Preface to the lecture, 1

98

 

radius of the electron

 

  

From

 

(6.2)

 

follows:

 

The speed of light determines the size of the elementary particles.

 

Energy of a capacitor:

 

 

(6.3) 

written down for the electron (with the Einstein relation):

 

 

(6.1) 

Capacity of a spherical capacitor: 

 

(6.4) 

"classical" radius of the electron

 is: 

 (6.5) 

r

e

   =  2,82 • 10

-15

 m 

(6.6) 

 

in the case of Kuchling

< ii>

 the radius of the electron is: 

r

e

   =   1,41 • 10

-15

 m . 

(6.7) 

Fig. 6.3:        Calculation of the radius of the electron.

 

:     Mende, Simon: Physik, Gl. 10.39, VEB-Leipzig, 4. Aufl.

 

:    Kuchling: Physik, Gl. At4, VEB-Leipzig, bis einschl. 11. Auflage 1974

 

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theory of objectivity

 

99

 

6.3 Radius of the electron

 

For the crucial process, in which the electromagnetic wave rolls up to a vortex, it is for 

reasons of continuity to be expected that the velocity of propagation remains equal that 

thus for the vortex oscillation exactly like for the electromagnetic wave the speed of light 

is determining. The direction of propagation in the case of the vortex takes place 

perpcndicular to the in fig. 6.2 shown field direction of the electric field strength. Not even

 

in that both field-phenomena differ.

 

Summarizing: the propagation takes place with the speed of light c along a circular path 

with the perimeter

Therefore holds:

 

 

(6.2)

 

According to this equation the radius and with that the size of the electron is determined 

by the speed of light. Therefore the question of the size of the electron is raised.

 

The energy interpretation predicts that for the theoretical case of a change of size the 

energy density in the inside of the particle is influenced that however the quantity of the 

included  energy  remains  unchanged.   We  therefore  can  further proceed  from the 

assumption that the bound amount of energy is independent of the size of the particle!

 

Consequently for the elementary quantum the energy W

e

 = 0,51 MeV is assumed, which it 

has acccording to the Einstein relation W

e

 = m

e

c

2

. For the electron of mass m

e

 the with

 

measuring techniques determined value is inserted.

 

The spherical electrode of a spherical capacitor with the above given energy W

e 

(according to eq. 6.1) and the capacity C

e

 (according to equation 6.4, fig. 6.3) represents a

 

very realistic model of the negatively charged particle.

 

In this manner the classical radius of the electron is calculated to be

: r

e

 = 2,82*10 

-15

 m.

 

But in the case of Kuchling it only is half this size

, what according to equation 6.2 

would mean that in the case of Kuchling the light would be on the way only half this 

fast 

. Therefore if one is careful, one prefers to be silent concerning this delicate theme 

and if one is honest, one admits not to know anything exact.

 

Not only the electron but also all the other elementary particles are according to the field- 

theoretical approach formed from concentrated potential vortices. For these equation 6.2 

hence has to hold in the same manner, so that more generalized we can conclude:

 

The speed of light determines the size of the elementary particles.

 

This statement is incompatible with the assumption of a constant speed of light! Because 

then all elementary particles would have identical size. As is known, however, are the 

building parts of the atomic nucleus, the protons and neutrons very much smaller than 

individual electrons. The constancy of the speed of light is to be questioned. 

This question is of such an elementary importance that we are not content with these 

considerations and in addition undertake a mathematical derivation in the sense of the 

field approach.

 

: Difference = Thomas factor

 

---

100

 

Maxwell field equations

 

 

Fig. 6.4:     Derivation of the laws of transformation

 

: Prof. G. Bosse in his text book in reversed direction derives the Faraday law 

of induction from the law of transformation 6.10, which he again derives 

from considerations about the Lorentz force. G. Bosse, Grundlagen der 

Elektrotechnik II, BI 183,  Hochschultaschenbucher-Verlag, Mannheim 1967

 

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theory of objectivity

 

101

 

6.4 The Maxwell field equations

 

The laws of transformation of the electromagnetic field shall form the starting-point for 

the coming up considerations. To exclude any doubts with regard to the interpretation, the

 

equations will be derived from the Maxwell laws under the assumption that no sources or 

charge carriers are present (fig. 3.2 and 3.3) and as a consequence no current density (j = 

0) is to be expected. 

This corresponds to the vanishing of the time independent terms, which consequently are

 

responsible for the occurring of force effects like e.g. the Lorentz force. Only at the end of 

this derivation we can understand the sense of this assumption (with 

= 0 and 

= 0). 

The procedure at first corresponds to that of fig. 5.1. Here the fundamental field equation 

had been derived from Faraday's law of induction and Ampere's law. With the 

assumptions made this time the in fig. 5.2 treated undamped wave equation is left (5.9, 

here 5.9*). Whom the derivation is still present can go in at this point.

 

In a sufficiently great distance from the source we are dealing with a plane wave, in which

 

the field factors only depend on the direction of propagation x. The Hertz' wave is a 

transverse wave, in which the field pointers oscillate perpendicular to the direction of 

propagation and in addition stand perpendicular to each other:

 

 

The curl, applied to the electric field pointer, itself points in the y-direction:

 

rot E = - dE/dx . This for the transverse wave carried out curl operation is now 

compared with Faraday's law of induction (5.4):

 

rot E   =  -dE/dx  =  - dB/dt 

(6.9)

 

The relation won in a mathematical way, with the speed fixed by (6.8), reads:

 

dE   = (dx/dt) • dB  =   v * dB 

(6.9*)

 

The result of this derivation at first only is valid for the introduced simplification, for 

instance for the case of the transverse electromagnetic wave. Better known is apart from 

that the generalized formulation, which among others by G. Bosse

 is called law of 

transformation.

 

 

(6.10) 

With Ampere's law (5.1) we now should proceed in an analogous manner. The result is:

 

 

(6.10*)

 

This equation 6.10* is given among others by Simonyi

. Now that we know, under 

which circumstances these equations of transformation can be derived from the Maxwell 

equations, the actual work can start.

 

:    K. Simonyi, Theoretische Elektrotechnik, 7. Auflage VEB Verlag Berlin 1979. 

pp. 921 - 924;  In addition see chapter 27.8 in part 3 of this book.

 

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