Preface to the lecture, 1

590

 

Gleanings concerning the theory of relativity

 

 

•  From the dual field-

theoretical approach

 

are derived:

 

• From Maxwell's field 

equations can be

 

derived:

 

=> Maxwell's

field equations

 

=>0

 

=> Quantum properties of

the elementary particles

 

=>0

 

=> Neutrino

 

(as an oscillating ring-like

vortex)

 

=> 0

 

=> Gravitation

 

(as a result of closed field

lines)

 

= > 0

 

=> Unified theory

 

(grand unification of all

interactions)

 

=>0

 

=> Temperature

 

(as an oscillation of size

depending on field)

 

=>0

 

=> Law of conservation of

energy

 

(and many other funda-

mental laws of physics)

 

=>0

 

=> Theory of objectivity

 

=> Theory of relativity

 

Fig. 28.10:       Comparison of the efficiency of the 

approaches 

(final balance)

 

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Mathematical gleanings ________________________________________________ 591

 

29. Mathematical gleanings

 

If, proceeding from the new field-physical approach, well-known and accepted theories 

are derived as special cases, this on the one hand can be valued as evidence for the 

correctness of the approach. On the other hand the new approach in part significantly 

influences the interpretation of the derived theories. That can involve a rethinking, with 

which not insightful people have difficulties, if for instance quantum physics, 

thermodynamics or the gravitation become partial aspects of electromagnetism. 

Over and above that are hidden many new thing in the new approach, which are there to 

discover. To that are counting among others the potential vortices and the scalar waves. 

One can work out these phenomena physically or mathematically, where the latter way as 

a rule is the faster one. Hence the summary shall be concluded with a kind of mathe- 

matical gleanings.

 

29.1 General and special theory of relativity

 

Albert Einstein distinguishes between general and special theory of relativity. Whereas the 

special (SRT), still is linked tightly with the prerequisites of the Lorentz-transformation, 

the general (GRT), deals with an extension to arbitrary systems, which mustn't be inertial 

systems. I would like not to dwell upon the GRT, as Einstein designed it, and merely 

notice that every generalization represents a possible source of errors and has to be well 

founded.

 

In the case of our derivation, the general case as it were resulted of its own accord. Let's 

turn back: If the root of Lorentz still was a component of the derived field dilatation 

(28.15) and equally of the length contraction (28.16), then it fell out in the comparison of 

both results (28.17). With that the important result, the proportionality (28.18), which 

among others results in the gravitation, becomes independent of the speed of light and the 

relative velocity v. This last step is obvious and still completely new. It cannot be found at 

Einstein, who in another way finds his GRT and his description of the gravitation. 

Even if here is striven for the same goal, then deviations in the result cannot be excluded 

because of the differences in the derivation, for which reason I additionally mark the by 

me derived general relativity (GRT'), to avoid confusion.

 

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592

 

 

 

 

 

Transformation table

 

Influence of the Lorentz-transformation in the: 

SRT    (special theory of relativity): one-dimensional, 

GRT' (general theory of relativity):  three-dimensional,  to  a 

large extent corresponding to the GRT of Albert Einstein,

 

GOT   (general theory of objectivity)

 

i

 

Fig. 29.2       Transformation table between SRT, GRT' and GOT

 

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Mathematical gleanings __________________________________________ 593 

29.2 Transformation table 

Let's speak again about the difference to the special relativity (SRT). This so to speak 

deals with the one-dimensional case of the uniform motion of a reference system in x- 

direction (v = v

x

), as specified by the Lorentz-transformation, where only the x- 

components and not those in y- or z-direction are being transformed. As already 

mentioned this is a purely theoretical case, which in practice occurs next to never. Normal 

is circular and vortical and with that accelerated motion, where the velocity component 

permanently changes its direction.

 

The derived result of the general relativity (GRT') does justice to this circumstance. Even 

if this at first only has been derived for the x-direction it nevertheless is valid equally in y- 

and z-direction. It even remains valid for the case that we base on a path of arbitrary form 

of a spatial field vortex. In this case some components continually occur in all directions 

of space, so that the relative velocity v as already the speed of light c loses its vectorial 

nature. With that the transition of the SRT to the GRT is carried out. 

By means of the spatial swirling the electric and magnetic field pointers at the same time 

turn into scalar factors, by taking over the function of the aether. Let us remember that 

even Einstein in his GRT was forced to again introduce the aether, which in the SRT still 

was unnecessary.

 

It therefore makes a difference in the transformation of physical factors, if we base on a 

one-dimensional (SRT) or a three-dimensional spatial description (GRT). Length 

measures in x-direction in both cases must be converted using the root of Lorentz. Usually 

the relativistic  -factor is introduced, which is inverse to the root of Lorentz

 

 

(29.2)

 

If thus individual length measures would be subject to a length contraction following the 

  -factor, then a volume V according to the SRT must be transformed with    according to 

the GRT' however with 

 

As is well-known a relativistic increase in mass is converted with the -factor and in the 

same manner the to that proportional energy E = m c

2

. If we however correlate the energy 

to the volume V and in that way determine an energy density w, then the difference 

between SRT 

 and GRT' 

 again has its maximum effect.

 

A relation to the field factors of E- and H-field is for instance provided by the energy 

density of a wave field

 

 (29.3)

 

According to that the field strengths in the one-dimensional case of the SRT should be 

converted with the  -factor, in the case of the GRT' however with    in accordance with 

the derivation in chapter 28. This circumstance willingly is overlooked, although it only 

concerns the textbooks and the today valid theory of relativity. I however point to the 

difference, since it does make a difference if we start with the SRT or the GRT when we 

change to the general theory of objectivity (GOT).

 

In the domain of the GOT all length measures should be transformed. The respective 

dimension gives information with which power the  -factor occurs (fig. 29.2). The unit 

meter is responsible for that.

 

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