Preface to the lecture, 1

102

 

Equations of transformation

 

Laws of transformation:

 

and 

(6.10) 

(6.10*)

 

We experience the magnetic field as an electric field

 

and the electric field as a magnetic field 

simply and solely for reason of the same relative motion!

 

The component of the direction of motion perpendicular to the 

area defined by the field pointers:

 

 

 

resp.

 

E

o

  =    E + E

z 

Ho =    H + H

z

 

(6.13) 

(6.13*)

 

Fig. 6.5:    Properties of transformation of the 

electromagnetic field.

 

 

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theory of objectivity

 

103

 

6.5 Equations of transformation

 

As a consequence of the in fig. 6.5 again written down laws of transformation of the

 

electromagnetic field (6.10 and 6.10*) magnetic phenomena can be traced back to electric

 

phenomena and vice versa. The mathematical formulation reveals us the two sides of the

 

same medal and points to a perfect duality between both fields and their factors of

 

description.

 

Because a way exists, as is shown here, in which the equations of transformation can be 

derived from the Maxwell field equations, the same generally valid and extensive 

importance should be attributed to them. They can with the same right be called the 

foundation of electromagnetism. Wherein does lie its message for physics, the always 

curious researcher will ask? For that the relations of material 3.5 and 3.6 are completed:

 

 

(6.10) 

und       

 

. (6.10*)

 

The here presented equations state, that we measure an electric field strength E, if we are 

moving with regard to a magnetic field H with the speed v and vice versa. 

The  electric and the magnetic field therefore prove to be an experience of the observing 

person and we can say:

 

We experience the magnetic field as electric field and the electric field 

 

as magnetic field simply and solely for reason of the relative motion!________

 

Let's assume, v is the component of the relative velocity (6.8), which stands perpendicular 

to the area defined by the field pointers (6.8*), then the equations of transformation (6.9* 

with 3.5) now read:

 

 (6.11) 

and       

 . (6.11*)

 

If we are moving with the velocity v in a basic field which is present with the field 

strength E, then according to equation 6.11* we observe a magnetic field, which again 

according to equation 6.11 is to be interpreted as an additional electric field E

z

:

 

 (6.12)

 

In duality  equation 6.11 inserted into equation 6.11* provides for the magnetic field 

strength a corresponding additional field H

z

:

 

 (6.12*)

 

W e obviously owe the measurable overlap fields in a laboratory simply and solely to the

 

relative velocity v with which the laboratory is moving. But now we must pay attention to

 

the fact that a terrestrial laboratory rotates along with the earth, that the earth orbits the sun

 

and the sun again rotates around the centre of the milky way. Eventually the whole milky

 

way is on the way in the cosmos with a galactic, for us hardly understandable speed. If we

 

further take into consideration that for every subsystem an additional field occurs as a

 

consequence of the relative motion with regard to the super ordinate system, then one

 

additonal field follows after the next and overlaps this one.

 

Let's imagine, the relative velocity could be reduced towards zero - and maybe we are 

moving around such a cosmic point - then here no overlapping field would be measurable.

 

<*>: A derivation using vectors is written in chapter 28 (part 3).

 

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104

 

Field overlap

 

Additional field (from fig. 6.5): 

(6.12) and 

 

(6.12*) 

 

 

Superposition of the fields: 

The additional field (E

z

 resp. H

z

) overlaps the basic field 

(E resp. H) to produce the measurable overall field (E

0

 resp. H

0

): 

(6.13) 

 

(6.13*) 

 

transformed: 

 

 

(6.14) 

for the Lorentz contraction holds apart from that: 

 

(6.14*) 

From the comparison 

Follows 

 

(6.14**) 

 

 

the proportionality: 

 

and       

     

(6.15) 

Fig. 6.6:        The field dependency of the Lorentz contraction

 

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theory of objectivity

 

105

 

6.6 Field overlap

 

Field vectors can be superpositioned. In this manner the additional field E

z

 resp. H

z

 which 

depends on the velocity, according to equation 6.10, overlaps the respective basic field (E 

resp. H)  to produce the measurable overall field (E

0

 resp. H

o

):

 

(6.13) 

 

(6.13*)

 

 

In the result something surprising the factor (l-v

2

/c

2

) appears, which is well-known from 

the special theory of relativity and for instance appears in the Lorentz contraction.

 

If we rewrite both equations for the characteristic factor and compare with the in a purely 

mathematical way, over the Lorentz transformation, won length contraction 

(1 - v

2

/c

2

) = (l/l

0

)

2

     , then it becomes clear that the Lorentz contraction physically seen 

should have its cause in the changed field conditions which a with relativistic speed 

moving body finds with regard to a resting body.

 

 

(6.14)

 

The equation is a compulsionless consequence of known physical laws. In this derivation

 

actually no new factor was introduced and nevertheless a completely new picture for the 

natural scientific reality results

.

 

In our observer system, where the field E

o

 exists, a rule has its proper length l

0

. In another

 

system, which is moving with the speed v relative to the observer, as a consequence of the

 

here prevailing field E the corresponding rule has a length 1. In which relation the factors

 

stand  to  each  other,   is  described  by  equation   6.14.   Accordingly  the   following

 

proportionality holds:

 

 

and           

       

(6.15)

 

If we are exterior to a very fast moving body with velocity v, we immediately can observe 

how this body for reason of its relative velocity experiences the calculated additional field 

and in this way experiences a length contraction. If the observer is moving along with the 

body, then he purely subjective seen doesn't detect a length contraction, because he

 

himself and his entire measuring technique is subjected to the same length contraction. 

From the axiomatic approach what would be, if the field, which itself only represents an 

experience, would determine perceptible space and its dimensions, quickly a fundamental 

realization   can   develop   if  the   described   experiences   should   coincide   with  real 

observations.

 

: Because in this point of view the subjective status of the observer is determining, 

it is not completely impossible that there is an error in the interpretation of the 

equations of transformation (6.10 and 6.10*). But because we started from the same 

point of view of the observer for the derivation of the length contraction from the 

Lorentz transformation, here the same error is to be expected. In putting both results 

equal (6.14), a like constituted error on both sides will cancel out in any case and the 

result stays above all doubts!

 

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