126
transformation
Fig. 6.17: Model-transformation between
theory of relativity and theory of objectivity.
theory of objectivity
127
6. 17 Transformation
The observation domain is, as the name already expresses, perceptible (observable) with
the help of our sense organs and measurable with corresponding apparatus. The special
theory of relativity for the most part provides us the mathematics needed for that. And in
that is assumed a constant speed of light. Because a length contraction is being observed
and can be measured, a time dilatation must arise as a consequence. Such is the consistent
statement of this theory. Because we already could make us clear that it concerns a
subjective theory, of course caution is advisable if generalizations are being made, like the
one of the inductive conclusion of the length contraction on the time dilatation. We'll
come to speak about that in this chapter (fig. 6.20).
The model domain however is not observable to us and only accessible in a mathematical
manner. Here the time is a constant. On the other hand do the radii of the particles and all
other distances and linear measures stand in direct proportionality to the speed of light. If
that changes, then does that lead to a change in length. The length contraction occurs
physically, which means actually. We propose the name "theory of objectivity" for the
valid theory which is derivable with this prerequisite and independent of the point of view
of the observer.
The importance of this model domain and of the possible model calculations is founded in
the circumstance that many physical relations within our observation domain aren't
recognized by us and can't be mathematically derived. Besides is only all to often worked
with unallowed generalizations and with pure hypotheses. Such a thing does not even exist
in the model domain.
The model domain can be tapped over a transformation. For that we select an approach
x(r) in the to us accessible observation domain. This then is transformed into the model
domain by a calculation instruction M{x(r)}. Here we can calculate the sought-for relation
In the usual manner and transform back again the result according to the same calculation
instruction M
-1
{x(r)} but in the reversed direction. After being returned in our familiar
observation domain, the result can be compared and checked with measurement results
(fig. 6.17).
In this way we will derive, calculate and compare the quantum properties of the
elementary particles with the known measurement values. Here we remind you of the fact
that all attempts to calculate the quantum properties conventionally, without
transformation, until now have failed. Not even a systematization may succeed, if it
concerns for instance explanations for the order of magnitude of the mass of a particle.
A transformation at first is nothing more than an in usefulness founded mathematical
measure. But if a constant of nature, and as such the quantum properties of elementary
particles until now have to be seen, for the first time can be derived and calculated with a
transformation then this measure with that also gains its physical authorization.
We now stand for the question: how does the instruction of transformation M{x(r)} read,
with which we should transform the approach and all equations from the observation
domain into the model domain?
128
transformation table
Fig. 6.18: Transformation of the dependencies on radius
theory of objectivity
129
6.18 Transformation table
The attempt to write down at this point already a closed mathematical relation as instruc-
tion of transformation, would be pure speculation. Such an instruction first must be
verified by means of numerous practical cases, i.e. be tested for its efficiency and
correctness. But we not even know the practical examples necessary for this purpose, if we
apply the transformation for the first time!
For his reason it unfortunately is not yet possible, to calculate absolute values in a direct
We have to be content to work with proportionalities and to carry out comparisons.
In fig. 6.18 the proportionalities are compared in the way, how they would have to be
transformed: on the left side, how they appear and can be observed in the view of the
special theory of relativity, and on the right side, how they can be represented and
calculated in the theory of objectivity.
The change, which here would have to be transformed, is the physical length contraction,
which is the change in length as it depends on the speed of light. For spherical symmetry
the length 1 becomes the radius r (eq. 6.26), of which is to be investigated the influence.
In the observation domain we had derived the proportionality (6.15 + 6.18):
E ~ 1/r
2
and H ~ 1/r
2
.
The field of a point charge or of a spherical capacitor confirms this relation:
Because the speed of light in our observation is constant, also both constants of material
which are related to it (eq.5.6:
= 1/c
2
), the dielectricity and the permeability are
to be taken constant.
With that the same proportionality as for the field strengths also holds for the induction B
and the dielectric displacement D:
B ~ 1/r
2
and D ~ 1/r
2
.
In the model domain everything looks completely different. Here the radius and any length
stands in direct proportionality to the speed of light. In this way we get problems with our
usual system of units, the M-K-S-A-system (Meter-Kilogram-Second-Ampere). The basic
u n i t Meter [m] and as a consequence also the unit of mass Kilogram [kg = VAs
3
/m
2
]
appear here as variable. It would be advantageous, to introduce instead the Volt [V] as
basic unit.
But in any case does the dimension of a quantity show us, in which proportionality it
stands to the unit of length. This in the model domain then is authoritative! As an example
does the speed of light have the dimension Meter per Second. In the model domain there
consequently has to exist a proportionality to the length r [m].
The speed of light determines with equation 5.6 again the constants of material:
[Vs/Am] ~ 1/r and [As/Vm] ~ 1/r
(6.28)
According to the model holds unchanged:
B [Vs/m
2
] ~ 1/r
2
and D [As/m
2
] ~ 1/r
2
. (6.29)
But if we insert the proportionalities 6.28 and 6.29 into the equations of material 3.5 and
3.6, then holds for the field strengths:
H [A/m] ~ 1/r and E [V/m] ~ 1/r.
(6.27)
Further dependencies of the radius can be read in the same manner either by inserting into
well-known laws or immediately from the dimension.