1.3 Extract energy from the vacuum?

The term vacuum energy is sometimes used by some scientists claiming that it is possible to extract energy—that is, mechanical work, heat … ., from the vacuum and dispose thus, ideally, a gigantic and virtually inexhaustible source of energy. Of course, these different hypotheses arouse great skepticism among many scientific researchers because they call into question a principle demonstrated mathematically by the theorem of the mathematician Emmy Noether in 1915, which involves the conservation of energy (like all invariances). This theorem is accepted in physics and has never been faulted until now!

In fact, the problem is less to extract energy from the vacuum than to extract it without spending more energy that we cannot hope to recover! This principle of Noether's theorem, still observed at the macroscopic scale, suggests that extracting energy from a vacuum would require at least as much energy, even probably more, than the process of its recovery would provide.

Thus, a cyclic system, on the model of a piston engine going from a position n°1 to n°2, then from n°2 to n°1, the existence of the Casimir force in 1=zs4, therefore greater in position (2) than in (1), would then imply spending more energy to return to (1), which would necessarily require an added energy!! This problem, like that of perpetual motion, then implies that this hope of extracting energy from a vacuum seems impossible and cannot be done with at least zero energy balance! But this is forgetting that an energy is not limited to a force but is, for example, the product of a force (intensity variable) by a displacement (position variable) (see Figure 3).

Indeed, imagine that the piston is a piezoelectric bridge, and that the deformation of this bridge is caused by the Casimir force. The deformation of this piezoelectric bridge induces fixed electric charges of opposite sign on each of its faces 1 and 2. Imagine that opposite mobile charge moves from the mass on each side of piezoelectric area. So, if it is possible to propagate, at the right moment, a part of the mobile charges of face 1 for example, on an electrically insulated surface opposite to face 2, then a Coulomb force opposite to the attractive Casimir force would practice. If this Coulomb force is greater than the Casimir force, for example by a factor of at least 2, then the total force Ft ¼ FCA–FCO, applied to the center of this piezoelectric bridge deforms it in the other direction, decreases then cancels out its deformation thus the electric charges on the two faces of the piezoelectric bridge. The disappearance of electric charges suppresses the Coulomb force (see Figures 4 and 5). The system would then return

Figure 3. Nomenclature of the different positions for the moving Casimir electrode.

Perspective Chapter: Device, Electronic,Technology for a M.E.M.S. Which Allow… DOI: http://dx.doi.org/10.5772/intechopen.105197

Figure 4.

Figure 5. Axes, forces, Casimir's electrodes.

Different view of the device without electronics.

to its original position and physical characteristics. Everything would start again, causing vibrations of the piezoelectric bridge of the Casimir reflector device without any external energy input!

Then, on the assumption that all the transient states of the system do not require any input of external energy and are only consequences of a primary cause which is the energy of the vacuum, the principle of Emmy Noether should not be contradicts!

The fixed electric charges on the two metallized faces of the piezoelectric bridge are of opposite signs and attracts from the mass of the mobile charges of opposite signs (Figure 3).

Let us imagine that the whole of the return electrode is in two parts of equal areas but separated by a switch circuit consisting of MOSN and MOSP enriched, in parallel and of threshold voltage VtNE <sup>¼</sup> ‐VtPE (Figure 3). The first part of this metallic return electrode and surface Sp1 consists of one of the faces of the piezoelectric bridge and carries mobile electric charges <sup>Q</sup> <sup>m</sup> <sup>¼</sup> ‐QF.

The second part of this metal electrode is earthed via another switch circuit made up of depleted MOSN and MOSP, in series and of the same threshold voltage as the enriched MOSN and MOSP: VtND ¼ VtPE >0 and VtPD ¼ VtNE <0 (see Figure 3).

These switch circuits (circuit 1 = MOSN and MOSP enriched in parallel, circuit 2 = MOSND and MOSPD in depletion and in series), are designed so that they open and close in opposition.

When circuit 1 opens or closes, at the same time switch circuit 2 closes or opens, thus isolating this return electrode from the ground (see Figure 3). This opposite behavior of the switch circuits can be seen in Figure 3.

So, when circuit 1 is open, the two parts of the return electrodes are grounded through circuits 2, on the other hand when circuit 1 closes the two parts of the return electrodes are isolated!

The electric field inside a perfect conductor being zero, the mobile charges attracted to the first part of the return electrode are redistributed on the two parts of this electrode in the ratio of the homogenization surfaces, that is to say ½ and are opposite the other electric charge face n°2 of the bridge! One then develops, between these isolated electrodes an attractive Coulomb force which is in the opposite direction to the Casimir force and can be greater than it (see Figures 3–5).

Now, we know that in the case of a deformation perpendicular to the polarization of a piezoelectric layer and caused by an FCA force, the fixed charges QF induced by the deformation of this piezoelectric layer are proportional to the Casimir force FCA and are therefore in 1=zs 4, with [5, 6].

$$\mathbf{Q}\_{\rm F} = (\mathbf{d}\_{\rm 31} \mathbf{F}\_{\rm CA} \mathbf{l}\_{\rm P}) / \mathbf{a}\_{\rm p},\tag{3}$$

With d31 = piezoelectric coefficient CN�<sup>1</sup> ,lp,ap respectively length and thickness (m) of the piezoelectric bridge (Figure 5). These fixed electric charges on the two metallized faces of the piezoelectric bridge have opposite signs and attract mobile charges of opposite signs from the mass (Figure 5). Thus, when it is effective, the Coulomb return force FCO is in 1=zs <sup>10</sup> because on the one hand in ð Þ QF=<sup>2</sup> <sup>2</sup> (therefore in 1=zs8) but also in 1=ð Þ zr <sup>þ</sup> z0 � zs <sup>2</sup> because depending of the distances zr þ z0 � zs between return electrode n°1 and face n°2 of the piezoelectric bridge. With zr the initial distance between the opposite face of the piezoelectric bridge and the return electrode, zs = distance between Casimir electrodes, time dependent, and z0 = initial distance between Casimir electrodes (see Figures 3–6) and Figure 2 bis. We will choose in the following MATLAB simulations (unless otherwise specified), the same interface between return electrode zr as that attributed to the initial interface z0 between Casimir reflectors. The distances over which the free Casimir electrode moves, correlated with

#### Figure 6.

General configuration of the device: MOS grid connections (face 2 of the piezoelectric bridge: Red), source connections (face 1 of the piezoelectric bridge: Green.

Perspective Chapter: Device, Electronic,Technology for a M.E.M.S. Which Allow… DOI: http://dx.doi.org/10.5772/intechopen.105197

the deformation of the piezoelectric bridge are very small and less than 100 A°. The variations z0,ze,zs are therefore <100 A° and are very small compared to the dimensions of the piezoelectric bridge and that of the Casimir electrodes. Although the rigorous calculation is possible, for the sake of simplification we will first consider that the Coulomb return electrodes remain strictly parallel (Figures 3–5).

Considering that the Coulomb force is zero when the piezoelectric bridge has no deformation, we thus obtain an attractive Coulomb force of direction opposite to that of Casimir with:

$$\begin{split} F\_{CO} &= \frac{Q\_F^2}{4\pi\varepsilon\_0\varepsilon\_r} \left( \left( \frac{1}{z\_r + z\_0 - z\_S} \right)^2 \right) = \\ & \left( S\_S \frac{\pi^2 \hbar c}{240} \frac{d\_{31} l\_P}{2^\*} \left( \frac{1}{z\_r^4} - \frac{1}{z\_0^4} \right) \right)^2 \left( \frac{1}{4\pi\varepsilon\_0\varepsilon\_r} \right) \left( \frac{1}{z\_r + z\_0 - z\_S} \right)^2 \end{split} \tag{4}$$

We note that FCO ¼ 0 when the bridge has no deflection (zs = z0), so no electrical charges! With zr = interface between the face 2 and the return electrode.

This Coulomb Force in 1=zs <sup>10</sup> can therefore become greater than that of Casimir which is in 1=zs 4.

Applied to the piezoelectric bridge, it reduces its deformation, and therefore the induced charges. So, Coulomb's force diminishes and then vanishes when the bridge goes to the starting position n°1 since zs ¼ z0.

For these Coulomb return electrodes generate only a Casimir force that is negligible compared to that of the reflector, it will be necessary to choose interfaces zr greater than 2z0. For example, if zr ¼ 2:z0 and the surface of Casimir reflector Ss2 <sup>¼</sup> <sup>5</sup> <sup>∗</sup> Sp then the Casimir force between the return electrodes will be about 100 times weaker than that linked to the reflector, which is negligible (Figure 3).

On the other hand, as FCO depends on the charge accumulated on the piezoelectric bridge in 1ð Þ =zs 8 , the electric voltage that the MOS switches will have to withstand, before being triggered increases with the interface zr, since the position where FCO ¼ FCA decreases with zr (see Figure 7).

This leads to an increase in the threshold voltages of the different MOS with the increase interface zr.

This electrostatic attraction of the piezoelectric bridge is possible because the fixed electric charges generated by the deformation of the piezoelectric bridge attract mobile electric charges Q <sup>m</sup> of opposite signs from the mass.

Note that if switch circuit n°1 is open, we have seen that circuit n°2 is closed and connected to ground, so the second part of the return electrode is to ground.


#### Figure 7.

Distribution of the threshold voltages of enriched and depleted N and P MOS switches.

Conversely, when circuit n°1 is closed then circuit n°2 is open, isolating the second part of the return electrode.

On the other hand, the mobile loads of face 2 by triggering, at the appropriate moment and depending on the threshold voltages, the automatic closing of circuit 1 and the opening of circuit 2, the charges of face 1 are distributed uniformly over the surfaces of the face n°1 of the piezoelectric bridge and the return electrode.

They create an attractive force FCO of Coulomb opposed to that of Casimir which can be superior to him in modulus. The total FCA FCO force then becomes repulsive and, applied to the piezoelectric bridge decreases and cancels out its deformation, which consequently automatically removes the electric charges on it and initiates the reopening of circuit 1 and the closing of circuit 2.

Thus, the repulsive force of Coulomb disappears, and the force of Casimir becomes preponderant again which allows this cycle to start again!

It seems the spatial and temporal omnipresence of the attractive Casimir force, with the spontaneous appearance and at the appropriate moment of the Coulomb force described above, then generate vibrations of the mobile Casimir reflector plate!

We will calculate the frequency of these vibrations with MATLAB.

Note that during the movement of the piezoelectric bridge from (1) to (2), only the force of Casimir FCA is exerted, because the circuit 2 is conducting and connects the return electrode to the mass suppressing the action of the force Coulomb. Note also that the fixed electrode of the Casimir reflector is constantly earthed (see Figure 3).

During the short homogenization time of the mobile charges on the fixed return electrode, an alternating current peak Ia is recovered which generates an alternating voltage peak Ua through its crossing of an integrated inductor (therefore without any additional energy).

This weak and ephemeral but always present electric power Ua:Ia is at the frequency of vibration of the structure. It then activates suitable electronics that must transform—without any external power source—this alternating voltage Ua into a direct voltage Uc which can be used (see Chapter 5).

This electronics was designed when I was working at ESIEE and on abandoned sensors. It works very well in SPICE simulation (see Part V).

If all the components of this project are successful (principle of extracting energy from the vacuum + device generating current peaks at the vibration frequency of the system and converted in peak of voltage by a coil + transformation electronics + technology for realization the device selected), all without any additional energy, the principle of Noether should be validated and the vacuum could then be considered as a simple medium, with which it is possible to exchange energy!
