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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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2.3. A circulation of energy of the magnetostatic field Because of some similarities between the electrostatic field and the magnetostatic field (the last-mentioned can be led back to the first-mentioned by a Lorentz-transformation, see [Sch 88], [Dob 06]), it should be possible to find a circulation of field energy also for the magnetic field in analogy with the circulation of field energy as found for the electric field. In section

2.3 it is demonstrated, that this analogy is going rather far. We want to demonstrate this with an example, for which we have to chose the geometry of the field source a bit different from

2.3. A circulation of energy of the magnetostatic field 15 the example of the energy circulation of the electric field. The reason can be understood in connection with the Lorentz-transformation mentioned above, which has the consequence (among others) that a magnetic field can not have a punctiform field source, because the creation of a magnetic fields need the movement of electrical charge. (The lowest order of the magnetic multiple is the dipole and not the monopole as in the case of the electric field.) Thus, our example in section 2.3 shall be built up on an electrical charge moving with constant velocity, emitting a constant magnetic field. And we want to follow the propagation of this field into the space, similar as we did in section 2.2.

–  –  –

We now analyze the propagation of the magnetic field respectively of its energy in the space.

This field together with its energy starts at the position of the z-axis and propagates perpendicularly to the z-axis (radially as shown in fig.5) with the speed of light. A component of propagation into the z-direction is not to be taken into account, because the whole setup is arranged with cylindrical symmetry around the z-axis (with infinite length in z-direction).

This can also be understood, if we look to a volume element with the shape of a cylinder of finite length z  0... z0 (see fig.5). The energy flux through the top and through the bottom end, going into the cylinder and coming out of the cylinder are identically the same, because the cylinder is neither source nor sink. In this way, we understand, that the energy being 16 2. Philosophical background emitted from the moving charge (which is located along the z-axis), is flowing with cylindrical symmetry into the xy-plane.

We now want to find out, how much magnetic field energy is flowing into the space within a time interval t. Therefore, we adjust the time-scale as following: The electrical current (i.e.

the movement of the electrical charge) is switched on in the moment t0  0. The time t1 (with t1  0 ) shall be defined as the moment, at which the magnetic field reaches the radius r1 in consideration of its finite speed of propagation (see again fig.5). Again a bit later, namely at the moment t2  t1  t (with t  0 ), the field will reach a cylinder with the radius r2.

Consequently, the magnetic energy, which has been emitted by the moving charge within the time interval t, has to be the same energy, which fills the cylindrical shell from the inner radius r1 up to the outer radius r2.

We calculate this amount of energy by integration of the energy density inside the cylindrical shell (with finite height z0 ), following equation (1.17) in which we introduce the magnetic

field according to (1.16):

–  –  –

In order to find out, whether the power P is constant in time (as it should be expected in the case that the vacuum would not interact with the propagating field), we have to express the radii r1 and r2 as a function of time. For this purpose, we can use (1.20) and (1.21) and

deduce:

–  –  –

Obviously, this expression is not constant in time. If it would be constant in time, it would not depend on the time t1. This means that the moving charge produces a magnetic field and thus it emits power, although the movement keeps constant speed. We understand this as the first aspect of the energy circulation (i.e. the first aspect of the solved paradox), regarding the emission of energy from a field source. But the moving (field producing) charge is in connection only with the vacuum, thus we have to find out the origin of the emitted energy (which will lead us soon to the second aspect of the energy circulation).

By the way, it shall be mentioned, that permanent magnets permanently emit field energy, which gives a very clear and simple explanation for the analogy with first aspect of the energy circulation of the electric field as shown in section 2.2.

But there is an additional further observation: Obviously, the emitted power is not constant in time, although there is no alteration of the field strength as a function of time. This explains the pendant for first aspect of the energy circulation (in analogy with the electric field), namely the fact that the vacuum takes energy out of the propagating field. This can be demonstrated by tracing a cylindrical volume (and the energy within this volume) along its propagation through the space, analyzing whether the energy inside this cylindrical volume remains constant during the propagation.

Therefore we follow the observed cylindrical shell with the inner radius r1 and the outer radius r2 for a further time interval t x  0. Within this time, the inner radius will be enlarged until it reaches r3  r1  c  t x and the outer radius will be enlarged until it reaches





r4  r2  c  t x. So we see the following development of the situation during time:

▪ At the moment t2  t1  t our cylindrical shell had had the inner radius r1 and the outer radius r2, this means that we look to the same cylindrical shell as in the calculation of (1.18).

▪ At the moment t2  t x  t1  t  t x this cylindrical shell from r1 … r2 has propagated radially into the space until it reaches the inner radius of r3 and the outer radius of r4.

The energy of this last mentioned cylinder can be calculated in both moments in analogy to

equation (1.18):

For those both moments of observation we compare the energy inside the cylindrical shell

according to (1.18) and we thus we come to the values of (1.23) and (1.24):

18 2. Philosophical background

–  –  –

Obviously, both expressions are different. If we want to understand the time dependency of

the energy, we put r1 and r2 from (1.20) into (1.23) and (1.24) and we come to:

–  –  –

which means in consideration of (1.25) and (1.26) that W12  W34. Consequently, the magnetostatic field gives energy to the vacuum during its propagation.

This makes the analogy between the circulation of energy of the electric field and the magnetic field complete. In both cases the field source is supplied with energy from the vacuum (in order to enable the field source to emit energy permanently), and in both cases the propagating field gives back energy to the vacuum.

2.3. A circulation of energy of the magnetostatic field 19 By the way it can be mentioned, that the energy and the power, which the field sources extracts from the vacuum (in the electrostatic case as well as in the magnetic case) is larger than the energy and the power, which the vacuum takes back during the propagation of the field. This is plausible, because the volume filled with field permanently grows during time (without a decrease of the field strength at a given position). The increase of the field strength during time has the consequence that the vacuum permanently loses some energy to the field.

Consequence: In analogy to the electric field and the circulation of energy herein, the circulation of energy of the magnetic field should also offer a possibility to extract energy from the vacuum. And both types of field- and energy- circulation should be observable in laboratory, if a mechanism can be found, which allows to extract energy and tu use it for the drive of a mechanical device (for instance to make a rotor rotate).

20 3. Theoretical fundament of the energy-flux

3. Theoretical fundament of the energy-flux

Of course, there is a connection between the energy-flux described in section 2 and the energy density of the vacuum.The energy density of the vacuum is still nowadays entitled as one of the unsolved puzzles of physics [Giu 00]. At least a certain part of the vacuum energy should be explainable by a summation of the eigen-values of the energy of the zero point oscillations of the vacuum (of electromagnetic harmonic oscillators resp. waves) [Whe 68].

Nevertheless, this statement does not want to express, that this special energy sum is the only energy within the vacuum. But this energy-sum can seen in relation with the energy-flux described in section 2. This will one of the topics of section 3.

The problem with the summation of the eigen-values of the energy of all zero point oscillations (these are infinitely many) is the divergence of the improper integral over all wave vectors of these zero point oscillations. One approach to the solution is discussed in Geometrodynamics, which is nowadays seen with large scepticism because it is in contradiction with measurements of Astrophysics (see section 3.5).

In section 3 of the present work a new solution for this convergence problem is introduced on the basis of Quantum electrodynamics (where improper integrals are not unknown), and this solution comes to values appearing realistic [e6]. The only necessary postulate is: It is well known that the speed of propagation of electromagnetic waves (in the vacuum) is influenced by electric and magnetic DC-fields [e7], [Eul 35], [Rik 00] [Bia 70], [Boe 02], [Ost 07]. The postulate is now to assume, that the zero point oscillations of the vacuum display the same behaviour as the other waves.

Based on this concept we will now investigate the energy of the zero point oscillations of the vacuum, and we will find an idea how this energy can be made manifest in the laboratory.

The experiments to realize this idea will be presented later in section 4.

–  –  –

The propagation of a photon in the vacuum without a field (electric and magnetic) follows the speed of light. Because the propagation of electrostatic and magnetic fields are understood as the exchange of photons [Hil 96], the logical consequence should be, that electric and magnetic DC-fields should also follow this speed of propagation. Assigning this conception to DC-fields is not usual for everybody, but we will find further justification in the following chapters with arguments within the Theory of Relativity and with arguments within Quantum Theory. The background will be understandable within the model presented in section 3 of the present work.

The fact, that even the ground state 0 of the “empty vacuum” contains the energy of harmonic oscillations of electromagnetic waves, is the reason that they got the name “zero point oscillations”. Their energy according to (1.28) defines the vacuum-energy of the ground state. If we want to have access to this energy (and to convert it into a classical form of energy), we have to understand their nature. A well-known example for a force coming out of this type of vacuum-energy is the Casimir-force [Cas 48], [Moh 98], [Bre 02], [Sve 00], [Ede 00], [Lam 97], which is explained on the basis of zero point oscillations. This explanation is based on the analysis of the influence of two ideally conducting (metallic) plates onto the spectrum of zero point oscillations of the vacuum. The free vacuum (i.e. without those plates) consists of a continuous spectrum of all imaginable wavelengths, whereas the space between the plates only contains a discrete spectrum of resonant (standing) waves, because the plates act as reflectors with a field strength of zero at the surface of each plate, defining nodal points of the oscillation. From the energy-difference between those both spectra (in the free vacuum and between the plates), Casimir deduces the energy density and the force between the plates.



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