line (H) with a closed course. Between both electrons a

space free of E-field stretches. If both vortices are a small distance apart they lay

themselves around this space like two half-shells of a sphere. A particle forms which seen

from the outside is magnetically neutral, but it carries the double elementary charge (fig.

7.4b).

The exceptional affinity is always restricted to two vortices of equal charge with an

opposite direction of rotation. Further vortices can't be integrated anymore and are

repelled. This property of vortices covers the quantum condition (Pauli's exclusion

principle) for the spin quantum number perfectly.

144 myon

Fig. 7.5: The mvon and the electric field E(x)

of the three elementary vortices

proof 145

7.5 Myon

We now have discussed all conceivable possibilities, which two elementary vortices can

form: the creation of a pair for like charge and the annihilation under emission of photons

via the formation of the positronium as an intermediate result for unequal charge. Next

another elementary vortex shall be added and all different possibilities and configurations

will be derived, which can be formed by amassing or overlapping.

The positronium can, as said, only take the in fig. 7.3 shown bound structure, if it is

stabilized from the outside. This task now a further electron shall take over. According to

the shell model the innermost elementary vortex an electron (e-), is overlapped by a

positron (e+) and that again overlapped by an electron (e-).

With an in the sum single negative charge, a completely symmetric structure as well as a

half-integer spin this particle will show a behaviour corresponding to a large extent to that

of the electron. Merely the mass will be considerably larger, because every vortex each

time compresses the other two.

It therefore concerns the myon which also is called "heavy electron". The myon

was discovered 1937 in the cosmic radiation (Anderson and others).

In fig. 7.5 are drawn above each other the shell-shaped structure of the myon and the

electric field E(x) of the three elementary vortices.

It is visible that merely in the proximity of the particle the actual course of the field

deviates from and is smaller, than the course which theoretically can be expected for a

single negatively charged body. The difference is marked by a hatching.

We now can tackle the calculation of the myon. For that the following considerations to

begin with are useful:

Mass is an auxiliary term founded in usefulness, which describes the influence of the

electromagnetic field on the speed of light and with that on the spatial extension of the

"point mass".

Without exception the local cosmic field Eo has an effect on a free and unbound

elementary vortex, thus on an individual e- or e+, and determines so its size and its mass.

But as long as we haven't determined this field strength, the calculation of its quantum

properties won't succeed.

Instead the masses of compound particles will be compared to each other, which are so

heavy that the field strength of the neighbouring vortices is predominant over the basic

field E0, so that a neglect of Eo seems to be allowed. The course of the calculation is made

for all elementary particles in the same manner, which is explained hereafter.

146 calculation of the vortex fields

Fig. 7.6: Calculation of the electric field strength E(r) of

the myon from its dependency on radius

proof 147

7.6 Calculation of the vortex fields

The tension voltage of an elementary vortex, like for a spherical capacitor, is determined

by integrating over the electric field strength from the inner radius ri up to the outer radius

ra:

(7.1)

For the electron (ri = 0 und ra = re) we already have carried out the integration and

determined the tension voltage to be 511 kV (equation 6.31 *).

Doing so we further had discovered that it won't change, if the radius r varies. Even for a

shell configuration, in which electrons and positrons alternately overlap, the approach is

valid:

U1 = U2 = U3 = U4 = ... = Un (7.2)

At a certain radius all elementary vortices show the same density of field lines and with

that also the identical field strength, so that we can solve the integral (7.1) for the each

time neighbouring vortex shells and can compare the results:

At the radius r1 with E(r1) = E1 the agreement, according to equation 7.1* (fig. 7.6), is

valid for the innermost and the overlapped vortex shell.

At the radius r2 with E(r2) = E2 the agreement according to equation 7.1** (fig. 7.6) is

valid analogously for the 2nd and 3rd shell.

If still more shells are present, then we can arbitrarily repeat this procedure. For the radius

of each shell we always obtain relation 7.3, which, related to the innermost radius,

provides the following simple expression for the individual radii:

r 2 = 2 * r 1 ; r3 = 3 • r1; ... ; rn = n * r1 (7.4)

From the comparison of the integration results 7.1* and 7.1** follows further that all

elementary vortices produce the same field strength:

E1 = E2 = E3 = ... = En (7.5)

We infer from the transformation table (fig. 6.18, eq. 6.27) that the field strengths E and H

decrease with 1/r. In fig. 7.5 the decrease of the fields with 1/r is shown. Up to the radius

r, the field of the innermost vortex E1 has worn off to the value E31 = - E1 • (r1/r3).

This field is overlapped by E32 = E2 * (r2/r3) as well as the cosmic basic field Eo:

E(r3) = E31+ E32+ E0 = E1 • (r2 - r1)/r3 + Eo (7.6)

The local basic field Eo is not known, but it is very small with regard to the field of the

neighbouring vortex shells, so that a neglect seems to be allowed.

From equation (7.6) in this way follows with the radius relation (7.4):

(7.7)

For the shell-shaped configuration of the myon (fig. 7.5) relation (7.7) indicates, which

field the outside vortex shell is exposed to. From this can already be seen, how much it is

compressed thanks to the field dependent speed of light and how much its mass as a

consequence is increased.

148 calculation of the proton

Structure of the proton p+:

Calculation:

structure consisting of two shells, inner vortices with 2 • E1,

field strength at the outer radius r2:

E ( r 2 ) = 2 * E2 1 = 2 * E 1 ( r 1 / r 2 ) = E1 (7.8)

Comparison of p+ (7.8) with u- (7.7) (ze = number of the elementary

vortices being involved with)

in building up the structure, here each time ze = 3):

Comparison of the radii with E ~ l / r (6.27)

(7.9)

Theory of objectivity (fig. 6.18): m~l/r2 (6.34)

(7.10)

mp/me = 9 * (mu/me) = 9 * 207 = 1863 (7.11)

Measurement value, proton mass: mp = 1836 • me

Resp.:

measurement value myon mass mu = 207 * me

myon calculated value: mp = 204 * me. (error = 1,5% )

Since we, by using this calculation method, for the first time succeeded

in deriving the mass of an elementary particle from that of another

particle, the particle mass isn't a constant of nature anymore!

Fig. 7.7: Calculation of the proton

proof________________________________________________________________ 149

7.7 Calculation of the proton

If we again remember the affinity of two elementary vortices, which rotate with opposite

spin. They align their axis of rotation antiparallel and form a very probable, but not

particularly tight bound pair (fig. 7.4).

If we this time start with a positron pair, then does this pair have a double positive

elementary charge. The two e+ hence exert a particularly big force of attraction on

electrons flying past them. If they have cached one and put it round as a shell, like a coat,

then they will never again give it back! To again remove the electron, a triple positive

charge would be necessary. But such a particle can't exist at all. The new particle

therefore has an absolute stability and a very big mass, because the positron pair is

considerably compressed by its outer shell. The total charge is single positive. With these

properties it actually only can concern the proton. Its structure is shown in fig. 7.7.

We can start from the assumption that both positrons are very close together in the inside

and thus each forms the half of a sphere. For the calculation of the proton mass we then

can assume as an approximation a structure of two shells, in which the inner vortex will

have the double charge and the double field (2 * E1). With equation 7.4 the field strength at

the outer radius r2 is:

E(r2) = 2*E21 = 2*E1*(r1/r2) = E1 (7.8)

If we want to compare the results of the p+ (7.8) and the (7.7), then it should be

considered that the field of the innermost elementary vortex E1 only is equal, if the number

ze of the elementary vortices involved in building up the particle is identical. Here with

each time ze = 3 this is the case. Because of equation 6.27 (E, H ~ 1/r) now also the radii

are comparable:

(7.9)

The mass of a particle first is determined by the number of the elementary vortices ze.

According to the theory of objectivity (fig. 6.18) however also the radius has an influence

on the mass: m ~ 1/r2 (6.34)

This proportionality should be applied to the - comparison.

(7.10)

The calculation provides a nine times bigger mass for the proton with regard to the mass

of the myon. Therefore the mass of the proton related to the mass of the electron is:

mp/me = 9* = 9*207 = 1863 (7.11)

It would be favourable, to start from the with measuring techniques determined value for

the mass of the proton mp/me = 1836 and calculate backwards the related mass of the

myon.

Then we obtain 204 as the calculated value instead of the measurement value =

207.

The reason for the deviation of 1.5 percent is caused by the neglect of the cosmic field Eo

with regard to the field of the neighbouring elementary vortex. This neglect takes very

much less effect for the relatively heavy proton than for the light myon.

The cosmic field therefore will compress the myon more strongly and increase the mass

more strongly as is calculated here, in agreement with the measurement results.

Summarizing: since we, by using this calculation method, for the first time succeeded in

deriving the mass of an elementary particle from that of another particle, the particle

mass isn't a constant of nature anymore!

150 ,,strong interaction"

Fig. 7.8: The proton and the electric field of the three

elementary vortices in x-, y- and z-direction

proof 151

7.8 "Strong interaction"

A central question of nuclear physics concerns the forces which keep the atomic nucleus,

which consists of many neutrons and protons, together and give it its very good stability in

spite of the like positive charge (key question XIV fig. 7.13).

According to today's textbook opinion (course of the field indicated with a in fig. 7.8) the

forces of repulsion between the individual protons increase further as the distance gets

smaller, to obtain immense values within the nucleus. They theoretically had to be

overcome by new and unknown nuclear forces. Therefore physicists assume the

hypothesis of a "strong interaction". But they are mistaken.

The answer to this open question is provided by the course of the field (b) for the proton,

sketched in fig. 7.8. We see that the electric field at first indeed still increases if we

approach the proton, but in the proximity it contrary to all expectations decreases again

until it is zero. With that then also any force of repulsion has vanished! But the course of

the field follows without compulsion from the overlap of the three individual elementary

vortex fields.

The field direction in the z-direction even is reversed! In this topsy-turvy world, in theory,

an electromagnetic force of attraction between two like charged protons can occur. We

conclude:

A strong interaction doesn't exist at all. The usually given values for "range" and

"strength" just represent a misinterpretation. The hatched drawn area marks the difference

which is misinterpreted by quantum physics. The model concept over and above that

answers another mysterious property of the proton. As an electrically charged particle with

a spin it first of all should form a magnetic moment for reason of the rotating charge. But

until now the measurable order of magnitude couldn't be explained.

7.9 Magnetic moment of the proton

If the inner positrons rotate around each other with oppositely pointing spin, then the

magnetic field line is already closed within the particle and no effect in x- or y-direction is

observable from the outside.

As pair they however still can rotate together around the z-axis and they'll do that. The

overlapping electron for reason of its rotation of its own will likewise build up a magnetic

dipole moment along its axis of rotation. It also will align its axis in the z-direction, so that

now all three elementary vortices have one field axis. Being comparable to individually

"elementary magnets" aligned in the same direction they produce a triple magnetic

moment (key question XII fig. 7.13).

If we namely would start with a single positively charged body according to the theory of

quantum mechanics, then we would have expected the value of the nuclear magneton

*pm*

as the magnetic moment for the proton pm = . Opposite to that provide

experiments with protons the approx. threefold value as already predictable by the new

vortex theory. In addition does the direction of the vector pmp correspond with the spinaxis,

so as if the proton were negatively charged. The reason for that is that only the

outermost elementary vortex determines the spin of the particle, and that is actually a

negatively charged electron! Also this excellent agreement in the case of the proton can be

judged as proof for the correctness of the vortex model.

as the magnetic moment for the proton pm = . Opposite to that provide

experiments with protons the approx. threefold value as already predictable by the new

vortex theory. In addition does the direction of the vector pmp correspond with the spinaxis,

so as if the proton were negatively charged. The reason for that is that only the

outermost elementary vortex determines the spin of the particle, and that is actually a

negatively charged electron! Also this excellent agreement in the case of the proton can be

judged as proof for the correctness of the vortex model.

*: The nuclear magneton has the value of: pmk = 5,0508 • 10-27 Am2*

152 structure of the neutron

Fig. 7.10: The neutron with magnetic dipole field H

proof 153

7.10 Structure of the neutron

Until now could not be solved, why despite its missing charge also the neutron n° has a

magnetic moment. The experimentally determined value is approx. the double of the

nuclear magneton. Further was with measuring techniques an only 0,14% bigger mass

with regard to the proton determined. The difference is approximately two and a half

electron masses. And how reads the answer in the view of the potential vortex theory?

It is obvious that a positively charged proton and a negatively charged electron mutually

attract and amass together (fig. 7.10a). A pair annihilation can't occur, because the

electron, which jackets both positrons, prevents this. The formation of an outer shell is not

permitted by the high stability of the proton. It would have to be a positron shell, which

instead of neutrality would produce a double positive charge. Conceivable is however the

configuration, in which one of the two e+ of the proton takes up the e- in its inside and

overlaps it (fig. 7.10b).

At first appears the amassing of p+ and e- to be the obvious answer to the structure of the

neutron also in view of the small increase in mass. Since both elementary particles (p+ and

e-) have a spin, will they align their axes of rotation antiparallelly and rotate against one

another, exactly like an electron pair. But we now have unequal conditions: the proton

brings the triple magnetic moment, the electron however only the single, and its field line

will be closed by the proton. The difference which remains is the measurable double

nuclear magneton, with which key question XIII (fig. 7.13) would be answered

exhaustively.

This structure is shown in fig. 7.10a and has as rest mass the by only one electron mass

increased proton mass, but it will deviate from this value, when the unequal partner come

closer. Doing so the electron will be more strongly compressed by the heavier proton as

vice versa.

Mass, magnetic moment and charge thus correspond to a large extent with the

measurement values. Problems are seen concerning the spin and the stability.

Set of problems concerning spin: both the e- and the p+ have a half-integer spin, for which

reason this configuration should have an integer spin.

Set of problems concerning stability: the neutron decays as is well-known in a p+ and an

e- , but this object should be shorter-lived as determined by experiments. If namely the

partner come each other very close, then the field strength of the p+, contrary to

expectation, doesn't increase but decreases, as is shown in fig. 7.8. The e- therefore can

only be bound very, very loosely; in z-direction it even will be repelled!

For these reasons is the open structure, which is shown in fig. 7.10a, not feasible as an

isolated elementary particle, but only in a spatially extended network, like it is present in

an atomic nucleus. In this case the neutron is, as is well-known, lighter by the mass defect,

which is interpreted as binding energy.

Possibly it only concerns an intermediate stage. The heavier final product of the n° then

could look like is shown in fig. 7.10b. For this version the line of the magnetic field

already is closed partly within the particle, so that also here the approx. double nuclear

magneton remains as a rest with a sense of orientation, as if the neutron were negatively

charged.

Without charge and with the 1/2 spin it in this configuration fulfils all important quantum

properties of the neutron, even that of the stability.

154 calculation of the neutron

the field of the e-: E31(-) = - E1 (r1/r3),

the field of the e+: E32 = E2 (r2/r3) = E1 (r2/r3)

and in addition the e+: E3 1 = E1 (r1/r3).

With the radius relation (eq. 7.4): r2 = 2*r1 und r3 = 3* r1

The total field is:

(7.12)

With zen = 4 elementary vortices

(7.13)

n0 is 12,5% bigger than p±

(7.14)

n0 is 5% heavier than p±

Fig. 7.11: Calculation of the mass of the neutron

proof 155

7.11 Calculation of the neutron

The calculation of the mass for the structure of the neutron according to fig. 7.10b has still

remained open.

Because in this book for the first time has been shown, how the mass can be calculated, if

the particles are understood as potential vortices, we also in this case again want to make

use of this possibility.

We have, like for the a structure of three shells with the radii r1, r2 and r3. At the outer

radius r3 the fields of the elementary vortices on the inside have an effect on the electron

On the outside: like is the case for the

the field of the e-: E31

(-) = -E1(r1/r3),

the field of the e+: E32 = E2 (r2/r3) = E1 (r2/r3)

and in addition the e+: E31 = E1 (r1/r3).

The total field is, with the radius relation equation 7.4:

(7.12)

If we compare the neutron, in which now ze = 4 elementary vortices are involved, with

the proton:

(7.13)

then we infer from the arithmetically determined result that the neutron according to the

radius is 12,5% bigger than the proton. The mass is calculated to:

(7.14)

The particle therefore has a mass which is 5% larger than for the proton, slightly more as

has been measured for the neutron. The difference is acceptable. The particle after all is

structured very asymmetrically, in which the reason is to be seen, why the uncharged

particle, looked at from close up, nevertheless shows an observable charge distribution.

156 beta-decay

Fig. 7.12: The electron-neutrino as a ring-like vortex

proof 157

7.12

In the case of the calculated quasistable particles, the and the n°, the verification by

means of the well-known decay processes is still due. Also free neutrons, those which are

not bound in an atomic nucleus, decay. But with an average life of 918 seconds they are

by far the longest living among the quasistable elementary particles.

Should the neutron decay be triggered by neutrinos, then obviously a distant flying past

does not suffice. For that the electron is bound in the proton too tight. There probably has

to occur a direct "crash", in which a neutrino is used, since the decay equation reads:

(7.15)

As could be expected a proton p+, an electron e- and the mentioned electron-antineutrino

are formed. What here is written down as the emission of an antiparticle, is equivalent

in the absorption of the particle152 structure of the neutron

Fig. 7.10: The neutron with magnetic dipole field H

proof 153

7.10 Structure of the neutron

Until now could not be solved, why despite its missing charge also the neutron n° has a

magnetic moment. The experimentally determined value is approx. the double of the

nuclear magneton. Further was with measuring techniques an only 0,14% bigger mass

with regard to the proton determined. The difference is approximately two and a half

electron masses. And how reads the answer in the view of the potential vortex theory?

It is obvious that a positively charged proton and a negatively charged electron mutually

attract and amass together (fig. 7.10a). A pair annihilation can't occur, because the

electron, which jackets both positrons, prevents this. The formation of an outer shell is not

permitted by the high stability of the proton. It would have to be a positron shell, which

instead of neutrality would produce a double positive charge. Conceivable is however the

configuration, in which one of the two e+ of the proton takes up the e- in its inside and

overlaps it (fig. 7.10b).

At first appears the amassing of p+ and e- to be the obvious answer to the structure of the

neutron also in view of the small increase in mass. Since both elementary particles (p+ and

e-) have a spin, will they align their axes of rotation antiparallelly and rotate against one

another, exactly like an electron pair. But we now have unequal conditions: the proton

brings the triple magnetic moment, the electron however only the single, and its field line

will be closed by the proton. The difference which remains is the measurable double

nuclear magneton, with which key question XIII (fig. 7.13) would be answered

exhaustively.

This structure is shown in fig. 7.10a and has as rest mass the by only one electron mass

increased proton mass, but it will deviate from this value, when the unequal partner come

closer. Doing so the electron will be more strongly compressed by the heavier proton as

vice versa.

Mass, magnetic moment and charge thus correspond to a large extent with the

measurement values. Problems are seen concerning the spin and the stability.

Set of problems concerning spin: both the e- and the p+ have a half-integer spin, for which

reason this configuration should have an integer spin.

Set of problems concerning stability: the neutron decays as is well-known in a p+ and an

e- , but this object should be shorter-lived as determined by experiments. If namely the

partner come each other very close, then the field strength of the p+, contrary to

expectation, doesn't increase but decreases, as is shown in fig. 7.8. The e- therefore can

only be bound very, very loosely; in z-direction it even will be repelled!

For these reasons is the open structure, which is shown in fig. 7.10a, not feasible as an

isolated elementary particle, but only in a spatially extended network, like it is present in

an atomic nucleus. In this case the neutron is, as is well-known, lighter by the mass defect,

which is interpreted as binding energy.

Possibly it only concerns an intermediate stage. The heavier final product of the n° then

could look like is shown in fig. 7.10b. For this version the line of the magnetic field

already is closed partly within the particle, so that also here the approx. double nuclear

magneton remains as a rest with a sense of orientation, as if the neutron were negatively

charged.

Without charge and with the 1/2 spin it in this configuration fulfils all important quantum

properties of the neutron, even that of the stability.

154 calculation of the neutron

the field of the e-: E31(-) = - E1 (r1/r3),

the field of the e+: E32 = E2 (r2/r3) = E1 (r2/r3)

and in addition the e+: E3 1 = E1 (r1/r3).

With the radius relation (eq. 7.4): r2 = 2*r1 und r3 = 3* r1

The total field is:

(7.12)

With zen = 4 elementary vortices

(7.13)

n0 is 12,5% bigger than p±

(7.14)

n0 is 5% heavier than p±

Fig. 7.11: Calculation of the mass of the neutron

proof 155

7.11 Calculation of the neutron

The calculation of the mass for the structure of the neutron according to fig. 7.10b has still

remained open.

Because in this book for the first time has been shown, how the mass can be calculated, if

the particles are understood as potential vortices, we also in this case again want to make

use of this possibility.

We have, like for the a structure of three shells with the radii r1, r2 and r3. At the outer

radius r3 the fields of the elementary vortices on the inside have an effect on the electron

On the outside: like is the case for the

the field of the e-: E31

(-) = -E1(r1/r3),

the field of the e+: E32 = E2 (r2/r3) = E1 (r2/r3)

and in addition the e+: E31 = E1 (r1/r3).

The total field is, with the radius relation equation 7.4:

(7.12)

If we compare the neutron, in which now ze = 4 elementary vortices are involved, with

the proton:

(7.13)

then we infer from the arithmetically determined result that the neutron according to the

radius is 12,5% bigger than the proton. The mass is calculated to:

(7.14)

The particle therefore has a mass which is 5% larger than for the proton, slightly more as

has been measured for the neutron. The difference is acceptable. The particle after all is

structured very asymmetrically, in which the reason is to be seen, why the uncharged

particle, looked at from close up, nevertheless shows an observable charge distribution.

156 beta-decay

Fig. 7.12: The electron-neutrino as a ring-like vortex

proof 157

7.12

In the case of the calculated quasistable particles, the and the n°, the verification by

means of the well-known decay processes is still due. Also free neutrons, those which are

not bound in an atomic nucleus, decay. But with an average life of 918 seconds they are

by far the longest living among the quasistable elementary particles.

Should the neutron decay be triggered by neutrinos, then obviously a distant flying past

does not suffice. For that the electron is bound in the proton too tight. There probably has

to occur a direct "crash", in which a neutrino is used, since the decay equation reads:

(7.15)

As could be expected a proton p+, an electron e- and the mentioned electron-antineutrino

are formed. What here is written down as the emission of an antiparticle, is equivalent

in the absorption of the particle

*, in this case of the neutrino. The reaction equation 7.15*

can be reformulated accordinglycan be reformulated accordingly

*:*

(7.15*)

Also for the decay of the myon an electron-neutrino is used. In both cases it provides the

energy necessary for the decay. But we can really understand the only, after we

have got to know these particles better.

Without charge and without mass neutrinos show hardly any interactions with matter and

as a consequence they possess the enormous ability of penetration - as is well-known.

They are said to participate in the ,,weak interaction", which should trigger a conversion of

the concerned particles, which is their decay. Pauli already has postulated the neutrino

1930 theoretically, because the transition from a half-integer spin to an integer spin for the

n0 -decay otherwise wouldn't have been explicable.

If we imagine an elementary vortex is being born, but the local field strength and energy

isn't sufficient for obtaining a quantized state. The result is an incomplete potential vortex,

which has an open vortex centre and as a consequence shows no localization at all. In the

form of a vortex ring it oscillates around itself, while it continually turns its inside to the

outside and then again to the inside.

One moment the vortex ring is green, then it is red again, one moment matter, then antimatter,

one moment positively charged and the next moment negatively charged. In

contrast to the photon the number of the involved elementary vortices ze for the neutrino is

odd (for the = 1). Perpendicular to the direction of propagation the neutrino has a spin

for reason of a rotation, which overlaps the pulsating oscillation.

This vortex ring is, as said, not a member of stationary matter, because it doesn't form a

"black hole" in its centre, where the speed of light becomes zero. But it has an absolute

stability like every elementary vortex, even if it only occurs incomplete and hence not in

any quantized form,. This concept of the electron-neutrino as an open oscillating

elementary vortex in the form of a ring-like vortex covers the experimentally determined

realizations unexpectedly well.

(7.15*)

Also for the decay of the myon an electron-neutrino is used. In both cases it provides the

energy necessary for the decay. But we can really understand the only, after we

have got to know these particles better.

Without charge and without mass neutrinos show hardly any interactions with matter and

as a consequence they possess the enormous ability of penetration - as is well-known.

They are said to participate in the ,,weak interaction", which should trigger a conversion of

the concerned particles, which is their decay. Pauli already has postulated the neutrino

1930 theoretically, because the transition from a half-integer spin to an integer spin for the

n0 -decay otherwise wouldn't have been explicable.

If we imagine an elementary vortex is being born, but the local field strength and energy

isn't sufficient for obtaining a quantized state. The result is an incomplete potential vortex,

which has an open vortex centre and as a consequence shows no localization at all. In the

form of a vortex ring it oscillates around itself, while it continually turns its inside to the

outside and then again to the inside.

One moment the vortex ring is green, then it is red again, one moment matter, then antimatter,

one moment positively charged and the next moment negatively charged. In

contrast to the photon the number of the involved elementary vortices ze for the neutrino is

odd (for the = 1). Perpendicular to the direction of propagation the neutrino has a spin

for reason of a rotation, which overlaps the pulsating oscillation.

This vortex ring is, as said, not a member of stationary matter, because it doesn't form a

"black hole" in its centre, where the speed of light becomes zero. But it has an absolute

stability like every elementary vortex, even if it only occurs incomplete and hence not in

any quantized form,. This concept of the electron-neutrino as an open oscillating

elementary vortex in the form of a ring-like vortex covers the experimentally determined

realizations unexpectedly well.

*: Kussner, H.G.: Grundlagen einer einheitlichen Theorie der physikalischen*

Teilchen und Felder, Musterschmidt, Gottingen 1976, S.155

158 "weak interaction"

A strong interaction doesn't exist. The electric field in

the proximity of the proton goes to zero within the range

which is determined with measuring techniques.

A weak interaction doesn't exist. That interaction only

is a special case of the electromagnetic interaction

which appears in a weakened form. ________________

XII: Why does the proton have approximately 3

times the magnetic moment which can be

expected for reason of the only single charge?

(3 elementary vortices)

XIII: Why does the neutron as an uncharged

particle anyway have a magnetic moment?

(Structure of the n°)

XIV: What owes the atomic nucleus, which consists

of like charges, its stability?

(Course of the field of the p+, instead of "strong interaction")

XV: Why does the free neutron decay, although it

is stable as a particle of the nucleus? _________

(Interaction with neutrinos)

XVI: Why do neutrinos nevertheless participate in

the "weak interaction", although they have no

mass and no charge? ________________________

(Oscillating charge)

XVII: How can be given reasons for the finite range

______of the "weak interaction"?

(Reaction cross-section for particle decay)

Fig. 7.13: Further key questions of quantum physics

(Continuation of figures 4.4 and 6.13)

proof 159

7.13 "Weak interaction"

Let's now look again at the -decay of the neutron, in which a neutrino is used. But this

by no means will be a process of the weak interaction. Instead will neutrinos, contrary to

the textbook opinion, participate in the electromagnetic interaction. They after all are one

moment positively charged and the next moment negatively charged. With slow-acting

gauges this it is true can't be proven, because the interaction is zero on the average. But

this charged oscillating vortex ring can exert a considerable effect while approaching a

neutron, which is based solely on the electromagnetic interaction.

The neutron is stimulated to synchronous oscillations of its own by the high-frequency

alternating field of the neutrino, until it in the case of the collision releases the bound

electron, which takes up the energy provided by the neutrino and transports it away. The

interaction obviously is only very weak due to the oscillation. But a physical

independency of it has to be disputed.

The finite range, which is given in this context, indicates the reaction cross-section around

the n°-particle, within which the "crash" and as a consequence the -decay occurs. This

range is considerable larger as the particle itself. The electromagnetic interaction for such

small distances after all is so violent, even if it only occurs in pulses, that the neutrino is

thrown out of its path and can fly directly towards the neutron.

Perhaps we now understand also the -decay of the myon. It actually were to be expected

that without outside disturbance an absolute stability could exist because of the ideal

symmetry of the On our planet we however are in every second bombarded with

approx. 66 milliard (billion) neutrinos per cm2Teilchen und Felder, Musterschmidt, Gottingen 1976, S.155

158 "weak interaction"

A strong interaction doesn't exist. The electric field in

the proximity of the proton goes to zero within the range

which is determined with measuring techniques.

A weak interaction doesn't exist. That interaction only

is a special case of the electromagnetic interaction

which appears in a weakened form. ________________

XII: Why does the proton have approximately 3

times the magnetic moment which can be

expected for reason of the only single charge?

(3 elementary vortices)

XIII: Why does the neutron as an uncharged

particle anyway have a magnetic moment?

(Structure of the n°)

XIV: What owes the atomic nucleus, which consists

of like charges, its stability?

(Course of the field of the p+, instead of "strong interaction")

XV: Why does the free neutron decay, although it

is stable as a particle of the nucleus? _________

(Interaction with neutrinos)

XVI: Why do neutrinos nevertheless participate in

the "weak interaction", although they have no

mass and no charge? ________________________

(Oscillating charge)

XVII: How can be given reasons for the finite range

______of the "weak interaction"?

(Reaction cross-section for particle decay)

Fig. 7.13: Further key questions of quantum physics

(Continuation of figures 4.4 and 6.13)

proof 159

7.13 "Weak interaction"

Let's now look again at the -decay of the neutron, in which a neutrino is used. But this

by no means will be a process of the weak interaction. Instead will neutrinos, contrary to

the textbook opinion, participate in the electromagnetic interaction. They after all are one

moment positively charged and the next moment negatively charged. With slow-acting

gauges this it is true can't be proven, because the interaction is zero on the average. But

this charged oscillating vortex ring can exert a considerable effect while approaching a

neutron, which is based solely on the electromagnetic interaction.

The neutron is stimulated to synchronous oscillations of its own by the high-frequency

alternating field of the neutrino, until it in the case of the collision releases the bound

electron, which takes up the energy provided by the neutrino and transports it away. The

interaction obviously is only very weak due to the oscillation. But a physical

independency of it has to be disputed.

The finite range, which is given in this context, indicates the reaction cross-section around

the n°-particle, within which the "crash" and as a consequence the -decay occurs. This

range is considerable larger as the particle itself. The electromagnetic interaction for such

small distances after all is so violent, even if it only occurs in pulses, that the neutrino is

thrown out of its path and can fly directly towards the neutron.

Perhaps we now understand also the -decay of the myon. It actually were to be expected

that without outside disturbance an absolute stability could exist because of the ideal

symmetry of the On our planet we however are in every second bombarded with

approx. 66 milliard (billion) neutrinos per cm2

*. Obviously it takes 2,2 on the average*

till a neutrino flies past a myon so close that it decays. In doing so it stimulates the

outside elementary vortex to violent oscillations by trying to synchronize it. In this case

the electron-neutrino carries away with it the two outer, and therefore weaker bound,

elementary vortices of the myon, which meanwhile are oscillating synchronously. The

innermost vortex, an electron e-, is left behind. The decay of the myon which takes place

with a probability of almost 100 % reads:

(7.16)

Thus a different neutrino is formed which can be distinguished from the ve and is

called myon-neutrino since it forms from the Actually it even has a similar structure of

three shells, as is shown in fig. 7.5. But the vortex centre is open and the particle isn't

stationary anymore. In the picture now only a momentarily state is shown, in which the

appears green on the outside and red in its open centre. As already for the oscillates also

here the inside to the outside and vice versa, this time merely as a packet of three shells, so

that also this particle shows all the typical neutrino properties discussed for the example of

the

The for potential vortices typical and already discussed phenomenon of transport here has

an effect. In particular in connexion with vortex rings this property is known from

hydrodynamics. It thus can be observed, how vortex rings bind matter and carry away with

them. Because the neutrino is not quantized, it neither is restricted with regard to its ability

to transport elementary vortices. Consequently even bigger configurations are

conceivable, like configurations of 5 shells, 7 shells etc..

till a neutrino flies past a myon so close that it decays. In doing so it stimulates the

outside elementary vortex to violent oscillations by trying to synchronize it. In this case

the electron-neutrino carries away with it the two outer, and therefore weaker bound,

elementary vortices of the myon, which meanwhile are oscillating synchronously. The

innermost vortex, an electron e-, is left behind. The decay of the myon which takes place

with a probability of almost 100 % reads:

(7.16)

Thus a different neutrino is formed which can be distinguished from the ve and is

called myon-neutrino since it forms from the Actually it even has a similar structure of

three shells, as is shown in fig. 7.5. But the vortex centre is open and the particle isn't

stationary anymore. In the picture now only a momentarily state is shown, in which the

appears green on the outside and red in its open centre. As already for the oscillates also

here the inside to the outside and vice versa, this time merely as a packet of three shells, so

that also this particle shows all the typical neutrino properties discussed for the example of

the

The for potential vortices typical and already discussed phenomenon of transport here has

an effect. In particular in connexion with vortex rings this property is known from

hydrodynamics. It thus can be observed, how vortex rings bind matter and carry away with

them. Because the neutrino is not quantized, it neither is restricted with regard to its ability

to transport elementary vortices. Consequently even bigger configurations are

conceivable, like configurations of 5 shells, 7 shells etc..

*: "Zeugen aus der Sonne", VDI-Nachrichten Nr. 45 vom 9.11.90, Seite 26*

160 tau particle

Fig. 7.14: Tau-neutrino and tau particle

161

7.14 Tau particle

In the table of the leptons after the e- and the as the next particle the tau particle is

found with its accompanying neutrino The obvious solution for the tau particle is the

structure of five shells, as is shown in fig. 7.14a. With that the electron would have

another particularly heavy relative with otherwise very similar properties.

For the myon the neutrino was stable, the particle itself however instable. We after all

huve explained the particle decay as a consequence of an outside disturbance, and

disturbances always are based on interactions. Correspondingly should, with the small

possibility for an interaction, also the neutrino of the tau particle have a better stability

than the particle itself.

Without doubt this structure of 5 shells fulfils all known quantum properties like spin,

charge etc. Merely the check of the mass is still due. This we now want to calculate for the

structure shown in fig. 7.14a.

(7.17)

(7.17*)

But the for the tau particle measured value is considerable higher!

Even if this structure is the only possible in the case of the neutrino for reason of the

complete symmetry, will the tau particle however change its structure by itself if another

structure exists, which is more stable, thus in which the particle can take a bigger mass.

Such a maximum provides the structure shown in fig. 7.14b after checking all possible

configurations with five elementary vortices:

(7.18)

(7.18*)

This value now lies 8% above the measurement values. It would be obvious, if unbound

tau particles predominantly would take the structure shown in fig. 7.14b. The remaining

error becomes explicable, if a very small number of tau particles in the lighter structure

according to fig. 7.14a are involved with a correspondingly smaller probability.

The enormous variety of kinds of decay, and not a single one of the dominating ones has a

probability of over 50%, makes it more difficult for us, to be able to directly infer the

inner structure of a particle from the decay products. It nevertheless should be mentioned

that after all 35% of all decays take place by taking up and using a neutrino or

entirely in accordance with the model of the myon decay (equation 7.16).

162 pions

7.15 Table of vortices of the calculated leptons and mesons

compared with measurement values (Part 1).

proof 163

7.l5 Pions

Unlike the leptons, which we could derive and calculate fairly completely, the mesons

don't have a half-integer spin. With this characteristic property they therefore can't

represent an individually overlapped elementary particle and they probably will consist of

the amassing in pairs of individual configurations of potential vortices. This kind of bond

can't be particularly tight. Consequently we don't know any stable mesons.

The most important basic building part of the mesons we have got to know over the

positronium in fig. 7.3. It necessarily has to amass to another particle, otherwise it

annihilates under emission of a -quanta, as already mentioned. This particle, as it will

be named here, has the mass of:

(7.19)

which only can be determined arithmetically. As a partner, to which the -particle can

amass, first of all another -particle should be considered. Because both partner will

rotate against one another, this new particle would not have a spin and moreover would be

uncharged. The mass now would be twice as big with:

(7.19*)

But the two -particles will come very close together and mutually feel the local, in the

same direction orientated, distribution of the field, which will lead to a weakening of the

field and as a consequence to a slight reduction of the mass.

With these properties it probably concerns the uncharged pion This model concept

finds an excellent confirmation in the two possible kinds of decay, which can be regarded

as equivalent:

with a probability of 99%

and

with a probability of 1%

Also in the case of the charged pion the observable decay offers a big help, which will

take place with a frequency of almost 100 %:

The equation doesn't state anything about the fact, if a neutrino ve is used in the process.

But it points at the circumstance that the partner of the -particle for the most likely is

a myon The mass will be smaller than the sum of both building parts:

(204+136) * me = 340 * me.

164 table of vortices of the mesons

Some compound configurations

Fig. 7.16: Table of vortices of the calculated leptons and

mesons compared with measurement values (Part 2).

proof 165

7.16 Table of vortices of the mesons

The numerous kinds of decay for K-mesons suggest that these strange particles will

consist of various combinations of amassed together and in pairs rotating and

particles. The possibilities of combination now already have increased in such a way that

for every kaon and other mesons several solutions can be proposed. To avoid unfounded

speculations, only a few clues will be given.

Besides the -particles also heavier arrangements should be considered as partner for the

spin and as a building part for kaons and other mesons.

If for instance a is overlapped by a then this particle has an arithmetically

determined mass of 918 me. It therefore can concern a building part of the uncharged kaon

The likewise with three formed configuration of 6 shells however, if it actually would

staystable for the duration of a measurement, would have the mass of 3672 electron

masses160 tau particle

Fig. 7.14: Tau-neutrino and tau particle

161

7.14 Tau particle

In the table of the leptons after the e- and the as the next particle the tau particle is

found with its accompanying neutrino The obvious solution for the tau particle is the

structure of five shells, as is shown in fig. 7.14a. With that the electron would have

another particularly heavy relative with otherwise very similar properties.

For the myon the neutrino was stable, the particle itself however instable. We after all

huve explained the particle decay as a consequence of an outside disturbance, and

disturbances always are based on interactions. Correspondingly should, with the small

possibility for an interaction, also the neutrino of the tau particle have a better stability

than the particle itself.

Without doubt this structure of 5 shells fulfils all known quantum properties like spin,

charge etc. Merely the check of the mass is still due. This we now want to calculate for the

structure shown in fig. 7.14a.

(7.17)

(7.17*)

But the for the tau particle measured value is considerable higher!

Even if this structure is the only possible in the case of the neutrino for reason of the

complete symmetry, will the tau particle however change its structure by itself if another

structure exists, which is more stable, thus in which the particle can take a bigger mass.

Such a maximum provides the structure shown in fig. 7.14b after checking all possible

configurations with five elementary vortices:

(7.18)

(7.18*)

This value now lies 8% above the measurement values. It would be obvious, if unbound

tau particles predominantly would take the structure shown in fig. 7.14b. The remaining

error becomes explicable, if a very small number of tau particles in the lighter structure

according to fig. 7.14a are involved with a correspondingly smaller probability.

The enormous variety of kinds of decay, and not a single one of the dominating ones has a

probability of over 50%, makes it more difficult for us, to be able to directly infer the

inner structure of a particle from the decay products. It nevertheless should be mentioned

that after all 35% of all decays take place by taking up and using a neutrino or

entirely in accordance with the model of the myon decay (equation 7.16).

162 pions

7.15 Table of vortices of the calculated leptons and mesons

compared with measurement values (Part 1).

proof 163

7.l5 Pions

Unlike the leptons, which we could derive and calculate fairly completely, the mesons

don't have a half-integer spin. With this characteristic property they therefore can't

represent an individually overlapped elementary particle and they probably will consist of

the amassing in pairs of individual configurations of potential vortices. This kind of bond

can't be particularly tight. Consequently we don't know any stable mesons.

The most important basic building part of the mesons we have got to know over the

positronium in fig. 7.3. It necessarily has to amass to another particle, otherwise it

annihilates under emission of a -quanta, as already mentioned. This particle, as it will

be named here, has the mass of:

(7.19)

which only can be determined arithmetically. As a partner, to which the -particle can

amass, first of all another -particle should be considered. Because both partner will

rotate against one another, this new particle would not have a spin and moreover would be

uncharged. The mass now would be twice as big with:

(7.19*)

But the two -particles will come very close together and mutually feel the local, in the

same direction orientated, distribution of the field, which will lead to a weakening of the

field and as a consequence to a slight reduction of the mass.

With these properties it probably concerns the uncharged pion This model concept

finds an excellent confirmation in the two possible kinds of decay, which can be regarded

as equivalent:

with a probability of 99%

and

with a probability of 1%

Also in the case of the charged pion the observable decay offers a big help, which will

take place with a frequency of almost 100 %:

The equation doesn't state anything about the fact, if a neutrino ve is used in the process.

But it points at the circumstance that the partner of the -particle for the most likely is

a myon The mass will be smaller than the sum of both building parts:

(204+136) * me = 340 * me.

164 table of vortices of the mesons

Some compound configurations

Fig. 7.16: Table of vortices of the calculated leptons and

mesons compared with measurement values (Part 2).

proof 165

7.16 Table of vortices of the mesons

The numerous kinds of decay for K-mesons suggest that these strange particles will

consist of various combinations of amassed together and in pairs rotating and

particles. The possibilities of combination now already have increased in such a way that

for every kaon and other mesons several solutions can be proposed. To avoid unfounded

speculations, only a few clues will be given.

Besides the -particles also heavier arrangements should be considered as partner for the

spin and as a building part for kaons and other mesons.

If for instance a is overlapped by a then this particle has an arithmetically

determined mass of 918 me. It therefore can concern a building part of the uncharged kaon

The likewise with three formed configuration of 6 shells however, if it actually would

staystable for the duration of a measurement, would have the mass of 3672 electron

masses

*.*

A very much better detectability must be attributed to the configuration of 4 shells which

consists of two so to speak a heavy relative of the and the It among others should

be able to decay like a With this property and with an arithmetically determined mass

of 1088 me it actually only can concern the meson. Solely according to the numeric

value the -meson could also consist of four mesons; but the decay in only two light

quants speaks against it.

The kaon-puzzle in addition is made more difficult by the spontaneously possible ability

to change of the involved -particles during a process of decay, as is made clear by the

numerous kinds of decay. These dependent pion halves can be "swallowed" or "spit out"

by neutrinos in the process, they can form from incident light or be emitted as photons and

eventually they even can break up in their individual parts.

In fig. 7.16 the possible configurations of potential vortices are sketched and the

respective, according to the new theory calculated, mass is given. If above that the other

decay products and quantum properties, which can be given for the vortex structures, are

added, like e.g. charge, spin and if need be magnetic moment, then an assignment without

doubts to the until now only from measurements known elementary particles is possible.

In order to better be able to assess the efficiency of the potential vortex theory, the

measurement values are compared to the calculated values.

Some terms are put in brackets, because it can be assumed that the calculated part only

concerns the dominating part, to which further or other small configurations of vortices

will amass for reason of its high mass. Correspondingly should the mass in that case be

corrected slightly.

A very much better detectability must be attributed to the configuration of 4 shells which

consists of two so to speak a heavy relative of the and the It among others should

be able to decay like a With this property and with an arithmetically determined mass

of 1088 me it actually only can concern the meson. Solely according to the numeric

value the -meson could also consist of four mesons; but the decay in only two light

quants speaks against it.

The kaon-puzzle in addition is made more difficult by the spontaneously possible ability

to change of the involved -particles during a process of decay, as is made clear by the

numerous kinds of decay. These dependent pion halves can be "swallowed" or "spit out"

by neutrinos in the process, they can form from incident light or be emitted as photons and

eventually they even can break up in their individual parts.

In fig. 7.16 the possible configurations of potential vortices are sketched and the

respective, according to the new theory calculated, mass is given. If above that the other

decay products and quantum properties, which can be given for the vortex structures, are

added, like e.g. charge, spin and if need be magnetic moment, then an assignment without

doubts to the until now only from measurements known elementary particles is possible.

In order to better be able to assess the efficiency of the potential vortex theory, the

measurement values are compared to the calculated values.

Some terms are put in brackets, because it can be assumed that the calculated part only

concerns the dominating part, to which further or other small configurations of vortices

will amass for reason of its high mass. Correspondingly should the mass in that case be

corrected slightly.

*: It could e.g. concern the D°-meson.*

166 table of vortices of the Baryons

Fig. 7.17: Table of vortices used for the calculation of the

most

important barvons with suggestions for the structure

(Part 3).

proof 167

7.17 Table of vortices of the baryons

The number of possibilities of combination quickly increases, if only a few elementary

vortices extend the structure of a particle. This probably is the reason for the large number

of observable hyperons, which recently have been produced artificially and observed with

the help of particle accelerators.

Both the neutron and the lambda particle can exist in a lighter and a heavier variant. At the

moment of the decay, as it for instance is observed in a bubble chamber, according to

expectation the state with the smaller mass takes the bigger probability. But in the

amassing with further particles as building part of bigger and heavier hyperons the heavier

structure is more likely. This circumstance should be considered in calculating the mass of

the hyperons.

In figures 7.17 and 7.18 the most important baryons are listed, which are characterised in

the way that one of the amassed together packets of vortices is a nucleon, thus a proton or

a neutron.

The given, from measurements known, kinds of decay are able to confirm the inner

structure pretty good. Of course an infinitely lot of combinations are conceivable and

numerous predictions are possible. But speculations are unnecessary from the time on

where we are able to calculate the particles!

The restriction to the few in the table listed particles seeming to be important hence

doesn't limit the universal importance of the theory of objectivity in any way!

168 unified theory

Fig. 7.18: Table of vortices used for the calculation of the

most

important baryons with suggestions for the structure

(Part 4).166 table of vortices of the Baryons

Fig. 7.17: Table of vortices used for the calculation of the

most

important barvons with suggestions for the structure

(Part 3).

proof 167

7.17 Table of vortices of the baryons

The number of possibilities of combination quickly increases, if only a few elementary

vortices extend the structure of a particle. This probably is the reason for the large number

of observable hyperons, which recently have been produced artificially and observed with

the help of particle accelerators.

Both the neutron and the lambda particle can exist in a lighter and a heavier variant. At the

moment of the decay, as it for instance is observed in a bubble chamber, according to

expectation the state with the smaller mass takes the bigger probability. But in the

amassing with further particles as building part of bigger and heavier hyperons the heavier

structure is more likely. This circumstance should be considered in calculating the mass of

the hyperons.

In figures 7.17 and 7.18 the most important baryons are listed, which are characterised in

the way that one of the amassed together packets of vortices is a nucleon, thus a proton or

a neutron.

The given, from measurements known, kinds of decay are able to confirm the inner

structure pretty good. Of course an infinitely lot of combinations are conceivable and

numerous predictions are possible. But speculations are unnecessary from the time on

where we are able to calculate the particles!

The restriction to the few in the table listed particles seeming to be important hence

doesn't limit the universal importance of the theory of objectivity in any way!

168 unified theory

Fig. 7.18: Table of vortices used for the calculation of the

most

important baryons with suggestions for the structure

(Part 4).

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