Ample evidence is available for the correctness of the theory of objectivity. The field
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
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:
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
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
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
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.
Fig. 7.3: Theoretical final state of the positronium
= static -quant (photon).
proof ______________________________________________________________ 141
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
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
Prerequisite for this point are two other, still unanswered, key questions of quantum
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
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
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.
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.
Fig. 7.5: The mvon and the electric field E(x)
of the three elementary vortices
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
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
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
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
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):
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+:
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)
Theory of objectivity (fig. 6.18): m~l/r2 (6.34)
mp/me = 9 * (mu/me) = 9 * 207 = 1863 (7.11)
Measurement value, proton mass: mp = 1836 • me
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
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
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.
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
Then we obtain 204 as the calculated value instead of the measurement value =
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
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
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
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.
: 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
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
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
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
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:
With zen = 4 elementary vortices
n0 is 12,5% bigger than p±
n0 is 5% heavier than p±
Fig. 7.11: Calculation of the mass of the neutron
7.11 Calculation of the neutron
The calculation of the mass for the structure of the neutron according to fig. 7.10b has still
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:
If we compare the neutron, in which now ze = 4 elementary vortices are involved, with
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:
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.
Fig. 7.12: The electron-neutrino as a ring-like vortex
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:
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 accordingly:
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? ________________________
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)
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:
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 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
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.
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:
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).
7.15 Table of vortices of the calculated leptons and mesons
compared with measurement values (Part 1).
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:
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:
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
with a probability of 99%
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).
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
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
: 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
important barvons with suggestions for the structure
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
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
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
important baryons with suggestions for the structure