# «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, ...»

The field source converts vacuum-energy into field energy by altering the wavelengths of the zero point oscillations. This alteration is stopped abruptly at the surface of the conductor plates (these are the blades of the rotor), so that the conductor plates absorb some field energy from the flux of the propagating field. (They absorb the percentage of the flux, which hits their surface.) Nevertheless, it is much easier to calculate the forces driving the vacuumenergy rotor if we follow the formalism of Classical Electrodynamics, using the image charge method [Bec 73], as will be done soon when developing the real concept of the experiment for the verification of the vacuum-energy and its conversion into mechanical energy.

3.5. Comparision of the QED-model with other models We now intend to compare our value for the energy-density of the vacuum (see (1.44) and (1.47)) with the values of other models in the context of other disciplines of physics. But we have to keep in mind, that our model only gives the energy-density of the electromagnetic zero point oscillations, not the total energy-density of the vacuum.

The total energy-density of the vacuum is a topic of Cosmology, because it refers to the gravitation, caused by the mass of the vacuum. The reason is that every type of energy corresponds to a mass, which (finally) gives rise to gravitation. And this is also the case for the vacuum-energy contained in the universe, which influences the expansion of the universe because of its gravitation. From the alteration of the speed of the expansion of the universe, it is possible to derive the total mass of the vacuum (together will all other matter within the universe). Thus the cosmological value gives the total energy-density of the vacuum, which should be larger than the value of our model. But this will lead to an open question, which can be seen as a contradiction (see (1.48) below).

The question of the energy density of the universe is known to be one of the unsolved puzzles in nowadays physics, and it is often called “the largest discrepancy known in Physics” with a range of more then 120 orders of magnitude between different values (for the same energydensity) from different branches on physics.

How can the discrepancy between (1.49) and (1.44) be interpreted ?

Well – the result of (1.49) is mostly regarded very sceptically, because there is not a serious argument for the way, how the convergence problems have been suppressed. In principle the idea of our model also begins with (1.30) same as the Geometrodynamical model, but our model has a serious physical argument to solve the convergence problems.

In principle, we could interpret the result in a way, that there is no contradiction at all. The model of the present work calculates only one part of the energy-density of the space, whereas the Geometrodynamical value gives the total energy-density of the space. So our values should be smaller than the Geometrodynamical value – and this is the case. But nevertheless, it is hard to imagine, that the difference is that large. Probably the discrepancy can not be dissolved that easy.

**Totally different is the interpretation of the values from cosmology and astrophysics in (1.48):**

The total energy density of cosmology should be larger than the value of the present work, giving only part of the energy density. But we observe the contrary. If the value of our model is larger than the value of (1.48) – can both values be possible ? The problem is gravitation: If our value would be correct – shouldn’t this mean that the attractive forces of gravitation should be larger than the observed values of cosmology ?

In reality, it is not that simple to construct a contradiction. Reason: On the one hand the question about the accelerated expansion of the universe is still unsolved [Cel 07] (and there are symptoms that the expansion of the universe might be decelerated). On the other hand,

3.5. Comparision of the QED-model with other models 35 expansion of the universe has to presume a special distribution of matter and dark matter – normally a distribution inside a sphere with a radius taken from the hypothesis, that the beginning of the universe was the “big bang” and the expansion of the matter and the dark matter is for sure not faster than the speed of light [Per 98], whereas the energy density of the zero point oscillations refer to the whole space 3. Hence there is also energy (and thus mass) in the space outside the sphere which we call universe. For gravitation, this difference is definitely important.

In this sense, there are too many open questions to see already a contradiction between the cosmological value of the energy density of the vacuum and the values of the model

**presented here. An interpretation could be like this:**

Obviously, the calculation of the energy density of the zero point oscillations of the vacuum runs into convergence problem with an improper integral, leading to an infinite energy density. Classical Quantum theory goes around this problem by ignoring the infinity and fixing the origin of the energy scale (energy zero) on top this infinite energy [Lin 97]. This perception is not fully satisfying, so Geometrodynamics tries to cut off the improper integral artificially by taking a finite range for the integration. It is clear that this approach avoids problems of divergence by principle, but it results in rather strange values, which are regarded with scepticism. A physical solution for this divergence problem is found in the work presented here, and it leads to sensible values for a certain part of the energy density, namely for this part which comes from the electromagnetic zero point oscillations. But it does not calculate the total energy density of the vacuum.

36 4. Experiments to convert vacuum-energy into classical mechanical energy

**4. Experiments to convert vacuum-energy into classical mechanical energy**

4.1. Concept of an electrostatic rotor Now we want to find a possible setup, with which we can extract some energy from the energy-flux of the circulation of the electrostatic field energy and the vacuum-energy (as described in sections 2 and 3). We want to convert this extracted energy into a classical type of energy, which can be experienced directly in the laboratory. If it would be possible to invent a rotor, which is driven by this energy-flux, this would be a direct experimental verification of the energy-flux.

A possible constellation, which fulfils this task, can be seen in fig.6. This is a principle sketch, which is made for sake of simplicity in order to be easy understandable, although this design does not yet have the maturity to be ready for the practical realization. For instance, it is impossible by principle to realize a punctiform field source, because the electrical charge has to be put onto a body of real existing material, but the fundamental explanations and considerations on the basis of this model can be understood very clear and easy.

a way, that the x-axis is exactly the middle-line of the rotor blade, which we take for our calculation. This rotor blade will be blade named as no.1 for further considerations.

The drive of the rotor by vacuum-energy is possible, because the charge q permanently emits field energy, which is continuously converted into mechanical energy, which has its reason in the fact, that the emitted electrical flux2 (as illustrated in textbooks by the use of flux-lines) is stopped or redirected by the metallic surfaces of the rotor blades, and this stop or redirection causes mechanical forces acting onto the rotor blades. These driving Coulomb-forces can be calculated by the use of the image-charge method [Bec 73], [Jac 81]. Thus in fig.6 the imagecharge q ' corresponding to the charge q with regard to rotor blade no.1 is marked. The Coulomb-force between the charge q and the rotor blade is (according to the image-charge method) the same as the Coulomb-force between the charge q and image-charge q '.

Consequently, the force driving rotor blade no.1 can be simply calculated by inserting the charges q and q ' into Coulomb’s law.

Because of the symmetry of the assembly, the considerations for the determination of the forces do not alter by principle, when the rotor-blades rotate during time. Also because of the symmetry, the forces are analogously for all three rotor-blades. Thus, it is sufficient to calculate the force and the torque in the moment of consideration chosen here, and to do this calculation just for the blade no.1 and to transform the results to all three rotor blades later. In any case, the axis of rotation is the z-axis, so that all rotor-blades move within the xy-plane.

A preliminary work (before the calculations of the forces onto rotor blade no.1 can start) is the determination of the position of the image-charge q ' with respect to the plane of (1.50).

The charge q is located at the z-axis at the z-coordinate z0. The location of the image-charge q ' can be found as drawn in fig.7, where we look from the direction of the x-axis onto the xz-plane. In this view, the rotor blade no.1 is drawn as a straight line with the mathematical function z y, which we already know from the parameterization of the mathematical function of the plane of the rotor blade. The position of the image-charge q ' is then on the y

charge because of “actio = reaction”), which causes a rotation of the rotor-blades around the z-axis, because the force has a tangential component with regard to the movement of the rotor blade around the z-axis. For illustration, we can again have a look to fig.6. This force is attractive, because the image-charge has the opposite algebraic sign as the charge itself. From this consideration, we understand the direction of the rotation as indicated in fig.6 with a bent arrow around the z-axis. This direction of the rotation is independent of the algebraic sign of the charge q (because q and q ' always hat opposite algebraic signs).

An additionally existing component of the force into the z-direction should not influence the rotation of the rotor blade, because it is absorbed by the bearing “B”. In the real experiment (section 5) we will later see, that this z-component of the force together with a radial component of the force (here in the direction of x) nevertheless causes practical technical problems depending on the type of bearing used.

In order to develop a feeling for the forces expected in the practical setup, an exemplary calculation with some arbitrary but realistic dimensions shall be demonstrated, for instance as done in fig.8. There we see the topview from the z-axis onto an exemplary rotor rotating in the xy-plane. Realistic dimensions also demand a realistic size field source, which is now a sphere with a real diameter.

For a really existing setup, the electrical charge q has to be put onto some really existing matter. Let us chose an electrically conducting sphere with a diameter of 2 R 1.0 cm, and let us mount its centre at the position z0 5 cm. The capacity of such a spherical capacitor (against infinity) is C 4π 0 R. If we put this sphere to an electrical voltage of U 10kV (which should be a good value in order to avoid electrical breakthrough), it will take an electrical charge of q C U 4π 0 U 5.56 109 C. The image-charge thus will have R 9 0.5 cm 10 kV a value of q ' 5.56 10 C.

Putting these values into (1.54) for the force between the charge and the image-charge, we come to 40 4. Experiments to convert vacuum-energy into classical mechanical energy

The z-component of this force, which is parallel to the direction of the axis of rotation will not be recognized (and not be important at all, besides for technical problems later), but the y-component of this force directly causes the rotation of blade no.1 around the z-axis (if this force is strong enough to overcome the force of friction), because it acts tangentially onto the rotor blade. Because of the symmetry of the assembly, the forces onto the other blades are understood analogously. This means that the principle of functioning of the motor is already explained now.