Claus W. Turtur (Fachbereich Elektrotechnik, University of Applied Sciences BraunschweigWolfenbuettel)
Published in physic.philica.com Abstract The fundamental principle of the conversion of zeropointenergy has been explained in [Tur 10]. This enables us to construct zeropointenergy converters systematically. The method of computation for such a construction was presented as dynamic FiniteElementMethod (DFEM), which is a FiniteElementAlgorithm with the supplement of taking the finite speed of propagation of the interactingfields (responsible for the forces between the partners of interaction) between the components of the zeropointenergy converter into account.
In order to illustrate the development from the fundamental principle to the real DFEMprogram, we now present a small example for this computation, including a short sourcecode as a working performance. This algorithm is explained in detail here, so that everybody can use and further develop it. Finally we analyse a possible zeropointenergy motor with this program, explaining its conditions of operation and its machine power. Article body
1. An uncomplicated setup This is the very first time that an algorithm for the construction of zeropointenergy converters is presented. Thus, the computerprogram was developed as uncomplicated as possible, in order to make it understandable to everybody. For the conversion of zeropointenergy is not something exotic, it is not difficult to find a very simple setup (as a basis for the analysis in our DFEMalgorithm), which can fulfill this task: For the sake of simplicity, we take a onedimensional example, and it is already sufficient to connect two masses with a helical spring, in order to build up a simple oscillator – nothing more – this is all we need. The only addition we will need is some electrical charge on the bodies No.1 and 2, or some magnets. The arrangement is drawn in figure 1 as it could be seen in every beginner’s textbook.
Fig. 1: Two masses, which are connected by a helical spring, can perform an oscillation. If we want to trace back the example of figure 1 directly to a simple beginner’s example, we can fix one ponderable mass with the use of a helical spring directly to a wall (as drawn in blue) in the middle of the setup and observe harmonic oscillations according to the differentialequation (1) without friction and without excitation. The solution according to equation (2) is generally known as: Of course, the amplitude is constant, and there is no conversion of zeropointenergy in this example. But if we put some electrical charge on the bodies m_{1} and m_{2}, or if we replace them by two magnets, an additional force will occur (it can be attractive or repulsive), which depends on the distance between the charged spheres or magnets. For the further course of our article, let us chose the direction of this interacting force to be attractive. In the case of electrically charged spheres, the force follows the (first) coulomb's law according to (3); in the case of permanent magnets the force follows the (second) coulomb's law for dipoledipole interactions according to (4), see [Ber 71]. Those both laws differ from each other only by the factor of proportionality, and by the fact that in the case of electrical charges, we have to put the charges Q_{1}, Q_{2} into the formula, whereas in the magnetic case, we have to put the magnetic dipolestrengths p_{1}, p_{2} into the formula. In both cases the forces decrease proportional to 1/r^{2}. Because of this reason, we can say, that the computation of electrostatic zeropointenergy motors has to be done in complete analogy with the computation of magnetic zeropointenergy motors, because the computations only differ by some constant factors. Nevertheless it has to be emphasized, that a totally different dependency between force and deflection would be absolutely no problem, because it would just require an alteration of two lines in the algorithm of section 3, namely FEL1:=+Q1*Q2/4/pi/epo/r/Abs(r); {electrostatic force between Q1 & Q2} FEL2:=Q1*Q2/4/pi/epo/r/Abs(r); {electrostatic force between Q1 & Q2} If L_{0} is the length of our helical spring in the moment without springforce, the description of the pendulum is now done by adding an expression for the electrostatic resp. for the magnetic force into the differentialequation of (1), so that we come to the differential equation of (5). The left expression is for body No.1, the right expression for body No.2. (5) where C_{EM} are the factors of proportionality mentioned above, which contain the information about Q_{1}, Q_{2} or p_{1}, p_{2}. Depending on the algebraic sign of the electrical charge Q_{1}, Q_{2}, or of the polarity of the dipoles p_{1}, p_{2}, the factor C_{EM} can be positive or negative. Besides the inertial forces and the forces of the helical spring, our differentialequation now takes also magnetic forces resp. electric forces into account. The solution of the differential equation (5) now is not any further a simple sineexpression as it has been in the harmonic oscillation of equation (2). With a numeric iteration, as shown in part 2 of the algorithm in section 3, we derive the solution as seen in figure 2. Fig. 2: Trajectories of the two bodies No.1 and 2, which are electrically charged or permanent magnets. The spring has to be imagined vertically, connecting the bodies No.1 and 2. Obviously the oscillation is not harmonic. Obviously classical potential energy (of the electrical or the magnetic field) is converted into the energy of spring energy and kinetic energy. Thus, we have an energyconversion between these three types of classical energy. Of course zeropointenergy is still not under discussion. The amplitudes are constant, confirming the conservation of classical energy. The computersimulation of the motion can be found in part 2 in the sourcecode printed in section 3. Because up to here, we did not yet deal with the zeropointenergy conversion, the algorithm is still a classical static FEMalgorithm (with only two elements). 2. Introducing Dynamics: From FEM to DFEM We now want to insert the finite speed of propagation of the electric field resp. the magnetic field into the considerations of figure 1 and section 1. In the static theory of electricity, the duration for the propagation of these fields is neglected. This means, that the speed of propagation of the fields is approximated to be infinitely fast. Of course, this is in clear contradiction to the Theory of Relativity, according to which the speed of light is a principle upper limit to all velocity and speed at all. So we regard the static theory of electricity as an approximation, which works rather well in many classical cases for engineering purpose, but which is not sufficient for the explanation of the zeropointenergy motors by principle (see [Tur 10]). Thus we decide to reject this approximation now, in order to make the conversion of zeropointenergy understandable. By the way, the speed of propagation of the fields is the speed of light only inside the vacuum. In matter, the fields propagate less fast. Consequently, we have to replace equation (5) and figure 2, which are based on the approximation of infinite speed of propagation of the fields, by a more precise consideration. This is what we do now: For the solution of equation (5), the forces in part 2 of the algorithm (see section 3) had been calculated only with the use of the static version of coulomb’s law. For the dynamic computation, we now have to accept the fields of interaction as selfreliant physical entities, and we have to take their finite speed of propagation into account, as illustrated in figure 3. There we see two bodies moving to the left and to the right, and the timedependant development of the situation is plotted in three steps from the top to the bottom. At the moment t_{a} the interacting partner No.1 (magnet or charge) is at the position x_{1,a} and the interacting partner No.2 is at the position x_{2,a}. At the moment t_{a}, No.1 emits a field, which propagates among others also into the direction towards No.2 (red arrow). This part of the field is responsible for force of No.1 acting on No.2. This field(package) now approaches towards No. 2, but at the same time, No.1 also moves a little bit to the right side, this means, that No.1 follows the direction of the field. But No.2 moves from the right to the left side, this is the direction towards the field(package). We can see this development, when we follow the course of the time from t_{a} to t_{b}. But finally we further follow the course of the time until we reach t_{c}. This is the moment, at which the field reaches the partner No.2. For the computation of coulomb's law we now face the question: Which fieldstrength does partner No.2 feel in this moment ? The answer is clear: We use Coulomb's law according to equation (3) or (4), and we apply the distance which the field had to pass really. This is the distance marked with the blue arrow in figure 3. This means that No.2 feels less field strength in the moment t_{c}, then it would be derived from the static version of Coulomb's law (for which the distance is marked with a green arrow). On the other hand, if both partners of interaction would not approach to each other, but run away from each other, the situation would be just the opposite, where No.2 would feel a field, which is a stronger then according to the static version of Coulomb's law. The situation is illustrated in figure 4.
Fig. 3: Illustration of the influence of the motion of the magnets or the electric charges on the emitted field strength. Basis of the understanding is the finite speed of propagation of the fields. The graph displays the situation of two bodies moving away from each other.
Fig. 4: Illustration of the influence of the motion of the magnets or the electric charges on the emitted field strength. Basis of the understanding is the finite speed of propagation of the fields. The graph displays the situation of two bodies moving towards each other. If we manage to organize the motion of the bodies (of Fig.1) in a tricky way, we can achieve that they oscillate relatively to each other (due to the helical spring connecting them to each other) in such a way, that they feel a reduced Coulombforce during the timeintervals when they increase their distance from each other, whereas they feel enhanced Coulombforce during the time, when they decrease the distance between each other. In the case of attractive Coulombforces, these leads to the consequence, that the amplitude of the oscillation increases more and more during time, without any support of classical energy. An illustration can be seen in figure 5, where different colours are used to represent different field strength. In the very first line of figure 5, we see a static field source at rest (charge or magnet), which emits a static field. As long as of the charge is at rest, the fieldstrength is constant, and thus it is not necessary to perform any dynamic consideration. But if the field source comes into motion, as in the second line of figure 5, the field is reduced on the right side (towards which the field source is moving), as we learned from t_{c} in Fig.3. The opposite case is a motion of the field source to the left side (third line of figure 5), corresponding to the moment t_{c} in Fig.4 and causing an enhancement of the field strength on the right side in comparison to the static version of Coulomb's law. Two field sources, which oscillate relatively to each other (this is our setup since figure 1), produce oscillating field strength at the position of each other. This causes, as soon as it is arranged properly, the modulation of the field strength, which leads to the enhancement of the amplitude as described above. Of course this is only possible, because it is supplied with the zeropointenergy of the quantumvacuum – as explained in [Tur 10]. Of course this is only possible, if the supply with zeropointenergy is kept during many periods of oscillation in good synchronization with the oscillating bodies. In this case, the supply of energy is resonant, and we have an efficient zeropointenergy motor, converting zeropointenergy into classical energy of an oscillation. In the opposite manner, it is also possible to synchronize the oscillating fields and the oscillating masses with reversed phases to each other, so that the phase of the enhanced field strength always occurs during the time when the attractive partners want to enhance their distance, whereas the phase of reduced field strength always occurs during the time when the attractive partners want to reduce their distance. In this case the dynamics of the fields in Coulomb's law reduces the oscillation. This means, that classical energy of the oscillation is converted into zeropointenergy of the quantum vacuum. Fig. 5: Illustration of the oscillating fields, as they are emitted by oscillating electrical charges or by oscillating magnets. The situation is not surprising, because the Hertz’ian dipoleemitter is known to work according to the same principle. From there, we understand that the principle of the conversion of zeropointenergy of the quantumvacuum can be applied in both directions (as soon as we understand it): On the one hand it can be used to convert zeropointenergy into classical energy, and on the other hand it can be used to convert classical energy into zeropointenergy. Which of those both directions is realized in an engine is mainly a question of the adjustment of the systemparameters. Especially the following both systemparameters have to be adjusted appropriately to each other:  the speed of propagation of the fields and  the speed of motion of the moving field sources. In our examplealgorithm this means, that we have to adjust the deflections and the amplitude of the oscillating bodies, their ponderable masses, Hooke’s spring force constant, and finally of course the electrical charges, which supply the Coulombforces necessary to convert zeropointenergy appropriately to each other. Instead of electrical charges, it would also be possible to use permanent magnets and to include the adjustment of their dipolestrengths into the adjustment of the systemparameters. In order to prove all these statements, within the preceding work, a dynamic Finiteelement algorithm (DFEM) was developped, which is a very short and easy to understand. It realizes the oscillation of two electrically charged spheres with a spring as drawn in figure 1, taking the finite speed of propagation of the Coulombfield into account when analyzing the oscillation. This means that we have the same geometrical setup as we had for our static consideration leading to figure 2. But due to the fact, that we now perform a dynamic analysis, we derive the deflections of figure 6, figures 7 and figure 8. Therefore, the adjustment of the systemparameters (in our algorithm) is given as following: With Fig.6:  speed of propagation of the fields c = 1.4 m/s  electrical charges Q_{1} and Q_{2} = 3•10^{5} C per each  Hooke’s spring force constant D = 2.7 N/m  length of the unloaded helical spring RLL = 8.0 m  startingposition of the bodies’ motion at x1=3.0 m and x2 = +3.0m. As can be seen, the amplitude increases rather fast at the begin of the oscillation. Obviously the motion of the bodies and the motion of the Coulombfields are adjusted in such a way to each other, that the oscillation gains energy from the quantum vacuum rather efficiently. But we further observe, that there is a certain limit for the amplitudes. This comes from the fact, that the speed of the motion of the bodies reaches a value in comparison with the speed of the propagation of the fields, that it will not be possible to gain more energy from the quantum vacuum than seen in this oscillation after time “30 seconds”. This means that the gain of energy from the quantum vacuum is saturated at these systemparameters reached here, and the amplitude will become constant. But it must be said: If we would extract mechanical energy from this oscillation (with constant amplitude), the mechanical extraction of energy would act back on the amplitude (as seen in section 5), but in this moment the regain of energy from the quantum vacuum would be enhanced, so that the amplitude would still be kept at its constant value (as long as we do not extract too much mechanical energy). The amount of mechanical energy which we can extract, is the enginepower, which we can gain from the zeropointenergy of the quantum vacuum in this mode of the operation of the zeropointenergy motor. Fig. 6: Example for the mode of operation of a harmonic oscillator according to figure 1 as a zeropointenergy converter. We can easily see, that the amplitude is increaseing due to the gain of zeropointenergy of the quantum vacuum. With Fig.7: If the systemparameters are altered only by a small amount, the system behaves completely different. Only a small alteration of the speed of propagation of the fields and of the dimensions of the spring (together with the starting positions of the bodies) in comparison to figure 6 leads to the consequence, that the oscillation can not gain energy from the quantum vacuum, because the speed of the fields and to the speed of the motion of the bodies are not adjusted appropriately to each other:  speed of propagation of the fields c = 1.4 m/s  electrical charges Q_{1} and Q_{2} = 3•10^{5} C per each  Hooke’s spring force constant D = 2.7 N/m  length of the unloaded helical spring RLL = 12.0 m  startingposition of the bodies’ motion at x1=5.0 m and x2 = +5.0m. Under this mode of operation, the engine is not any further a zeropointenergy converter. Abb. 7: Under this mode of operation, the harmonic oscillator according to figure 1 does not gain any energy from the zeropointoscillations of the quantum vacuum. With Fig.8: One tiny further alteration of a systemparameter leads us into the opposite direction, at which the system destroys classical energy by converting it into zeropointenergy. In comparison to figure 6, just only Hooke’s spring force constant was altered, nothing else. Nevertheless, the consequence is, that the capability of the system to oscillate was altered in a way, that the duration time for the speed of propagation of the fields work in such way, that they reduce the energy of oscillation of the both bodies. The parameters for this case are:  speed of propagation of the fields c = 1.4 m/s  electrical charges Q_{1} and Q_{2} = 3•10^{5} C per each  Hooke’s spring force constant D = 3.5 N/m  length of the unloaded helical spring RLL = 8.0 m  startingposition of the bodies’ motion at x1=3.0 m and x2 = +3.0m. Under this mode of operation, we have an "inverted" zeropointenergy converter, which produces zeropointenergy instead of utilizing it. This provides us with the knowledge, to handle the zeropointenergy of the quantum vacuum just as we need to do, such as to convert it into classical energy back and forth. We may compare this with the situation of a Stirlingengine in Thermodynamics, which can convert mechanical energy into thermal energy as well as thermal energy into mechanical energy, just depending on the direction into which we make him operate. In similar manner we are now able to adjust zeropointenergy converters just as we like them. Abb. 8: Under this mode of operation, the harmonic oscillator according to figure 1 converts mechanical energy into zeropointenergy of the quantum vacuum. The consequence is an enhancement of the fieldstrength flowing away from the apparatus. Remark, regarding the absolute values of the parameters: These absolute values have been chosen in the way that they are handy, in order to make the article most easy to understand. Of course, in reality the speed of propagation of the fields is much larger than in our little numerical example. We decided to choose such values, because handy figures are easier to fit into the reader’s imagination. The presentation of the DFEMcomputeralgorithm in this publication has the sense, to bring everybody who reads this article into the capability to construct his or her zeropointenergy motor. This construction is now possible for every engineer and scientist on the basis of the article presented here. The explanations in [Tur 10] are somehow abstract, so that it became necessary, to support them by a real examplecalculation as presented here, giving definite results, which can be used by every technician. Particularly clear is the answer to the question about the reproducibility of the results presented here: Everybody is invited, to “copy and paste” the DFEMalgorithm as printed in section 3 on his own computer and to run it. All you need is PASCALcompiler (for instance [Bor 99]). Those who furthermore try the systematic variation of the systemparameters can gain a lot of experience regarding the operation of zeropointenergy converters. Real zeropointenergy motors, which can be produced and technically applied, are of course more complicated than this simple example presented here. Real zeropointenergy motors rarely consist of only two magnets and one helical spring. But for people with technical training it should not be a principle problem, to expand the algorithm to additional partners of interaction, representing additional components of a machine. The decision to demonstrate a DFEMprogram with only two finite elements has the reason, to maximize their understandability. For the same reason, the sourcecode of the DFEMalgorithm is published below. 3. Sourcecode of the DFEMalgorithm
A convenient download of the algorithm is also possible for free at: http://www.ostfalia.de/export/sites/default/de/pws/turtur/FundE/English/DFEMALGO.TXT 4. Background explanation The conception, showing the way to the DFEMcomputation, which is based on the dynamic propagation of the interacting fields, has been discussed in [Tur 10]: According to this conception, the occurrence of electric and magnetic fields can be understood as a reduction of the wavelengths of the zeropointwaves of the quantum vacuum. This reduction of the wavelengths is to be understood as a consequence of the reduction of the speed of propagation of the zeropointwaves due to electric and magnetic fields as one of the consequences of the work of [Hei 36]. If we switch on and off the electric charge suddenly, this would cause gaps between the wavepackets, which are differently emitted during the time when the charge is switched on, or when the charge is switched off. Less sharp than this sudden action of switching on and off, we can understand a continuous motion of the field sources, as explained in figure 3, figure 4 and figure 5. The continuous motion of the fieldsources, which we see there, leads to the consequence of a continuous modulation of the fieldstrength, which goes back to a continuous alteration of the position and velocity of the fieldsource. In order to complete the explanations of section 2, we again want to regard the case of a static fieldsource at rest, as it can be seen in the first line of figure 5. Its field reduces the wavelengths of the zeropointwaves and it reduces their speed of propagation. Close to the fieldsource, this effect is much stronger, then more far away from the field source, because the field is the stronger the more close to the fieldsource. This means, that the zeropointwaves which run away from the fieldsource and transport the field have to decrease their reduction of the wavelength and the speed of propagation. This has to be done in such a way, that there will not occur any gaps between the waves, because static fields, produced by electric charges in rest do not have any dynamics, but they are continuous. This decrease of the reduction of the wavelength and of the speed of propagation explains the energy dissipating from the field into the quantum vacuum during the propagation of the field. Let us look to the following consideration: As we know from [Boe 07] for magnetic fields and from [Rik 00], [Rik 03] for electric fields, the reduction of the speed of propagation v of the zeropointwaves is a function of the field strength as following: If we dissolve these equations to the speed of propagation v, we can derive the reduction of the length of a given wavepacket and furthermore the reduction of its speed of propagation, while it is running through an alternating field strength, as it is illustrated in figure 9:
The factor between L_{1} and L_{2} is the factor, by which the length of the wavepackage is altered because of its way through varying fieldstrength.
Fig. 9: Illustration of the propagation of the wavepackets of the zeropointwaves through zones of varying field strength. This consideration corresponds to the fact, that the zeropoint wavepackets adjust their compression or prolongation as well as their speed of propagation to the requirements of the field strength which they pass, according to figure 3 and figure 4. 5. Converted machine power Of course we want to dedicate our attention to the question, how much zeropoint energy is converted per time. This means, we want to find out the converted machinepower. Indeed, this question makes sense only if the systemparameters are adjusted as done in figure 6, because under this operation, the machine is a zeropoint energy converter. Power can only be extracted from a motor, if there is some (mechanical) resistor, and not as long as it is running without any force. This makes it necessary to introduce an additional force into our DFEMalgorithm, for instance a force of friction. In order to keep the comprehensibility of our calculationexample as easy as possible, let us decide to introduce dry friction, which is independent from the relative speed of the motion, as it known as Coulomb’s friction. This allows us to introduce a force F_{R}, which is defined in the third part of the algorithm with the name “Reib”. This force is switched on at the time of 10 seconds, and from there on it remains constant until to the end of the computation at time of 100 seconds. This is also the time interval over which the machinepower is determined as the average of the absolute value of the machine power (even if the graphicplot is continued only to the time of few more than 65 seconds). For the purpose of supervision, we begin with a force of F_{R}=0, and we identically reproduce the behaviour, which we already know from figure 6 with an enhancement of the amplitude of 3.20 meters. Please compare this result of figure 10. After this verification of the algorithm, we now decide to enhance the force of friction stepbystep, and to our surprise, we detect that the enhancement of the amplitude does not decrease with increasing friction. We find out that an enhancement of the energy being extracted by friction, enhances the amplitude of the oscillation. Friction does not reduce the speed of the motion, but it additionally empowers it ! The finding is the following: When we extract energy from the oscillating system, the amplitude is a little bit larger, compared to the system without energyoutput (see blue curve in figure 10). This indicates the following: When we try to slow down the motion, we optimize the adjustment of the phasedifference between the bodies and the fields in such a way, that the extraction of zeropoint energy from the quantum vacuum is increasing. This is the reason, why we see a linear growth of the purple curve, representing the machinepower as a function of the force of friction, in figure 10. This indicates, that it should be possible by principle, to maximize the amount of energy being extracted from the quantum vacuum, by doing a search of the maximum of the purple curve in figure 10. This finding is confirmed by the reports of several vacuumenergy experimentalists. Although they built their engines from intuition (and not on the basis of an existing theory), they observe this phenomenon several times. And sometimes this observation is dangerous for these experimentalists, because their engines suddenly begin to run too fast, so that they lose the control over the engines. Some of them report, that they tried to slow down their engines by using a strong break (enhancing friction very much), and they have been astonished that this extraction of kinetic energy from their apparatus did not reduce its speed. There are even reports, according to which vacuumenergy motors began to run so fast, that the they burst into pieces (one of them is [Har 10]). From our theoretical calculations now we fully understand the reason for this problem: It is just the fact, that the phasedifference between the field’s propagation and the motion of the components of the zeropoint engine can be optimized by friction. Every practical experimentalist will express the objection: Very strong and rigid friction can bring every motion to standstill. Certainly this is true. As we see in figure 10, there is a critical value for the friction, at which the powerconversion more or less suddenly collapses and the amplitude of the oscillation goes to zero. Obviously the effect of friction is so strong at this point, that the moving components of the engine can not follow the speed of propagation of the fields any further. This means that the moving components of the engine and the moving fields can not keep the phasedifference necessary for resonant excitation of the engine any further. If we apply a “zoom” to this part of figure 10 with F_{R} = 0.334 … 0.344 N, we come to figure 11. There we can see, that there is a certain interval, during which the phasedifference for resonance is being lost. This means, that the zone of maximum powerextraction from the quantum vacuum has some certain width. If a zeropointenergy motor can be operated within this range, friction will be just a little bit too weak to stop the engine.
Abb. 10: Enhancement of the amplitude (blue curve and blue scale at the right ordinate) and the converted power (purple curve and purple scale at the left ordinate) of a zeropoint energy motor as a function of the converted energy (here represented as friction).
Abb. 11: „Zoom“ to Fig.10 at the range of the powermaximum of a zeropointenergy motor.
By the way, a negative enhancement of the amplitude (blue curve below zero) is understandable very easy. It indicates, that there friction is so strong, that the amplitude is reduced in comparison to its value at the beginning of the oscillation. If we would continue our DFEMsimulation to a longer time interval, the engine would come to standstill under this operation. Under practical operation is necessary, to drive the machine in a way, that the amplitude will be kept constant over long time interval. This should not be difficult, if the extraction of energy (and power) is kept on the left side apart from the maximum of the purple curve. References [Ber 71] Gobrecht, H. (1971). BergmannSchaefer, Lehrbuch der Experimentalphysik, Verlag Walter de Gruyter, ISBN 3110020900 [Boe 07] Boer, D. and van Holten, J.W. (2007). Exploring the QED vacuum with laser interferometers, arXiv:hepph/0204207v1, different Versions 17. April 2002 up to 1. Feb. 2008 [Bor 99] Borland Pascal (Delphi 5 aus 1999 oder neuere Version) [Har 10] Hary, G. (2010). Example by Guy Hary at the Congress „Autonome Energiesysteme“, 3.5.Sept.2010 at Schloss Hofen, Bregenz: Schweizerische Vereinigung für Raumenergie SVR, JupiterVerlag/TransAltec AG, Zürich [Hei 36] Heisenberg, W. and Euler, H. (1936). Folgerungen aus der Diracschen Theorie des Positrons, 22.Dez.1935, Zeitschrift für Physik (1936), S.714 [Rik 00] Rikken, G. L. J. A. and Rizzo, C. (2000). Magnetoelectric birefringences of the quantum vacuum, Phys. Rev. A, Vol.63, 012107 [Rik 03] Rikken, G. L. J. A. and Rizzo, C. (2003). Magnetoelectric anisotropy of the quantum vacuum, Phys. Rev. A, Vol.67, 015801 [Tur 10] Turtur, C. W. (2010) The fundamental Principle of the Conversion of Zeropointenergy of the Vacuum, PHILICA.COM, ISSN 17513030, Article no.206, (28. Sept. 2009) [Information] An extended list of literaturereferences is to be found at [Tur 10].
Adress of the Author: Prof. Dr. Claus W. Turtur University of Applied Sciences BraunschweigWolfenbüttel Salzdahlumer Strasse 46 / 48 Germany – 38302 Wolfenbüttel Email: cw.turtur@ostalia.de Tel.: (++49) 5331 / 939 – 42220 Internetpage: http://www.ostfalia.de/cms/de/pws/turtur/FundE Information about this Article This Article has not yet been peerreviewed This Article was published on 9th October, 2010 at 10:09:26 and has been viewed 13805 times. This work is licensed under a Creative Commons Attribution 2.5 License. 
The full citation for this Article is: Turtur, C. (2010). Example of a simple Algorithm for the Construction of Zeropointenergy Converters. PHILICA.COM Article number 207. 
