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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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Remark: The thickness  d of the spherical shells has been regarded as d  0 in our example.

2.1. Static fields versus Theory of Relativity 7

–  –  –

If the calculation of the field strength is conducted with continuously ongoing time and the superposition of those field strengths which reach the observer at the position x at the same moment (they have to be calculated individually for each of the four point charges), the result will be the total electric (DC-)field at the position x as a function of time, following Coulomb’s law under consideration of the finite speed of propagation of the field.

An exemplary result, calculated with the input-values of q  1.60217653  1019 C (elementary charge), d1  0.5 m, d 2  3.5 m,   107 sec. and x  10 m, is plotted in fig.3. Obviously, the field strength at the position of the observer is not zero. This is plausible, because those field strengths which compensate each other in (1.5) will not compensate to zero now, because they arrive at the position x at different moments in time, because they have to pass different distances on their way to the observer. On the other hand those field-strengths which reach at the position x have been produced at different moments and thus at different positions not being able to compensate each other according to (1.5), because there are different distances to be used in Coulomb’s law.

–  –  –

The most important statement of the result is obvious: The field strength is not zero at the position x.

But there is a further observation: Although the four point charges oscillate following a cosine during time, the field strength (at the position x ) as a function of time does not exactly follow a sine or cosine. Its deviation from a sine can be seen in equation (1.7), where the first sine-term gives the dominant part of the field strength, and the next both sine-terms give the continuation of a series (which is not a Fourier-series because of the individual phase of every sine-term). By the way: The maximum of the speed, with which the electrical charges move in our example is a bit less than 2  108 m s. If the charges move slower, the difference between the shape of E  t  and a sine decreases.

–  –  –

Of course, such forces do not have an explanation within Classical Electrodynamics – they do not exist within this Theory. Consequently, they should have an explanation within Electromagnetic Field Theory or within Quantum Electrodynamics (going back to the structure of the vacuum / space). From this point of view it can be concluded, that the finite speed of propagation of electric (DC-)fields (as well as of magnetic (DC-)fields) should offer a possibility to convert some of the energy within the vacuum (space) into some classical type of energy – as will be demonstrated in the further course of the present work. (The logics behind this conclusion will be seen soon.)

Additional remark:

The contradictions between Classical Electrodynamics on the one hand and Electromagnetic Field Theory and the Theory of Relativity on the other hand can be solved in favour of Field Theory and Relativity – if it is possible to conduct an experiment, which converts vacuumenergy into classical energy, which is developed and explained on the basis of the finite speed of propagation of the field. This will be done in the experimental part of the present work.

From this point of view it is clear, that Classical Electrodynamics is an approximation under terrestric circumstances for normal technical applications, where the finite speed of propagation of electric and magnetic fields will not be recognized, because the distances inside a laboratory, which the fields have to transit are so small, that the duration of propagation is not noticed. This is not astonishing if we have a look to the time scale in fig.3 ( Pikoseconds ) in comparison distances of some meters ( x  10 Meter ).

But there is one additional question arising: From where does the energy originate, which the propagating field contains and transports ?

This question is important and helpful, because the mentioned energy is this type of energy, which shall be converted into a classical type of energy. We want to trace this energy exemplarily in section 2.2 for the electric field and in section 2.3 for the magnetic field. This leads us to the logical background, from which was said, that it will understood soon.

10 2. Philosophical background

2.2. A circulation of energy of the electrostatic field If electrostatic fields propagate with the speed of light, they transport energy, because they have a certain energy density [Chu 99]. It should be possible to trace this transport of energy if is really existing. That this is really the case can be seen even with a simple example regarding a point charge, as will be done on the following pages. When we trace this energy, we come to situation, which looks paradox at the very first glance, but the paradox can be dissolved, introducing a circulation of energy [e5]. This is also demonstrated on the following pages. By the way there are colleagues who also began with considerations of this propagating energy (for instance [Eng 05]), but they do not primarily discuss the circulation of energy but rather the idea to transmit information with a speed faster than the speed of light, which could only be possible according to the conception of the infinite speed of propagation of electric (or magnetic) DC-fields.





The first aspect of the mentioned paradox regards the emission of energy at all1 [e16]. If a point charge (for instance an elementary charge) exists since a given moment in time, it emits electric field and field’s energy from the time of its birth without any alteration of its mass.

The volume of the space filled with this field increases permanently during time and with it the total energy of the field. But from where does this “new energy” originate ? For the charged particle does not alter its mass (and thus its energy), the “new energy” can not originate from the particle itself. This means: The charged particle has to be permanently supplied with energy from somewhere. The situation is also possible for particles, which are in contact with nothing else but only with the vacuum. The consequence is obvious: The particle can be supplied with energy only from the vacuum. This sounds paradox, so it can be regarded as the first aspect of the mentioned paradox. But it is logically consequent, and so we will have to solve it later.

Remark: Electrically charged particles can be “born” by pair production process, but there might also be charged particles existing since the big bang. Both types of particles are well within the explanations given here. The difference is only the duration of their existence, which is proportional to the diameter of the sphere, which is filled with the field. But for our paradox, this difference does not play any role.

The second aspect of the mentioned paradox regards the propagation of the emitted field’s energy into the space. In order to understand this, we want to regard the electrical field emitted from a charged elementary particle Q (see fig.4). For the our consideration it does not play a role, whether the elementary particle has punctiform shape (for instance as the electron in scattering experiments, leading to a radius of rstreu  1018 m, see for instance [Loh 05], [Sim 80]) or whether we regard an electron with its classical radius For the sake of illustration it should be mentioned that periodically moving stars (for instance such as rotating double stars [Sha 83] or a star rotating around a black hole) emit gravitational waves because of the emission of gravitational (DC-)fields. The fact that we see gravitational waves (at our position) goes back to the mechanism described in section 2.1 for moving point charges in similar way as for moving point masses. In this context it might be remembered, that this is not the gravimagnetic field known from the Thirring-Lense-effect (see for instance [Sch 02], [Thi 18], [Gpb 07]), which can be understood in analogy with the magnetic field of Elecrodynamic and which is emitted additionally.

2.2. A circulation of energy of the electrostatic field 11 ( rklass.  2.82... 1015 m according to [Cod 00], [Fey 01]). In order to evade such questions, we want to put a sphere with the radius x1 around the particle Q. Furthermore we want to fix our time scale at this moment t  0, at which the electrostatic field fills exactly the sphere with the radius x1. From there on, we trace the field along its propagation through the space.

Let us now come to a moment t  0, which is later than the begin of our consideration, so that the field with its finite speed of propagation c fills a sphere with the radius x1  c  t, so that the energy which the charge emitted during the time-interval t is the energy within the spherical shell from x1 to x1  c  t, because this is the amount of energy, by which the total energy of the field was enhanced during the time interval t. This energy is larger than zero, so that we clearly see that the charge Q indeed emitted field and field’s energy.

Let us now observe the situation at a moment t2, which is later than the moment in the consideration before. And let us further add the time interval t, so that the spherical shell from x1 to x1  c  t had developed itself into the spherical shell from x2 to x2  c  t. This means that the energy from the shell x1 … x1  c  t moved into the shell x2 … x2  c  t. If the vacuum (inside which the field propagates) would not extract energy from the field, we expect the energy within the shell x1 … x1  c  t to be the same as the energy within the shell x2 … x2  c  t.

Will now check this expectation by the following calculations and we will find a violation of the energy conservation during the propagation of the field into the space. We will see that the field loses energy during its propagation. With other words: We regard a given package of space filled with electric field (inside a spherical shell) and trace it along its propagation through the space. We calculate the field’s energy inside the field package and we will find that it does not keep its field’s energy constant. This is the second aspect of the mentioned paradox of the electric field, which will also be solved later in the present work.

–  –  –

 Obviously, the energy Einner shell is more than the energy Eouter shell. This means that the empty space decreases the energy of the shell. This proofs the validity of the second paradox, and we see that the vacuum (the mere space) takes away energy from the field during its propagation.

–  –  –

Important is the conclusion, which can be found with logical consequence:

On the one hand the vacuum (= the space) permanently supplies the charge with energy (first paradox aspect), which the charge (as the field source) converts into field energy and emits it in the shape of a field. On the other hand the vacuum (= the space) permanently takes energy away from the propagating field, this means, that space gets back its energy from field during the propagation of the field. This indicates that there should be some energy inside the “empty” space, which we now can understand as a part of the vacuum-energy. In section 3, we will understand this energy more detailed.

But even now, we can come to the statement:

During time, the field of every electric charge (field source) increases. Nevertheless the space (in the present work the expressions “space” and “vacuum” are use as synonyms) causes a permanent circulation of energy, supplying charges with energy and taking back this energy during the propagation of the fields. This is the circulation of energy, which gave the title for present section 2.2.

This leads us to a new aspect of vacuum-energy:

The circulating energy (of the electric field) is at least a part of the vacuum-energy. We found its existence and its conversion as well as its flow. On the basis of this understanding it should be possible to extract at least a part of this circulating energy from the vacuum – in section 4 a description is given of a possible method how to extract such energy from the vacuum.



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