Preface to the lecture, 1

576

 

Field overlap

 

•  concerning the development of the power series:

 

 

•  for q < 1 the power series with q = (v/c)

2

  will converge (28.11)

 

 

(28.12)

 

•  for  (v/c)

2

 < 1  resp. for   v < c   therefore is valid:

 

 

The square root of Lorentz appears in squared form

:

 

 

(28.14)

 

The derivation for the magnetic field strength analogous to that 

provides the identical result

:

 

 

(28.15)

 

Fig. 28.3   The field dilatation depending on velocity

 

:     see part 1, chap. 6.6

 

:    Prof. Dr. H.-J. Runckel, Abteilung fur Mathematik IV der Universitat Ulm

 

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Objectivity versus relativity

 

577

 

28.3 Field overlap

 

But it doesn't abide by this one overlap. In the case of vortex fields the effect overlaps the 

cause and itself becomes the cause for a new effect. The overlapped cause produces a 

further effect, which for its part is overlapping (see chap. 3).

 

Vortices thus arise, if overlaps for their part are overlapping and that theoretically reaches

 

to infinity, to which I already repeatedly have pointed (fig. 3.0). In addition do vortices 

represent a fundamental physical principle. The Greek philosopher Demokrit has traced 

back the whole nature to vortex formation and that already 2500 years ago!

 

In the field-theoretical approach this interpretation seems to experience a mathematical 

confirmation, since also the fields are overlapping in vortex structures. According to that 

we owe our observations and our being the relative movements and the vortex formation. 

If reversed there wouldn't be any movement, then there also would not exist fields, light 

nor matter. If we observe the sky, then everything visible follows the movement of its own 

of the Earth, of the solar system and the whole galaxy, which is on its way with unknown 

galactic velocity, and all movements take place in vortex structures (fig. 10.2).

 

The field overlap dictated by the Faraday-approach as well reaches to infinity, what has 

stimulated my colleagues of mathematics to also mathematically put into practice this 

physical requirement

. This leads to an infinite power series, which converges under the 

condition that v < c.

 

As a result of the power series development the well-known square root 

 of

 

Lorentz occurs in squared form (see also fig. 6.6). It determines the relation of the 

observed and the causing field strength of the electric or the magnetic field. 

Physically the found relation describes a dilatation field depending on velocity. The field 

strength thus increases, if the relative velocity v increases, or inversely no difference is 

observable anymore, if v tends towards zero.

 

Whoever wants to compete with Albert Einstein (1879-1955), who has developed the 

theory of relativity from the length contraction, which depends on velocity, could be 

inclined to derive a new field physics from the field dilatation. But I must warn of such a 

step. The derivation of the length contraction by the mathematician Hendrik Lorentz 

(Lorentz contraction) assumes a number of limiting conditions. The relative velocity v for 

instance may not experience any acceleration. Actually however almost all motion takes 

place as circular vortex motion, so that due to the occurring centripetal acceleration the 

conditions for the theory of relativity aren't fulfilled anymore. Neglects or generalizations 

thereby can lead to considerable errors, of which I would like to warn. 

It in general is a delicate enterprise, if one wants to provide a physical interpretation for

 

a purely mathematically won result.

 

This warning to the same extent also is valid for the here shown derivation of the field

 

dilatation. The limiting conditions practically are the same as for Einstein and the

 

problems with a provided physical interpretation won't be less. Also here lots of

 

paradoxes will occur, which are nothing but errors of the theory. So we won't reach our

 

destination.

 

There now only one further mathematical step is necessary, which links the theory of

 

relativity with the new notion of a field dilatation depending on velocity.

 

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578

 

The derivation of the length contraction

 

Example:

 

Measurement of length by means of a measurement of propaga- 

tion time (sound or light) with c = L/t in a vehicle moving with v.

 

 

From driving time t:

 

 

= signal propagation time:

 

follows 

 

According to Pythagoras:

 

 

the shortening of the rule results in:

 

 

(28.16)

 

Fig. 28,4: ______Derivation of the length contraction

 

Examples: contraction according to Lorentz transformation, 

measurable length shortening, curvature of space.

 

Counterexample:       unsuccessful aether detection (Michelson experiment)

 

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