1. Introduction Generating electromagnetic radiation at extremely-low frequencies is difficult because the long wavelengths require long antennas, extending for hundreds of kilometers. Natural ionospheric currents provide such an antenna if they can be modulated at the desired frequency [1-6]. The generation of ELF electromagnetic radiation by modulated heating of the ionosphere has been the subject matter of numerous papers [7-13]. In 1974, it was shown that ionospheric heater can generate ELF waves by heating the ionosphere with high-frequency (HF) radiation in the megahertz range [7]. This heating modulates the electron’s temperature in the D region ionosphere, leading to modulated conductivity and a time-varying current, which then radiates at the modulation frequency. Several HF ionospheric heaters have been built in the course of the latest decades in order to study the ELF waves produced by the heating of the ionosphere with HF radiation. Currently, the HAARP heater is the most powerful ionospheric heater, with 3.6GW of effective power using HF heating beam, modulated at ELF (2.5Hz) [14, 15]. This paper shows that high-power ELF
radiation generated by modulated HF heating of the lower ionosphere, such as that produced by the current HAARP heater, can cause Earthquakes, Cyclones and strong localized heating. 2. Gravitational Shielding The contemporary greatest challenge of the Theoretical Physics was to prove that, Gravity is a quantum phenomenon. Since General Relativity describes gravity as related to the curvature of space-time then, the quantization of the gravity implies the quantization of the proper space-time. Until the end of the century XX, several attempts to quantize gravity were made. However, all of them resulted fruitless [16, 17]. In the beginning of this century, it was clearly noticed that there was something unsatisfactory about the whole notion of quantization and that the quantization process had many ambiguities. Then, a new approach has been proposed starting from the generalization of the action function * . The result has been the derivation of a theoretical background, which finally led to the sosought quantization of the gravity and of the
*
The formulation of the action in Classical Mechanics extends to Quantum Mechanics and has been the basis for the development of the Strings Theory.
2 space-time. Published with the title “Mathematical Foundations of the Relativistic Theory of Quantum Gravity”[18], this theory predicts a consistent unification of Gravity with Electromagnetism. It shows that the strong equivalence principle is reaffirmed and, consequently, Einstein’s equations are preserved. In fact, Einstein’s equations can be deduced directly from the mentioned theory. This shows, therefore, that the General Relativity is a particularization of this new theory, just as Newton’s theory is a particular case of the General Relativity. Besides, it was deduced from the new theory an important correlation between the gravitational mass and the inertial mass, which shows that the gravitational mass of a particle can be decreased and even made negative, independently of its inertial mass, i.e., while the gravitational mass is progressively reduced, the inertial mass does not vary. This is highly relevant because it means that the weight of a body can also be reduced and even inverted in certain circumstances, since Newton’s gravity law defines the weight P of a body as the product of its gravitational mass m g by the local gravity acceleration g , i.e.,
P = mg g
equivalent but correlated by means of the following factor [18]:
2 ⎧ ⎡ ⎤⎫ ⎛ Δp ⎞ ⎪ ⎥⎪ = ⎨1 − 2⎢ 1 + ⎜ ⎜ m c ⎟ − 1⎥⎬ ⎟ ⎢ mi 0 ⎪ ⎝ i0 ⎠ ⎣ ⎦⎪ ⎩ ⎭
mg
(3)
Where mi 0 is the rest inertial mass and Δp is the variation in the particle’s kinetic momentum; c is the speed of light. This equation shows that only for Δp = 0 the gravitational mass is equal to the inertial mass. Instances in which Δp is produced by electromagnetic radiation, Eq. (3) can be rewritten as follows [18]:
2 ⎧ ⎤⎫ ⎡ ⎛ nr2 D ⎞ ⎪ ⎟ − 1⎥⎪ = ⎨1 − 2⎢ 1 + ⎜ 3 ⎟ ⎥⎬ ⎢ ⎜ρ c mi 0 ⎪ ⎝ ⎠ ⎥⎪ ⎢ ⎦⎭ ⎣ ⎩
mg
(4)
Where nr is the refraction index of the particle; D is the power density of the electromagnetic radiation absorbed by the particle; and ρ , its density of inertial mass. From electrodynamics we know that v= dz ω = = dt κ r c
(1)
ε r μr ⎛ 2 ⎞ ⎜ 1 + (σ ωε ) + 1⎟
2 ⎝ ⎠
(5)
It arises from the mentioned law that the gravity acceleration (or simply the gravity) produced by a body with gravitational mass M g is given by g= GM g r2
the real part of the r propagation vector k (also called phase r constant ); k = k = k r + iki ; ε , μ and σ, are the electromagnetic characteristics of the medium in which the incident radiation is propagating ( ε = εrε0 ; ε0 = 8.854×10−12 F / m ;
where
kr
is
(2 )
The physical property of mass has two distinct aspects: gravitational mass mg and inertial mass mi. The gravitational mass produces and responds to gravitational fields; it supplies the mass factor in Newton's famous inverse-square law of 2 gravity F = GM g m g r . The inertial mass
μ = μ r μ 0 , where μ0 = 4π ×10−7 H / m ).
From (5), we see that the index of refraction nr = c v , for σ >> ωε , is given by μrσ (6) nr = 4πfε 0 Substitution of Eq. (6) into Eq. (4) yields
(
)
is the mass factor in Newton's 2nd Law of Motion (F = mi a ) . These two masses are not
It was shown that there is an additional effect - Gravitational Shielding effect produced by a substance whose gravitational mass was reduced or made negative [18]. This effect shows that just beyond the substance the gravity acceleration g 1 will be reduced at the same proportion χ 1 = m g mi 0 , i.e., g1 = χ 1 g , ( g is the gravity acceleration before the substance). Consequently, after a second gravitational shielding, the gravity will be given by g 2 = χ 2 g 1 = χ 1 χ 2 g , where χ 2 is the value of the ratio m g mi 0 for the
Inner belt
0
Outer belt
3600km 6600km
Earth
Magnetic axis
Fig.1 – Van Allen belts
second gravitational shielding. In a generalized way, we can write that after the nth gravitational shielding the gravity, g n , will be given by g n = χ 1 χ 2 χ 3 ...χ n g
The dependence of the shielding effect on the height, at which the samples are placed above a superconducting disk with radius rD = 0.1375 m , has been recently measured up to a height of about 3m [19]. This means that the gravitational shielding effect extends, beyond the disk, for approximately 20 times the disk radius.
3. Gravitational Shieldings in the Van Allen belts The Van Allen belts are torus of plasma around Earth, which are held in place by Earth's magnetic field (See Fig.1). The existence of the belts was confirmed by the Explorer 1 and Explorer 3 missions in early 1958, under Dr James Van Allen at the University of Iowa. The term Van Allen belts refers specifically to the radiation belts surrounding Earth; however, similar radiation belts have been discovered around other planets. Now consider the ionospheric heating with HF beam, modulated at ELF (See Fig. 2). The amplitude-modulated HF heating
wave is absorbed by the ionospheric plasma, modulating the local conductivity σ . The current density j = σE 0 radiates ELF electromagnetic waves that pass through the Van Allen belts producing two Gravitational Shieldings where the densities are minima, i.e., where they are approximately equal to density of the interplanetary medium near Earth. The quasi-vacuum of the interplanetary space might be thought of as beginning at an altitude of about 1000km above the Earth’s surface [20]. Thus, we can assume that the densities ρi and ρo respectively, at the first gravitational shielding Si (at the inner Van Allen belt) and at So (at the outer Van Allen belt) are ρo ≅ ρi ≅ 0.8 ×10−20 kg.m−3 (density of the interplanetary medium near the Earth [21]). The parallel conductivities, † σ 0i and σ0o , respectively at Si and So, present values which lie between those for metallic conductors and those for semiconductors [20], i.e., σ 0i ≅ σ 0o ~ 1S / m . Thus, in these two Gravitational Shielding, according to Eq. (7), we have, respectively:
⎧ 2 ⎡ ⎤⎫ ⎛ ⎞ ⎪ ⎢ ⎥⎪ 4 Di ⎟ −1⎥⎬ χi = ⎨1− 2⎢ 1+ ⎜ 4.1×10 ⎜ ⎟ f ⎠ ⎪ ⎝ ⎢ ⎥⎪ ⎣ ⎦⎭ ⎩
(8)
†
Conductivity in presence of the Earth’s magnetic field
4 d ~ 100km
Outer Van Allen belt
So
6,600 km
Inner Van Allen belt
Si
3,600 km
ELF radiation
~10× d ~1,000km mair g’sun g
Electrojet Electric Field, E0
E σ 100km
D ρ air < 0.01kg.m −3 ρ air ~ 0.7kg .m −3
30km 60km
ELF – modulated HF heating radiation
Fig. 2 – Ionospheric Gravitational Shieldings - The amplitude-modulated HF heating wave is absorbed by the ionospheric plasma, modulating the local conductivity σ 0 . The current density j = σ 0 E 0 (E0 is the Electrojet Electric Field), radiates ELF electromagnetic waves (d is the length of the ELF dipole). Two gravitational shieldings (So and Si) are formed at the Van Allen belts. Then, the gravity due to the Sun, after the shielding Si, becomes g’sun =χoχi gsun. The effect of the gravitational shielding reaches ~ 20 × rD = ~ 10 × d ≅ 1,000km .
5
Sun to Earth, 1 AU), g = 9.8m / s 2 and and
⎧ 2 ⎡ ⎤⎫ ⎛ ⎞ ⎪ ⎢ ⎥⎪ 4 Do ⎟ − 1⎥ ⎬ χo = ⎨1 − 2⎢ 1 + ⎜ 4.1×10 ⎜ ⎟ f ⎠ ⎪ ⎝ ⎢ ⎥⎪ ⎣ ⎦⎭ ⎩
2 g sun = − GM sun rse = 5.92 × 10 −3 m / s 2 , is the
(9)
where
Di ≅ Do ≅ PELF Sa
(10)
gravity due to the Sun at the Earth. The gravitational potential energy related to m air , with respect to the Sun’s center, considering the effects produced by the gravitational shieldings So and Si, is
E p = mairrse (g − χo χi g sun )
PELF is the ELF radiation power, radiated from the ELF ionospheric antenna; S a is the
(14)
area of the antenna. Substitution of (10) into (8) and (9) leads to
⎧ ⎡ 2 ⎤⎫ ⎛ ⎞ ⎪ ⎢ ⎥⎪ 4P ELF ⎟ −1⎥⎬ χoχi = ⎨1− 2⎢ 1+ ⎜ 4.1×10 ⎜ Sa f ⎟ ⎪ ⎢ ⎝ ⎠ ⎥⎪ ⎦⎭ ⎩ ⎣
2
Thus, the decrease in the gravitational potential energy is
ΔEp = Ep − Ep0 = 1− χo χi mairrsegsun
4. Effect of the gravitational shieldings Si and So on the Earth and its environment.
Based on the Podkletnov experiment, previously mentioned, in which the effect of the Gravitational Shielding extends for approximately 20 times the disk radius (rD ) , we can assume that the effect of the gravitational shielding Si extends for approximately 10 times the dipole length ( d ). For a dipole length of about 100km, we can conclude that the effect of the gravitational shielding reaches about 1,000Km below Si (See Fig.2), affecting ‡ therefore an air mass, m air , given by mair = ρ airVair =
= ~ 0.7kg.m −3 (100,000m)2 (30,000m) = ~ 1014 kg
The HF power produced by the HAARP transmitter is PHF = 3.6GW modulated at f = 2.5Hz . The ELF conversion efficiency at HAARP is estimated to be ~ 10 −4 % for wave generated using sinusoidal amplitude modulation. This means that
PELF ~ 4kW
Substitution of PELF ~ 4kW , f = 2.5Hz and
S a = (100,000 )2 = 1 × 1010 m 2 into (16) yields
ΔEp ~ 10−4 mairrsegsun ~ 1019 joules
(17)
This decrease in the gravitational potential energy of the air column, ΔE p , produces a decrease Δp in the local pressure p ( Bernoulli principle). Then the pressure equilibrium between the Earth’s mantle and the Earth’s atmosphere, in the region corresponding to the air column, is broken. This is equivalent to an increase of pressure Δp in the region of the mantle corresponding to the air column. This phenomenon is similar to an Earthquake, which liberates an energy equal to ΔE p (see Fig.3).
(
)
(12)
The gravitational potential energy related to m air , with respect to the Sun’s center, without the effects produced by the gravitational shieldings So and Si is
E p0 = mair rse ( g − g sun )
(13)
where, rse = 1.49 × 1011 m (distance from the
‡
The mass of the air column above 30km height is negligible in comparison with the mass of the air column below 30km height, whose average density is ~0.7kg./m3.
6
Curst Earth’s atmosphere
Air column
Sun
p − Δp
p
Core Mantle Earth
Fig. 3 - The decrease in the gravitational potential energy of the air column, Δ E p , produces a decrease Δ p in the local pressure p (Principle of Bernoulli). Then the pressure equilibrium between the Earth’s mantle and the Earth’s atmosphere, in the region corresponding to the air column, is broken. This is equivalent to an increase of pressure Δ p in the region of the mantle corresponding to the air column. This phenomenon is similar to an Earthquake, which liberates an amount of energy equal to ΔE p .
The magnitude M s in the Richter scales, corresponding to liberation of an amount of energy, ΔEp ~ 1019 joules, is obtained by means of the well-known equation:
Note that, by reducing the diameter of the HF beam radiation, it is possible to reduce dipole length (d) and consequently to reduce the reach of the Gravitational Shielding, since the effect of the gravitational shielding reaches approximately18 times the dipole length. By reducing d, we also reduce the area S a , increasing consequently the value of χ o χ i (See Eq. (18)). This can cause an increase in the velocity V0 air (See Eq. (22)). On the other hand, if the dipole length (d) is increased, the reach of the Gravitational Shielding will also be increased. For example, by increasing the value of d for d = 101km , the effect of the Gravitational Shielding reaches approximately 1010 km , and can surpass the surface of the Earth or the Oceans (See Fig.2). In this case, the decrease in the gravitational potential energy at the local, by analogy to Eq.(15), is (21) ΔEp = (1− χo χi )m rsegsun where m is the mass of the soil, or the mass of the ocean water, according to the case. The decrease, ΔE p , in the gravitational potential energy increases the kinetic energy of the local at the same ratio, in such way that the mass m acquires a kinetic energy E k = ΔE p . If this energy is not enough to pluck the mass m from the soil or the ocean, and launch it into space, then E k is converted into heat, raising the local temperature by ΔT , the value of which can be obtained from the following expression:
Ek ≅ kΔT N
(18) 1019 = 10 (5+1.44M s ) which gives M s = 9.1 . That is, an Earthquake
with magnitude of about 9.1 in the Richter scales. The decrease in the gravitational potential energy in the air column whose mass is m air gives to the air column an initial kinetic energy E k = 1 mairV02air = ΔE p , where 2 ΔE p is given by (15).
(22)
In the previously mentioned HAARP conditions, Eq.(11) gives (1 − χ o χ i ) ~ 10 −4 . Thus, from (15), we obtain
ΔE p ~ 10 −4 mair rse g sun
(19)
Thus, the initial air speed V0 air is
V0air ≅ 10 g sunrse ~ 10 m / s ~ 400km/ h
2 −4
where N is the number of atoms in the volume V of the substance considered; k = 1.38 × 10 −23 J / K is the Boltzmann constant. Thus, we get
ΔT ≅ =
(20)
This velocity will strongly reduce the pressure in the air column (Bernoulli principle) and it is sufficient to produce a powerful Cyclone around the air column (Coriolis Effect).
(1− χ χ ) ρ rse g sun o i
Ek 1− χ o χ i m rse g sun = = (nV )k Nk nk
(
)
(23)
where n is the number of atoms/m3 in the substance considered.
7
In the previously mentioned HAARP conditions, Eq. (11) gives (1 − χ o χ i ) ~ 10 −4 . Thus, from (23), we obtain
ΔT ≅ 6.4 × 10 27 ρ n
(24)
For most liquid and solid substances the value of n is about 10 28 atoms / m 3 , and ρ ~ 10 3 kg / m 3 . Therefore, in this case, Eq. (24) gives
ΔT ≅ 640K ≅ 400°C
It was experimentally observed that ELF radiation escapes from the Earth– ionosphere waveguide and reaches the Van Allen belts [25-28]. In the ionospheric spherical cavity, the ELF radiation power density, D , is related to the energy density inside the cavity, W , by means of the wellknown expression: c D= W 4
(25)
where
W=
c is
This means that, the region in the soil or in the ocean will have its temperature increased by approximately 400°C. By increasing PELF or decreasing the frequency, f , of the ELF radiation, it is possible to increase ΔT (See Eq.(16)). In this way, it is possible to produce strong localized heating on Land or on the Oceans. This process suggests that, by means of two small Gravitational Shieldings built with Gas or Plasma at ultra-low pressure, as shown in the processes of gravity control [22], it is possible to produce the same heating effects. Thus, for example, the water inside a container can be strongly heated when the container is placed below the mentioned Gravitational Shieldings. Let us now consider another source of ELF radiation, which can activate the Gravitational Shieldings So and Si. It is known that the Schumann resonances [23] are global electromagnetic resonances (a set of spectrum peaks in the extremely low frequency ELF), excited by lightning discharges in the spherical resonant cavity formed by the Earth’s surface and the inner edge of the ionosphere (60km from the Earth’s surface). The Earth– ionosphere waveguide behaves like a resonator at ELF frequencies and amplifies the spectral signals from lightning at the resonance frequencies. In the normal mode descriptions of Schumann resonances, the fundamental mode (n = 1) is a standing wave in the Earth–ionosphere cavity with a wavelength equal to the circumference of the Earth. This lowest-frequency (and highestintensity) mode of the Schumann resonance occurs at a frequency f1 = 7.83Hz [24].
1 ε E2 2 0
the speed of light, and . The electric field E , is given by
E= q
2 4πε 0 r⊕
where q = 500,000C [24] and r⊕ = 6.371×106 m .
Therefore, we get E = 110.7V / m,
W = 5.4 ×10−8 J / m3 ,
(26) D ≅ 4.1 W / m 2 The area, S , of the cross-section of the cavity is S = 2πr⊕ d = 2.4 × 10 m 2 . Thus, the ELF radiation power is P = DS ≅ 9.8 × 1012 W . The total power escaping from the Earthionosphere waveguide, Pesc , is only a fraction of this value and need to be determined.
12
When this ELF radiation crosses the Van Allen belts the Gravitational Shieldings So and Si can be produced (See Fig.4).
So
d⊕
ELF radiation
Si
Crust Mantle Outer core Inner core Earth
Reach of the Gravitational Shielding
~ 10 × d ⊕ = 126 ,000 km
Fig.4 – ELF radiation escaping from the Earth– ionosphere waveguide can produce the Gravitational Shieldings So and Si in the Van Allen belts.
The ELF radiation power densities Di and Do , respectively in Si and So, are given by
8
Di = P esc 4πri2 P esc
2 4πro
(27)
(28)
and
Do =
where ri and ro are respectively, the distances from the Earth’s center up to the Gravitational Shieldings Si and So . Under these circumstances, the kinetic energy related to the mass, m oc , of the Earth’s outer core § , with respect to the Sun’s center, considering the effects produced by the Gravitational Shieldings So and Si ** is
2 Ek = 1 − χ o χ i moc rse g sun = 1 mocVoc 2
(
)
(29)
Thus, we get
Voc = 1 − χ o χ i rse g sun
(
)
(30)
The average radius of the outer core is roc = 2.3 × 10 6 m . Then, assuming that the average angular speed of the outer core, ϖ oc , has the same order of magnitude of the average angular speed of the Earth’s crust, ϖ ⊕ , i.e., ϖ oc ~ ϖ ⊕ = 7.29 × 10 −5 rad / s , then we get Voc = ϖ oc roc ~ 10 2 m / s . Thus, Eq. (30) gives
speed Voc will be null. After a time interval, the progressive increasing of the power density of the ELF radiation makes χ o χ i greater than 1. Equation (29) shows that, at this moment, the velocity Voc resurges, but now in the opposite direction. The Earth's magnetic field is generated by the outer core motion, i.e., the molten iron in the outer core is spinning with angular speed, ϖ oc , and it's spinning inside the Sun’s magnetic field, so a magnetic field is generated in the molten core. This process is called dynamo effect. Since Eq. (31) tells us that the factor (1− χ o χ i ) is currently very close to zero, we can conclude that the moment of the reversion of the Earth’s magnetic field is very close.
5. Device for moving very heavy loads.
(1− χ
o
χ i ~ 10−5
)
(31)
This relationship shows that, if the power of the ELF radiation escaping from the Earth-ionosphere waveguide is progressively increasing (for example, by the increasing of the dimensions of the holes in the Earth-ionosphere waveguide †† ), then as soon as the value of χ o χ i equals 1, and the
§
Based on the phenomenon of reduction of local gravity related to the Gravitational Shieldings So and Si, it is possible to create a device for moving very heavy loads such as large monoliths, for example. Imagine a large monolith on the Earth’s surface. At noon the gravity acceleration upon the monolith is basically given by g R = g − g sun
2 where gsun = −GMsun rse = 5.92×10−3 m/ s2 is the gravity due to the Sun at the monolith and g = 9.8m/ s2 . If we place upon the monolith a mantle with a set of n Gravitational Shieldings inside, the value of g R becomes
The Earth is an oblate spheroid. It is composed of a number of different layers. An outer silicate solid crust, a highly viscous mantle, a liquid outer core that is much less viscous than the mantle, and a solid inner core. The outer core is made of liquid iron and nickel.
g R = g − χ n g sun
Note that the reach of the Gravitational Shielding is ~ 10 × d ⊕ = 126,000km . †† The amount of ELF radiation that escapes from the Earth-ionosphere waveguide is directly proportional to the number of holes in inner edge of the ionosphere and the dimensions of these holes. Thus, if the amount of holes or its dimensions are increasing, then the power of the ELF radiation escaping from the Earthionosphere waveguide will also be increased.
**
This shows that, it is possible to reduce g R down to values very close to zero, and thus to transport very heavy loads (See Fig.5). We will call the mentioned mantle of Gravitational Shielding Mantle. Figure 5 shows one of these mantles with a set of 8
Gravitational Shieldings. Since the mantle thickness must be thin, the option is to use Gravitational Shieldings produced by layers of high-dielectric strength semiconductor [22]. When the Gravitational Shieldings are active the
Set of 8 Gravitational Shieldings inside the Mantle
Cross-section of the Mantle (c)
V
~
ELF f
Fig. 5 – Device for transporting very heavy loads. It is possible to transport very heavy loads by using a Gravitational Shielding Mantle - A Mantle with a set of 8 semiconductor layers or more (each layer with 10μm thickness, sandwiched by two metallic foils with 10μm thickness). The total thickness of the mantle (including the insulation layers) is ~1mm. The metallic foils are connected to the ends of an ELF voltage source in order to generate ELF electromagnetic fields through the semiconductor layers. The objective is to create 8 Gravitational Shieldings as shown in (c). When the Gravitational Shieldings are active the gravity due to the Sun is multiplied by the factor χ 8 , in such way that the gravity resultant upon the monoliths (a) and (b) becomes g R = g − χ 8 g Sun . Thus, for example, if χ = −2.525 results g R = 0.028m / s 2 . Under these circumstances, the weight of the monolith becomes 2.9 × 10 −3 of the initial weight.
10 gravity due to the Sun is multiplied by the factor χ 8 , in such way that the gravity resultant upon the monolith becomes g R = g − χ 8 g Sun . Thus, for example, if χ = −2.525 the result is g R = 0.028m / s 2 . Under these circumstances,
the total charge[24], then Q = ηAσ q = ηq n ( q n = Aσ q is the normal amount of charge in the area A ). By substituting (33) into (32), we get
⎛ Qr ⎞ 2 3 ⎟ ⎜ 3 ⎜ 2ε A⎟ 2α ⎛ Q ⎞ 2 V2 ⎝ 0 ⎠ ⎟ = ⎜ jw = 2 j = 2α 2 = 2α ⎟ ⎜ r ⎝ 2ε 0 A⎠ r r2
3
the weight of the monolith becomes 2.9 × 10 −3 of the initial weight.
(34)
6. Gates to the imaginary spacetime in the Earth-ionosphere waveguide.
It is known that strong densities of electric charges can occur in some regions of the upper boundary of the Earth-ionosphere waveguide, for example, as a result of the lightning discharges [29]. These anomalies increase strongly the electric field E w in the mentioned regions, and possibly can produce a tunneling effect to the imaginary spacetime. The electric field E w will produce an electrons flux in a direction and an ions flux in an opposite direction. From the viewpoint of electric current, the ions flux can be considered as an “electrons” flux at the same direction of the real electrons flux. Thus, the current density through the air, j w , will be the double of the current density expressed by the well-known equation of LangmuirChild
3 3 3
Since Ew = σ Q 2ε 0 and j w = σ w E w , we can write that
3 ⎡ ⎤ 2 3 4 3 ⎢ 2α ⎛ Q ⎞ ⎥ Q = ⎜ ⎟ σ w Ew = jw Ew = ⎢ r ⎜ 2ε 0 A ⎟ ⎥ 2ε 0 A ⎠ ⎥ ⎢ ⎝ ⎣ ⎦
3
=
0.18 3Q5.5 α r1.5ε 05.5 A5.5
=
0.18 3σ Q5.5 α r1.5ε 05.5
=
0.18 3 ησq α r1.5ε 05.5
( )5.5
=
= 2.14×1016η 5.5
(35)
The electric field E w has an oscillating component, E w1 , with frequency, f , equal to the lowest Schumann resonance frequency f1 = 7.83 Hz . Then, by using Eq. (7), that can be rewritten in the following form [18]: χ= mg
we can write that χw = mg 4 2e V 2 V2 V2 =α 2 = 2.33×10−6 2 j = εrε0 9 me r2 r r
(32)
where ε r ≅ 1 for the air; α = 2.33 × 10 −6 is the called Child’s constant; r , in this case, is the distance between the center of the charges and the Gravitational Shieldings S w1 and S w 2 (see Fig.6) ( r = 1 1.4×10−15m = 7×10−16m); V is the 2
By
⎧ ⎡ μ σ 3 E4 ⎤⎫ ⎪ ⎪ = ⎨1− 2⎢ 1+1.758×10−27 rw 2 w 3 w1 −1⎥⎬ (37) mi ⎥⎪ ρw f1 ⎪ ⎢ ⎦⎭ ⎩ ⎣ substitution of Eq. (35), μ rw = 1 ,
voltage drop given by σQ Qr (33) V = Ewr = r= 2ε 0 2ε 0 A where Q is the anomalous amount of charge in the region with area A , i.e., σ Q = Q A = ησ q , η is the ratio of proportionality, and σ q = q 4πR2 ≅ 9.8×10−10C / m2
The gravity below S w 2 will be decreased by the effect of the Gravitational Shieldings S w1 and S w 2 , according to the following expression
(g − χ w1 χ w2 g sun ) where χ w1 = χ w 2 = χ w . Thus, we get
is the normal charge density ; q = 500,000C is
11
Region with much greater
Ionosphere r σq
concentration of electric charges
σQ
+
+
+
+ + + + + + + + +
Ew
+
+
+
S w1
S w2
A
Upper boundary of the Earth-Ionosphere waveguide
Earth-Ionosphere waveguide
60 km
Reach of the Gravitational Shielding
~10 X d
R
g
g − χ w 1 χ w 2 g sun
g
d
ground
Fig. 6 - Gravitational Shieldings S w1 and S w2 produced by strong densities of electric charge in the upper boundary of the Earth-Ionosphere.
where χ = ⎨1 − ⎧1 − 2⎡ 1 + 7.84 ×10 −10 η 5.5 − 1⎤ ⎫ ⎨ ⎢ ⎥⎬
⎩ ⎣ ⎧ ⎪ ⎪ ⎩ g sun ⎫ ⎪ ⎬ (39) ⎦⎭ g ⎪ ⎭
2
In a previous article [18], it was shown that, when the gravitational mass of a body is reduced to a value in the range of + 0.159 mi to − 0.159 mi or the local gravity (g ) is reduced to a value in the range of + 0.159 g to − 0.159 g , the body performs a transition to the imaginary spacetime. This means that, if the value of χ given by Eq.(39) is in the range 0.159 < χ < −0.159 , then any body (aircrafts, ships, etc) that enters the region defined by the volume ( A × ~ 10d ) below the Gravitational Shielding S w 2 , will perform a transition to the imaginary spacetime. Consequently, it will disappear from our Real Universe and will appear in the Imaginary Universe. However, the electric field E w1 , which reduces the gravitational mass of the body (or the gravitational shieldings, which reduce the local gravity) does not accompany the body; they stay at the Real Universe. Consequently, the body returns immediately from the Imaginary Universe. Meanwhile, it is important to note that, in the case of collapse of the wavefunction Ψ of the body, it will never more come back to the Real Universe. Equation (39) shows that, in order to obtain χ in the range of 0.159< χ < −0.159 the value of η must be in the following range:
127 . 1 < η < 135 . 4
gravitational mass (Eq. (4)). Now, it will be shown that it also affects the length of an object. Length contraction or Lorentz contraction is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer. If L0 is the length of the object in its rest frame, then the length L , observed by an observer in relative motion with respect to the object, is given by
L= L0 = L0 1 − V 2 c 2 γ (V )
(40)
where V is the relative velocity between the observer and the moving object and c the speed of light. The function γ (V ) is known as the Lorentz factor. It was shown that Eq. (3) can be written in the following form [18]:
⎧ ⎡ 2 ⎤⎫ ⎧ ⎡ ⎤⎫ ⎛ Δp ⎞ 1 ⎪ ⎢ ⎪ ⎜ ⎟ −1⎥⎪ = ⎪1− 2⎢ −1⎥⎬ = ⎨1− 2 1+ ⎜ ⎟ ⎥⎬ ⎨ ⎢ ⎢ 2 2 ⎥⎪ mi0 ⎪ ⎝ mi0c ⎠ ⎥⎪ ⎪ ⎣ 1−V c ⎢ ⎦⎭ ⎦⎭ ⎩ ⎩ ⎣ mg
This expression shows that
⎛ Δp ⎞ 1 ⎟ 1+ ⎜ = γ (V ) ⎜m c⎟ = 2 2 ⎝ i0 ⎠ 1 −V c
2
(41)
By substitution of Eq. (41) into Eq.(40) we get
(42) 2 ⎛ Δp ⎞ ⎟ 1+ ⎜ ⎜m c⎟ ⎝ i0 ⎠ It was shown that, the term, Δp mi 0 c , in the
L=
L0 = γ (V )
L0
Since the normal charge density is σq ≅ 9.8×10−10C / m2 then it must be increased by about 130 times in order to transform the region ( A × ~ 10d ) , below the Gravitational Shielding S w 2 , in a gate to the imaginary spacetime. It is known that in the Earth's atmosphere occur transitorily large densities of electromagnetic energy across extensive areas. We have already seen how the density of electromagnetic energy affects the
equation above is equal to Wn r ρ c 2 , where W is the density of electromagnetic energy absorbed by the body and nr the index of refraction, given by ε μ c nr = = r r ⎛ 1 + (σ ωε )2 +1⎞ ⎜ ⎟ v 2 ⎝ ⎠
In the case of σ >> 2πfε , W = (σ 8πf )E 2 and n r = c v = μσc 2 4πf [30]. Thus, in this case,
Eq. (42) can be written as follows
L= L0 ⎛ μ σ3 ⎞ 1 +1.758×10−27⎜ r 3 ⎟E4 ⎜ ρ2 f ⎟ ⎝ ⎠
(43)
Note that E = E m sin ωt .The average value
2 for E 2 is equal to 1 2 E m because E varies sinusoidaly ( E m is the maximum value
where ϕ is the gravitational potential. Then, it follows that
⎛ Δp ⎜ ⎜m ⎝ i0
2 2
13
for E ). On the other hand, E rms = E m
4
2.
4 rms
Consequently we can change E by E , and the equation above can be rewritten as follows
L= L0 ⎛ μ σ3 ⎞ 4 1 +1.758×10−27⎜ r 3 ⎟Erms ⎜ 2 ⎟
⎞ ⎛ Δp ⎞ V 2 2ϕ ⎟ = V 2 = 2ϕ and ⎜ ⎟ = = ⎟ ⎜m c⎟ c2 c2 ⎠ ⎝ i0 ⎠ Consequently, the expression of T becomes
T= T0 1 −V c
2 2
= T0 1+
2ϕ c2
(44)
⎝ρ f ⎠ Now, consider an airplane traveling in a region of the atmosphere. Suddenly, along a distance L0 of the trajectory of the airplane arises an ELF electric field with intensity E rms ~ 10 5 V .m −1 and frequency f ~ 1Hz . The
which is the well-known expression obtained in the General Relativity. Based on Eq. (41) we can also write the expression of T in the following form:
⎛ μ σ3 ⎞ 4 ⎛ Δp ⎞ ⎟ = T0 1+1.758×10−27⎜ r ⎟Erms (45) T = T0 1+ ⎜ ⎜ m c⎟ ⎜ ρ2 f 3 ⎟ ⎝ i0 ⎠ ⎝ ⎠
2
Aluminum density is ρ = 2.7 × 10 3 kg .m −3 and its conductivity is σ = 3.82 × 10 7 S .m −1 . According to Eq. (44), for the airplane the distance L0 is shortened by 2.7 × 10 −5 . Under these conditions, a distance L0 of about 3000km will become just 0.08km. Time dilation is an observed difference of elapsed time between two observers which are moving relative to each other, or being differently situated from nearby gravitational masses. This effect arises from the nature of space-time described by the theory of relativity. The expression for determining time dilation in special relativity is:
T = T0γ (V ) = T0
Now, consider a ship in the ocean. It is made of steel ( μr = 300; σ = 1.1×106 S.m−1 ; ρ = 7.8 × 103 kg.m −3 ). When subjected to a
uniform ELF electromagnetic field, with intensity and E rms = 1.36 × 10 3 V .m −1 frequency f = 1Hz , the ship will perform a transition in time to a time T given by
⎛ μ σ3 ⎞ 4 T = T0 1 + 1.758×10−27 ⎜ r 3 ⎟Erms = ⎜ ρ2 f ⎟ ⎝ ⎠ ) = T0 (1.0195574
(46)
1−V 2 c2
where T0 is the interval time measured at the object in its rest frame (known as the proper time); T is the time interval observed by an observer in relative motion with respect to the object. Based on Eq. (41), we can write the expression of T in the following form:
T= ⎛ Δp ⎞ ⎟ = T0 1+ ⎜ ⎜m c⎟ 2 2 ⎝ i0 ⎠ V c 1− T0
2
