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)
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.
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
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.