Preface to the lecture, 1

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.

 

---