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«PACS-classification: 84.60.-h, 89.30.-g, 98.62.En, 12.20.-m, 12.20.Ds, 12.20.Fv Summary of a Scientfic Work by Claus Wilhelm Turtur Germany, ...»

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This arises the expectation that the conversion of vacuum-energy into mechanical energy as reported in [e8] can be understood in analogy to the Casimir-effect. If this energy conversion shall be done in a perpetual process, we have to find a possibility to move the plates 22 3. Theoretical fundament of the energy-flux relatively to each other without alteration of the distance between them. This has been developed in the present work. Thus, there is some similarity with the Casimir-effect, but there is also an important difference: If some of the energy of the zero point oscillation shall be converted into mechanical energy, the conducting plates have to move relatively to each other, but they are not allowed to alter their distance (which leads us to a parallel shift) – otherweise the conversion would not be perpetual. This is imaginable if the plates perform an appropriate rotation. The practical setup is presented in section 4.

Although the Casimir-effect helped to invent a machine which verifies the existence of the energy of the zero point oscillations and converts it into mechanical energy, it was clear from the very beginning of the development, that the metal plates (whose position have to be different from the position in the Casimir configuration) and the vacuum, necessary for the Casimir-effect are not enough for the endless conversion of vacuum-energy. Additionally to those objects, there has to be an electric (or a magnetic) field, which has to provide the possibility to interact with the energy circulation of section 2.

The experiments which finally succeeded in converting vacuum-energy into classical mechanical energy [e8, e9] confirm this approach. The first explanation of the functioning principle of the energy-converting rotor was given on the basis of an electrostatic field within classical electrodynamics [e5], [e9], [e10]. The logical connection between the zero point oscillations and classical electrodynamics is topic of [e6]. A central aspect thereby is the mechanism how the electric and the magnetic fields propagate in the vacuum (i.e. into the space). The crucial question is: How do those fields and their propagation influence the zero point oscillations. This question will also be answered in the following chapters.

3.2. Connection with the classical model of vacuum-energy Before we answer the crucial concluding question of section 3.1 (the interaction between the propagating field and the zero point oscillations), we want to recapitulate the basics of the model of section 2, which already showed the way how to convert vacuum-energy into

classical energy:

Electric and magnetic fields as regarded in Classical Electrodynamics are normally regarded to be “everywhere in space at the same moment” [Kli 03]. This means, that normally their time dependent propagation into the space is not taken into consideration, but only their presence. For most of the technical and practical applications of electrodynamics (with typical distances inside the laboratory and velocities negligible in comparison with the speed of light) this is fully sufficient. But as a matter of principle, this is in clear contradiction with the Theory of Relativity [Goe 96], according to which the propagation of the field strength has to respect at least the limit of the speed of light [Chu 99]. Thus, it appears sensible to take the propagation (of DC-fields) with the speed of light into account. But this conception leads to important consequences – one of them is the awareness, that electric and magnetic fields give energy to the vacuum during their propagation (as stated in section 2).

3.3. New microscopic model for the electromagnetic part of the vacuum-energy 23 Even though this fundamental logic of Classical Electrodynamics is sufficient to explain the existence and the nature of the energy circulation in the vacuum, we want to look at the inner structure of the vacuum in order to find the backgrounds of the described behaviour. In order to prepare the microscopic model of energy conversion, we want to outline the circulation of

the energy in the vacuum:

The propagation of an electric field as well as a magnetic field (in the model to be developed now) influences the wavelength of the zero point oscillations. We will find the correlation between the field strength and the alteration of the wavelength soon. The central assumption of the model is, that quantum electrodynamical corrections such as vacuum polarisation do not only occur with photons but also with zero point oscillations (and we will find, that this causes the extraction of energy from the field). But the particles of vacuum polarisation do not follow the propagation of the field, and so they can distribute their energy all over the space. This is the “drain” into which the field loses its energy during its propagation. On the other hand, this mechanism also gives us the explanation of the source, from which the electrical charges are permanently supplied with energy in order to produce field strength: It indicates the reason for the transportation of field energy to be an alteration of the wavelength of the zero point oscillations. And there is further conclusion, that the lost field energy during the propagation of the field is the energy necessary for vacuum polarization.

In the following sections 3.3 and 3.4 we will see, that this model does not only explain the experiments of the conversion of vacuum-energy but it furthermore also allows to determine the energy density of the zero point oscillations in the vacuum.

3.3. New microscopic model for the electromagnetic part of the vacuum-energy Annotation: It should be mentioned, that the present work only analyzes the connections between the field energy of the electric and the magnetic field on the one hand and its part of the vacuum-energy on the other hand. The present work does not give any answer to the question whether there are some further other items in the vacuum, giving further contributions to the vacuum-energy, which we do not know today. In the moment, mankind does not have an imagination how to answer this question, and it is not topic of the present work.

Clear in any case is, that the zero point oscillations mentioned above can be understood in connection with several effects of vacuumpolarization (such as for instance virtual electrons and positrons) [Fey 97], [Gia 00]. Thus, the energy of the zero point oscillations should be explainable with such physical items. With other words: An explanation has to be searched which helps to understand the propagation of electric and magnetic fields, as well as the supply of field sources with energy, on the basis of the items of the vacuum.

The model for this explanation has been found in the present work in such simple (and elementary) manner, that it is advantageous according to Occam’s razor [Sim 04], which always prefers explanations as easy as possible. Our model finally goes back to the year 1935, when Heisenberg and Euler [Hei 36] performed quantum theoretical calculations of the 24 3. Theoretical fundament of the energy-flux Lagrangeian of photons in electric and magnetic fields, coming to the conclusion that photons propagate in such fields with lower speed than in the vacuum without field. The reasons are found in vacuum polarisation, which influences the Lagrangeian as calculated by Heisenberg and Euler. The experimental verification is not yet completely done. It was regarded as complete in [Zav 06], but this scientist later withdrew his results [Zav 07] by himself. But it is supposed that the verification will be done in not too far future [Che 06], [Lam 07], [Bes 07].

Logical consequence leads to a conclusion, which is the only assumption of our model:

If electromagnetic waves (such as photons) undergo retarded propagation within electric and magnetic fields (in comparison with field free vacuum), zero point oscillations should undergo the same retardation of propagation, because they have the same nature (to be electromagnetic waves). This means that electric and magnetic fields have an influence on the  wave vectors k and on the frequencies  of the zero point oscillations. This causes an influence on the energy eigen-values of the zero point oscillations. This postulate is one of the main fundamental considerations of the present work.

We want to use it as a hypothesis (and the experiment will confirm it later):

The alteration of the energy of the zero point oscillations in electric and magnetic fields should be sufficient to explain the energy of those fields.

The development of out QED-model can now be done in similarity with Casimir’s considerations (and the effect with his name) by comparing the energy of the continuous spectrum of the zero point oscillations with and without intervention. Casimir’s intervention was to mount two conducting plates (without electrical charge). The intervention of the present work is to switch on an electric (or a magnetic) field between some nonparallel plates.

The result, which we have to find, is the difference of the total energy of the spectra with and without field. The difference of those both total energy sums should be directly the energy of the field. In principle, our calculation has the same problems with the convergence of improper integrals as Casimir’s calculation. And the similar problems should be solvable in a similar way. The typical method for the solution is renormalization in Quantum field theory [She 01], [She 03], see also [Hoo 72], [Dow 78], [Bla 91]. The mathematical methods are presented also very clearly in [Kle 08]. But the result can be obtained most easy, if we can

find and use utilisable results somewhere in literature as done in the following calculation:

–  –  –

where the indices “WITH” and “WITHOUT” represent the situation with and without external field. This difference must be the energy density of the field, as marked by the index “FIELD”.

–  –  –

where me is the mass of the electron and the other symbols are to be interpreted as usually.

There are several articles in which the speed of propagation of electromagnetic waves in electric, magnetic and electromagnetic DC-fields are calculated on the basis of this Heisenberg-Euler-Lagrangeian (see for instance [Lam 07], [Hec 05], [Lig 03], [Rik 00], [Rik 03], [Riz 07], [Sch 07], [Zav 07]). And we want to assign this speed of propagation also to the electromagnetic waves of the zero point oscillations of the vacuum, thus we will take the speed of propagation from those articles in order to determine the influence of the external  field (the electric as well as the magnetic) onto the k -vector of the zero point oscillations and thereby the influence on energy density of the zero point oscillations of the vacuum, which is E. These results contain the solution of the improper integrals mentioned above.

V Z We will do this now for both probes (types of fields interacting with the zero point oscillations, i.e. the electric and the magnetic field) separately, beginning with the magnetic field (first calculation) and later followed with the electric field (second calculation).

–  –  –

which is confirmed by [Rik 00] quantitatively for an angle of   90 and also by [Bia 70].

The last-mentioned reference is often regarded as a milestone on the way to the comprehension of electromagnetic waves in electric and magnetic DC-fields, because it is the first work giving quantitative predictions of the birefringence (and thus of the speed of propagation) of electromagnetic waves in the fields, which is a quantity that can be really measured.

–  –  –

at an excitation with   90, where me is the mass of the electron and  is the constant of hyperfine structure.

This is the way how all convergence problems of improper integrals over spectra of zero point oscillations have been traced back to existing solutions in literature.

Free from any problems of convergence of improper integrals, and free from any cut-off functions (with uncertain motivation), we found in literature, some results, that help to calculate the energy density of the zero point oscillations of the vacuum. We have in mind that the calculation was done with a magnetic field as a probe, but the influence of the magnetic field was eliminated during the course of the calculation.

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