Preface to the lecture, 1

564

 

Derivation of the fundamental field equation

 

•

 

Under the assumption: E = E(r,t); H = H(r,t)   , 

•

 

using the relations of material: 

 and     

    :

 

•  the complete and extended law of induction reads:

 

 

(27.20)

 

•  and the well-known law of Ampere:

 

 

(27.21)

 

if we again apply the curl operation to eq. 27.20 and insert 

eq. 27.21:

 

 

with the definition for the speed of light c:     

 

 

(27.25)

 

the fundamental field equation reads:

 

 

Fig. 27.11:       Derivation of the fundamental field 

equation 

from the equations of transformation of the 

electromagnetic field.

 

:     The fundamental field equation mathematically describes a wave damped 

with the vortices of the electric and the vortices of the magnetic field. 

It is formulated only in space and time. From it can be deduced numerous 

eigenvalue equations, (i.e. the equation of Schrodinger, fig. 5.1).

 

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Faraday versus Maxwell ________________________________________________ 565

 

27.11 Derivation of the ,,fundamental field equation"

 

The two equations of transformation and also the from that derived field equations (27.20 

and 27.21) show the two sides of a medal, by mutually describing the relation between the 

electric and magnetic field strength (between E and H). We get on the track of the 

meaning of the ,,medal" itself, by inserting the dually formulated equations into each 

other. If the calculated H-field from one equation is inserted into the other equation then 

as a result a determining equation for the E-field remains. The same vice versa also 

functions to determine the H-field. Since the result formally is identical and merely the H- 

field vector appears at the place of the E-field vector and since it equally remains valid for 

the B-, the D-field and all other known field factors, the determining equation is more than 

only a calculation instruction. It reveals a fundamental physical principle. I call it the 

"fundamental field equation".

 

The derivation always is the same: If we again apply the curl operation to rot E (law of 

induction 27.20) also the other side of the equation should be subjected to the curl. If for 

both terms rot H is expressed by Ampere's law 27.21, then in total four terms are formed 

(27.26): the wave equation (a-b) with the two damping terms, on the one hand the eddy 

currents (a-c) and on the other hand the potential vortices (a-d) and as the fourth term the 

Poisson equation (a-e), which is responsible for the spatial distribution of currents and 

potentials 

.

 

Not in a single textbook a mathematical linking of the Poisson equation with the wave 

equation can be found, as we here succeed in for the first time. It however is the 

prerequisite to be able to describe the conversion of an antenna current into 

electromagnetic waves near a transmitter and equally the inverse process, as it takes place 

at a receiver. Numerous model concepts, like they have been developed by HF- and EMC- 

technicians as a help, can be described mathematically correct by the physically founded 

field equation.

 

In addition further equations can be derived, for which this until now was supposed to be 

impossible, like for instance the Schrodinger equation (chapter 5.6-5.9). This contrary to 

current opinion isn't a wave equation at all, since the term (b) with the second time 

derivation is missing. As diffusion equation it has the task to mathematically describe field 

vortices and their structures.

 

As a consequence of the Maxwell equations in general and specifically the eddy currents 

not being able to form structures, every attempt has to fail, which wants to derive the 

Schrodinger equation from the Maxwell equations.

 

The fundamental field equation however contains the newly discovered potential vortices, 

which owing to their concentration effect (in duality to the skin effect) form spherical 

structures, for which reason these occur as eigenvalues of the equation. For these 

eigenvalue-solutions numerous practical measurements are present, which confirm their 

correctness and with that have probative force with regard to the correctness of the new 

Held approach and the fundamental field equation. By means of the pure formulation in 

space and time and the interchangeability of the field pointers here a physical principle is 

described, which fulfills all requirements, which a world equation must meet.

 

:     see also fig. 5.1

 

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566

 

The Maxwell field as a derived special case

 

Comparison: 

 

 

Fig. 27.12: 

Comparison of the field-theoretical approaches 

according to Faradav and according to Maxwell. 

 

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Faraday versus Maxwell

 

567

 

27.12 The Maxwell field as a derived special case

 

As the derivations show, nobody can claim there wouldn't exist potential vortices and no 

propagation as a scalar wave, since only the Maxwell equations are to blame that these 

already have been factored out in the approach. One has to know that the field equations, 

and may they be as famous as they are, are nothing but a special case, which can be 

derived.

 

The field-theoretical approach however, which among others bases on the Faraday-law, is 

universal and can't be derived on its part. It describes a physical basic principle, the 

alternating of two dual experience or observation factors, their overlapping and mixing by 

continually mixing up cause and effect. It is a philosophic approach, free of materialistic 

or quantum physical concepts of any particles.

 

Maxwell on the other hand describes without exception the fields of charged particles, the 

electric field of resting and the magnetic field as a result of moving charges. The charge 

carriers are postulated for this purpose, so that their origin and their inner structure remain 

unsettled and can't be derived. The subdivision e.g. in quarks stays in the domain of a 

hypothesis, which can't be proven. The sorting and systematizing of the properties of 

particles in the standard-model is nothing more than unsatisfying comfort for the missing 

calculability.

 

With the field-theoretical approach however the elementary particles with all quantum 

properties can be calculated as field vortices (chap. 7). With that the field is the cause for 

the particles and their measurable quantization. The electric vortex field, at first source 

free, is itself forming its field sources in form of potential vortex structures. The formation 

of charge carriers in this way can be explained and proven mathematically, physically, 

graphically and experimentally understandable according to the model.

 

Where in the past the Maxwell theory has been the approach, there in the future should be 

proceeded from the equations of transformation of the field-theoretical approach. If now 

potential vortex phenomena occur, then these also should be interpreted as such in the 

sense of the approach and the derivation, then the introduction and postulation of new and 

decoupled model descriptions isn't allowed anymore, like the near-field effects of an 

antenna, the noise, dielectric capacitor losses, the mode of the light and a lot else more.

 

The at present in theoretical physics normal scam of at first putting a phenomenon to zero, 

to afterwards postulate it anew with the help of a more or less suitable model, leads to a 

breaking up of physics into apparently not connected individual disciplines and an 

inefficient specialisthood. There must be an end to this now! The new approach shows the 

way towards a unified theory, in which the different areas of physics again fuse to one 

area. In this lies the big chance of this approach, even if many of the specialists at first 

should still revolt against it.

 

This new and unified view of physics shall be summarized with the term "theory of 

objectivity". As we shall derive, it will be possible to deduce the theory of relativity as a 

partial aspect of it (chapter 6 and 28).

 

Let us first cast our eyes over the wave propagation.

 

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