Preface to the lecture, 1

84

 

atomistic interpretation!

 

  

  

Fig. 5.5:    The structure of atoms in the view of the 

fundamental field equation 

condition for equilibrium: 

(5.13)

 

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Derivation and interpretation 

85 

5.5 Atomistic interpretation of the fundamental field equation

 

Let's again turn to the smaller, the atomistic dimensions. Here positively charged protons

 

and negatively charged electrons are found. Both are matter particles and that means that

 

seen from the outside both have the identical swirl direction. For reason of the unequal

 

charge conditions they attract each other mutually and according to fig. 4.9 rotate around a

 

common centre of mass as differently heavy pair. Chemists say: "the light electron orbits

 

the heavy atomic nucleus". With small balls they try to explain the atomic structure.

 

But the model is no good: it contradicts causality in the most elementary manner. We are

 

dealing with the problem that according to the laws of electrodynamics a centripetally

 

accelerated electron should emit electromagnetic waves and continuously lose energy, to

 

eventually plunge into the nucleus.

 

Our experience teaches that this fortunately is not true - and Niels Bohr in order to save 

his model of the atom was forced to annul the laws of physics with a postulate founded in 

arbitrariness.

 

Actually this state only exists for a very short time and then something unbelievable 

happens: the electron can't be distinguished as an individual particle anymore. "It is 

smeared 

over the electron orbit" do certain people say; "it possesses a dual nature" says 

Heise

nberg. Besides the corpuscular nature the electron should in case of its "second 

nature" form a matter wave, "the position of the electron is to be looked at as a resonance 

which is the maximum of a probability density", do explain us de Broglie and 

Schrodinger.

 

These explanations can hardly convince. If the electron loses its particle nature in its

 

second nature, then it also will lose its typical properties, like for instance its mass and its

 

charge. but this is not the case.

 

T

HE 

vortex theory provides clear and causal answers: if the electron were a ball it con- 

tinuosly would lose energy, therefore another configuration forms that does not know 

this problem. Here the phenomenon of transport takes an effect. The electron opens its 

vortex centre and takes the tiny protons and neutrons as atomic nucleus up into itself. The 

Bohr electron orbit with that is not a path anymore, but is occupied by the whole particle 

as spherical shell. This is confirmed by the not understood measurements exactly like the 

photos of individual atoms with the scanning electron microscope.

 

But now an electron does in its inside have the opposite swirl direction as the proton seen

 

from the outside. As a consequence a force of repulsion will occur, which can be

 

interpreted as the to the outside directed current eddy, the force of attraction for reason of

 

the opposite charge works in the opposite direction and can be interpreted as the potential

 

vortex effect.

 

If both vortices are equally powerful:                    

                         (5.13)

 

or if both forces are balanced, as one usually would say, then the object which we call an 

atom is in a stable state.

 

It probably will be a result of the incompatible swirl direction, why a very big distance

 

results, if the electron becomes an enveloping electron. On such a shell not too many

 

electrons have room. Because of the rotation of their own, the electron spin, they form a

 

magnetic dipole moment, which leads to a magnetic attraction of two electrons if they put

 

their spin axis antiparallelly.

 

As a "frictionless" against one another rotating pair they form two half-shells of a sphere 

and with that occupy the innermost shell in the hull of an atom. If the positive charge of 

the nucleus is still not balanced with that, then other electrons is left only the possibility to 

form another shell. Now this next electron takes the whole object up into itself. The new 

shell lies further on the outside and naturally offers room to more as only two vortices.

 

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86

 

Klein-Gordon equation

 

 

Fig.   5.6:   Derivation of the Klein-Gordon equation (5.20) 

from the fundamental field equation (5.7) 

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Derivation and interpretation

 

87

 

5.6 Derivation of the Klein-Gordon equation

 

The valid model of the atom today still raises problems of causality, as has been

 

explained. An improvement was provided by an equation, which was proposed by the

 

mathematician Schrodinger 1926 as a model description. This equation in this way missed

 

the physical root, but it nevertheless got international acknowledgment, because it could

 

be confirmed experimentally. Looking backwards from the result then the physical

 

interpretation of the probability density of the resonance of the waves could be pushed

 

afterwards. 

 (5.14)

 

The Schrodinger equation is valid for matter fields (of mass m), while the interaction 

with a outside force field the energy U indicates. It can be won from a wave equation by 

conversion, which possibly is the reason why it usually is called a wave equation,

 

although in reality it is a diffusion equation, so a vortex equation!

 

For the derivation Schrodinger gives the approach of a harmonic oscillation for the 

complex wave function

 

 

(5.15)

 

if the entire time dependency can be described by one frequency   f = W/h 

(de-Broglie relation):               

               (5.16)

 

The high-put goal is: if the structure of the atom is determined by the fundamental field 

equation 5.7 then one should be able to derive the experimentally secured Schrodinger 

equation and to mathematically describe the discussed special case. Also we select at first 

an approach periodic in time:

 

 

(5.17)

 

with                                        

  . (5.18)

 

We insert the approach 5.17 and its derivations into the field equation 5.7 and divide by 

the damping term e

-wt

:

 

 

If as the next step the angular frequency according to equation 5.18 is inserted, then 

summarized the provisional intermediate result results:

 

 

(5.20)

 

The derived equation 5.20 represents formally seen the Klein-Gordon equation, which is

 

used for the description of matter waves in quantum mechanics and which particularly in

 

the quantum field theory (e.g. mesons) plays an important role. Even if it often is regarded

 

as the relativistic invariant generalization of the Schrodinger equation, it at a closer look is

 

incompatible with this equation and as "genuine" wave equation it is not capable of

 

treating vortex problems correctly, like e.g. the with the Schrodinger equation calculable

 

quantization of our microcosm.

 

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