The Gravitational Spacecraft

There is an electromagnetic factor of correlation between gravitational mass and inertial mass, which in specific electromagnetic conditions, can be reduced, made negative and increased in numerical value. This means that gravitational forces can be reduced, inverted and intensified by means of electromagnetic fields. Such control of the gravitational interaction can have a lot of practical applications. For example, a new concept of spacecraft and aerospace flight arises from the possibility of the electromagnetic control of the gravitational mass. The novel spacecraft called Gravitational Spacecraft possibly will change the paradigm of space flight and transportation in general. Here, its operation principles and flight possibilities, it will be described. Also it will be shown that other devices based on gravity control, such as the Gravitational Motor and the Quantum Transceivers, can be used in the spacecraft, respectively, for Energy Generation and Telecommunications.

Key words: Gravity, Gravity Control, Quantum Devices.

CONTENTS

1. Introduction 02

2. Gravitational Shielding 02

3. Gravitational Motor: Free Energy 05

4. The Gravitational Spacecraft 06

5. The Imaginary Space-time 13

6. Past and Future 18

7. Instantaneous Interstellar Communications 20

8. Origin of Gravity and Genesis of Gravitational Energy 23

Appendix A 26 Appendix B 58 Appendix C 66 Appendix D 71 References 74

2 1. Introduction

The discovery of the correlation In the beginning of this century, between gravitational mass and inertial it has been clearly noticed that there mass [1] has shown that the gravity was something unsatisfactory about can be reduced, nullified and inverted. the whole notion of quantization and Starting from this discovery several that the quantization process had many ways were proposed in order to obtain ambiguities. Then, a new approach has experimentally the local gravity been proposed starting from the control [2]. Consequently, new generalization of the action function*. concepts of spacecraft and aerospace The result has been the derivation of a flight have arisen. This novel theoretical background, which finally spacecraft, called Gravitational led to the so-sought quantization of the Spacecraft, can be equipped with other gravity and of the space-time. devices also based on gravity control, Published under the title: such as the Gravitational Motor and “Mathematical Foundations of the the Quantum Transceiver that can be Relativistic Theory of Quantum used, respectively, for energy Gravity”†, this theory predicts a generation and telecommunications. consistent unification of Gravity with Based on the theoretical background Electromagnetism. It shows that the which led to the gravity control, the strong equivalence principle is operation principles of the reaffirmed and, consequently Gravitational Spacecraft and of the Einstein’s equations are preserved. In devices above mentioned, will be fact, Einstein’s equations can be described in this work. deduced directly from the Relativistic Theory of Quantum Gravity. This 2. Gravitational Shielding shows, therefore, that the General Relativity is a particularization of this The contemporary greatest new theory, just as the Newton’s challenge of the Theoretical Physics theory is a particular case from the was to prove that, Gravity is a General Relativity. Besides, it was quantum phenomenon. Since the deduced from the new theory an General Relativity describes gravity as important correlation between the related to the curvature of the space- gravitational mass and the inertial time then, the quantization of the mass, which shows that the gravity implies the quantization of the gravitational mass of a particle can be proper space-time. Until the end of the decreased and even made negative, century XX, several attempts to independently of its inertial mass, i.e., quantify gravity were accomplished. while the gravitational mass is However, all of them resulted fruitless [3, 4]. * The formulation of the action in Classical Mechanics extends to the Quantum Mechanics and it has been the basis for the development of the Strings Theory. † http://arxiv.org/abs/physics/0212033

3 progressively reduced, the inertial kinetic momentum; c is the speed of mass does not vary. This is highly light. relevant because it means that the This equation shows that only weight of a body can also be reduced for Δp = 0 the gravitational mass is and even inverted in certain equal to the inertial mass. Instances in circumstances, since Newton’s gravity which Δp is produced by law defines the weight P of a body as electromagnetic radiation, Eq. (3) can the product of its gravitational mass be rewritten as follows:

mg by the local gravity acceleration g , 2 ⎧ ⎡ 2 ⎤⎫ mg ⎪ ⎛ Dn ⎞ ⎪ i.e., ⎢ 121 +−= ⎜ r ⎟ − ⎥ ()41 ⎨ ⎢ ⎜ 3 ⎟ ⎥⎬ mi0 ⎪ ⎝ ρ c ⎠ ⎪ ⎩ ⎣⎢ ⎦⎥⎭ = gmP (1) g Where n is the refraction index of the It arises from the mentioned law r particle; D is the power density of the that the gravity acceleration (or simply electromagnetic radiation absorbed by the gravity) produced by a body with the particle; and ρ its density of gravitational mass M is given by g inertial mass. It was shown [1] that there is an GM g additional effect of gravitational g = 2 ()2 r shielding produced by a substance whose gravitational mass was reduced The physical property of mass or made negative. This effect shows has two distinct aspects: gravitational that just above the substance the mass mg and inertial mass mi. The gravity acceleration g will be reduced gravitational mass produces and 1 at the same proportion χ = mm , responds to gravitational fields. It ig 0 = χ gg g supplies the mass factors in Newton's i.e., 1 , ( is the gravity famous inverse-square law of acceleration bellow the substance). 2 Equation (4) shows, for gravity ( = gg rmGMF ). The inertial example, that, in the case of a gas at mass is the mass factor in Newton's ultra-low pressure (very low density of 2nd Law of Motion (= amF ). These i inertial mass), the gravitational mass two masses are not equivalent but of the gas can be strongly reduced or correlated by means of the following made negative by means of the factor [1]: incidence of electromagnetic radiation with power density relatively low. ⎧ ⎡ 2 ⎤⎫ mg ⎪ ⎛ Δp ⎞ ⎪ Thus, it is possible to use this ⎨ ⎢ 121 +−= ⎜ ⎟ −1⎥⎬ ()3 ⎢ ⎜ ⎟ ⎥ effect in order to produce gravitational mi0 ⎪ ⎝ i0cm ⎠ ⎪ ⎩ ⎣ ⎦⎭ shieldings and, thus, to control the local gravity.

Where mi0 is the rest inertial mass and The Gravity Control Cells Δp is the variation in the particle’s (GCC) shown in the article “Gravity Control by means of Electromagnetic 4 Field through Gas or Plasma at Ultra- detectors can only be dangerous if Low Pressure”‡, are devices designed inhaled. on the basis, of this effect, and usually The Relativistic Theory of are chambers containing gas or plasma Quantum Gravity also shows the at ultra-low pressure. Therefore, when existence of a generalized equation for an oscillating electromagnetic field is the inertial forces which has the applied upon the gas its gravitational following form mass will be reduced and, consequently, the gravity above the = gi aMF (5) mentioned GCC will also be reduced at the same proportion. This expression means a new law for It was also shown that it is the Inertia. Further on, it will be possible to make a gravitational shown that it incorporates the Mach’s shielding even with the chamber filled principle to Gravitation theory [5]. with Air at one atmosphere. In this Equation (3) tell us that the case, the electric conductivity of the gravitational mass is only equal to the air must be strongly increased in order inertial mass when p =Δ 0 . Therefore, to reduce the intensity of the we can easily conclude that only in electromagnetic field or the power this particular situation the new density of the applied radiation. expression of Fi reduces to = ii amF , This is easily obtained by which is the expression for Newton's ionizing the air in the local where we 2nd Law of Motion. Consequently, want to build the gravitational this Newton’s law is just a particular shielding. There are several manners case from the new law expressed by of ionizing the air. One of them is by the Eq. (5), which clearly shows how means of ionizing radiation produced the local inertial forces are correlated by a radioactive source of low to the gravitational interaction of the intensity, for example, by using the local system with the distribution of radioactive element Americium (Am- cosmic masses (via m ) and thus, 241). The Americium is widely used g as air ionizer in smoke detectors. incorporates definitively the Mach’s Inside the detectors, there is just a little principle to the Gravity theory. amount of americium 241 (about of The Mach’s principle postulates that: “The local inertial forces would 1/5000 grams) in the form of AmO2. Its cost is very low (about of US$ be produced by the gravitational 1500 per gram). The dominant interaction of the local system with the radiation is composed of alpha distribution of cosmic masses”. particles. Alpha particles cannot cross However, in spite of the several a paper sheet and are also blocked by attempts carried out, this principle had some centimeters of air. The not yet been incorporated to the Americium used in the smoke Gravitation theory. Also Einstein had carried out several attempts. The ad ‡ http://arxiv.org/abs/physics/0701091 hoc introduction of the cosmological

5 term in his gravitation equations has anything during the maneuvers of the been one of these attempts. car. With the advent of equation (5), the origin of the inertia - that was 3. Gravitational Motor: Free Energy considered the most obscure point of the particles’ theory and field theory – It is known that the energy of becomes now evident. the gravitational field of the Earth can In addition, this equation also be converted into rotational kinetic reveals that, if the gravitational mass energy and electric energy. In fact, this of a body is very close to zero or if is exactly what takes place in there is around the body a hydroelectric plants. However, the gravitational shielding which reduces construction these hydroelectric plants closely down to zero the gravity have a high cost of construction and accelerations due to the rest of the can only be built, obviously, where Universe, then the intensities of the there are rivers. inertial forces that act on the body The gravity control by means of become also very close to zero. any of the processes mentioned in the This conclusion is highly article: “Gravity Control by means of relevant because it shows that, under Electromagnetic Field through Gas or these conditions, the spacecraft could Plasma at Ultra-Low Pressure” allows describe, with great velocities, unusual the inversion of the weight of any trajectories (such as curves in right body, practically at any place. angles, abrupt inversion of direction, Consequently, the conversion of the etc.) without inertial impacts on the gravitational energy into rotational occupants of the spacecraft. mechanical energy can also be carried Obviously, out of the above- out at any place. mentioned condition, the spacecraft In Fig. (1), we show a schematic and the crew would be destroyed due diagram of a Gravitational Motor. The to the strong presence of the inertia. first Gravity Control Cell (GCC1) When we make a sharp curve changes the local gravity from g with our car we are pushed towards a to ′ = −ngg , propelling the left side of direction contrary to that of the motion the rotor in a direction contrary to the of the car. This happens due to motion of the right side. The second existence of the inertial forces. GCC changes the gravity back again to However, if our car is involved by a g i.e., from ′ = −ngg to g , in such a gravitational shielding, which reduces way that the gravitational change strongly the gravitational interaction of occurs just on the region indicated in the car (and everything that is inside Fig.1. Thus, a torque T given by the car) with the rest of the Universe, then in accordance with the Mach’s ()−= ′ []−=+ ()′ + ()22 rgmgmrFFT = principle, the local inertial forces g g would also be strongly reduced and, ()+= 1 1 grmn consequently, we would not feel 2 g 6 Is applied on the rotor of gravitational means that the gravitational motors mass mg , making the rotor spin with can produce energy practically free. angular velocity ω . It is easy to see that gravitational The average power, P , of the motors of this kind can be designed for motor is = TP ω . However, powers needs of just some watts up to − ′ =+ ω 2rgg .Thus, we have millions of kilowatts.

1 3 3 2 i ()+= 1 rgnmP ()6 g’’=χ g’ = g Consider a cylindrical rotor of iron air(2) −3 -1 (ρ = .7800 mKg ) with height = .50 mh , χar(2)= (χar(1)) GCC (2) radius Rr == 0545.03 m and inertial 2 mass i ρπ == 05.327 kghRm . By adjusting the GCC 1 in order to obtain g’= -ng R χair()1 = () ()airiairg = −nmm −= 19 and, since r −2 Rotor = .81.9 smg , then Eq. (6) gives r g

5 P 1019.2 watts 219 KW ≅≅×≅ 294HP g’=χ g air(1)

GCC (1) This shows that this small motor can be used, for example, to substitute χar(1)= -n = mg(ar)/mi(ar) the conventional motors used in the g cars. It can also be coupled to an electric generator in order to produce electric energy. The conversion of the Fig. 1 – Gravitational Motor - The first Gravity Control Cell rotational mechanical energy into (GCC1) changes the local gravity from g to ′ −= ngg , propelling electric energy is not a problem since the left side of the rotor in contrary direction to the motion of the right side. The second GCC changes the gravity back again to g i.e., it is a problem technologically from ′ = −ngg to g , in such a way that the gravitational change resolved several decades ago. Electric occurs just on the region shown in figure above. generators are usually produced by the 4. The Gravitational Spacecraft industries and they are commercially available, so that it is enough to couple Consider a metallic sphere with a gravitational motor to an electric radius rs in the terrestrial atmosphere. generator for we obtaining electric If the external surface of the sphere is energy. In this case, just a gravitational recovered with a radioactive substance motor with the power above (for example, containing Americium mentioned it would be enough to 241) then the air in the space close to supply the need of electric energy of, the surface of the sphere will be for example, at least 20 residences. strongly ionized by the radiation Finally, it can substitute the emitted from the radioactive element conventional motors of the same and, consequently, the electric power, with the great advantage of not conductivity of the air close to sphere needing of fuel for its operation. What will become strongly increased. 7 By applying to the sphere an shielding the gravity produced by the 2 electric potential of low frequencyVrms , sphere is −= g rMGg , then, out of the in order to produce an electric field shielding it becomes ′=χairgg .Thus,

Erms starting from the surface of the 2 2 2 ′ χair(−= g ) −= ()χ gair −= g rGmrMGrMGg , sphere, then very close to the surface, where the intensity of the electric field will = χ Mm gairg be = rVE and, in agreement with rms srms Therefore, for the Universe out of the Eq. (4), the gravitational mass of the shielding the gravitational mass of the Air in this region will be expressed by sphere is mg and not M g . In these ⎧ ⎡ 3 4 ⎤⎫ ⎛σμ ⎞ V ⎪ ⎢ 0 air rms ⎥⎪ circumstances, the inertial forces m ()airg ⎨ 121 +−= ⎜ ⎟ −1 ⎬m0()airi ()7 ⎢ 2 ⎜44 πfc ⎟ r 4ρ2 ⎥ acting on the sphere, in agreement ⎪ ⎣ ⎝ ⎠ airs ⎦⎪ ⎩ ⎭ with the new law for inertia, expressed Therefore we will have by Eq. (5), will be given by ⎧ ⎡ 3 4 ⎤⎫ = amF 9 m airg ⎪ ⎛σμ ⎞ V ⎪ igii ( ) χ () ⎢ 121 +−== 0 ⎜ air ⎟ rms − ⎥ 81 air ⎨ 2 ⎜ ⎟ 4 2 ⎬ () m0()airi ⎢ ⎝44 πfc ⎠ r ρairs ⎥ Thus, these forces will be almost null ⎩⎪ ⎣ ⎦⎭⎪ when m becomes almost null by The gravity accelerations acting on the g sphere, due to the rest of the Universe means of the action of the gravitational (See Fig. 2), will be given by shielding. This means that, in these circumstances, the sphere practically ′ = χ = ,...,2,1 nigg loses its inertial properties. This effect iairi leads to a new concept of spacecraft

and aerospatial flight. The spherical Note that by varying V or the rms form of the spacecraft is just one form frequency f , we can easily to reduce that the Gravitational Spacecraft can and control χ air . Consequently, we can have, since the gravitational shielding also control the intensities of the can also be obtained with other gravity accelerations g i′ in order to formats. produce a controllable gravitational An important aspect to be shielding around the sphere. observed is that it is possible to control Thus, the gravitational forces the gravitational mass of the acting on the sphere, due to the rest of spacecraft, M (spacecrafg ), simply by the Universe, will be given by controlling the gravitational mass of a = ′ = ()χ gMgMF iairgiggi body inside the spacecraft. For where M g is the gravitational mass of instance, consider a parallel plate the sphere. capacitor inside the spacecraft. The The gravitational shielding gravitational mass of the dielectric around of the sphere reduces both the between the plates of the capacitor can gravity accelerations acting on the be controlled by means of the ELF sphere, due to the rest of the Universe, electromagnetic field through it. Under and the gravity acceleration produced these circumstances, the total by the gravitational mass M of the gravitational mass of the spacecraft g will be given by own sphere. That is, if inside the 8

Gravitational Shielding total M ()spacecrafg = M ()spacecrafg mg =+

M i0 += χdielectricmi0 ()10

where M i0 is the rest inertial mass of S the spacecraft(without the dielectric) and mi0 is the rest inertial mass of the Erms Mg 2 dielectric; χ dielectric = mm ig 0 , where mg g = - G Mg / r g1’ = χair g1 is the gravitational mass of the dielectric. By decreasing the value of χ χ dielectric , the gravitational mass of the air spacecraft decreases. It was shown, 2 g1 = - G M’g / r that the value of χ can be negative. 2 g’ = - χair g = - χair G Mg / r = r Thus, when χdielectric −≅ mM ii 00 , the 2 = - Gmg / r gravitational mass of the spacecraft M’g m = χ M gets very close to zero. g air g When χdielectric −< mM ii 00 , the gravitational Fig.2- The gravitational shielding reduces the gravity accelerations ( g1’) acting on the sphere (due to the rest of the mass of the spacecraft becomes Universe) and also reduces the gravity acceleration that the sphere negative. produces upon all the particles of the Universe (g’). For the Universe, the gravitational mass of the sphere will be m = χ M Therefore, for an observer out g air g. of the spacecraft, the gravitational As we have shown [2], a mass of the spacecraft is gravitational repulsion is established between the mass M g and any positive M ()spacecrafg M i0 += χ dielectricmi0 , and not gravitational mass below the + mM ii 00 . Another important aspect to be mentioned system. This means that the observed is that we can control the particles in this region will stay subjected to a gravity acceleration a , gravity inside the spacecraft, in order b to produce, for example, a gravity given by M acceleration equal to the Earth’s 3 rr 3 g ˆ −2 b ≅ ()χ ga Mair −≅ ()χair G 2 μ ()11 gravity ( = .81.9 smg ). This will be r0 very useful in the case of space flight, If the Air inside the GCCs is and can be easily obtained by putting sufficiently ionized, in such way that −13 in the ceiling of the spacecraft the σair ≅ .10 mS , and if =1 Hzf , system shown in Fig. 3. This system ρ ≅ .1 mkg −3, V ≅ 10 KV and = 1 cmd has three GCC with nuclei of ionized air rms then the Eq.8 shows that inside the air (or air at low pressure). Above GCCs we will have these GCC there is a massive block ⎧ ⎡ 3 4 ⎤⎫ with mass M . m ()airg ⎪ ⎛σμ ⎞ V ⎪ 3 g χ ⎢ 121 +−== 0 ⎜ air ⎟ rms − ⎥ −≅ 101 air ⎨ 2 ⎜ ⎟ 24 ⎬ m0()airi ⎢ ⎝44 fc ⎠ d ρπ air ⎥ ⎩⎪ ⎣ ⎦⎭⎪

9 We can also use the system FM shown in Fig. 3 as a thruster in order Ceiling to propel the spacecraft. Note that the Mg gravitational repulsion that occurs GCC 1 χ air between the block with mass M g and GCC 2 χ air d any particle after the GCCs does not G CC3 χ air depend on of the place where the system is working. Thus, this

Gravitational Thruster can propel the r0 gravitational spacecraft in any direction. Moreover, it can work in the

terrestrial atmosphere as well as in the cosmic space. In this case, the energy that produces the propulsion is a b obviously the gravitational energy,

μ Floor which is always present in any point of M the Universe. ar ≅ ()χ 3 gr −≅ ()χ 3 G g μˆ b Mair air r 2 The schematic diagram in Fig. 4 0 Fig.3 – If the Air inside the GCC is sufficiently shows in details the operation of the −13 Gravitational Thruster. A gas of any ionized, in such way that σ air ≅ .10 mS and −3 type injected into the chamber beyond if f =1 Hz; =1cmd ; ρair ≅ .1 mkg and Vrms ≅10 KV then Eq. 8 shows that inside the CCGs we will have the GCCs acquires an acceleration 3 a χair −≅ 10 . Therefore, for ig ≅≅ 100kgMM and gas , as shown in Fig.4, the intensity of

o ≅1mr the gravity acceleration inside the spacecraft which, as we have seen, is given by will be directed from the ceiling to the floor of the 3 3 M g −2 a = ()χ g −≅ ()χ G ()14 spacecraft and its intensity will be b ≈ .10 sma . gas Mgas gas 2 r0 Therefore the equation (11) gives 9 Thus, if inside of the GCCs, χgas −≅ 10

M then the equation above gives +≈ 109 Ga g ()12 M b r 2 a +≅ 1027 G g ()15 0 gas r 2 For ≅≅ 100kgMM and ≅1mr (See 0 ig 0 For ≅ ≅10kgMM , ≅1mr we have Fig.3), the gravity inside the spacecraft ig 0 a ×≅ .106.6 sm −217 . With this enormous will be directed from the ceiling to the gas floor and its intensity will have the acceleration the particles of the gas following value reach velocities close to the speed of −2 b ≈ .10 sma (13) the light in just a few nanoseconds. Therefore, an interstellar travel in a Thus, if the emission rate of the gas is −3 gravitational spacecraft will be gas skgdtdm ≅≅ litres/4000/10 hour, then particularly comfortable, since we can the trust produced by the gravitational travel during all the time subjected to thruster will be the gravity which we are accustomed to here in the Earth. 10

dmgas dmgas 5 where the spacecraft is placed. By = vF gas c ≅≅ 10 N ()16 dt dt adjusting the shielding for χ out = 01.0 4 and if M spacecraft =10 Kg then for a thrust ≅ 105 NF , the acceleration of the Gas spacecraft will be −2 aspacecraft = .1000 sm (18) Mg m μ GCC GCC GCC r0 g With this acceleration, in just at 1(one) F M 1 2 3 agas day, the velocity of the spacecraft will Fm be close to the speed of light. Gas However it is easy to see that χ out can still be much more reduced and, consequently, the thrust much more Fig. 4 – Gravitational Thruster – Schematic diagram showing the operation of the Gravitational Thruster. Note increased so that it is possible to

that in the case of very strong χair , for increase up to 1 million times the 9 example χair −≅ 10 , the gravity accelerations upon the acceleration of the spacecraft. boxes of the second and third GCCs become very strong. It is important to note that, the Obviously, the walls of the mentioned boxes cannot to stand the enormous pressures. However, it is possible to build a inertial effects upon the spacecraft will similar system [2] with 3 or more GCCs, without material be reduced by χout MM ig ≅= 01.0 . Then, boxes. Consider for example, a surface with several radioactive sources (Am-241, for example). The alpha in spite of its effective acceleration to particles emitted from the Am-241 cannot reach besides be = .1000 sma −2 , the effects for the crew 10cm of air. Due to the trajectory of the alpha particles, three or more successive layers of air, with different electrical of the spacecraft will be equivalents to

conductivitiesσ1, σ2 and σ3 , will be established in the an acceleration of only ionized region. It is easy to see that the gravitational shielding effect produced by these three layers is similar to M the effect produced by the 3 GCCs above. a′ g ≈= .10 sma −1

M i It is easy to see that the gravitational thrusters are able to produce strong This is the magnitude of the trusts (similarly to the produced by the acceleration on the passengers in a powerful thrusters of the modern contemporary commercial jet. aircrafts) just by consuming the Then, it is noticed that the injected gas for its operation. gravitational spacecrafts can be It is important to note that, if subjected to enormous accelerations F is the thrust produced by the (or decelerations) without imposing gravitational thruster then, in any harmful impacts whatsoever on agreement with Eq. (5), the spacecraft the spacecrafts or its crew. acquires an acceleration a spacecraft , We can also use the system expressed by the following equation shown in Fig. 3, as a lifter, inclusively F F within the spacecraft, in order to lift aspacecraft = = ()17 M g()spacecraft χ M ()spacecraftiout peoples or things into the spacecraft as

Where χ out , given by Eq. (8), is the shown in Fig. 5. Just using two GCCs, factor of gravitational shielding which the gravitational acceleration produced depends on the external medium below the GCCs will be 11 r 2 2 2 g = ()χ ga Mair −≅ ()χair g rMG 0 μˆ (19) Thus, if the gravitational mass of Note that, in this case, if χ is the particle is reduced by means of the air absorption of an amount of negative, the acceleration ar will have g electromagnetic energy U , for a direction contrary to the versor μˆ , example, then we have i.e., the body will be attracted in the M g ⎧ 2 ⎫ χ ⎡ 121 +−== cmU 2 −1⎤ direction of the GCCs, as shown in ⎨ ⎢ ()i0 ⎥⎬ Mi ⎩ ⎣ ⎦⎭ Fig.5. In practice, this will occur when This shows that the energy U the air inside the GCCs is sufficiently continues acting on the particle turned ionized, in such a way that imaginary. In practice this means that σ ≅ .10 mS −13 . Thus, if the internal air electromagnetic fields act on thickness of the GCCs is now d =1 mm imaginary particles. Therefore, the −3 and if =1 Hzf ; ρair ≅ .1 mkg and internal electromagnetic field of a

Vrms ≅ 10 KV , we will then have GCC remains acting upon the particles 5 inside the GCC even when their χair −≅ 10 . Therefore, for ≅ ≅100kgMM ig gravitational masses are in the range and, for example, 0 ≅ 10mr the + .1590 M i to − .1590 M i , turning them gravitational acceleration acting on the imaginaries. This is very important body will be ≈ .6.0 sma −2 . It is obvious b because it means that the GCCs of a that this value can be easily increased gravitational spacecraft remain or decreased, simply by varying the working even when the spacecraft V voltage rms . Thus, by means of this becomes imaginary. Gravitational Lifter, we can lift or Under these conditions, the lower persons or materials with great gravity accelerations acting on the versatility of operation. imaginary spacecraft, due to the rest of It was shown [1] that, when the the Universe will be, as we have see, gravitational mass of a particle is given by reduced into the range, + .1590 M i to i′ = χ i = ,...,2,1 nigg − 1590 M , it becomes imaginary, i.e., . i Where χ = M g ()(imaginary M imaginaryi ) and its masses (gravitational and inertial) 2 i −= Gmg gi ()imaginary ri . Thus, the becomes imaginary. Consequently, the gravitational forces acting on the particle disappears from our ordinary spacecraft will be given by Universe, i.e., it becomes invisible for us. This is therefore a manner of to = gMF ′ = obtain the transitory invisibility of gi g ()imaginary i = M − χGm r 2 = persons, animals, spacecraft, etc. g ()imaginary ()gj ()imaginary j 2 2 However, the factor g ()−= χ riGmiM igi += χ rmGM igig ()20.

χ = M g()(imaginary M imaginaryi ) remains real because Note that these forces are real. By calling that, the Mach’s principle says M iM M that the inertial effects upon a particle χ = g ()imaginary g g === real are consequence of the gravitational M ()imaginaryi i iM M i interaction of the particle with the rest 12 of the Universe. Then we can conclude It is easy to show that the that the inertial forces acting on the gravitational forces between two thin spacecraft in imaginary state are also layers of air (with masses mg1 and real. Therefore, it can travel in the mg 2 ) around the spacecraft , are imaginary space-time using the expressed by gravitational thrusters. rr 2 mm ii 21 ˆ 12 FF 21 −=−= ()χair G 2 μ ()21 r Mg Note that these forces can be strongly GCC 1 χ air increased by increasing the value of GCC 2 χ air χ . In these circumstances, the air air around the spacecraft would be strongly compressed upon the external rb surface of the spacecraft creating an atmosphere around it. This can be

particularly useful in order to minimize the friction between the spacecraft and the atmosphere of the planet in the case of very high speed ab movements of the spacecraft. With the

atmosphere around the spacecraft the μ friction will occur between the M atmosphere of the spacecraft and the ≅ ()χ 2 ga rr −≅ ()χ 2 G g μˆ b Mair air r 2 atmosphere of the planet. In this way, b the friction will be minimum and the Fig.5 – The Gravitational Lifter – If the air inside the GCCs is sufficiently ionized, in such way that spacecraft could travel at very high −13 speeds without overheating. σair ≅ .10 mS and the internal thickness of the GCCs is now d =1 mm then, if =1 Hzf ; However, in order for this to occur, it is necessary to put the gravitational ρ ≅ .1 mkg −3 andV ≅ 10 KV , we have air rms shielding in another position as shown 5 χair −≅ 10 . Therefore, for ig ≅≅ 100kgMM and in Fig.2. Thus, the values of χ airB 0 ≅ 10mr the gravity acceleration acting on the and χ airA will be independent (See body will be ≈ .6.0 sma −2 . b Fig.6). Thus, while inside the It was also shown [1] that gravitational shielding, the value of imaginary particles can have infinity χ airB is put close to zero, in order to velocity in the imaginary space-time. strongly reduce the gravitational mass Therefore, this is also the upper limit of the spacecraft (inner part of the of velocity for the gravitational shielding), the value of χ airA must be spacecrafts traveling in the imaginary reduced to about −10 8 in order to space-time. On the other hand, the strongly increase the gravitational travel in the imaginary space-time can attraction between the air molecules be very safe, because there will not be around the spacecraft. Thus, by any material body in the trajectory of the spacecraft. 13 8 substituting χairA −≅ 10 intoEq.21, we 5. The Imaginary Space-time get rr mm The speed of light in free space −=−= 1016GFF ii 21 μˆ ()22 12 21 r 2 is, as we know, about of 300.000 km/s. If, mm ρρ ≅≅=≅ 10VV −8 kg and The speeds of the fastest modern 21 airii 1 air 2 airplanes of the present time do not = 10−3 mr then Eq. 22 gives r r reach 2 km/s and the speed of rockets −≅−= 10−4 NFF 23 12 21 ( ) do not surpass 20 km/s. This shows These forces are much more intense how much our aircraft and rockets are than the inter-atomic forces (the forces slow when compared with the speed of that unite the atoms and molecules) the light. intensities of which are of the order of The star nearest to the Earth −8 ×− 1010001 N . Consequently, the air (excluding the Sun obviously) is the around the spacecraft will be strongly Alpha of Centaur, which is about of 4 compressed upon the surface of the light-years distant from the Earth spacecraft and thus will produce a (Approximately 37.8 trillions of crust of air which will accompany the kilometers). Traveling at a speed about spacecraft during its displacement and 100 times greater than the maximum will protect it from the friction with speed of our faster spacecrafts, we the atmosphere of the planet. would take about 600 years to reach Gravitational Shielding Alpha of Centaur. Then imagine how (GCC) many years we would take to leave our

E own galaxy. In fact, it is not difficult rms to see that our spacecrafts are very

Atmosphere χ slow, even for travels in our own solar airB of the

Spacecraft system. Gravitational One of the fundamental

Spacecraft characteristics of the gravitational χ airA spacecraft, as we already saw, is its capability to acquire enormous

accelerations without submitting the crew to any discomfort. Impelled by gravitational thrusters gravitational spacecrafts can

−28 Fig. 6 – Artificial atmosphere around the gravitational acquire accelerations until .10 sm or spacecraft - while inside the gravitational shielding more. This means that these the value of χ airB is putted close to zero, in order to spacecrafts can reach speeds very strongly reduces the gravitational mass of the close to the speed of light in just a few spacecraft (inner part of the shielding), the value of 8 seconds. These gigantic accelerations χairA must be reduced for about −10 in order to strongly increase the gravitational attraction between can be unconceivable for a layman, the air molecules around the spacecraft. however they are common in our Universe. For example, when we submit an electron to an electric field

14 of just /1 mVolt it acquires an impracticable. Besides, to travel at acceleration a , given by such a speed would be very dangerous, because a shock with other celestial −19 eE ()× ( /1106.1 mVC ) −211 bodies would be inevitable. However, a == −31 ≅ .10 sm me ×1011.9 as we showed [1] there is a possibility of a spacecraft travel quickly far As we see, this acceleration is about beyond our galaxy without the risk of 100 times greater than that acquired by being destroyed by a sudden shock the gravitational spacecraft previously with some celestial body. The solution mentioned. is the gravitational spacecraft travel By using the gravitational through the Imaginary or Complex shieldings it is possible to reduce the Space-time. inertial effects upon the spacecraft. As It was shown [1] that it is we have shown, they are reduced by possible to carry out a transition to the Imaginary space-time or Imaginary the factor χ out = MM ig . Thus, if the Universe. It is enough that the body inertial mass of the spacecraft is has its gravitational mass reduced to a M i = 000.10 kg and, by means of the value in the range of + .1590 M i gravitational shielding effect the to − 1590 M . In these circumstances, gravitational mass of the spacecraft is . i reduced to M ≈ 10−8 M then , in spite the masses of the body (gravitational g i and inertial) become imaginaries and, of the effective acceleration to be so does the body. (Fig.7). gigantic, for example, ≈ .10 sma −29 , the Consequently, the body disappears effects for the crew of the spacecraft from our ordinary space-time and would be equivalents to an appears in the imaginary space-time. acceleration a′of only In other words, it becomes invisible M a′ g a == ()()− 98 ≈ .101010 sm −2 for an observer at the real Universe. M i Therefore, this is a way to get This acceleration is similar to that temporary invisibility of human which the passengers of a beings, animals, spacecrafts, etc. contemporary commercial jet are Thus, a spacecraft can leave our subjected. Universe and appear in the Imaginary Therefore the crew of the Universe, where it can travel at any gravitational spacecraft would be speed since in the Imaginary Universe comfortable while the spacecraft there is no speed limit for the would reach speeds close to the speed gravitational spacecraft, as it occurs in of light in few seconds. However to our Universe, where the particles travel at such velocities in the cannot surpass the light speed. In this Universe may note be practical. Take way, as the gravitational spacecraft is for example, Alpha of Centaur (4 propelled by the gravitational light-years far from the Earth): a round thrusters, it can attain accelerations up trip to it would last about eight years. to .10 sm −29 , then after one day of trip Trips beyond that star could take then with this acceleration, it can several decades, and this obviously is 15

of the spacecraft in such way that it leaves the range of + 1590 M . i to − 1590 M . Thus the spacecraft can . i transition reappear in our Universe near its ( −0.159 > mg > +0.159 ) target. B The return trip would be done in ΔtAB =1 second similar way. That is to say, the 1 light-year Vmax = ∞ Vmax = c spacecraft would transit in the imaginary Universe back to the ΔtAB =1 year departure place where would reappear dAB = 1 light-year in our Universe and it would make the photon approach flight to the wanted point. Thus, trips through our Universe that

would delay millions of years, at transition speeds close to the speed of light, ( −0.159 < mg < +0.159 ) mg A could be done in just a few months in Gravitational Spacecraft the imaginary Universe. Fig. 7 – Travel in the Imaginary Space-time. What will an observer see when in the imaginary space-time? It will reach velocities ≈ .10 smV −114 (about 1 see light, bodies, planets, stars, etc., million times the speed of light). With everything formed by imaginary this velocity, after 1 month of trip the photons, imaginary atoms, imaginary spacecraft would have traveled protons, imaginary neutrons and about10 21 m . In order to have idea of imaginary electrons. That is to say, this distance, it is enough to remind the observer will find an Universe that the diameter of our Universe similar to ours, just formed by (visible Universe) is of the order particles with imaginary masses. The of10 26 m . term imaginary adopted from the Due to the extremely low Mathematics, as we already saw, gives density of the imaginary bodies, the the false impression that these masses collision between them cannot have do not exist. In order to avoid this the same consequences of the collision misunderstanding we researched the between the dense real bodies. true nature of that new mass type and Thus for a gravitational matter. spacecraft in imaginary state the The existence of imaginary mass problem of the collision doesn't exist associated to the neutrino is well- in high-speed. Consequently, the known. Although its imaginary mass is gravitational spacecraft can transit not physically observable, its square freely in the imaginary Universe and, is. This amount is found in this way reach easily any point of experimentally to be negative. our real Universe once they can make Recently, it was shown [1] that quanta the transition back to our Universe by of imaginary mass exist associated to only increasing the gravitational mass the photons, electrons, neutrons, and 16 protons, and that these imaginary indicated by Ψ . The wave function masses would have psychic properties associated to a material particle (elementary capability of “choice”). describes the dynamic state of the Thus, the true nature of this new kind particle: its value at a particular point of mass and matter shall be psychic x, y, z, t is related to the probability of and, therefore we should not use the finding the particle in that place and term imaginary any longer. instant. Although Ψ does not have a Consequently from the above exposed physical interpretation, its square Ψ 2 we can conclude that the gravitational (or Ψ Ψ* ) calculated for a particular spacecraft penetrates in the Psychic point x, y, z, t is proportional to the Universe and not in an “imaginary” probability of experimentally finding Universe. the particle in that place and instant. In this Universe, the matter Since Ψ 2 is proportional to the would be, obviously composed by probability P of finding the particle psychic molecules and psychic atoms described by Ψ , the integral of Ψ 2 on formed by psychic neutrons, psychic the whole space must be finite – protons and psychic electrons. i.e., the inasmuch as the particle is someplace. matter would have psychic mass and Therefore, if consequently it would be subtle, much +∞ 2d =Ψ 0V less dense than the matter of our real ∫ ∞− Universe. The interpretation is that the particle Thus, from a quantum viewpoint, does not exist. Conversely, if +∞ the psychic particles are similar to the 2 dV ∞=Ψ ∫ ∞− material particles, so that we can use the particle will be everywhere the Quantum Mechanics to describe simultaneously. the psychic particles. In this case, by The wave function Ψ analogy to the material particles, a corresponds, as we know, to the particle with psychic mass m will be Ψ displacement y of the undulatory described by the following motion of a rope. However, Ψ as expressions: opposed to y , is not a measurable

r quantity and can, hence, being a r = kp ψ h ψ complex quantity. For this reason, it is Eψ = hωψ admitted that Ψ is described in the x - direction by r r −(2π )()− pxEthi Where ψ = ΨVmp is the momentum =Ψ Be carried by the wave and Eψ its energy; This equation is the mathematical r description of the wave associated k = 2 λπ is the propagation number ψ ψ with a free material particle, with total and λψ = Ψ Vmh the wavelength and energy E and momentum p , moving in

ωψ = 2πfψ its cyclic frequency. the direction + x . The variable quantity that As concerns the psychic characterizes DeBroglie’s waves is particle, the variable quantity called Wave Function, usually characterizing psyche waves will also 17 be called wave function, denoted by dynamic state, represented by Ψ1 e Ψ Ψ ( to distinguish it from the material Ψ2 in the formation of the general particle wave function), and, by dynamic state described by Ψ . analogy with equation of Ψ , In the case of psychic particles expressed by: (psychic bodies, consciousness, etc.), −(2π )()− ΨΨ xptEhi Ψ Ψ=Ψ 0e by analogy, if ΨΨ1 , ΨΨ2 ,..., ΨΨn refer If an experiment involves a to the different dynamic states the large number of identical particles, all psychic particle takes, then its general described by the same wave function dynamic state may be described by the

Ψ , the real density of mass ρ of wave function ΨΨ , given by: these particles in x, y, z, t is ΨΨ = ΨΨ + cc ΨΨ2211 ... c Ψ++ Ψnn proportional to the corresponding The state of superposition of wave value Ψ 2 (Ψ 2 is known as density of functions is, therefore, common for probability. If Ψ is complex then both psychic and material particles. In 2 2 ΨΨ=Ψ * . Thus, ρ .ΨΨ=Ψ∝ * ). the case of material particles, it can be Similarly, in the case of psychic verified, for instance, when an electron particles, the density of psychic mass, changes from one orbit to another. Before effecting the transition to ρΨ , in x, y, z, will be expressed by 2 * 2 another energy level, the electron ρ Ψ Ψ ΨΨ=Ψ∝ ΨΨ . It is known that ΨΨ is always real and positive while carries out “virtual transitions” [6]. A ρ = Vm is an imaginary quantity. kind of relationship with other Ψ Ψ electrons before performing the real Thus, as the modulus of an imaginary transition. During this relationship number is always real and positive, we period, its wave function remains can transform the proportion ρ Ψ∝ 2 , Ψ Ψ “scattered” by a wide region of the in equality in the following form: space [7] thus superposing the wave 2 =Ψ k ρ Ψ Ψ functions of the other electrons. In this Where k is a proportionality constant relationship the electrons mutually (real and positive) to be determined. influence each other, with the In Quantum Mechanics we have possibility of intertwining their wave studied the Superposition Principle, functions§. When this happens, there which affirms that, if a particle (or occurs the so-called Phase system of particles) is in a dynamic Relationship according to quantum- state represented by a wave function mechanics concept.

Ψ1 and may also be in another In the electrons “virtual” dynamic state described by Ψ2 then, transition mentioned before, the the general dynamic state of the “listing” of all the possibilities of the particle may be described by Ψ , electrons is described, as we know, by where Ψ is a linear combination Schrödinger’s wave equation.

(superposition) of Ψ1 and Ψ2 , i.e., § Since the electrons are simultaneously waves and cc Ψ+Ψ=Ψ 2211 particles, their wave aspects will interfere with each other; besides superposition, there is also the The Complex constants c1 e c2 possibility of occurrence of intertwining of their wave respectively express the percentage of functions. 18 Otherwise, it is general for material human consciousnesses establish particles. By analogy, in the case of among themselves and with the psychic particles, we may say that the Ordinary Universe. Besides, we have “listing” of all the possibilities of the shown that the Psychic Interaction psyches involved in the relationship postulates a new model for the will be described by Schrödinger’s evolution theory, in which the equation – for psychic case, i.e., evolution is interpreted not only as a 2 2 pΨ biological fact, but mainly as psychic Ψ 2 Ψ =Ψ+Ψ∇ 0 h fact. Therefore, is not only the Because the wave functions are mankind that evolves in the Earth’s capable of intertwining themselves, planet, but all the ecosystem of the the quantum systems may “penetrate” Earth. each other, thus establishing an internal relationship where all of them are affected by the relationship, no 6. Past and Future longer being isolated systems but becoming an integrated part of a larger It was shown [1,9] that the system. This type of internal collapse of the psychic wave function relationship, which exists only in must suddenly also express in reality quantum systems, was called (real space-time) all the possibilities Relational Holism [8]. described by it. This is, therefore, a We have used the Quantum point of decision in which there occurs Mechanics in order to describe the the compelling need of realization of foundations of the Psychic Universe the psychic form. We have seen that which the Gravitational Spacecrafts the materialization of the psychic will find, and that influences us daily. form, in the real space-time, occurs These foundations recently discovered when it contains enough psychic mass †† – particularly the Psychic Interaction, for the total materialization of the show us that a rigorous description of psychic form (Materialization the Universe cannot to exclude the Condition). When this happens, all the psychic energy and the psychic psychic energy contained in the particles. This verification makes psychic form is transformed in real evident the need of to redefine the energy in the real space-time. Thus, in Psychology with basis on the quantum the psychic space-time just the foundations recently discovered. This holographic register of the psychic has been made in the article: “Physical form, which gives origin to that fact, Foundations of Quantum survives, since the psychic energy Psychology”**[9], recently published, deforms the metric of the psychic ‡‡ where it is shown that the Psychic space-time , producing the Interaction leads us to understand the †† By this we mean not only materialization proper but Psychic Universe and the also the movement of matter to realize its psychic extraordinary relationship that the content (including radiation). ‡‡ As shown in General Theory of Relativity the ** energy modifies the metric of the space-time http://htpprints.yorku.ca/archive/00000297 (deforming the space-time). 19 holographic register. Thus, the past Since both registrations are in survive in the psychic space-time just the psychic space-time, then the access in the form of holographic register. to their information only occur by That is to say, all that have occurred in means of the interaction with another the past is holographically registered psychic body, for example, our in the psychic space-time. Further consciousness or a psychic observer ahead, it will be seen that this register (body totally formed by psychic mass). can be accessed by an observer in the We have seen that, if the gravitational psychic space-time as well as by an mass of a body is reduced to within the observer in the real space-time. range + .1590 M i to − .1590 M i , its A psychic form is intensified by gravitational and inertial masses means of a continuous addition of become imaginaries (psychics) and, psychic mass. Thus, when it acquires therefore, the body becomes a psychic sufficiently psychic mass, its body. Thus, a real observer can also realization occurs in the real space- become in a psychic observer. In this time. Thus the future is going being way, a gravitational spacecraft can built in the present. By means of our transform all its inertial mass into current thoughts we shape the psychic psychic mass, and thus carry out a forms that will go (or will not) take transition to the psychic space-time place in the future. Consequently, and become a psychic spacecraft. In those psychic forms are continually these circumstances, an observer being holographically registered in the inside the spacecraft also will have its psychic space-time and, just as the mass transformed into psychic mass, holographic registrations of the past and, therefore, the observer also will these future registration can also be be transformed into a psychic accessed by the psychic space-time as observer. What will this observer see well as by the real space-time. when it penetrates the psychic The access to the holographic Universe? According to the registration of the past doesn't allow, Correspondence principle, all that obviously, the modification of the exists in the real Universe must have past. This is not possible because there the correspondent in the psychic would be a clear violation of the Universe and vice-versa. This principle of causality that says that the principle reminds us that we live in causes should precede the effects. more than one world. At the present However, the psychic forms that are time, we live in the real Universe, but being shaped now in order to manifest we can also live in the psychic themselves in the future, can be Universe. Therefore, the psychic modified before they manifest observer will see the psychic bodies themselves. Thus, the access to the and their correspondents in the real registration of those psychic forms Universe. Thus, a pilot of a becomes highly relevant for our gravitational spacecraft, in travel present life, since we can avoid the through the psychic space-time, won't manifestation of many unpleasant facts have difficulty to spot the spacecraft in in the future. its trips through the Universe. 20 The fact of the psychic forms If the gravitational mass of a manifest themselves in the real space- particle is positive, then t is always time exactly at its images and likeness, positive and given by it indicates that real forms (forms in the real space-time) are prior to all 22 0 1−+= cVtt reflective images of psychic forms of the past. Thus, the real space-time is a This leads to the well-known mirror of the psychic space-time. relativistic prediction that the particle Consequently, any register in the goes to the future if → cV . However, psychic space-time will have a if the gravitational mass of the particle correspondent image in the real space- is negative, then t is also negative and, time. This means that it is possible that therefore, given by we find in the real space-time the image of the holographic register 1−−= cVtt 22 existing in the psychic space-time, 0 corresponding to our past. Similarly, every psychic form that is being In this case, the prevision is that the shaped in the psychic space-time will particle goes to the past if → cV . In have reflective image in the real space- this way, negative gravitational mass time. Thus, the image of the is the necessary condition to the holographic register of our future particle to go to the past. (existing in the psychic space-time) Since the acceleration of a can also be found in the real space- spacecraft with gravitational mass mg , time. is given by = mFa g , where F is the Each image of the holographic thrust of its thrusters, then the more we register of our future will be obviously reduce the value of mg the bigger the correlated to a future epoch in the acceleration of the spacecraft will be. temporal coordinate of the space-time. However, since the value of m cannot In the same way, each image of the g + 1590 M holographic registration of our past be reduced to the range . i to will be correlated to a passed time in − .1590 M i because the spacecraft the temporal coordinate of the referred would become a psychic body, and it space-time. Thus, in order to access needs to remain in the real space-time the mentioned registrations we should in order to access the past or the future accomplish trips to the past or future in the real space-time, then, the ideal in the real space-time. This is possible values for the spacecraft to operate now, with the advent of the with safety would be ± 2.0 mi . Let us gravitational spacecrafts because they consider a gravitational spacecraft allow us to reach speeds close to the whose inertial mass is mi = 000.10 kg . If speed of light. Thus, by varying the its gravitational mass was made gravitational mass of the spacecraft for negative and equal to negative or positive we can go = − 2.0 mm = −2000kg and, at this respectively to the past or future [1]. g i instant the thrust produced by the 21 thrusters of the spacecraft was of the ionized air inside the GCC 5 = 10 NF then, the spacecraft would and ρ ()ar is its density; f is the −2 acquire acceleration g == .50 smmFa frequency of the magnetic field. and, after dayst ×== 105.230 6 s , the By varying B one can vary speed of the spacecraft would be m ()airg and consequently to vary the v −18 =×= 4.0.102.1 csm . Therefore, right gravitational field generated by m ()airg , after that the spacecraft returned to the producing then Gravitational Earth, its crew would find the Earth in Radiation. Then a GCC can work as a the past (due to the negative Gravitational Antenna. gravitational mass of the spacecraft) at Apparently, Newton’s theory of 22 a time 0 1−−= cVtt ; t0 is the time gravity had no gravitational waves measured by an observer at rest on the because, if a gravitational field

Earth. Thus, if t0 = 2009 AD, the time changed in some way, that change would have taken place interval −=Δ ttt 0 would be expressed by instantaneously everywhere in space, and one can think that there is not a wave in this case. However, we have ⎛ 1 ⎞ ⎛ 1 ⎞ −=−=Δ tttt ⎜ −1⎟ −= t ⎜ −1⎟≅ already seen that the gravitational 00 ⎜ 22 ⎟ 0 ⎝ 1− cV ⎠ ⎝ − 16.01 ⎠ interaction can be repulsive, besides t −≅−≅ 183091.0 years 0

Graviphotons That is, the spacecraft would be in the v = ∞ year 1826 AD. On the other hand, if GCC Air the gravitational mass of the spacecraft would have become positive Coil m g 2.0 mi +=+= 2000kg , instead of i Real gravitational waves negative, then the spacecraft would be v = c f in the future at t +=Δ 183 years from 2009. That is, it would be in the year

2192 AD. (a) Antenna GCC

7. Instantaneous Interestelar

Communications GCC GCC Consider a cylindrical GCC Graviphoton v = ∞ (GCC antenna) as shown in Fig.8. The gravitational mass of the air inside the GCC is i i

⎧ ⎡ 4 ⎤⎫ ⎪ σ ()air B ⎪ f f m ()airg ⎨ ⎢ 121 +−= −1⎥⎬m ()airi ()24 ⎢ 4 μρπ cf 22 ⎥ ⎪ ⎣ ()air ⎦⎪ ⎩ ⎭ Transmitter (b) Receiver Where σ ()ar is the electric conductivity

Fig. 8 – Transmitter and Receiver of Virtual Gravitational Radiation. 22 attractive. Thus, as with virtual gravitational radiation. In electromagnetic interaction, the addition, the scattering of this gravitational interaction must be radiation is null. Therefore the virtual produced by the exchange of "virtual" gravitational radiation is very suitable quanta of spin 1 and mass null, i.e., the as a means of transmitting information gravitational "virtual" quanta at any distances, including (graviphoton) must have spin 1 and astronomical distances. not 2. Consequently, the fact that a As concerns detection of the change in a gravitational field reaches virtual gravitational radiation from instantaneously every point in space GCC antenna, there are many options. occurs simply due to the speed of the Due to Resonance Principle a similar graviphoton to be infinite. It is known GCC antenna (receiver) tuned at the that there is no speed limit for same frequency can absorb energy “virtual” photons. On the other hand, from an incident virtual gravitational the electromagnetic quanta (“virtual” radiation (See Fig.8 (b)). photons) can not communicate the Consequently, the gravitational mass electromagnetic interaction to an of the air inside the GCC receiver will infinite distance. vary such as the gravitational mass of Thus, there are two types of the air inside the GCC transmitter. gravitational radiation: the real and This will induce a magnetic field virtual, which is constituted of similar to the magnetic field of the graviphotons; the real gravitational GCC transmitter and therefore the waves are ripples in the space-time current through the coil inside the generated by gravitational field GCC receiver will have the same changes. According to Einstein’s characteristics of the current through theory of gravity the velocity of the coil inside the GCC transmitter. propagation of these waves is equal to However, the volume and pressure of the speed of light [10]. the air inside the two GCCs must be Unlike the electromagnetic exactly the same; also the type and the waves the real gravitational waves quantity of atoms in the air inside the have low interaction with matter and two GCCs must be exactly the same. consequently low scattering. Therefore Thus, the GCC antennas are simple real gravitational waves are suitable as but they are not easy to build. a means of transmitting information. Note that a GCC antenna However, when the distance between radiates graviphotons and transmitter and receiver is too gravitational waves simultaneously large, for example of the order of (Fig. 8 (a)). Thus, it is not only a magnitude of several light-years, the gravitational antenna: it is a Quantum transmission of information by means Gravitational Antenna because it can of gravitational waves becomes also emit and detect gravitational impracticable due to the long time "virtual" quanta (graviphotons), necessary to receive the information. which, in turn, can transmit On the other hand, there is no delay information instantaneously from any during the transmissions by means of 23 distance in the Universe without Universe, by means of the above scattering. mentioned systems of transmission Due to the difficulty to build and reception of “virtual” gravitational two similar GCC antennas and, waves. considering that the electric current in the receiver antenna can be detectable 8. Origin of Gravity and Genesis of even if the gravitational mass of the the Gravitational Energy nuclei of the antennas are not strongly reduced, then we propose to replace It was shown [1] that the the gas at the nuclei of the antennas by “virtual” quanta of the gravitational a thin dielectric lamina. When the interaction must have spin 1 and not 2, virtual gravitational radiation strikes and that they are “virtual” photons upon the dielectric lamina, its (graviphotons) with zero mass outside gravitational mass varies similarly to the coherent matter. Inside the the gravitational mass of the dielectric coherent matter the graviphotons mass lamina of the transmitter antenna, is non-zero. Therefore, the inducing an electromagnetic field gravitational forces are also gauge ( E , B ) similar to the transmitter forces, because they are yielded by the antenna. Thus, the electric current in exchange of "virtual" quanta of spin 1, the receiver antenna will have the such as the electromagnetic forces and same characteristics of the current in the weak and strong nuclear forces. the transmitter antenna. In this way, it Thus, the gravitational forces is then possible to build two similar are produced by the exchanging of antennas whose nuclei have the same “virtual” photons (Fig.9). volumes and the same types and Consequently, this is precisely the quantities of atoms. origin of the gravity. Note that the Quantum Newton’s theory of gravity does Gravitational Antennas can also be not explain why objects attract one used to transmit electric power. It is another; it simply models this easy to see that the Transmitter and observation. Also Einstein’s theory Receiver can work with strong does not explain the origin of gravity. voltages and electric currents. This Einstein’s theory of gravity only means that strong electric power can describes gravity with more precision be transmitted among Quantum than Newton’s theory does. Gravitational Antennas. This Besides, there is nothing in both obviously solves the problem of theories explaining the origin of the wireless electric power transmission. energy that produces the gravitational Thus, we can conclude that the forces. Earth’s gravity attracts all spacecrafts do not necessarily need to objects on the surface of our planet. have a system for generation of This has been going on for over 4.5 electric energy inside them. Since the billions years, yet no known energy electric energy to be used in the source is being converted to support spacecraft can be instantaneously this tremendous ongoing energy transmitted from any point of the expenditure. Also is the enormous 24 continuous energy expended by The Uncertainty Principle Earth’s gravitational field for tells us that, due to the occurrence of maintaining the Moon in its orbit - exchange of graviphotons in a time millennium after millennium. In spite interval Δ < h ΔEt (where ΔE is the of the ongoing energy expended by energy of the graviphoton), the energy Earth’s gravitational field to hold variation ΔE cannot be detected in the objects down on surface and the Moon system − mM gg . Since the total energy in orbit, why the energy of the field W is the sum of the energy of the n never diminishes in strength or drains graviphotons, i.e., Δ+Δ= + +ΔEEEW , its energy source? Is this energy 21 ... n then the energy W cannot be detected expenditure balanced by a conversion as well. However, as we know it can of energy from an unknown energy be converted into another type of source? energy, for example, in rotational kinetic energy, as in the hydroelectric plants, or in the Gravitational Motor, g as shown in this work.

It is known that a quantum of energy Δ = hfE , which varies during a Exchanging of “virtual” photons

(graviphotons) time interval 1 ==Δ λ < h ΔEcft

(wave period) cannot be experimentally detected. This is an imaginary photon or a “virtual” photon. Thus, the graviphotons are

imaginary photons, i.e., the energies ΔEi of the graviphotons are imaginaries energies and therefore the

energy = Δ 1 + EEW 2 ... Δ++Δ En is also an imaginary energy. Consequently, it belongs to the imaginary space-time. Fig. 9 – Origin of Gravity: The gravitational forces are produced by the exchanging of “virtual” photons It was shown [1] that, imaginary (graviphotons). energy is equal to psychic energy. Consequently, the imaginary space- The energy W necessary to support time is, in fact, the psychic space-time, the effort expended by the which contains the Supreme gravitational forces F is well-known Consciousness. Since the Supreme and given by Consciousness has infinite psychic r mM mass [1], then the psychic space-time −== GFdrW gg ∫∞ r contains infinite psychic energy. This According to the Principle of Energy is highly relevant, because it confers to Conservation, the spending of this the Psychic Universe the characteristic energy must be compensated by a of unlimited source of energy. Thus, conversion of another type of energy. as the origin of the gravitational energy it is correlated to the psychic 25 energy, then the spending of gravitational energy can be supplied indefinitely by the Psychic Universe. This can be easily confirmed by the fact that, in spite of the enormous amount of energy expended by Earth’s gravitational field to hold objects down on the surface of the planet and maintain the Moon in its orbit, the energy of Earth’s gravitational field never diminishes in strength or drains its energy source.

Acknowledgement

The author would like to thank Dr. Getúlio Marques Martins (COPPE – UFRJ, Rio de Janeiro-Brasil) for revising the manuscript.

APPENDIX A: The Simplest Method to Control the Gravity

In this Appendix we show the i simplest method to control the gravity. 0 Consider a body with mass density ρ and the following electric characteristics: μr ,ε r ,σ (relative IDC permeability, relative permittivity and electric conductivity, respectively). Through this body, passes an electric I = IDC + iosc current I , which is the sum of a sinusoidal current osc = 0 sinωtii and the

DC current I DC , i.e., DC += 0 sinωtiII

;ω = 2πf . If 0 << Ii DC then ≅ II DC . Thus, the current I varies with the t frequency f , but the variation of its intensity is quite small in comparison Fig. A1 - The electric current I varies with frequency f . But the variation of I is quite small with I DC , i.e., I will be practically in comparison with I due to << Ii . In this constant (Fig. A1). This is of DC o DC way, we can consider ≅ II . fundamental importance for DC maintaining the value of the gravitational mass of the body, mg , where, = VUW is the density of sufficiently stable during all the time. electromagnetic energy and ρ = mi0 V The gravitational mass of the is the density of inertial mass. body is given by [1] The instantaneous values of the density of electromagnetic energy in ⎧ ⎡ 2 ⎤⎫ an electromagnetic field can be ⎪ ⎛ Un ⎞ ⎪ m ⎢ 121 +−= ⎜ r ⎟ −1⎥ Am 1 g ⎨ ⎜ 2 ⎟ ⎬ i0 () deduced from Maxwell’s equations ⎢ ⎝ i0cm ⎠ ⎥ ⎩⎪ ⎣ ⎦⎭⎪ and has the following expression

1 2 1 2 whereU , is the electromagnetic energy 2 += 2 με HEW (A3) absorbed by the body and nr is the index of refraction of the body. where = m sinωtEE and = sinωtHH are Equation (A1) can also be rewritten in the instantaneous values of the electric the following form field and the magnetic field respectively. ⎧ ⎡ 2 ⎤⎫ m ⎛ ⎞ It is known that = μHB , g ⎪ ⎢ rWn ⎥⎪ ⎨ 121 +−= ⎜ ⎟ − ⎬ ()A21 ⎢ ⎜ 2 ⎟ ⎥ = ω kBE r [11] and mi0 ⎪ ⎝ ρ c ⎠ ⎪ ⎩ ⎣⎢ ⎦⎥⎭

27 dz ω c B2 v === ()A4 W = ()A8 dt κ r με 2 μ rr ⎜⎛ 1 ()ωεσ ++ 1⎟⎞ 2 ⎝ ⎠ or 2 where kr is the real part of the = ε EW (A9) r propagation vector k (also called For σ >> ωε , Eq. (A4) gives r phase constant ); +== ikkkk ir ; ε , μ 2ω v = ()A10 and σ, are the electromagnetic μσ characteristics of the medium in which Then, from Eq. (A7) we get the incident (or emitted) radiation is propagating(ε = ε ε ;ε ×= −12 /10854.8 mF ⎡ ⎛ 2ω ⎞ ⎤ ⎛ωε⎞ r 0 0 W = 1 ε⎜ ⎟ 2 1 μμμ HH 2 =+ 2 1 μμ HH 2 ≅+ 2 ⎢ ⎜ ⎟ ⎥ 2 ⎜ ⎟ 2 −7 μσ ⎝ σ ⎠ ; μ = μ r μ0 where 0 πμ ×= 104 m/H ). It is ⎣ ⎝ ⎠ ⎦ 1 2 known that for free-space ≅ 2 μH ()A11

σ = 0 andε μrr == 1. Then Eq. (A4) gives Since = = μHvvBE , we can rewrite = cv (A11) in the following forms: From (A4), we see that the index of B 2 W ≅ ()A12 refraction r = vcn is given by 2μ or c με ⎛ σ ⎞ 2 n == rr ⎜⎛ 1 ()ωεσ 2 ++ ⎟⎞ ()A51 W ≅ ⎜ ⎟E ()A13 r v 2 ⎝ ⎠ ⎝ 4ω ⎠ By comparing equations (A8) (A9) Equation (A4) shows that (A12) and (A13), we can see that Eq. (A13) shows that the best way to ω κ r = v .Thus, ω r == vkBE , i.e., = = μHvvBE (A6) obtain a strong value of W in practice Then, Eq. (A3) can be rewritten in the is by applying an Extra Low- following form: Frequency (ELF) electric field 1 22 1 2 ( = π << 12 Hzfw ) through a medium = 2 ( ) + 2 μμμε HHvW (A7) with high electrical conductivity. Forσ << ωε , Eq. (A4) reduces to Substitution of Eq. (A13) into c Eq. (A2), gives v = ⎧ ⎡ 3 4 ⎤⎫ με ⎪ ⎛ σμ ⎞ E ⎪ rr m ⎢ 121 +−= ⎜ ⎟ −1⎥ m = g ⎨ 2 ⎜ ⎟ 2 ⎬ i0 ⎢ 4c ⎝ 4πf ⎠ ρ ⎥ ⎩⎪ ⎣ ⎦⎭⎪ Then, Eq. (A7) gives ⎧ ⎡ 3 ⎤⎫ ⎪ ⎛ μ ⎞⎛ σμ ⎞ 4 ⎪ ⎢ 121 +−= ⎜ 0 ⎟⎜ r ⎟ −1⎥ mE = 2 ⎨ 23 ⎜ 32 ⎟ ⎬ i0 ⎡ ⎛ c ⎞ ⎤ ⎢ ⎝ 256π ⎠ ρ fc ⎥ W = 1 ε⎜ ⎟ 2 1 2 =+ μμμμ HHH 2 ⎩⎪ ⎣ ⎝ ⎠ ⎦⎭⎪ 2 ⎢ ⎜ ⎟ ⎥ 2 ⎣ ⎝ με rr ⎠ ⎦ ⎧ ⎡ 3 ⎤⎫ ⎪ −27 ⎛ rσμ ⎞ 4 ⎪ ⎨ ⎢ ×+−= 10758.1121 ⎜ ⎟ −1⎥⎬mE i0 ⎢ ⎜ ρ f 32 ⎟ ⎥ This equation can be rewritten in the ⎩⎪ ⎣ ⎝ ⎠ ⎦⎭⎪ following forms: ()A14

Note that = m sinωtEE .The average 2 1 2 value for E is equal to 2 Em because 28 4 E varies sinusoidaly ( Em is the ⎧ ⎡ ⎤⎫ ⎪ −25 I DC ⎪ mg ⎨ ⎢ ×+−= 1089.7121 −1⎥⎬mi0 = maximum value for E ). On the other S 4 ⎩⎪ ⎣⎢ ⎦⎥⎭⎪ hand, rms = EE m 2 . Consequently we 4 4 4 {}[]DC −+−= 113.0121 mI i0 ()A18 can change E by Erms , and the equation above can be rewritten as Then, follows m χ g I 4 −+−≅= 113.0121 A19 ⎧ ⎡ 3 ⎤⎫ { [ DC ]} () ⎪ −27 ⎛ rσμ ⎞ 4 ⎪ mi0 mg ⎨ ⎢ ×+−= 10758.1121 ⎜ ⎟ rms −1⎥⎬mE i0 ⎢ ⎜ ρ f 32 ⎟ ⎥ ⎩⎪ ⎣ ⎝ ⎠ ⎦⎭⎪ For = 2.2 AI , the equation above Substitution of the well-known DC equation of the Ohm's vectorial Law: gives ⎛ m ⎞ = σEj into (A14), we get ⎜ g ⎟ χ = ⎜ ⎟ −≅ 1 ()A20 4 ⎝ m i0 ⎠ ⎪⎧ ⎡ μ j ⎤⎪⎫ m ⎢ ×+−= 10758.1121 −27 rmsr − ⎥ Am 151 g ⎨ 32 ⎬ i0 () This means that the gravitational ⎢ σρ f ⎥ ⎩⎪ ⎣ ⎦⎭⎪ shielding produced by the aluminum where rms = jj 2 . foil can change the gravity Consider a 15 cm square acceleration above the foil down to Aluminum thin foil of 10.5 microns thickness with the following ′ χ −≅= 1ggg (A21) −17 characteristics:μr =1 ; σ ×= .1082.3 mS ; ρ = .2700 mKg −3 . Then, (A15) gives Under these conditions, the Aluminum ⎧ ⎡ 4 ⎤⎫ foil works basically as a Gravity ⎪ −42 jrms ⎪ mg ⎨ ⎢ −×+−= ⎥⎬ i0 ()Am 16110313.6121 Control Cell (GCC). f 3 ⎩⎪ ⎣⎢ ⎦⎥⎭⎪ In order to check these Now, consider that the ELF electric theoretical predictions, we suggest an current DC += 0 sin ωtiII , (0 << Ii DC ) experimental set-up shown in Fig.A2. passes through that Aluminum foil. A 15cm square Aluminum foil Then, the current density is of 10.5 microns thickness with the I I following composition: Al 98.02%; Fe j rms ≅= DC ()A17 rms S S 0.80%; Si 0.70%; Mn 0.10%; Cu where 0.10%; Zn 0.10%; Ti 0.08%; Mg 0.05%; Cr 0.05%, and with the −6 − 26 μ =1 = mS ( m) ×=× 1057.1105.1015.0 m following characteristics: r ; −3 σ ×= .1082.3 mS −17 ; ρ = .2700 mKg , is fixed If the ELF electric current has on a 17 cm square Foam Board §§ frequency μHzf ×== 1022 −6 Hz, then, the plate of 6mm thickness as shown in gravitational mass of the aluminum Fig.A3. This device (the simplest foil, given by (A16), is expressed by §§ Foam board is a very strong, lightweight (density: 24.03 kg.m-3) and easily cut material used for the mounting of photographic prints, as backing in picture framing, in 3D design, and in painting. It consists of three layers — an inner layer of polystyrene clad with outer facing of either white clay coated paper or brown Kraft paper. 29 Gravity Control Cell GCC) is placed φ = 10mm ; area S πφ2 ×== 108.74 − m25 ; on a pan balance shown in Fig.A2. wire#12AWG; = 21 NNN == 20; = 42mml ; Above the Aluminum foil, a 2 −7 21 === μ0 ( lSNLLL ) ×= 103.9 H .Thus, sample (any type of material, any we get mass) connected to a dynamometer 2 ωLrRZ 2 501Ω≅++= will check the decrease of the local 1 ()()i11 gravity acceleration upon the sample and ′ = χ gg 2 2 ( ), due to the gravitational 2 ( 22 pi ) ++++= ()ωLRRrRZ shielding produced by the decreasing of gravitational mass of the Aluminum min For R = 0 we get ZZ 22 4Ω≅= ; for foil (χ = mm ig 0 ). Initially, the sample max R = 10Ω the result is ZZ 22 14Ω≅= . lies 5 cm above the Aluminum foil. As Thus, shown in Fig.A2, the board with the 2 ⎛ N ⎞ dynamometer can be displaced up to min min +=+= ZZZZZ min ⎜ 1 ⎟ 505Ω≅ ,1 total ,11 reflected 21 ⎜ N ⎟ few meters in height. Thus, the initial ⎝ 2 ⎠ 2 ⎛ N ⎞ distance between the Aluminum foil max max max⎜ 1 ⎟ ,1 total ,11 reflected +=+= ZZZZZ 21 ⎜ ⎟ 515Ω≅ and the sample can be increased in ⎝ N2 ⎠ order to check the reach of the gravitational shielding produced by the The maxima rms currents have Aluminum foil. the following values: In order to generate the ELF I max = 1 40 ZV min = 56mA 1 2 pp ,1 total electric current of = 2μHzf , we can (The maximum output current of the use the widely-known Function Function Generator HP3325A (Op.002 Generator HP3325A (Op.002 High High Voltage Output) is Voltage Output) that can generate mA ≅ 5.5680 mA ); sinusoidal voltages with extremely-low pp rms −6 ε frequencies down to f ×= 101 Hz and max 2 I 2 min == 3A Z 2 amplitude up to 20V (40Vpp into 500Ω load). The maximum output current and max max max 3 2 1 ≅+= 3AIII is 080 A. pp ; output impedance <2Ω at ELF . The new expression for the Figure A4 (a) shows the r inertial forces, (Eq.5) = aMF r , shows equivalent electric circuit for the gi experimental set-up. The that the inertial forces are proportional electromotive forces are:ε1 (HP3325A) to gravitational mass. Only in the

particular case of g = mm i 0 , the and ε 2 (12V DC Battery).The values of the resistors are expression above reduces to the well- : R −Ω= 2500 W ;;r 2Ω< R Ω= − 404 W known Newtonian expression 1 i1 2 r −3 r ; r 1.0 Ω< ; R 105.2 Ω×= ; Rheostat = ii 0 amF . The equivalence between i 2 p r r ≡FF (0≤ R ≤10Ω - 90W). The coupling gravitational and inertial forces ( gi ) transformer has the following [1] shows then that a balance measures characteristics: air core with diameter the gravitational mass subjected to 30 acceleration = ga . Here, the decrease than − .1590 M i , or when it becomes in the gravitational mass of the greater than + .1590 M i . Aluminum foil will be measured by a Equation (A18) shows that the pan balance with the following gravitational mass of the Aluminum characteristics: range 0-200g; foil, m ()Alg , goes close to zero when readability 0.01g. ≅ 76.1 AI . Consequently, the gravity The mass of the Foam Board 3 plate is: ≅ 17.4 g , the mass of the acceleration above the Aluminum foil also goes close to zero since Aluminum foil is: ≅ 64.0 g , the total ′ χ == mmgg . Under these mass of the ends and the electric wires ()0 ()AliAlg of connection is ≅ 5g . Thus, initially circumstances, the Aluminum foil remains invisible. the balance will show ≅ 81.9 g . Now consider a rigid Aluminum According to (A18), when the electric wire # 14 AWG. The area of its cross current through the Aluminum foil section is (resistance * σSlr 105.2 −3 Ω×== ) reaches p the value ≅ 2.2 AI , we will get −3 2 − 26 3 S π ( ×= m) ×= 1008.2410628.1 m ()Alg −≅ mm 0 ()Ali . Under these circumstances, the balance will show: If an ELF electric current with frequency μHzf ×== 1022 −6 Hz passes − − ≅ 53.864.064.081.9 gggg through this wire, its gravitational mass, given by (A16), will be and the gravity acceleration g′ above expressed by the Aluminum foil, becomes ⎪⎧ ⎡ j 4 ⎤⎪⎫ m ⎢ −42 rms −×+−= 110313.6121 ⎥ m = ′ χ −≅= 1ggg . g ⎨ 3 ⎬ i0 ⎪ ⎢ f ⎥⎪ It was shown [1] that, when the ⎩ ⎣ ⎦⎭ ⎧ ⎡ 4 ⎤⎫ gravitational mass of a particle is ⎪ −25 IDC ⎪ ⎨ ⎢ −×+−= 11089.7121 ⎥⎬mi0 = reduced to the gravitational mass S 4 ⎩⎪ ⎣⎢ ⎦⎥⎭⎪ ranging between + .1590 M i to 4 {}[]DC −+−= 113.0121 mI i0 ()A22 − .1590 M i , it becomes imaginary, i.e., the gravitational and the inertial For ≅ 3AI the equation above gives masses of the particle become DC imaginary. Consequently, the particle m −≅ 8.3 m disappears from our ordinary space- g i0 time. This phenomenon can be observed in the proposed experiment, Note that we can replace the i.e., the Aluminum foil will disappear Aluminum foil for this wire in the when its gravitational mass becomes experimental set-up shown in Fig.A2. It is important also to note that an ELF smaller than + .1590 M i . It will become visible again, only when its electric current that passes through a gravitational mass becomes smaller wire - which makes a spherical form, as shown in Fig A5 - reduces the gravitational mass of the wire (Eq. 31 A22), and the gravity inside sphere at in this case, the electric field *** the same proportion, χ= mm ig 0 , through it will be null . (Gravitational Shielding Effect). In According to Eq. A14, max max this case, that effect can be checked by when pp == /036.0 mVhVE , = 2μHzf and 7 3 means of the Experimental set-up 2 σ Al ×= /1082.3 mS , ρ Al = /2700 mkg (Fig.A6). Note that the spherical form (Aluminum), we get can be transformed into an ellipsoidal m ()Al χ = −≅ 9.0 form or a disc in order to coat, for m ()Ali example, a Gravitational Spacecraft. It Under these conditions, the maximum is also possible to coat with a wire current density through the plate with several forms, such as cylinders, thickness h will be given by cones, cubes, etc. max σ Ej max ×== /104.1 mA 26 (It is well- The circuit shown in Fig.A4 (a) pAl can be modified in order to produce a known that the maximum current new type of Gravitational Shielding, as density supported by the Aluminum 28 shown in Fig.A4 (b). In this case, the is ≈ /10 mA ). Gravitational Shielding will be Since the area of the plate is 2 produced in the Aluminum plate, with A ( ) ×== 1042.0 − m22 , then the maximum thickness h , of the parallel plate current is max max == 56kAAji . Despite capacitor connected in the point P of this enormous current, the maximum the circuit (See Fig.A4 (b)). Note that, dissipated power will be just in this circuit, the Aluminum foil max max 2 = ( ) RiP plate = 2.6 W , because the (resistance R ) (Fig.A4(a)) has been p resistance of the plate is very small, replaced by a Copper wire # 14 AWG −9 i.e., plate σ Al AhR 102 Ω×≅= . with 1cm length ( =1cml ) in order to Note that the area A of the plate produce a resistance R 1021.5 −5 Ω×= . φ (where the Gravitational Shielding Thus, the voltage in the point P of the takes place) can have several circuit will have the maximum value geometrical configurations. For max −4 V p ×= 101.1 V when the resistance of example, it can be the area of the the rheostat is null (R = 0) and the external surface of an ellipsoid, sphere, min −5 minimum value V p ×= 1003.4 V when etc. Thus, it can be the area of the external surface of a Gravitational R 10Ω= . In this way, the voltage 2 V (with frequency = 2μHzf ) applied Spacecraft. In this case, if ≅100mA , p for example, the maximum dissipated on the capacitor will produce an electric field E with intensity *** p When the voltage Vp is applied on the capacitor, the = hVE through the Aluminum plate charge distribution in the dielectric induces positive pp and negative charges, respectively on opposite sides of of thickness = 3mmh . It is important to the Aluminum plate with thickness h. If the plate is note that this plate cannot be not connected to the ground (Earth) this charge distribution produces an electric field Ep=Vp/h through connected to ground (earth), in other the plate. However, if the plate is connected to the words, cannot be grounded, because, ground, the negative charges (electrons) escapes for the ground and the positive charges are redistributed along the entire surface of the Aluminum plate making null the electric field through it. 32 max 1 q ε rV power will be P ≅ 4.15 kW , i.e., V == r 00 ()A28 2 b approximately /154 mW . 4πε 0 b b

All of these systems work with Consequently, the electric field Eb is Extra-Low Frequencies ( <<10−3 Hzf ). given by

Now, we show that, by simply 1 q ε r rV 00 Eb 2 == 2 ()A29 changing the geometry of the surface 4πε0 b b of the Aluminum foil, it is possible to From = rr 0 up to == + dabr the increase the working frequency f up electric field is approximately constant to more than 1Hz. (See Fig. A7). Along the distance d it Consider the Aluminum foil, will be called Eair . For > + dar , the now with several semi-spheres electric field stops being constant. stamped on its surface, as shown in Thus, the intensity of the electric field Fig. A7 . The semi-spheres have at = = + dabr is approximately equal radius r0 = 9.0 mm , and are joined one to E0 , i.e., b ≅ EE 0 . Then, we can write to another. The Aluminum foil is now that coated by an insulation layer with ε rV V r 00 ≅ 0 ()A30 relative permittivity ε r and dielectric 2 b r0 strength k . A voltage source is whence we get connected to the Aluminum foil in ≅ rb ε (A31) order to provide a voltage V (rms) 0 r 0 Since the intensity of the electric field with frequency f . Thus, the electric through the air, Eair , is ≅ bair ≅ EEE 0 , potential V at a distance r , in the then, we can write that r a interval from 0 to , is given by 1 q ε rV E == r 00 A32 1 q air 2 2 () V = ()A23 4πε0 b b 4 r επε 0 r Note that, ε r refers to the relative In the interval ≤< bra the electric permittivity of the insulation layer, potential is which is covering the Aluminum foil. 1 q V = ()A24 If the intensity of this field is 4πε r 0 greater than the dielectric strength of since for the air we have ε ≅ 1. 6 r the air ( × /103 mV ) there will occur the Thus, on the surface of the well-known Corona effect. Here, this = rr metallic spheres (0 ) we get effect is necessary in order to increase 1 q the electric conductivity of the air at V0 = ()A25 4 rεπε r00 this region (layer with thickness d). Consequently, the electric field is Thus, we will assume 1 q min min min ε r 0 rV 0 V0 6 E0 = 2 ()A26 E ×=== /103 mV 4 επε r air 2 r 0 0 b r0 By comparing (A26) with (A25), we and obtain ε maxrV V max E max r 0 0 0 ×=== 7 AmV 33/101 V air 2 () 0 b r E0 = ()A27 0 r0 min max The electric field air air ≤≤ EEE air will The electric potential Vb at = br is 33 produce an electrons flux in a direction thickness =Δ 6.0 mm , ε r ≅ 5.3 (1- and an ions flux in an opposite 60Hz), = /17 mmkVk (Acrylic sheet direction. From the viewpoint of 1.5mm thickness), and the semi- electric current, the ions flux can be spheres stamped on the metallic considered as an “electrons” flux at the surface have r0 = 9.0 mm (See Fig.A7) same direction of the real electrons then ra =Δ+= 5.1 mm. Thus, we obtain flux. Thus, the current density through 0 from Eq. (A33) that the air, j , will be the double of the air min = 7.2 kVV current density expressed by the well- 0 max = 9kVV (A40) known equation of Langmuir-Child 0 3 3 3 From equation (A31), we obtain the 4 2e V2 V2 V2 j = εε α ×== 1033.2 −6 A34 following value for b : r 0 22 2 () 9 me d d d where ε ≅ 1 for the air; α ×= 1033.2 −6 −3 r = rb 0 ε r ×= 1068.1 (Am 41) is the called Child’s constant. Thus, we have Since = + dab we get 3 V2 j =2α ()A35 air d2 d 8.1 ×= 10−4 m where d , in this case, is the thickness of the air layer where the electric field Substitution of a , b , d and A(32) into is approximately constant and V is the (A39) produces 1 1 voltage drop given by σ ×= 10117.4 −4 E 2 ×= 10375.1 −2V 2 1 q 1 q air air 0 VVV ba =−=−= 4 0 a 4πεπε 0 b Substitution of σ air , air ()rmsE and ⎛ − ab ⎞ ⎛ε r 0dr ⎞ −3 = rV 00 ε r ⎜ ⎟ = ⎜ ⎟V0 ()A36 ρ air = .2.1 mkg into (A14) gives ⎝ ab ⎠ ab ⎠⎝ m ⎧ ⎡ 43 ⎤⎫ By substituting (A36) into (A35), we ()airg ⎪ −27 σ Eairair ⎪ ⎨ ⎢ ×+−= 10758.1121 −1⎥⎬= m ρ f 32 get 0()airi ⎩⎪ ⎣⎢ air ⎦⎥⎭⎪ 3 3 3 2 2 2 2α ⎛ε dVr ⎞ 2α⎛ε Vr ⎞ ⎛b⎞ 5.5 r 00 r 00 ⎧ ⎡ V ⎤⎫ jair = 2 ⎜ ⎟ = 1 ⎜ 2 ⎟ ⎜ ⎟ = ⎪ −21 0 ⎪ 2 ⎢ ×+−= 10923.4121 −1⎥ ()A42 d ⎝ ab ⎠ d ⎝ b ⎠ ⎝a⎠ ⎨ 3 ⎬ ⎢ f ⎥ 3 ⎩⎪ ⎣ ⎦⎪⎭ 3 2 2α ⎛b⎞ max 2 == 9kVVV = 2Hzf = 1 Eair⎜ ⎟ ()A37 For 00 and , the 2 a d ⎝ ⎠ result is According to the equation of the m ()airg Ohm's vectorial Law: = σEj , we can −≅ 2.1 mi0()air write that Note that, by increasing V0 the jair σair = ()A38 values of Eair and σ air are increased. Eair Substitution of (A37) into (A38) yields Thus, as show (A42), there are two 1 3 m 2 2 ways for decrease the value of (airg ): ⎛ Eair ⎞ ⎛b⎞ air = 2ασ ⎜ ⎟ ⎜ ⎟ ()A39 increasing the value of V or ⎝ d ⎠ ⎝ a⎠ 0 If the insulation layer has decreasing the value of f . 34 max 7 Since 0 == /10/10 mmkVmVE and Gravitational Shielding is max max 2 =Δ 6.0 mm then the dielectric strength air = (iRP airair ) ≅10kW . This means that of the insulation must be ≥ kV /7.16 mm . a very strong light will be radiated As mentioned above, the dielectric from this type of Gravitational strength of the acrylic is 17kV / mm. Shielding. Note that this device can It is important to note that, due also be used as a lamp, which will be to the strong value of Eair (Eq. A37) much more efficient than conventional the drift velocity vd , lamps.

(aird == σ airair neEnejv ) of the free Coating a ceiling with this charges inside the ionized air put them lighting system enables the entire area of ceiling to produce light. This is a at a distance dd ≅== 4.02 mfvtvx , which is much greater than the distance form of lighting very different from those usually known. d ×= 108.1 −4 m. Consequently, the number max ≅10kWP n of free charges decreases strongly Note that the value air , ††† inside the air layer of thickness d , defines the power of the transformer except, obviously, in a thin layer, very shown in Fig.A10. Thus, the close to the dielectric, where the maximum current in the secondary is max number of free charges remains s = = 9.0109 AkWkVi . sufficiently increased, to maintain the Above the Gravitational air conductivity with σair ≅ /1.1 mS (Eq. Shielding, σ air is reduced to the A39). normal value of conductivity of the The thickness h of this thin air atmospheric air (≈ −14 /10 mS ). Thus, the layer close to the dielectric can be power radiated from this region is easily evaluated starting from the charge distribution in the max max 2 ()−= (ihdP ) σ A = neighborhood of the dielectric, and of air air air max 2 −4 the repulsion forces established among ()−= σ ()EAhd airair ≅10 W them. The result is −9 Now, we will describe a method = πε0 Eeh ×≅ 104406.0 m . This is, therefore, the thickness of the Air to coat the Aluminum semi-spheres Gravitational Shielding. If the area of with acrylic in the necessary dimension (Δ = − ra ). First, take an this Gravitational Shielding is equal to 0 the area of a format A4 sheet of paper, Aluminum plate with × 1.2921 cmcm i.e., A =×= 0582.0291.020.0 m2 , we obtain (A4 format). By means of a convenient the following value for the resistance process, several semi-spheres can be stamped on its surface. The semi- Rair of the Gravitational Shielding: −8 spheres have radius r0 = 9.0 mm , and air = σ air AhR 106 Ω×≅ . Since the maximum electrical current through are joined one to another. Next, take an acrylic sheet (A4 format) with this air layer is max max ≅= 400kAAji , then 1.5mm thickness (See Fig.A8 (a)). the maximum power radiated from the Put a heater below the Aluminum plate

††† in order to heat the Aluminum (Fig.A8 Reducing therefore the conductivity, σ air , to the normal value of the conductivity of atmospheric air. (b)). When the Aluminum is 35 sufficiently heated up, the acrylic sheet around bodies or spacecrafts with and the Aluminum plate are pressed, several formats (spheres, ellipsoids, one against the other, as shown in Fig. etc); Fig. A11 (d) shows a A8 (c). The two D devices shown in Gravitational Shielding around a this figure are used in order to impede Spacecraft with ellipsoidal form. that the press compresses the acrylic The previously mentioned and the aluminum to a distance shorter Gravitational Shielding, produced on a than + ay . After some seconds, remove thin layer of ionized air, has a the press and the heater. The device is behavior different from the Gravitational Shielding produced on a ready to be subjected to a voltage V0 with frequency f , as shown in Fig.A9. rigid substance. When the Note that, in this case, the balance is gravitational masses of the air not necessary, because the substance molecules, inside the shielding, are reduced to within the range that produces the gravitational + 159.0 < mm < − 159.0 m , they go to shielding is an air layer with thickness gi i d above the acrylic sheet. This is, the imaginary space-time, as therefore, more a type of Gravity previously shown in this article. Control Cell (GCC) with external However, the electric field Eair stays at gravitational shielding. the real space-time. Consequently, the It is important to note that this molecules return immediately to the GCC can be made very thin and as real space-time in order to return soon flexible as a fabric. Thus, it can be after to the imaginary space-time, due used to produce anti- gravity clothes. to the action of the electric field Eair . These clothes can be extremely useful, In the case of the Gravitational for example, to walk on the surface of Shielding produced on a solid high gravity planets. substance, when the molecules of the Figure A11 shows some substance go to the imaginary space- geometrical forms that can be stamped time, the electric field that produces on a metallic surface in order to the effect, also goes to the imaginary produce a Gravitational Shielding space-time together with them, since in effect, similar to the produced by the this case, the substance of the semi-spherical form. Gravitational Shielding is rigidly An obvious evolution from the connected to the metal that produces semi-spherical form is the semi- the electric field. (See Fig. A12 (b)). cylindrical form shown in Fig. A11 This is the fundamental difference (b); Fig.A11(c) shows concentric between the non-solid and solid metallic rings stamped on the metallic Gravitational Shieldings. surface, an evolution from Fig.A11 Now, consider a Gravitational (b). These geometrical forms produce Spacecraft that is able to produce an the same effect as the semi-spherical Air Gravitational Shielding and also a form, shown in Fig.A11 (a). By using Solid Gravitational Shielding, as concentric metallic rings, it is possible to build Gravitational Shieldings 36 shown in Fig. A13 (a) ‡‡‡. Assuming time. Under these circumstances, that the intensity of the electric field, the gravitational mass of the

Eair , necessary to reduce the Gravitational Shielding can be reduced −4 gravitational mass of the air molecules to mg ≅ 0 . For example, mg ≅ 10 kg . to within the range Thus, if the inertial mass of the

159.0 mm gi −<<+ 159.0 mi , is much Gravitational Shielding is i0 ≅ 1kgm , −4 smaller than the intensity of the then χ = g mm i0 ≅ 10 . As we have electric field, Ers , necessary to reduce seen, this means that the inertial the gravitational mass of the solid effects on the spacecraft will be substance to within the range reduced by χ ≅10−4 . Then, in spite of the

159.0 mm gi −<<+ 159.0 mi , then we effective acceleration of the spacecraft conclude that the Gravitational be, for example, = .10 sma −25 , the effects Shielding made of ionized air goes to on the crew of the spacecraft will be the imaginary space-time before the equivalent to an acceleration of only

Gravitational Shielding made of solid mg a′ χ ≈== .10 smaa −1 substance. When this occurs the mi0 spacecraft does not go to the This is the magnitude of the imaginary space-time together with the acceleration upon the passengers in a Gravitational Shielding of air, because contemporary commercial jet. the air molecules are not rigidly Then, it is noticed that connected to the spacecraft. Thus, Gravitational Spacecrafts can be while the air molecules go into the subjected to enormous accelerations imaginary space-time, the spacecraft (or decelerations) without imposing stays in the real space-time, and any harmful impacts whatsoever on remains subjected to the effects of the the spacecrafts or its crew. Gravitational Shielding around it, Now, imagine that the intensity since the shielding does not stop to of the electric field that produces the work, due to its extremely short Gravitational Shielding around the permanence at the imaginary space- spacecraft is increased up to reaching

the value Ers that reduces the ‡‡‡ The solid Gravitational Shielding can also be obtained by means of an ELF electric current through gravitational mass of the solid a metallic lamina placed between the semi-spheres Gravitational Shielding to within the and the Gravitational Shielding of Air (See Fig.A13 (a)). The gravitational mass of the solid Gravitational range + 159.0 < mm gi −< 159.0 mi . Under Shielding will be controlled just by means of the these circumstances, the solid intensity of the ELF electric current. Recently, it was discovered that Carbon nanotubes (CNTs) can be Gravitational Shielding goes to the added to Alumina (Al2O3) to convert it into a good imaginary space-time and, since it is electrical conductor. It was found that the electrical conductivity increased up to 3375 S/m at 77°C in rigidly connected to the spacecraft, samples that were 15% nanotubes by volume [12]. It also the spacecraft goes to the is known that the density of α-Alumina is imaginary space-time together with the 3.98×103kg.m-3 and that it can withstand 10-20 KV/mm. Thus, these values show that the Alumina- Gravitational Shielding. Thus, the CNT can be used to make a solid Gravitational spacecraft can travel within the Shielding.

37 imaginary space-time and make use of departure place where would the Gravitational Shielding around it. reappear in our Universe. Thus, trips As we have already seen, the through our Universe that would delay maximum velocity of propagation of millions of years, at speeds close to the the interactions in the imaginary speed of light, could be done in just a space-time is infinite (in the real few months in the imaginary Universe. space-time this limit is equal to the In order to produce the light velocity c ). This means that there acceleration of ≈ .10 sma −29 upon the are no limits for the velocity of the spacecraft we propose a Gravitational spacecraft in the imaginary space- Thruster with 10 GCCs (10 time. Thus, the acceleration of the Gravitational Shieldings) of the type spacecraft can reach, for example, with several semi-spheres stamped on = .10 sma −29 , which leads the spacecraft the metallic surface, as previously to attain velocities ≈ .10 smV −114 (about shown, or with the semi-cylindrical 1 million times the speed of light) after form shown in Figs. A11 (b) and (c). one day of trip. With this velocity, The 10 GCCs are filled with air at 1 after 1 month of trip the spacecraft atm and 300K. If the insulation layer is 21 would have traveled about10 m . In made with Mica (ε r ≅ 4.5 ) and has order to have idea of this distance, it is thickness =Δ 1.0 mm , and the semi- enough to remind that the diameter of spheres stamped on the metallic our Universe (visible Universe) is of surface have r0 = 4.0 mm (See Fig.A7) the order of10 26 m . then ra 0 =Δ+= 5.0 mm. Thus, we get Due to the extremely low rb ε ×== 10295.9 −4m density of the imaginary bodies, the 0 r and collision between them cannot have abd ×=−= 10295.4 −4 m the same consequences of the collision Then, from Eq. A42 we obtain between the real bodies. m ⎧ ⎡ 43 ⎤⎫ Thus, for a Gravitational ()airg ⎪ −27 σ Eairair ⎪ χair ⎨ ⎢ ×+−== 10758.1121 −1⎥⎬ = m ρ f 32 Spacecraft in imaginary state, the 0()airi ⎩⎪ ⎣⎢ air ⎦⎥⎭⎪ problem of the collision in high-speed ⎧ ⎡ 5.5 ⎤⎫ ⎪ −18 V ⎪ doesn't exist. Consequently, the ⎨ ⎢ 0 −×+−= 1100.1121 ⎥⎬ f 3 Gravitational Spacecraft can transit ⎩⎪ ⎣⎢ ⎦⎥⎭⎪ max freely in the imaginary Universe and, For VV 00 == 6.15 kV and f = 12.0 Hz, the in this way, reach easily any point of result is our real Universe once they can make the transition back to our Universe by m ()airg 4 χair ×−≅= 106.1 only increasing the gravitational mass m 0()airi of the Gravitational Shielding of the spacecraft in such way that it leaves max max Since 0 = 0 rVE 0 is now given by the range of + .1590 M i to − .1590 M i . max 0 = = kVmmkVE /3.179.06.15 mm and =Δ 1.0 mm The return trip would be done in then the dielectric strength of the similar way. That is to say, the insulation must be ≥ /173 mmkV . As spacecraft would transit in the imaginary Universe back to the 38 §§§ −19 shown in the table below , 0.1mm - 10 ⎛10 ⎞ a ×−−= 4 ×1067.6106.1 −11 ⎜ ⎟ = ()()⎜ 2 ⎟ thickness of Mica can withstand 17.6 ⎝ 30 ⎠ max kV (that is greater thanV = 6.15 kV ), in −29 0 −= .10 sm such way that the dielectric strength is In spite of this gigantic acceleration, 176 kV/mm. the inertial effects for the crew of the The Gravitational Thrusters are spacecraft can be strongly reduced if, positioned at the spacecraft, as shown for example, the gravitational mass of in Fig. A13 (b). Then, when the the Gravitational Shielding is reduced spacecraft is in the intergalactic space, down to ≅ 10−6 kgm and its inertial the gravity acceleration upon the g mass is i0 ≅ 100kgm . Then, we get gravitational mass mgt of the bottom χ mm ≅= 10−8 of the thruster (See Fig.A13 (c)), is ig 0 . Therefore, the given by [2] inertial effects on the spacecraft will M be reduced by χ ≅10−8 , and ar ≅ ()χ 10 gr −≅ ()χ 10 G g μˆ air M air r 2 consequently, the inertial effects on the crew of the spacecraft would be where M is the gravitational mass in g equivalent to an acceleration a′of only front of the spacecraft. m a′ g a == ()()− 98 ≈ .101010 sm −2 For simplicity, let us consider m just the effect of a hypothetical volume i0 3733 Note that the Gravitational Thrusters V =××= 10101010 m of intergalactic in the spacecraft must have a very matter in front of the spacecraft small diameter (of the order of (≅ 30mr ). The average density of millimeters) since, obviously, the hole matter in the intergalactic medium through the Gravitational Shielding −− 326 **** (IGM) is ρig ≈ .10 mkg ) . Thus, cannot be large. Thus, these thrusters 4 for χair ×−≅ 106.1 we get are in fact, Micro-Gravitational Thrusters. As shown in Fig. A13 (b), §§§ The dielectric strength of some dielectrics can have it is possible to place several micro- different values in lower thicknesses. This is, for example, the case of the Mica. gravitational thrusters in the Dielectric Thickness (mm) Dielectric Strength (kV/mm) spacecraft. This gives to the Mica 0.01 mm 200 Gravitational Spacecraft, several Mica 0.1 mm 176 Mica 1 mm 61 degrees of freedom and shows the enormous superiority of this spacecraft **** Some theories put the average density of the Universe as the equivalent of one hydrogen atom per in relation to the contemporaries cubic meter [13,14]. The density of the universe, spacecrafts. however, is clearly not uniform. Surrounding and The density of matter in the stretching between galaxies, there is rarefied plasma [15] that is thought to possess a cosmic filamentary intergalactic medium (IGM) is about structure [16] and that is slightly denser than the 10 -26 kg.m-3 , which is very less than average density in the universe. This material is called the density of matter in the interstellar the intergalactic medium (IGM) and is mostly ionized -21 -3 hydrogen; i.e. a plasma consisting of equal numbers of medium (~10 kg.m ) that is less than electrons and protons. The IGM is thought to exist at a the density of matter in the density of 10 to 100 times the average density of the -20 -3 Universe (10 to 100 hydrogen atoms per cubic meter, interplanetary medium (~10 kg.m ). i.e., ≈ −26 .10 mkg −3 ). The density of matter is enormously 39 increased inside the Earth’s atmosphere. Also, the gravity can be atmosphere (1.2kg.m-3 near to Earth’s controlled inside of the Gravitational surface). Figure A14 shows the Spacecraft in order to maintain a value gravitational acceleration acquired by close to the Earth’s gravity as shown a Gravitational Spacecraft, in these in Fig.3. media, using Micro-Gravitational Finally, it is important to note thrusters. that a Micro-Gravitational Thruster In relation to the Interstellar and does not work outside a Gravitational Interplanetary medium, the Shielding, because, in this case, the Intergalactic medium requires the resultant upon the thruster is null due greatest value of χ air (χ inside the to the symmetry (See Fig. A15 (a)). Micro-Gravitational Thrusters), i.e., Figure A15 (b) shows a micro- 4 gravitational thruster inside a χair ×−≅ 106.1 . This value strongly decreases when the spacecraft is Gravitational Shielding. This thruster within the Earth’s atmosphere. In this has 10 Gravitational Shieldings, in case, it is sufficient only†††† χ ≅ −10 in such way that the gravitational air acceleration upon the bottom of the order to obtain: thruster, due to a gravitational mass 10 ρ V a −= ()χ G atm ≅ M in front of the thruster, is air r 2 g 10 2 7 10 = χ air aa 0 where 0 −= g rMGa is the 10 −11 ()102.1 −24 ()−−≅ ()×1067.610 ≅ .10 sm ()20 2 gravitational acceleration acting on With this acceleration the the front of the micro-gravitational Gravitational Spacecraft can reach thruster. In the opposite direction, the about 50000 km/h in a few seconds. gravitational acceleration upon the Obviously, the Gravitational Shielding bottom of the thruster, produced by a gravitational mass M , is of the spacecraft will reduce strongly g 2 the inertial effects upon the crew of the a0′ χ s (−= g rGM ′ )≅ 0 spacecraft, in such way that the inertial since χ s ≅ 0 due to the Gravitational effects of this strong acceleration will Shielding around the micro-thruster not be felt. In addition, the artificial (See Fig. A15 (b)). Similarly, the atmosphere, which is possible to build acceleration in front of the thruster is around the spacecraft, by means of 10 10 2 ′ = aa ′ [χχ ()−= rGM ′ ] χ gravity control technologies shown in 10 air 0 air g s where χ 10 − ′2 < arGM , since r′ > r . this article (See Fig.6) and [2], will [ air ( g )] 10 −29 −8 protect it from the heating produced Thus, for 10 ≅ .10 sma and χ s ≈10 we −2 by the friction with the Earth’s conclude that 10′ < .10 sma . This means

that 10′ << aa 10 . Therefore, we can write †††† This value is within the range of values of χ 3 that the resultant on the micro-thruster (χ −< AEqSee 15..10 ), which can be produced by can be expressed by means of the means of ELF electric currents through metals as Aluminum, etc. This means that, in this case, if following relation convenient, we can replace air inside the GCCs of the Gravitational Micro-thrusters by metal laminas with 10 ELF electric currents through them. 10 =≅ χ air FFR 0

Figure A15 (c) shows a Micro- E(acrylic)are not sufficient to produce Gravitational Thruster with 10 Air the ionization effect, which increases Gravitational Shieldings (10 GCCs). the electrical conductivity. Thin Metallic laminas are placed after Consequently, the conductivities of the each Air Gravitational Shielding in water and the acrylic remain<< .1 mS −1. order to retain the electric In this way, with E(OH ) and E()acrylic field = xVE , produced by metallic 2 b 0 much smaller than E , and σ <<1, surface behind the semi-spheres. The air ()2OH laminas with semi-spheres stamped on σ ()acrylic <<1 , the decrease in both the its surfaces are connected to the ELF gravitational mass of the acrylic and voltage source V0 and the thin laminas the gravitational mass of water, in front of the Air Gravitational according to Eq.A14, is negligible. Shieldings are grounded. The air This means that only in the air layer inside this Micro-Gravitational the decrease in the gravitational mass Thruster is at 300K, 1atm. will be relevant. We have seen that the insulation Equation A39 gives the electrical layer of a GCC can be made up of conductivity of the air layer, i.e., 1 3 Acrylic, Mica, etc. Now, we will 2 2 1 ⎛Eair⎞ ⎛b⎞ 2 air=2ασ ⎜ ⎟ ⎜ ⎟ = 029.0 V0 ()A46 design a GCC using Water (distilled ⎝ d ⎠ ⎝a⎠ water,ε ()OHr = 80 ) and Aluminum semi- = rb ε 2 Note that 0 (2OHr ). Therefore, here cylinders with radius 0 = 3.1 mmr . Thus, the value of b is larger than in the case for =Δ 6.0 mm , the new value of a of the acrylic. Consequently, the is = 9.1 mma . Then, we get electrical conductivity of the air layer = rb ε ×= 1063.11 −3 Am 43 0 ()2OHr ( ) will be larger here than in the case of abd ×=−= 1073.9 −3m (A44) acrylic. and Substitution of σ ()air , Eair (rms) 1 q and ρ = .2.1 mkg −3 into Eq. A14, gives E = = air air 2 4 ()airr επε 0 b ⎧ ⎡ 5.5 ⎤⎫ m ()airg ⎪ −20V0 ⎪ ⎨ ⎢ −×+−= 11054.4121 ⎥⎬ ()A47 rV 00 3 =ε = m0()airi ⎪ ⎢ f ⎥⎪ r H ⎩ ⎣ ⎦⎭ ()2O ε b2 ()airr max For 00 == 9kVVV and = 2Hzf , the VrV 000 =≅= 1.1111 V0 ()A45 result is ε ()airr r0 m ()airg Note that −≅ 4.8 m 0()airi rV E = 00 ()2OH This shows that, by using water ε ()OHr 2 instead of acrylic, the result is much and better. rV 00 E()acrylic = In order to build the GCC based ε ()acrylicr on the calculations above (See Fig. Therefore, E and E are much (2OH ) (acrylic) A16), take an Acrylic plate with smaller than Eair . Note that for 885mm X 885m and 2mm thickness, ≤ 9kVV E then paste on it an Aluminum sheet 0 the intensities of (2OH )and 41 with 895.2mm X 885mm and 0.5mm frequency is decreased). A precision thickness(note that two edges of the balance is placed below the GCC in Aluminum sheet are bent as shown in order to measure the mentioned mass Figure A16 (b)). Next, take 342 decrease for comparison with the Aluminum yarns with 884mm length values predicted by Eq. A(47). In total, and 2.588mm diameter (wire # 10 this GCC weighs about 6kg; the air AWG) and insert them side by side on layer 7.3grams. The balance has the the Aluminum sheet. See in Fig. A16 following characteristics: range 0-6kg; (b) the detail of fixing of the yarns on readability 0.1g. Also, in order to the Aluminum sheet. Now, paste prove the Gravitational Shielding acrylic strips (with 13.43mm height Effect, we can put a sample (connected and 2mm thickness) around the to a dynamometer) above the GCC in Aluminum/Acrylic, making a box. Put order to check the gravity acceleration distilled water (approximately 1 litter) in this region. inside this box, up to a height of In order to prove the exponential exactly 3.7mm from the edge of the effect produced by the superposition of acrylic base. Afterwards, paste an the Gravitational Shieldings, we can Acrylic lid (889mm X 889mm and 2mm take three similar GCCs and put them thickness) on the box. Note that above one above the other, in such way that the water there is an air layer with above the GCC 1 the gravity 885mm X 885mm and 7.73mm acceleration will be ′=χ gg ; above the thickness (See Fig. A16). This GCC2 ′′ = χ 2 gg , and above the GCC3 thickness plus the acrylic lid thickness ′′′ = χ 3 gg . Where χ is given by Eq. (2mm) is equal to =−= 73.9 mmabd (A47). where = rb ε = 63.11 mm and 0 ()2OHr It is important to note that the ra 0 =Δ+= 99.1 mm , since 0 = 3.1 mmr , intensity of the electric field through ε = 80 =Δ 6.0 mm ()2OHr and . the air below the GCC is much smaller Note that the gravitational action than the intensity of the electric field through the air layer inside the GCC. of the electric field Eair , extends itself only up to the distance d , which, in In addition, the electrical conductivity this GCC, is given by the sum of the of the air below the GCC is much Air layer thickness (7.73mm) plus the smaller than the conductivity of the air thickness of the Acrylic lid (2mm). layer inside the GCC. Consequently, Thus, it is ensured the the decrease of the gravitational mass gravitational effect on the air layer of the air below the GCC, according to while it is practically nullified in the Eq.A14, is negligible. This means that acrylic sheet above the air layer, since the GCC1, GCC2 and GCC3 can be simply overlaid, on the experiment E()acrylic << Eair and σ ()acrylic <<1 . proposed above. However, since it is With this GCC, we can carry out necessary to put samples among them an experiment where the gravitational mass of the air layer is progressively in order to measure the gravity above reduced when the voltage applied to each GCC, we suggest a spacing of the GCC is increased (or when the 30cm or more among them. 42

Dynamometer

50 mm g g ′ = χ gg Sample Aluminum foil Foam Board

GCC

Flexible Copper wire # 12 AWG Pan balance

Battery 12V

4Ω - 40W R ε 2 R Rheostat 2 10Ω - 90W Coupling Transformer

Function Generation Flexible Copper wire HP3325A # 12 AWG

ε 1

R 1 500Ω - 2W Fig. A2 – Experimental Set-up 1.

Flexible Copper Wire # 12 AWG

15 cm square Aluminum foil (10.5 microns thickness)

Gum (Loctite Super Bonder)

17 cm square Foam Board plate (6mm thickness)

Aluminum foil Foam Board

Fig. A3 – The Simplest Gravity Control Cell (GCC). 44

I1 ε 2

+ − ri2 R I 2

GCC ri1

ε R 1 ~ p = 2μHzf Wire # 12 AWG Gravitational Shielding R1

= + III 213 R2

(a)

ε1 = Function Generator HP3325A(Option 002 High Voltage Output)

ri1 ;2 R1 −Ω=Ω< W;2500 ε 2 = rDCV i2 1.0;12 Ω< ()Battery ;

−3 R2 −Ω= ;404 RW p Ω×= ;105.2 Reostat R −Ω≤≤= 90100 W max max max I1 = 56 (); 2 = ;3 3 ≅ 3 ()rmsAIAIrmsmA Transforme Coupling Transforme r to theisolate Function Generator thefrom Battery

• coreAir mm-10 diameter; wire # 12 AWG; N 21 === 42;20 mmlN

I1 ε 2 T

+ − ri2 R I 2

ri1 GCC −5 ε l = 1cml → Rφ 1023.5 Ω×= 1 ~ 0.5 2 h =3mm = 2μHzf d i Wire # 12 AWG e l e Al 200 mm R c 1 t = + III R2 r 213 # 12 AWG i P c (b) 0 VR max ×=⇒= 101.1 −4V Gravitational p Shielding min −5 10 VR p ×=⇒= 100.4 V

Fig. A4 – Equivalent Electric Circuits 45

j ELF electric current Wire

⎧ ⎡ 4 ⎤⎫ ⎪ −27 μr j ⎪ mg ⎨ ⎢ ×+−= 10758.1121 −1⎥⎬mi0 σρ f 32 ⎩⎪ ⎣⎢ ⎦⎥⎭⎪

Fig. A5 – An ELF electric current through a wire, that makes a spherical form as shown above, reduces the gravitational mass of the wire and the gravity inside sphere at the same proportion

χ = mm ig 0 (Gravitational Shielding Effect). Note that this spherical form can be transformed into an ellipsoidal form or a disc in order to coat, for example, a Gravitational Spacecraft. It is also possible to coat with a wire several forms, such as cylinders, cones, cubes, etc. The characteristics of the wire are expressed by: μ r ,σ , ρ ; j is the electric current density and f is the frequency.

Dynamometer

Rigid Aluminum wire 50 mm # 14 AWG

Length = 28.6 m

RS= 0.36 Ω

Flexible Copper wire # 12 AWG

Battery 12V

4Ω - 40W R ε 2 R Rheostat 2 Coupling Transformer

Function Generation HP3325A Flexible Copper wire # 12 AWG

ε 1

R 1 Fig. A6 – Experimental set-up 2.

Gravitational Shielding Air d Eair ,σair b Insulation Δ ε a r

Aluminum Foil

~ V0 , f

Fig A7 – Gravitational shielding produced by semi-spheres stamped on the Aluminum foil - By simply changing the geometry of the surface of the Aluminum foil it is possible to increase the working frequency f up to more than 1Hz.

a =1.5 mm Acrylic sheet

r0 =0.9 mm y Aluminum Plate (a)

Heater (b)

Press

D D y + a

(c)

Δ =0.6 mm a = 1.5 mm r0 =0.9 mm

(d)

Fig A8 – Method to coat the Aluminum semi-spheres with acrylic ()0 =−=Δ 6.0 mmra . (a)Acrylic sheet (A4 format) with 1.5mm thickness and an Aluminum plate (A4) with several semi-spheres (radius 0 = 9.0 mmr ) stamped on its surface. (b)A heater is placed below the Aluminum plate in order to heat the Aluminum. (c)When the Aluminum is sufficiently heated up, the acrylic sheet and the Aluminum plate are pressed, one against the other (The two D devices shown in this figure are used in order to impede that the press compresses the acrylic and the aluminum besides distance y + a ). (d)After some seconds, the press and the heater are removed, and the device is ready to be used. 49

Dynamometer

50 mm g g ′ = χ gg GCC Sample Acrylic/Aluminum

Flexible Copper wire # 12 AWG

High-voltage V0 Rheostat Oscillator Transformer f > 1Hz

Fig. A9 – Experimental Set-up using a GCC subjected to high-voltage V0 with frequency > 1Hzf . Note that in this case, the pan balance is not necessary because the substance of the Gravitational Shielding is an air layer with thickness d above the acrylic sheet. This is therefore, more a type of Gravity Control Cell (GCC) with external gravitational shielding. 50

Gravitational Shielding d R V0

GCC A crylic /Aluminum

max V0 = 9 kV Oscillator min V0 = 7.2 kV ~ > 1Hzf

(a)

Acrylic Pin wire

Aluminum

Connector (High-voltage) (b) 10kV

Fig. A10 – (a) Equivalent Electric Circuit. (b) Details of the electrical connection with the Aluminum plate. Note that others connection modes (by the top of the device) can produce destructible interference on the electric lines of the Eair field.

(a) (b)

Metallic Rings

Metallic base

(c)

Eair

Gravitational Shielding εr

Ellipsoidal metallic base

Metallic Rings Oscillator f

Transformer V Dielectric layer 0 Ionized air (d)

Fig. A11 – Geometrical forms with similar effects as those produced by the semi-spherical form – (a) shows the semi-spherical form stamped on the metallic surface; (b) shows the semi-cylindrical form (an obvious evolution from the semi-spherical form); (c) shows concentric metallic rings stamped on the metallic surface, an evolution from semi-cylindrical form. These geometrical forms produce the same effect as that of the semi-spherical form, shown in Fig.A11 (a). By using concentric metallic rings, it is possible to build Gravitational Shieldings around bodies or spacecrafts with several formats (spheres, ellipsoids, etc); (d) shows a Gravitational Shielding around a Spacecraft with ellipsoidal form.

Dielectric Metal Dielectric Metal (rigidly connected to the spacecraft)

Spacecraft Spacecraft E E

Non-solid Gravitational Shielding Solid Gravitational Shielding (rigidly connected to the dielectric)

(a) (b)

Fig. A12 – Non-solid and Solid Gravitational Shieldings - In the case of the Gravitational Shielding produced on a solid substance (b), when its molecules go to the imaginary space-time, the electric field that produces the effect also goes to the imaginary space-time together with them, because in this case, the substance of the Gravitational Shielding is rigidly connected (by means of the dielectric) to the metal that produces the electric field. This does not occur in the case of Air Gravitational Shielding.

Metal Dielectric Metal Dielectric i ELF electric current A l u Spacecraft E Spacecraft m rs Eair i n u m

Solid Gravitational Shielding Air Gravitational Shielding (a)

Micro-Gravitational Thruster

(b)

Volume V of the Micro-Gravitational Thruster with 10 gravitational shieldings Intergallactic medium (IGM) a Gravitational Spacecraft r mgt Mg M g ρigmV = χ 10Ga = χ 10G r 2 r 2 Gravitational Shielding -26 -3 ρ igm∼10 kg.m

(c)

Fig. A13 – Double Gravitational Shielding and Micro-thrusters – (a) Shows a double gravitational shielding that makes possible to decrease the inertial effects upon the spacecraft when it is traveling both in the imaginary space-time and in the real space-time. The solid Gravitational Shielding also can be obtained by means of an ELF electric current through a metallic lamina placed between the semi-spheres and the Gravitational Shielding of Air as shown above. (b) Shows 6 micro-thrusters placed inside a Gravitational Spacecraft, in order to propel the spacecraft in the directions x, y and z. Note that the Gravitational Thrusters in the spacecraft must have a very small diameter (of the order of millimeters) because the hole through the Gravitational Shielding of the spacecraft cannot be large. Thus, these thrusters are in fact Micro- thrusters. (c) Shows a micro-thruster inside a spacecraft, and in front of a volume V of the intergalactic medium (IGM). Under these conditions, the spacecraft acquires an acceleration a in the direction of the volume V.

Volume V of the Micro-Gravitational Thruster with 10 gravitational shieldings Interstellar medium (ISM)

Gravitational Spacecraft a r Mg M ρ V = χ 10Ga g = χ 10G ism r 2 r 2 Gravitational Shielding -21 -3 ρ ism∼10 kg.m

(a)

Volume V of the Interplanetary Micro-Gravitational Thruster with 10 gravitational shieldings medium (IPM)

a Gravitational Spacecraft r Mg 10 M g 10 ρipmV = χ Ga 2 = χ G 2 Gravitational Shielding r r -20 -3 ρ ipm∼10 kg.m

(b)

Volume V of the Earth’s Micro-Gravitational Thruster with 10 gravitational shieldings atmospheric

a Gravitational Spacecraft r Mg M ρ V = χ 10Ga g = χ 10G atm Gravitational Shielding r 2 r 2

-3 ρ atm∼1.2kg.m (c) Fig. A14 – Gravitational Propulsion using Micro-Gravitational Thruster – (a) Gravitational acceleration produced by a gravitational mass Mg of the Interstellar Medium. The density of the Interstellar Medium is about 105 times greater than the density of the Intergalactic Medium (b) Gravitational acceleration produced in the Interplanetary Medium. (c) Gravitational acceleration produced in the Earth’s atmosphere. Note that, in this case, ρatm (near to the Earth’s surface)is about 26 10 times greater than the density of the Intergalactic Medium.

F’ 2 2 F r 0 F2 =χair F0 F’2=χair F’0 0 r F1 =χairF0 F’1 =χairF’0 Mg Mg S2 S 1 F’0 = F0 => R = (F’0 – F2) + (F1 – F’1 ) + (F’2 – F0) = 0

(a)

Micro-Gravitational Thruster with 10 gravitational shieldings Gravitational Shielding

r’ χ −≅ 10−8 r s a’0 2 10 2 a’0 =χs(-GMg /r’ ) a10=χair a0 a0 = - GMg/r Mg Mg 10 10 =≅ χ air FFR 0 Hole in the Gravitational Shielding

Metal Mica (b) Grounded Metallic laminas 1 GCC Air Gravitational Shielding x

10mm

ELF ~

V0 ~ 400 mm

(c) Fig. A15 – Dynamics and Structure of the Micro-Gravitational Thrusters - (a) The Micro- Gravitational Thrusters do not work outside the Gravitational Shielding, because, in this case, the resultant −8 upon the thruster is null due to the symmetry. (b) The Gravitational Shielding (χ s ≅ 10 ) reduces strongly the intensities of the gravitational forces acting on the micro-gravitational thruster, except obviously, through the hole in the gravitational shielding. (c) Micro-Gravitational Thruster with 10 Air Gravitational Shieldings (10GCCs). The grounded metallic laminas are placed so as to retain the electric field produced by metallic surface behind the semi-spheres. 56

0.885 m Sample Acrylic Box Any type of material; any mass (2mm thickness) g’= χ g 2 mm d = 9.73 mm Air layer mg (air) = χ mi (air) 7.73 mm a = 1.9 mm 3.2 mm Distilled Water 1.8 mm 2 mm Aluminum sheet max (0.5 mm thickness) V0 = 9 kV 342 Aluminum yarns (# 10 AWG) Balance (2.558 mm diameter; 0.884 mm length) ~ 2 Hz

Transformer g

GCC Cross-section Front view (a)

0.885 m

0.884 m 1mm 1mm

Aluminum sheet (0.5 mm thickness) Balance 342 Aluminum yarns (# 10 AWG) 1.5mm (2.558 mm diameter; 0.884 mm length) 0.5 mm 3.6mm

0.885 m

GCC Cross-section Side View (b)

Fig. A16 – A GCC using distilled Water. In total this GCC weighs about 6kg; the air layer 7.3 grams. The balance has the following characteristics: Range 0 – 6kg; readability 0.1g. The yarns are inserted side by side on the Aluminum sheet. Note the detail of fixing of the yarns on the Aluminum sheet.

140 cm

70 cm Sample 5Kg mg Any type of material; any mass

′′′ = χ 3gg GCC 3 Balance

70 cm 5Kg mg

′′ = χ 2 gg GCC 2 Balance

70 cm 5Kg mg

′ = χ gg GCC 1 Balance

Fig. A17 – Experimental set-up. In order to prove the exponential effect produced by the superposition of the Gravitational Shieldings, we can take three similar GCCs and put them one above the other, in such way that above the GCC 1 the gravity acceleration will be ′=χ gg ; above the GCC2 ′′ = χ 2 gg , and above the GCC3 ′′′ = χ 3gg . Where χ is given by Eq. (A47). The arrangement above has been designed for values of g <13gm and χ up to -9 or g <1kgm and χ up to -2 .

58 APPENDIX B: Gravity Control Cells (GCCs) made from Semiconductor Compounds.

There are some semiconductors BACKGROUND FOR EXPERIMENTAL compounds with electrical conductivity TM between 104S/m to 1 S/m, which can The Duracap 86103 is sold have their gravitational mass strongly under the form of small cubes. Its decreased when subjected to ELF melting temperature varies from 177ºC electromagnetic fields. to 188ºC. Thus, a 15cm square Duracap For instance, the polyvinyl plate with 1 mm thickness can be shaped chloride (PVC) compound, called by using a suitable mold, as the shown DuracapTM 86103. in Fig.B1. It has the following characteristics: Figure B2(a) shows the Duracap plate between the Aluminum plates of a parallel plate capacitor. The plates have μr =1; εr =3 the following dimensions: 19cm X 15cm σ = /3.3333 mS −3 X 1mm. They are painted with an ρ =1400 m.kg insulating varnish spray of high dieletric strength = /98 mmKV dielectric strength (ISOFILM). They are connected to the secondary of a Then, according to the following transformer, which is connected to a equation below (derived from Eq.A14) Function Generator. The distance ⎧ ⎡ ⎛ 3 ⎞ ⎤⎫ ⎪ ⎢ −27⎜ rσμ ⎟ 4 ⎥⎪ between the Aluminum plates is =1mmd . mg ⎨ ×+−= 10758.1121 − ⎬ irms 0 ()BmE 11 ⎢ ⎜ρ f 32 ⎟ ⎥ Thus, the electric field through the ⎪ ⎣ ⎝ ⎠ ⎦⎪ ⎩ ⎭ Duracap is given by the gravitational mass, mg , of the m VE 0 TM Erms == ()B3 Duracap 86103, when subjected to an ε r d 22 electromagnetic field of frequency f , is where ε r is the relative permittivity of given by the dielectric (Duracap), and V0 is the ⎧ ⎡ 4 ⎤⎫ ⎪ −23 Erms ⎪ amplitude of the wave voltage applied mg ⎨ ⎢ ×+−= 103.3121 −1⎥⎬ i0 ()Bm 2 ⎢ f 3 ⎥ on the capacitor. ⎩⎪ ⎣ ⎦⎭⎪ In order to generate ELF wave Note that, if the electromagnetic field voltage of = 2Hzf , we can use the through the Duracap has extremely-low widely-known Function Generator frequency, for example, if = 2Hzf , and HP3325A (Op.002 High Voltage

Output) that can generate sinusoidal E ×= 5 mV ()/94.0/104.9 mmkV rms voltages with extremely-low frequencies

and amplitude up to 20V (40Vpp into Then, its gravitational mass will be 500Ω load). The maximum output reduced down to g −≅ 1.1 mm i0 , reducing current is 080 A. pp ; output impedance in this way, the initial weight <2Ω at ELF. ( 0 == ig 0 gmgmP ) of the Duracap down to The turns ratio of the transformer − 1.1 P0 . (Bosch red coil) is 1:200 . Thus, since the 59 maximum value of the amplitude of the body inside the spacecraft (Eq.(10)). voltage produced by the Function This body can be, for example, the max Generator is V p = 20 V , then the dielectric between the plates of a maximum secondary voltage will capacitor, whose gravitational mass can max max be easily controlled by means of an ELF be == 4kVVV .Consequently, Eq. s 0 electromagnetic field produced between (B3) gives max 6 the plates of the capacitor. We will call Erms ×= /108.2 mV this type of capacitor of Capacitor of Thus, for = 2Hzf , Eq. (B2) gives Gravitational Mass Control (CGMC). mg −= 5.29 mi0 Figure B 4(a) shows a CGMC The variations on the placed in the center of the spacecraft. gravitational mass of the Duracap plate Thus, the gravitational mass of the can be measured by a pan balance with spacecraft can be controlled simply by the following characteristics: range 0 − varying the gravitational mass of the 1.5kg ; readability 0.01g, using the set- dielectric of the capacitor by means of up shown in Fig. B2(a). an ELF electromagnetic field produced Figure B2(b) shows the set-up to between the plates of the capacitor. Note measure the gravity acceleration that the Capacitor of Gravitational Mass variations above the Duracap plate Control can have the spacecraft's own (Gravitational Shielding effect). The form as shown in Fig. B 4(b). The samples used in this case, can be of dielectric can be, for example, a several types of material. Duracap plate, as shown in this Since voltage waves with appendix. In this case, the gravitational frequencies very below 1Hz have a very mass of the dielectric is expressed by long period, we cannot consider, in Eq. (B2). Under these circumstances, practice, their rms values. However, we the total gravitational mass of the can add a sinusoidal voltage spacecraft will be given by Eq.(10):

osc = 0 sin ωtVV with a DC voltage VDC , by means of the circuit shown in Fig.B3. M ()spacecrafg M i0 += χ dielectric mi0

Thus, we obtain DC += 0 sinωtVVV ;ω = 2πf .

If 0 << VV DC then ≅ VV DC . Thus, the where M i0 is the rest inertial mass of voltage V varies with the frequency f , the spacecraft(without the dielectric) and but its intensity is approximately equal mi0 is the rest inertial mass of the to VDC , i.e., V will be practically dielectric; χ dielectric = mm ig 0 , where mg is constant. This is of fundamental the gravitational mass of the dielectric. importance for maintaining the value of By decreasing the value of χ dielectric , the the gravitational mass of the body, mg , gravitational mass of the spacecraft sufficiently stable during all the time, in decreases. It was shown, that the value the case of f << Hz . of χ can be negative. Thus, for example,

We have shown in this paper that when χdielectric ≅ − mM ii 00 , the gravitational it is possible to control the gravitational mass of the spacecraft gets very close to mass of a spacecraft, simply by zero. When χdielectric −< mM ii 00 , the controlling the gravitational mass of a 60 gravitational mass of the spacecraft spacecraft can be reduced just down becomes negative. to 159.0 g . In addition, since the Mach’s Therefore, for an observer out of principle says that the local inertial the spacecraft the gravitational mass of forces are produced by the gravitational the spacecraft is M ()spacecrafg Mi0 += χ midielectric 0 , interaction of the local system with the and not + mM ii 00 . distribution of cosmic masses then the Since the dielectric strength of the inertial effects upon the crew would be Duracap is /98 mmkV , a Duracap plate reduced just by χ dielectric = 159.0 . with 1mm thickness can withstand up to However, there is a way to

98kV . In this case, the value of χ dielectric strongly reduce the inertial effects upon for = 2Hzf , according to Eq. (B2), is the crew of the spacecraft without making it imaginary. As shown in Fig. χ mm −≅= 104 dielectric ig 0 B4 (c), we can build an inertial Thus, for example, if the inertial mass of shielding, with n superimposed the spacecraft is M i0 ≅ 0014.10021 kg and, CGMCs. In this case, according to the the inertial mass of the dielectric of the Gravitational Shielding Principle, the Capacitor of Gravitational Mass Control is gravity upon the crew will be given by mi0 ≅ 0021.1 kg , then the gravitational n g n = χ dielectric g , where g is the gravity mass of the spacecraft becomes acceleration out of the spacecraft (in a M M += χ m ≅ 10−3 kg ()spacecrafg i0 dielectric i0 given direction) and χdielectric= mm ig 0 ; mg This value is much smaller than and mi0 are, respectively, the + 159.0 M i0 . gravitational mass and the inertial mass It was shown [1] that, when the of the dielectric. Under these conditions gravitational mass of a particle is the inertial effects upon the crew will be reduced to values between + 1590 M n . i reduced by χ dielectric . and − .1590 Mi , it becomes imaginary, i.e., Thus, for n =10 (ten superimposed the gravitational and the inertial masses CGMCs), and χ dielectric ≅ 2.0 , the inertial of the particle become imaginary. effects upon the crew will be reduced Consequently, the particle disappears 10 −7 by χ dielectric ×≅ 101 . Therefore, if the from our ordinary space-time. maximum thrust produced by the This means that we cannot reduce thrusters of the spacecraft is =105 NF , the gravitational mass of the spacecraft then the intensities of the inertial forces + 1590 M below . i , unless we want to upon the crew will not exceed 01.0 N , make it imaginary. i.e. they will be practically negligible. Obviously this limits the Under these circumstances, the minimum value of χ dielectric , i.e. gravitational mass of the spacecraft, for min χ dielctric = 159.0 . Consequently, if the an observer out of the spacecraft, will be gravity acceleration out of the spacecraft just approximately equal to the (in a given direction) is g , then, gravitational mass of the inertial according to the Gravitational Shielding shielding, i.e. M g()(spacecraft ≅ M inertialg .shield ). 3 Principle, the corresponding gravity If M ()inertialg .shield ≅ 10 kg , and the acceleration upon the crew of the thrusters of the spacecraft are able to 61 produces up to F ×= 103 5 N , the KV/mm; maximum working spacecraft will acquires an acceleration temperature of 1600°C. given by Another material is the Alumina- §§§§ F −22 CNT, recently discovered . It has aspacecraft = ×≅ .103 sm M g()spacecraft electrical conductivity of 3375 S/m at With this acceleration it can reach 77°C in samples that were 15% velocities close to Mach 10 in some nanotubes by volume [17]; ε r = 8.9 ; seconds. ρ = .3980 mkg −3 ; dielectric strength 10- The velocity that the spacecraft 20KV/mm; maximum working can reach in the imaginary spacetime is temperature of 1750°C. much greater than this value, since

M g(spacecraft), as we have seen, can be reduced down to ≅ 10 −3 kg or less. Thus, if the thrusters of the spacecraft are able to produces up 5 −3 to F ×= 103 N , and M g()spacecraft ≅ 10 kg , the spacecraft will acquires an acceleration given by F −28 aspacecraft = ×≅ .103 sm M g()spacecraft The novel Carbon Nanotubes With this acceleration it can reach ***** Aerogels , called CNT Aerogels are velocities close to the light speed in less also suitable to produce Gravitational than 1 second. After 1 month, the Shieldings, mainly due to their very velocity of the spacecraft would be 15 small densities. The electrical about /10 sm (remember that in the conductivity of the CNT Aerogels is imaginary spacetime the maximum 70.4S/m for a density of ρ = .5.7 mkg −3 [18]; velocity of propagation of the ε ≈10. Recently (2010), it was announced interactions is infinity [1]). r the discovered of Graphene Aerogel OTHER SEMICONDUCTOR COMPOUNDS with σ ×= 2 /101~ mS and ρ = .10 mkg −3 [19] (Aerogels exhibit higher dielectric A semiconductor compound, strength than expected for porous which can have its gravitational mass materials). strongly decreased when subjected to ELF electromagnetic fields is the §§§§ Recently, it was discovered that Carbon nanotubes CoorsTek Pure SiCTM LR CVD Silicon (CNTs) can be added to Alumina (Al2O3) to convert it ‡‡‡‡ into a good electrical conductor. Carbide, 99.9995% . This Low- ***** In 2007, Mateusz Brying et al. working with Prof. resistivity (LR) pure Silicon Carbide has Arjun Yodh at the University of Pennsylvania produced the first aerogels made entirely of carbon nanotubes electrical conductivity of 5000S/m at (CNT Aerogels) [20] that, depending on the processing room temperature; ε r = 8.10 ; conditions, can have their electrical conductivity ranging −3 as high as 100 S/m. ρ = .3210 mkg ; dielectric strength >10

‡‡‡‡ www.coorstek.com

Aluminum

2mm

150mm

3mm 150mm

200mm 5mm 150mm

3mm 200mm 150mm

Aluminum

Fig.B1 – Mold design

Aluminum 190mmX150mmX1mm Duracap 150mmX150mmX1mm Acrylic 1kg 150mmX40mmX1mm Wood

Bosch 20 mm ELF Wave Voltage red 20 mm Balance Generator coil 20 mm (a)

Sample

1kg

Bosch ELF Wave Voltage red Balance Generator coil

(b)

Fig.B2 – Schematic diagram of the experimental set-up 64

− V + DC

ELF voltage DC + VV osc w aves V >> V Generato r DC 0 V 200:1 osc ~ V = sin ωtVV f osc osc 0

Bosch red coil Coupling Transformer

Fig. B3 – Equivalent Electric Circuit

Capacitor of Gravitational Mass Control

Gravitational Thrusters

y x

col 1 col 2

(a)

Capacitor of Gravitational Mass Control dielectric (CGMC)

(b)

n dielectrics n 3 2 1

n g n = χ dielectric g g

Inertial Shielding (c) Fig.B4 – Gravitational Propulsion System and Inertial Shielding of the Gravitational Spacecraft – (a) eight gravitational thrusters are placed inside a Gravitational Spacecraft, in order to propel the spacecraft along the directions x, y and z. Two gravitational thrusters are inside the columns 1 and 2, in order to rotate the spacecraft around the y-axis. The functioning of the Gravitational Thrusters is shown in Fig.A14. The gravitational mass of the spacecraft is controlled by the Capacitor of Gravitational Mass Control (CGMC). Note that the CGMC can have the spacecraft's own form, as shown in (b). In order to strongly reduce the inertial effects upon the crew of the spacecraft, we can build an inertial shielding, with several CGMCs, as shown above (c). In this case, the gravity upon the crew will be n given by g n = χ dielectric g , where g is the gravity acceleration out of the spacecraft (in a given direction) and χ dielectric = mm ig 0 ; mg and mi0 are, respectively, the gravitational mass and the inertial mass of n the dielectric. Under these conditions the inertial effects upon the crew will be reduced by χ dielectric . Thus, for example, if n =10 and χ dielectric ≅ 2.0 , the inertial effects will be reduced 10 −7 5 by χ dielectric ×≅ 101 . If the maximum thrust produced by the thrusters is =10 NF , then the intensities of the inertial forces upon the crew will not exceed 01.0 N .

66 APPENDIX C: Longer-Duration Microgravity Environment Produced by Gravity Control Cells (GCCs).

The acceleration experienced by deep vertical mine shaft in Japan that an object in a microgravity has been converted to a drop facility. environment, by definition, is one- Drop towers are used for millionth (10-6) of that experienced at experiments that only need a short Earth’s surface (1g). Consequently, a duration of microgravity, or for an microgravity environment is one initial validation for experiments that where the acceleration induced by will be carried out in longer duration gravity has little or no measurable of microgravity. effect. The term zero-gravity is, obviously inappropriate since the quantization of gravity [1] shows that the gravity can have only discrete values different of zero [1, Appendix B]. Only three methods of creating a microgravity environment are currently known: to travel far enough into deep space so as to reduce the effect of gravity by attenuation, by falling, and by orbiting a planet. The first method is the simplest in conception, but requires traveling an Aircraft can fly in parabolic arcs enormous distance, rendering it most to achieve period of microgravity of impractical with the conventional 20 to 25 seconds with g-level of spacecrafts. The second method, approximately 0.02 g. The airplane falling, is very common but climbs rapidly until its nose is about approaches microgravity only when 45-degree angle to the horizon then the the fall is in a vacuum, as air resistance engines are cut back. The airplane will provide some resistance to free slows; the plane remains in free fall fall acceleration. Also it is difficult to over the top of the parabola, then it fall for long enough periods of time. nose-dives to complete the parabola, There are also problems which involve creating microgravity conditions. avoiding too sudden of a stop at the Aircraft parabolic flights give end. The NASA Lewis Research the opportunity to perform medical Center has several drop facilities. One experiments on human subjects in real provides a 132 meter drop into a hole microgravity environment. They also in the ground similar to a mine shaft. offer the possibility of direct This drop creates a reduced gravity intervention by investigators on board environment for 5.2 seconds. The the aircraft during and between longest drop time currently available parabolas. In the mid-1980s, NASA (about 10 seconds) is at a 490 meter KC-135, a modified Boeing 707,

67 provided access to microgravity and potential loss of data. environment. A parabolic flight Unmanned capsules, platforms or provided 15 to 20 seconds of 0.01 g or satellites, such as the European less, followed by a 2-g pull out. On a retrievable carrier Eureka, DLR's typical flight, up to 40 parabolic retrievable carrier SPAS, or the trajectories can be performed. The Russian Photon capsules, the US KC-135 can accommodate up to 21 Space Shuttle (in connection with the passengers performing 12 different European Spacelab laboratory or the experiments. In 1993, the Falcon-20 US Spacelab module), provide weeks performed its first parabolic flight with or months of microgravity. microgravity experiment on board. A space station, maintaining a This jet can carry two experimenters low earth orbit for several decades, and perform up to 3 experiments. Each greatly improves access to flight can make up to 4 parabolic microgravity environment for up to trajectories, with each parabola lasting several months. 75 seconds, with 15 to 20 seconds of Thus, microgravity environment microgravity at 0.01g or less. can be obtained via different means, providing different duration of microgravity. While short-duration microgravity environments can be achieved on Earth with relative easiness, longer-duration microgravity environments are too expensive to be obtained. Here, we propose to use the Gravity Control Cells (GCCs), shown in this The third method of creating a work, in order to create longer- microgravity environment is orbiting a duration microgravity environments. planet. This is the environment As we have seen, just above a GCC commonly experienced in the space the gravity can be strongly reduced shuttle, International Space Station, (down to 1μg or less). In this way, the Mir (no longer in orbit), etc. While this gravity above a GCC can remain at the scenario is the most suitable for >>1m scientific experimentation and >>1m commercial exploitation, it is still quite expensive to operate in, mostly longer-duration microgravity due to launch costs. environment ~1 μ g up to 3m A space shuttle provides an ideal laboratory environment to conduct microgravity research. A large panoply GCC of experiments can be carried out in microgravity conditions for up to 17 days, and scientists can make 1 g adjustment to avoid experiment failure

68 promise to develop new materials microgravity ranging during a very which can not be made on Earth due to long time (several years). Thus, GCCs gravity. These new materials shall can be used in order to create longer- have properties that are superior to duration microgravity environments on those made on Earth and may be used Earth. In addition, due to the cost of to: the GCCs to be relatively low, also the -increase the speed of future longer-duration microgravity computers, environments will be produced with -improve fiber optics, low costs. -make feasible Room Temperature This possibility appears to be Superconductors, absolutely new and unprecedented in -enable medical breakthroughs to cure the literature since longer-duration several diseases (e.g., diabetes). microgravity environments are usually In a microgravity environment obtained via airplanes, sounding protein crystals can be grown larger rockets, spacecraft and space station. and with a purity that is impossible to It is easy to see that the GCCs obtain under gravity of 1g. By can be built with width and length of analyzing the space-grown crystals it until some meters. On the other hand, is possible to determine the structure as the effect of gravity reduction above and function of the thousands of the GCC can reach up to 3m, we can proteins used in the human body and then conclude that the longer-duration in valuable plants and animals. The microgravity environments produced determination of protein structure above the GCCs can have sufficiently represents a huge opportunity for large volumes to perform any pharmaceutical companies to develop microgravity experiment on Earth. new drugs to fight diseases. The longer-duration microgravity Crystal of HIV protease environment produced by a GCC will inhibitor grown in microgravity are be a special tool for microgravity significantly larger and of higher research. It will allow to improve and quality than any specimens grown to optimize physical, chemical and under gravity of 1g. This will help in biological processes on Earth that are defining the structure of the protein important in science, engineering and crucial in fighting the AIDS virus. also medicine. The reduction of Protein Crystal Isocitrate Lysase gravitational effects in a microgravity is an enzyme for fungicides. The environment shows, for example, that isocitrate lysase crystals grown in temperature differences in a fluid do microgravity environments are of not produce convection, buoyancy or larger sizes and fewer structural sedimentation. The changes in fluid defects than crystals grown under behavior in microgravity lie at the gravity of 1g. They will lead to more heart of the studies in materials powerful fungicides to treat serious science, combustion and many aspects crop diseases such as rice blast, and of space biology and life sciences. increase crop output. Microgravity research holds the 69 Improved crystals of human purity fiber optics, optical switches insulin will help improve treatment for for computing, telecommunications, diabetes and potentially create a cure. medical surgery and cauterization, Anchorage dependent cells temperature monitoring, infrared attached to a polymer and grown in a imaging, fiber-optic lasers, and optical bioreactor in microgravity will lead to power transmission. A ZBLAN fiber the production of a protein that is optic cable manufactured in a closer in structure and function to the microgravity environment has the three-dimensional protein living in the potential to carry 100 times the body. amount of data conveyed by conventional silica-based fibers. In microgravity environment where complications of gravity-driven convection flows are eliminated, we can explore the fundamental processes in fluids of several types more easily and test fundamental theories of three- dimensional laminar, oscillatory and turbulent flow generated by various other forces. This should help reduce or By improving the basics for eliminate transplant rejection and is predicting and controlling the behavior therefore critical for organ transplant of fluids, we open up possibilities for and for the replacement of damaged improving a whole range of industrial bone and tissues. Cells grown on Earth processes: are far from being three-dimensional due to the effect of 1g gravity. -aCivil engineers can design safe The ZBLAN is a new substance buildings in earthquake-prone areas with the potential to revolutionize fiber thanks to a better understanding of the optics communications. A member of fluid-like behavior of soils under the heavy metal fluoride family of stress. glasses, ZBLAN has promising applications in fiber optics. It can be - Materials engineers can benefit from used in a large array of industries, a deeper knowledge of the including manufacture of ultra high determination of the structure and properties of a solid metal during its formation and can improve product quality and yield, and, in some cases, lead to the introduction of new products.

- Architects and engineers can design more stable and performing power 70 plants with the knowledge of the flow appears to have unique radiation characteristics of vapor-liquid mixture. shielding capabilities, including an ability to block alpha, beta, gamma - Combustion scientists can improve rays). Terrafoam can be constructed to fire safety and fuel efficiency with the be extremely lightweight. Altering the knowledge of fluid flow in manufacturing process and the microgravity. inclusion of other materials can vary In microgravity environment, the properties of Terrafoam. Properties medical researchers can observe the such as cell structure, tensile strength, functional changes in cells when the bulk density and temperature effect of gravity is practically resistance can be varied to suit specific removed. It becomes possible to study applications. It self-welds to concrete, fundamental life processes down to the aluminum and other metals. The useful cellular level. variations on the base product are Access to microgravity will potentially in the thousands. Perhaps provide better opportunities for the most exciting potential research, offer repeated testing applications for Terrafoam stem from procedures, and enormously improve its extraordinary capability as an ultra- the test facilities available for life lightweight thermal and radioactive sciences investigations. This will shield. provide valuable information for Also, the formation of medical research and lead to nanoscale carbon structures by improvements in the health and electrical arc discharge plasma welfare of the six billion people, which synthesis has already been investigated live under the influence of 1g gravity in microgravity experiments by on the Earth's surface. NASA. Furthermore, complex The utilization of microgravity plasmas are relevant for processes in to develop new and innovative which a particle formation is to be materials, pharmaceuticals and other prevented, if possible, as, for example, products is waiting to be explored. within plasma etching processes for Access to microgravity environments microchip production. currently is limited. Better access, as the produced by GCCs, will help researchers accelerate the experimentation into these new products. Terrafoam is a rigid, silicate based inorganic foam. It is nonflammable and does not five off People will benefit from noxious fumes when in the presence of numerous microgravity experiments fire. It does not conduct heat to any that can be conducted in Longer- measurable degree and thus is an Duration Microgravity Environment outstanding and possible unsurpassed Produced by Gravity Control Cells thermal insulator. In addition, it (GCCs) on Earth. 71

APPENDIX D: Antenna with Gravitational Transducer for Instantaneous Communications at any distance

It was previously shown in this is decreased down to the range of article that Quantum Gravitational + 159.0 miS to − 159.0 miS . By analogy, it Antennas (GCC antennas, Fig.8) can becomes imaginary and goes to the emit and detect virtual gravitational imaginary Universe. It is easy to show radiation. The velocity of this radiation that, in these circumstances, also a is infinite, as we have seen. This means body inside the shielding S becomes that these quantum antennas can imaginary and goes to the imaginary transmit and receive communications Universe together with the gravitational instantaneously to and from anywhere shielding S . In order to prove it, in the Universe. Here, it is shown how consider, for example, Fig.D1 where to transmit and receive we clearly see that the Gravitational communications instantaneously from Shielding Effect is equivalent to a any distance in the Universe by decrease of χ = mm iSgS in the utilizing virtual electromagnetic (EM) gravitational masses of the bodies A radiation instead of virtual and B , since the initial gravitational gravitational radiation. Starting from masses: ≅ mm and ≅ mm become the principle that the antennas of usual gA iA gB iB = χmm = χmm transceivers (real antennas) radiate real respectively gA iA and gB iB , EM radiation, then we can expect that when the gravitational shielding is imaginary antennas radiate imaginary activated. Thus, when χ becomes less EM radiation or virtual EM radiation. than + 159.0 , both the gravitational The velocity of this radiation is also masses of S and A become infinite, in such a way that respectively: it can transmit communications instantaneously from any distance in mgS < + 159.0 miS the Universe. and It was shown [1] that when the mgA < + 159.0 miA gravitational mass of a body is decreased down to the range of This proves, therefore, that when a + 159.0 m to − 159.0 m (m is its inertial i i i Gravitational Shielding S becomes mass), the body becomes imaginary imaginary, any particle (including and goes to an imaginary Universe photons‡‡‡‡‡) inside S , also becomes which contains our real Universe. imaginary and goes to the imaginary Thus, we have the method to convert ‡‡‡‡‡ real antennas to imaginary antennas. As shown in the article “Mathematical Now, consider a Gravitational Foundations of the Relativistic Theory of Quantum Shielding S , whose gravitational mass Gravity”, real photons become imaginary photons or virtual photons.

72 antenna becomes imaginary, and, m m A Gg gB −≅−= G iB together with S , it goes to the BA r 2 r 2 imaginary Universe. In these r m m circumstances, the real photons Gg gA G iA AB 2 −≅−= 2 radiated from the antenna also become B r r imaginary photons or virtual photons. Since the velocity of these photons is (a) infinite, they can reach instantaneously the receiving antenna, if it is also an

imaginary antenna in the imaginary mgB χ m Universe. Gg −=−= G iB BA r 2 r 2 Therefore, we can say that the S Gravitational Shielding around the m χ m χ = mm χ <1, gA iA antenna works as a Gravitational iSgS AB Gg −=−= G r2 r2 Transducer ****** converting real EM

energy into virtual EM energy. (b) In practice, we can encapsulate antennas of transceivers with Aluminum cylinders, as shown in S Fig.D2(a). By applying an appropriate mgS +< 159.0 miS ELF electric current through the Al

Virtual photon cylinders, in order to put the A mgA +< 159.0 miA gravitational masses of the cylinders

within the range of + 159.0 miCyl to − 159.0 m , we can transform real (c) iCyl antennas into imaginary antennas, Fig.D1 – (a) (b) The Gravitational Shielding making possible instantaneously

Effect is equivalent to a decrease of χ = mm iSgS communications at any distance, in the gravitational masses of the bodies A including astronomical distances. and B . (c) When a Gravitational Shielding S Figure D2 (b) shows usual becomes imaginary, any particle (including transceivers operating with imaginary photons) inside S , also becomes imaginary. antennas, i.e., real antennas turned into imaginary antennas. It is important to Universe together with the §§§§§ note that the communications between Gravitational Shielding S . them occur through the imaginary Now, consider a transceiver space-time. At the end of antenna inside a Gravitational transmissions, when the Gravitational Shielding S . When the gravitational Transducers are turned off, the mass of S , m , is reduced down to the gS antennas reappear in the real space- range of + 159.0 miS to − 159.0 miS , the time, i.e., they become real antennas again. §§§§§ Similarly, the bodies inside a Gravitational Spacecraft become also imaginaries when the ****** A Transducer is substance or device that converts Gravitational Spacecraft becomes imaginary. input energy of one form into output energy of another. 73 Imagine now cell phones using to put the transceiver totally inside a antennas with gravitational transducers. Gravitational Shielding. Then, consider There will not be any more need of cell a transceiver X inside the gravitational phone signal transmission stations shielding of a Gravitational Spacecraft. because the reach of the virtual EM When the spacecraft becomes radiation is infinite (without imaginary, so does the transceiver X . scattering). The new cell phones will Imagine then, another real transceiver transmit and receive communications Y with imaginary antenna. With their directly to and from one another. In antennas in the imaginary space-time, addition, since the virtual EM radiation both transceivers X and Y are able to does not interact with matter, then there transmit and receive communications will not be any biological effects, as it instantaneously between them, by happens in the case of usual cell means of virtual EM radiation (See phones. Fig. D3(a)). Figure D3(b) shows another possibility: instantaneous Aluminum cylinder Antenna communications between two transceivers at virtual state.

Imaginary Space-time ~ ELF electric current

(a) Virtual photons

v → ∞ Imaginary antennas + Imaginary transducers Virtual Transceiver X

Real Transceiver Y Virtual photons v → ∞ (a)

Real Transceiver 1

Imaginary Space-time

Real Space-time Real Transceiver 2 Virtual photons

(b) v → ∞ Fig. D2 – (a) Antenna with Gravitational Transducer. (b) Transceivers operating with imaginary antennas (instantaneous Virtual Transceivers communications at any distance, including astronomical distances). (b) Let us now consider the case Fig. D3 – (a) Instantaneous communications where a transceiver is totally turned between the real Universe and the imaginary into imaginary (Fig.D3). In order to Universe.(b) Instantaneous communications convert real antennas into imaginary between two Virtual Transceivers in the antennas, we have used the imaginary Universe. gravitational shielding effect, as we have already seen. Now, it is necessary 74 References

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