Preface to the lecture, 1

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 E

o

 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 E

0

, so that a neglect of E

o

 seems to be allowed. The course of the calculation is made

 

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

 

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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 

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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 r

i

 up to the outer radius

 

r

a

: 

 

(7.1)

 

For the electron (r

i

 = 0 und r

a

 = r

e

) 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:

 

U

1

 = U

2

 = U

3

 = U

4

 = ... = U

n 

(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 r

1

 with E(r

1

) = E

1

  the agreement, according to equation 7.1* (fig. 7.6), is

 

valid for the innermost and the overlapped vortex shell.

 

At the radius r

2

 with E(r

2

) = E

2

 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

;       r

3

 = 3 • r

1

;      ... ;      r

n

 = n * r

1 

(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:

 

E

1

 =   E

2

   =   E

3

   = ...   =   E

n 

(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 E

1

 has worn off to the value  E

31

 = - E

1

 • (r

1

/r

3

). 

This field is overlapped by    E

32

 = E

2

 * (r

2

/r

3

)    as well as the cosmic basic field E

o

:

 

E(r

3

) = E

31

+ E

32

+ E

0

 = E

1

 • (r

2

 - r

1

)/r

3

 + E

o 

(7.6)

 

The local basic field E

o

 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.

 

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