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High-power ELF radiation generated by modulated HF heating of the ionosphere can cause Earthquakes, Cyclones and localized heating
Journal Article: JEP 01/2011;
Abstract
The High Frequency Active Auroral Research Program (HAARP) is actually the most important facility used to generate extremely low frequency (ELF) electromagnetic radiation in the ionosphere. In order to produce this ELF radiation the HAARP transmitter radiates a strong beam of high-frequency (HF) waves modulated at ELF. This HF heating modulates the electron temperature in the D region ionosphere and leads to modulated conductivity and a time-varying current which then radiates at the modulation frequency. Recently, the HAARP HF transmitter operated with 3.6GW of effective radiated power modulated at frequency of 2.5Hz. It is shown that high-power ELF radiation generated by HF ionospheric heaters, such as the current HAARP heater, can cause Earthquakes, Cyclones and strong localized heating.
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Page 1
High-power ELF radiation generated by modulated HF heating of the
ionosphere can cause Earthquakes, Cyclones and localized heating
Fran De Aquino
Maranhao State University, Physics Department, S.Luis/MA, Brazil.
Copyright © 2011 by Fran De Aquino. All Rights Reserved
The High Frequency Active Auroral Research Program (HAARP) is currently the most important
facility used to generate extremely low frequency (ELF) electromagnetic radiation in the ionosphere.
In order to produce this ELF radiation the HAARP transmitter radiates a strong beam of high-
frequency (HF) waves modulated at ELF. This HF heating modulates the electrons’ temperature in the
D region ionosphere and leads to modulated conductivity and a time-varying current which then
radiates at the modulation frequency. Recently, the HAARP HF transmitter operated with 3.6GW of
effective radiated power modulated at frequency of 2.5Hz. It is shown that high-power ELF radiation
generated by HF ionospheric heaters, such as the current HAARP heater, can cause Earthquakes,
Cyclones and strong localized heating.
.
Key words: Physics of the ionosphere, radiation processes, Earthquakes, Tsunamis, Storms.
PACS: 94.20.-y ; 94.05.Dd ; 91.30.Px ; 91.30.Nw; 92.60.Qx
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 so-
sought 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.
ionosphere can cause Earthquakes, Cyclones and localized heating
Fran De Aquino
Maranhao State University, Physics Department, S.Luis/MA, Brazil.
Copyright © 2011 by Fran De Aquino. All Rights Reserved
The High Frequency Active Auroral Research Program (HAARP) is currently the most important
facility used to generate extremely low frequency (ELF) electromagnetic radiation in the ionosphere.
In order to produce this ELF radiation the HAARP transmitter radiates a strong beam of high-
frequency (HF) waves modulated at ELF. This HF heating modulates the electrons’ temperature in the
D region ionosphere and leads to modulated conductivity and a time-varying current which then
radiates at the modulation frequency. Recently, the HAARP HF transmitter operated with 3.6GW of
effective radiated power modulated at frequency of 2.5Hz. It is shown that high-power ELF radiation
generated by HF ionospheric heaters, such as the current HAARP heater, can cause Earthquakes,
Cyclones and strong localized heating.
.
Key words: Physics of the ionosphere, radiation processes, Earthquakes, Tsunamis, Storms.
PACS: 94.20.-y ; 94.05.Dd ; 91.30.Px ; 91.30.Nw; 92.60.Qx
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 so-
sought 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.
Page 2
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 by the
local gravity acceleration , i.e.,
gm
g
( )1gmP g=
It arises from the mentioned law that the
gravity acceleration (or simply the gravity)
produced by a body with gravitational mass
is given by gM
( )22r
GM
g g=
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
gravity ( )2rmGMF gg= . The inertial mass
is the mass factor in Newton's 2nd Law of
Motion . These two masses are not
equivalent but correlated by means of the
following factor [
( amF i= )
18]:
( )31121
2
00 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+−=
cm
p
m
m
ii
g
Where is the rest inertial mass and 0im pΔ is
the variation in the particle’s kinetic
momentum; c is the speed of light.
This equation shows that only for
0=Δp the gravitational mass is equal to the
inertial mass. Instances in which pΔ is
produced by electromagnetic radiation, Eq.
(3) can be rewritten as follows [18]:
( )41121
2
3
2
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛+−=
c
Dn
m
m
r
i
g
ρ
Where is the refraction index of the
particle; is the power density of the
electromagnetic radiation absorbed by the
particle; and
rn
D
ρ , its density of inertial mass.
From electrodynamics we know that
( )
( )5
11
2
2 ⎟⎠
⎞⎜⎝
⎛ ++
===
ωεσμεκ
ω
rrr
c
dt
dz
v
where is the real part of the
propagation vector
rk
k
r
(also called phase
constant ); ir ikkkk +==
r
; ε , μ and σ, are
the electromagnetic characteristics of the
medium in which the incident radiation is
propagating ( 0εεε r= ; ; mF /10854.8 120 −×=ε
0μμμ r= , where ). m/H70 104 −×= πμ
From (5), we see that the index of
refraction vcnr = , for ωεσ >> , is given
by
( )6
4 0επ
σμ
f
n rr =
Substitution of Eq. (6) into Eq. (4) yields
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 by the
local gravity acceleration , i.e.,
gm
g
( )1gmP g=
It arises from the mentioned law that the
gravity acceleration (or simply the gravity)
produced by a body with gravitational mass
is given by gM
( )22r
GM
g g=
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
gravity ( )2rmGMF gg= . The inertial mass
is the mass factor in Newton's 2nd Law of
Motion . These two masses are not
equivalent but correlated by means of the
following factor [
( amF i= )
18]:
( )31121
2
00 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+−=
cm
p
m
m
ii
g
Where is the rest inertial mass and 0im pΔ is
the variation in the particle’s kinetic
momentum; c is the speed of light.
This equation shows that only for
0=Δp the gravitational mass is equal to the
inertial mass. Instances in which pΔ is
produced by electromagnetic radiation, Eq.
(3) can be rewritten as follows [18]:
( )41121
2
3
2
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛+−=
c
Dn
m
m
r
i
g
ρ
Where is the refraction index of the
particle; is the power density of the
electromagnetic radiation absorbed by the
particle; and
rn
D
ρ , its density of inertial mass.
From electrodynamics we know that
( )
( )5
11
2
2 ⎟⎠
⎞⎜⎝
⎛ ++
===
ωεσμεκ
ω
rrr
c
dt
dz
v
where is the real part of the
propagation vector
rk
k
r
(also called phase
constant ); ir ikkkk +==
r
; ε , μ and σ, are
the electromagnetic characteristics of the
medium in which the incident radiation is
propagating ( 0εεε r= ; ; mF /10854.8 120 −×=ε
0μμμ r= , where ). m/H70 104 −×= πμ
From (5), we see that the index of
refraction vcnr = , for ωεσ >> , is given
by
( )6
4 0επ
σμ
f
n rr =
Substitution of Eq. (6) into Eq. (4) yields
Page 3
3
( )71
4
121
2
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛+−==
cf
D
m
m
i
g
πρ
μσχ
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 will be
reduced at the same proportion
1g
01 ig mm=χ ,
i.e., gg
11 χ= , ( is the gravity acceleration
before the substance). Consequently, after a
second gravitational shielding, the gravity
will be given by
g
ggg
21122 χχχ == , where
2
χ is the value of the ratio 0ig mm for the
second gravitational shielding. In a
generalized way, we can write that after the
nth gravitational shielding the gravity, ,
will be given by
ng
gg
nn χχχχ ...321=
The dependence of the shielding
effect on the height, at which the samples are
placed above a superconducting disk with
radius , has been recently
measured up to a height of about 3m [
mrD 1375.0=
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
Fig.1 – Van Allen belts
Inner
belt
Outer
belt
Magnetic
axis
Earth
Van Allen belts
0 3600km 6600km
wave is absorbed by the ionospheric plasma,
modulating the local conductivityσ . The
current density 0Ej σ= 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 iρ and oρ
respectively, at the first gravitational
shielding Si (at the inner Van Allen belt) and
at So (at the outer Van Allen belt) are
(density of the
interplanetary medium near the Earth [
320 .108.0 −−×≅≅ mkgio ρρ
21]).
The parallel conductivities,† i0σ
and o0σ , respectively at Si and So, present
values which lie between those for metallic
conductors and those for semiconductors
[20], i.e., mSoi /1~00 σσ ≅ . Thus, in these
two Gravitational Shielding, according to Eq.
(7), we have, respectively:
( )81101.4121
2
4
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ ×+−=
f
Di
iχ
† Conductivity in presence of the Earth’s magnetic field
( )71
4
121
2
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛+−==
cf
D
m
m
i
g
πρ
μσχ
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 will be
reduced at the same proportion
1g
01 ig mm=χ ,
i.e., gg
11 χ= , ( is the gravity acceleration
before the substance). Consequently, after a
second gravitational shielding, the gravity
will be given by
g
ggg
21122 χχχ == , where
2
χ is the value of the ratio 0ig mm for the
second gravitational shielding. In a
generalized way, we can write that after the
nth gravitational shielding the gravity, ,
will be given by
ng
gg
nn χχχχ ...321=
The dependence of the shielding
effect on the height, at which the samples are
placed above a superconducting disk with
radius , has been recently
measured up to a height of about 3m [
mrD 1375.0=
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
Fig.1 – Van Allen belts
Inner
belt
Outer
belt
Magnetic
axis
Earth
Van Allen belts
0 3600km 6600km
wave is absorbed by the ionospheric plasma,
modulating the local conductivityσ . The
current density 0Ej σ= 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 iρ and oρ
respectively, at the first gravitational
shielding Si (at the inner Van Allen belt) and
at So (at the outer Van Allen belt) are
(density of the
interplanetary medium near the Earth [
320 .108.0 −−×≅≅ mkgio ρρ
21]).
The parallel conductivities,† i0σ
and o0σ , respectively at Si and So, present
values which lie between those for metallic
conductors and those for semiconductors
[20], i.e., mSoi /1~00 σσ ≅ . Thus, in these
two Gravitational Shielding, according to Eq.
(7), we have, respectively:
( )81101.4121
2
4
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ ×+−=
f
Di
iχ
† Conductivity in presence of the Earth’s magnetic field
Page 4
4
Fig. 2 – Ionospheric Gravitational Shieldings - The amplitude-modulated HF heating wave is absorbed by the
ionospheric plasma, modulating the local conductivity 0σ . The current density 00 Ej σ= (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 kmdrD 000,110~20~ ≅×=× .
100km
60km
D
E
So
ELF – modulated
HF heating radiation
d ~ 100km
mair g’sun
~10× d ~1,000km
σ
6,600 km
Outer Van Allen belt
Inner Van Allen belt
3,600 km
Si
ELF radiation
g
30km
3.7.0~ −mkgairρ
3.01.0 −< mkgairρ
Electrojet Electric Field, E0
Fig. 2 – Ionospheric Gravitational Shieldings - The amplitude-modulated HF heating wave is absorbed by the
ionospheric plasma, modulating the local conductivity 0σ . The current density 00 Ej σ= (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 kmdrD 000,110~20~ ≅×=× .
100km
60km
D
E
So
ELF – modulated
HF heating radiation
d ~ 100km
mair g’sun
~10× d ~1,000km
σ
6,600 km
Outer Van Allen belt
Inner Van Allen belt
3,600 km
Si
ELF radiation
g
30km
3.7.0~ −mkgairρ
3.01.0 −< mkgairρ
Electrojet Electric Field, E0
Page 5
5
and
( )91101.4121
2
4
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ ×+−=
f
Do
oχ
where
( )10
a
ELF
oi S
P
DD ≅≅
ELFP is the ELF radiation power, radiated
from the ELF ionospheric antenna; is the
area of the antenna.
aS
Substitution of (10) into (8) and (9)
leads to
( )111101.4121
2
2
4
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ ×+−=
fS
P
a
ELF
ioχχ
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 ( )Dr ,
we can assume that the effect of the
gravitational shielding Si extends for
approximately 10 times the dipole length
( ). For a dipole length of about 100km, we
can conclude that the effect of the
gravitational shielding reaches about
1,000Km below S
d
i (See Fig.2), affecting
therefore an air mass, , given by airm
‡
( )( ) ( )
( )1210~
000,30000,100.7.0~
14
23
kg
mmmkg
Vm airairair
==
==
−
ρ
The gravitational potential energy
related to , with respect to the Sun’s
center, without the effects produced by the
gravitational shieldings S
airm
o and Si is ( ) ( )130 sunseairp ggrmE −=
where, (distance from the mrse
111049.1 ×=
‡ 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.
Sun to Earth, 1 AU), and 2/8.9 smg =
232 /1092.5 smrGMg sesunsun
−×=−= , is the
gravity due to the Sun at the Earth.
The gravitational potential energy
related to , with respect to the Sun’s
center, considering the effects produced by
the gravitational shieldings S
airm
o and Si, is
( ) ( )14sunioseairp ggrmE χχ−=
Thus, the decrease in the gravitational
potential energy is
( ) ( )1510 sunseairppp grmEEE ioχχ−=−=Δ
Substitution of (11) into (15) gives
( )161101.41211
2
2
4
sunseair
a
ELF
p grmfS
P
E
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ ×+−−=Δ
The HF power produced by the
HAARP transmitter is GWPHF 6.3=
modulated at Hzf 5.2= . The ELF conversion
efficiency at HAARP is estimated to be
for wave generated using sinusoidal
amplitude modulation. This means that
%10~ 4−
kWPELF 4~
Substitution of , and kWPELF 4~ Hzf 5.2=
( ) 2102 101000,100 mSa ×== into (16) yields
( )1710~10~ 194 joulesgrmE sunseairp −Δ
This decrease in the gravitational potential
energy of the air column, , produces a
decrease
pEΔ
pΔ 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 pΔ in the region of the
mantle corresponding to the air column. This
phenomenon is similar to an Earthquake, which
liberates an energy equal to (see Fig.3). pEΔ
and
( )91101.4121
2
4
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ ×+−=
f
Do
oχ
where
( )10
a
ELF
oi S
P
DD ≅≅
ELFP is the ELF radiation power, radiated
from the ELF ionospheric antenna; is the
area of the antenna.
aS
Substitution of (10) into (8) and (9)
leads to
( )111101.4121
2
2
4
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ ×+−=
fS
P
a
ELF
ioχχ
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 ( )Dr ,
we can assume that the effect of the
gravitational shielding Si extends for
approximately 10 times the dipole length
( ). For a dipole length of about 100km, we
can conclude that the effect of the
gravitational shielding reaches about
1,000Km below S
d
i (See Fig.2), affecting
therefore an air mass, , given by airm
‡
( )( ) ( )
( )1210~
000,30000,100.7.0~
14
23
kg
mmmkg
Vm airairair
==
==
−
ρ
The gravitational potential energy
related to , with respect to the Sun’s
center, without the effects produced by the
gravitational shieldings S
airm
o and Si is ( ) ( )130 sunseairp ggrmE −=
where, (distance from the mrse
111049.1 ×=
‡ 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.
Sun to Earth, 1 AU), and 2/8.9 smg =
232 /1092.5 smrGMg sesunsun
−×=−= , is the
gravity due to the Sun at the Earth.
The gravitational potential energy
related to , with respect to the Sun’s
center, considering the effects produced by
the gravitational shieldings S
airm
o and Si, is
( ) ( )14sunioseairp ggrmE χχ−=
Thus, the decrease in the gravitational
potential energy is
( ) ( )1510 sunseairppp grmEEE ioχχ−=−=Δ
Substitution of (11) into (15) gives
( )161101.41211
2
2
4
sunseair
a
ELF
p grmfS
P
E
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ ×+−−=Δ
The HF power produced by the
HAARP transmitter is GWPHF 6.3=
modulated at Hzf 5.2= . The ELF conversion
efficiency at HAARP is estimated to be
for wave generated using sinusoidal
amplitude modulation. This means that
%10~ 4−
kWPELF 4~
Substitution of , and kWPELF 4~ Hzf 5.2=
( ) 2102 101000,100 mSa ×== into (16) yields
( )1710~10~ 194 joulesgrmE sunseairp −Δ
This decrease in the gravitational potential
energy of the air column, , produces a
decrease
pEΔ
pΔ 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 pΔ in the region of the
mantle corresponding to the air column. This
phenomenon is similar to an Earthquake, which
liberates an energy equal to (see Fig.3). pEΔ
Page 6
6
Fig. 3 - The decrease in the gravitational potential energy
of the air column, pEΔ , produces a decrease pΔ 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 pΔ 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
pEΔ .
Sun
Earth
Earth’s
atmosphere
Air column
Core
Mantle
p pp Δ−
Curst
The magnitude in the Richter
scales, corresponding to liberation of an
amount of energy,
sM
joulesEp
1910~Δ , is obtained
by means of the well-known equation:
( ) ( )181010 44.1519 sM+=
which gives . That is, an Earthquake
with magnitude of about 9.1 in the Richter
scales.
1.9=sM
The decrease in the gravitational
potential energy in the air column whose
mass is gives to the air column an initial
kinetic energy
airm
pairairk EVmE Δ== 2021 , where
is given by (15). pEΔ
In the previously mentioned HAARP
conditions, Eq.(11) gives .
Thus, from (15), we obtain
( ) 410~1 −− ioχχ
( )1910~ 4 sunseairp grmE −Δ
Thus, the initial air speed is airV0
( )20/400~/10~10 240 hkmsmrgV sesunair −≅
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).
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 , increasing consequently the
value of
aS
ioχχ (See Eq. (18)). This can cause
an increase in the velocity (See Eq. (22)). airV0
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 for d kmd 101= , the effect of the
Gravitational Shielding reaches
approximately , 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
km1010
( ) ( )211 sunsep grmE ioχχ−=Δ
where is the mass of the soil, or the mass
of the ocean water, according to the case.
m
The decrease, pEΔ , in the gravitational
potential energy increases the kinetic energy
of the local at the same ratio, in such way
that the mass acquires a kinetic
energy
m
pk EE Δ= . If this energy is not enough
to pluck the mass from the soil or the
ocean, and launch it into space, then is
converted into heat, raising the local
temperature by
m
kE
TΔ , the value of which can
be obtained from the following expression:
( )22Tk
N
Ek Δ≅
where is the number of atoms in the
volume of the substance considered;
is the Boltzmann
constant. Thus, we get
N
V
KJk /1038.1 23−×=
( )
( )
( ) ( )231
1
nk
gr
knV
grm
Nk
E
T
sunse
sunsek
io
io
ρχχ
χχ
−=
=−=≅Δ
where is the number of atoms/mn 3 in the
substance considered.
Fig. 3 - The decrease in the gravitational potential energy
of the air column, pEΔ , produces a decrease pΔ 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 pΔ 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
pEΔ .
Sun
Earth
Earth’s
atmosphere
Air column
Core
Mantle
p pp Δ−
Curst
The magnitude in the Richter
scales, corresponding to liberation of an
amount of energy,
sM
joulesEp
1910~Δ , is obtained
by means of the well-known equation:
( ) ( )181010 44.1519 sM+=
which gives . That is, an Earthquake
with magnitude of about 9.1 in the Richter
scales.
1.9=sM
The decrease in the gravitational
potential energy in the air column whose
mass is gives to the air column an initial
kinetic energy
airm
pairairk EVmE Δ== 2021 , where
is given by (15). pEΔ
In the previously mentioned HAARP
conditions, Eq.(11) gives .
Thus, from (15), we obtain
( ) 410~1 −− ioχχ
( )1910~ 4 sunseairp grmE −Δ
Thus, the initial air speed is airV0
( )20/400~/10~10 240 hkmsmrgV sesunair −≅
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).
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 , increasing consequently the
value of
aS
ioχχ (See Eq. (18)). This can cause
an increase in the velocity (See Eq. (22)). airV0
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 for d kmd 101= , the effect of the
Gravitational Shielding reaches
approximately , 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
km1010
( ) ( )211 sunsep grmE ioχχ−=Δ
where is the mass of the soil, or the mass
of the ocean water, according to the case.
m
The decrease, pEΔ , in the gravitational
potential energy increases the kinetic energy
of the local at the same ratio, in such way
that the mass acquires a kinetic
energy
m
pk EE Δ= . If this energy is not enough
to pluck the mass from the soil or the
ocean, and launch it into space, then is
converted into heat, raising the local
temperature by
m
kE
TΔ , the value of which can
be obtained from the following expression:
( )22Tk
N
Ek Δ≅
where is the number of atoms in the
volume of the substance considered;
is the Boltzmann
constant. Thus, we get
N
V
KJk /1038.1 23−×=
( )
( )
( ) ( )231
1
nk
gr
knV
grm
Nk
E
T
sunse
sunsek
io
io
ρχχ
χχ
−=
=−=≅Δ
where is the number of atoms/mn 3 in the
substance considered.
Page 7
7
In the previously mentioned HAARP
conditions, Eq. (11) gives ( ) 410~1 −− ioχχ .
Thus, from (23), we obtain
( )24104.6 27 ρ
n
T
×≅Δ
For most liquid and solid substances
the value of is about , and
. Therefore, in this case, Eq.
(24) gives
n 328 /10 matoms
33 /10~ mkgρ
CKT °≅≅Δ 400640
This means that, the region in the soil or in
the ocean will have its temperature increased
by approximately 400°C.
By increasing or decreasing the
frequency, , of the ELF radiation, it is
possible to increase
ELFP
f
TΔ (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 ( is a standing wave
in the Earth–ionosphere cavity with a
wavelength equal to the circumference of the
Earth. This lowest-frequency (and highest-
intensity) mode of the Schumann resonance
occurs at a frequency
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 well-
known expression:
( )25
4
W
c
D =
where is the speed of light, and c
2
02
1 EW ε= . The electric field E , is given by
2
04 ⊕
=
r
q
E πε
where Cq 000,500= [24] and .
Therefore, we get
mr 610371.6 ×=⊕
( )26/1.4
,/104.5
,/7.110
2
38
mWD
mJW
mVE
≅
×=
=
−
The area, , of the cross-section of the cavity
is . Thus, the ELF
radiation power is . The
total power escaping from the Earth-
ionosphere waveguide, , is only a fraction of
this value and need to be determined.
S
212104.22 mdrS ×== ⊕π
WDSP 12108.9 ×≅=
escP
When this ELF radiation crosses the
Van Allen belts the Gravitational Shieldings
So and Si can be produced (See Fig.4).
Fig.4 – ELF radiation escaping from the Earth–
ionosphere waveguide can produce the Gravitational
Shieldings So and Si in the Van Allen belts.
kmd 000,12610~ =× ⊕
Inner
core
Outer
core
Crust
Mantle
Earth
So
Si
⊕d
ELF
radiation
Reach of the Gravitational Shielding
)1=n
Hzf 83.71 = [24].
The ELF radiation power densities and
, respectively in S
iD
oD i and So, are given by
In the previously mentioned HAARP
conditions, Eq. (11) gives ( ) 410~1 −− ioχχ .
Thus, from (23), we obtain
( )24104.6 27 ρ
n
T
×≅Δ
For most liquid and solid substances
the value of is about , and
. Therefore, in this case, Eq.
(24) gives
n 328 /10 matoms
33 /10~ mkgρ
CKT °≅≅Δ 400640
This means that, the region in the soil or in
the ocean will have its temperature increased
by approximately 400°C.
By increasing or decreasing the
frequency, , of the ELF radiation, it is
possible to increase
ELFP
f
TΔ (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 ( is a standing wave
in the Earth–ionosphere cavity with a
wavelength equal to the circumference of the
Earth. This lowest-frequency (and highest-
intensity) mode of the Schumann resonance
occurs at a frequency
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 well-
known expression:
( )25
4
W
c
D =
where is the speed of light, and c
2
02
1 EW ε= . The electric field E , is given by
2
04 ⊕
=
r
q
E πε
where Cq 000,500= [24] and .
Therefore, we get
mr 610371.6 ×=⊕
( )26/1.4
,/104.5
,/7.110
2
38
mWD
mJW
mVE
≅
×=
=
−
The area, , of the cross-section of the cavity
is . Thus, the ELF
radiation power is . The
total power escaping from the Earth-
ionosphere waveguide, , is only a fraction of
this value and need to be determined.
S
212104.22 mdrS ×== ⊕π
WDSP 12108.9 ×≅=
escP
When this ELF radiation crosses the
Van Allen belts the Gravitational Shieldings
So and Si can be produced (See Fig.4).
Fig.4 – ELF radiation escaping from the Earth–
ionosphere waveguide can produce the Gravitational
Shieldings So and Si in the Van Allen belts.
kmd 000,12610~ =× ⊕
Inner
core
Outer
core
Crust
Mantle
Earth
So
Si
⊕d
ELF
radiation
Reach of the Gravitational Shielding
)1=n
Hzf 83.71 = [24].
The ELF radiation power densities and
, respectively in S
iD
oD i and So, are given by
Page 8
8
( )27
4 2i
esc
i
r
P
D π=
and
( )28
4 2o
esc
o
r
P
D π=
where and are respectively, the
distances from the Earth’s center up to the
Gravitational Shieldings S
ir or
i and So .
Under these circumstances, the kinetic
energy related to the mass, , of the
Earth’s outer core
ocm
§, with respect to the Sun’s
center, considering the effects produced by
the Gravitational Shieldings So and Si ** is ( ) ( )291 221 ococsunseock VmgrmE io =−= χχ
Thus, we get ( ) ( )301 sunseoc grV io χχ−=
The average radius of the outer core
is mroc
6103.2 ×= . Then, assuming that the
average angular speed of the outer core, ocϖ ,
has the same order of magnitude of the
average angular speed of the Earth’s
crust, ⊕ϖ , i.e., ,
then we get
sradoc /1029.7~
5−⊕ ×=ϖϖ
smrV ocococ /10~
2ϖ= . Thus, Eq.
(30) gives ( ) ( )3110~1 5−−
io
χχ
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 ioχχ equals 1, and the
§ 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.
** Note that the reach of the Gravitational Shielding
is . kmd 000,12610~ =× ⊕
†† 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 Earth-
ionosphere waveguide will also be increased.
speed ocV will be null. After a time
interval, the progressive increasing of the
power density of the ELF radiation makes
ioχχ greater than 1. Equation (29) shows
that, at this moment, the velocity
resurges, but now in the opposite direction.
ocV
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, ocϖ , 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 ( )
io
χχ−1 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.
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
sunR ggg −=
where 232 /1092.5 smrGMg sesunsun
−×=−= is the
gravity due to the Sun at the monolith and
. 2/8.9 smg=
If we place upon the monolith a mantle
with a set of Gravitational Shieldings
inside, the value of becomes
n
Rg
sun
n
R ggg χ−=
This shows that, it is possible to reduce
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 [
Rg
22].
When the Gravitational Shieldings are active the
( )27
4 2i
esc
i
r
P
D π=
and
( )28
4 2o
esc
o
r
P
D π=
where and are respectively, the
distances from the Earth’s center up to the
Gravitational Shieldings S
ir or
i and So .
Under these circumstances, the kinetic
energy related to the mass, , of the
Earth’s outer core
ocm
§, with respect to the Sun’s
center, considering the effects produced by
the Gravitational Shieldings So and Si ** is ( ) ( )291 221 ococsunseock VmgrmE io =−= χχ
Thus, we get ( ) ( )301 sunseoc grV io χχ−=
The average radius of the outer core
is mroc
6103.2 ×= . Then, assuming that the
average angular speed of the outer core, ocϖ ,
has the same order of magnitude of the
average angular speed of the Earth’s
crust, ⊕ϖ , i.e., ,
then we get
sradoc /1029.7~
5−⊕ ×=ϖϖ
smrV ocococ /10~
2ϖ= . Thus, Eq.
(30) gives ( ) ( )3110~1 5−−
io
χχ
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 ioχχ equals 1, and the
§ 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.
** Note that the reach of the Gravitational Shielding
is . kmd 000,12610~ =× ⊕
†† 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 Earth-
ionosphere waveguide will also be increased.
speed ocV will be null. After a time
interval, the progressive increasing of the
power density of the ELF radiation makes
ioχχ greater than 1. Equation (29) shows
that, at this moment, the velocity
resurges, but now in the opposite direction.
ocV
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, ocϖ , 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 ( )
io
χχ−1 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.
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
sunR ggg −=
where 232 /1092.5 smrGMg sesunsun
−×=−= is the
gravity due to the Sun at the monolith and
. 2/8.9 smg=
If we place upon the monolith a mantle
with a set of Gravitational Shieldings
inside, the value of becomes
n
Rg
sun
n
R ggg χ−=
This shows that, it is possible to reduce
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 [
Rg
22].
When the Gravitational Shieldings are active the
Page 9
9
(a) (b)
Cross-section of the Mantle
(c)
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 8χ , in such way that the gravity resultant upon the
monoliths (a) and (b) becomes SunR ggg
8χ−= . Thus, for example, if 525.2−=χ results 2/028.0 smg R = .
Under these circumstances, the weight of the monolith becomes 3109.2 −× of the initial weight.
~
~ 1 mm
g
Sung
8χ
g
Sung
8χ
Set of 8 Gravitational Shieldings inside the Mantle
ELF
f
V
mμ10 mμ100
dielectric metallic
foils
High-dielectric strength
semiconductor
Mantle
(a) (b)
Cross-section of the Mantle
(c)
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 8χ , in such way that the gravity resultant upon the
monoliths (a) and (b) becomes SunR ggg
8χ−= . Thus, for example, if 525.2−=χ results 2/028.0 smg R = .
Under these circumstances, the weight of the monolith becomes 3109.2 −× of the initial weight.
~
~ 1 mm
g
Sung
8χ
g
Sung
8χ
Set of 8 Gravitational Shieldings inside the Mantle
ELF
f
V
mμ10 mμ100
dielectric metallic
foils
High-dielectric strength
semiconductor
Mantle
Page 10
10
gravity due to the Sun is multiplied by the
factor , in such way that the gravity resultant
upon the monolith becomes .
Thus, for example, if
8χ
SunR ggg
8χ−=
525.2−=χ the result is
. Under these circumstances,
the weight of the monolith becomes of
the initial weight.
2/028.0 smg R =
3109.2 −×
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 in the
mentioned regions, and possibly can produce
a tunneling effect to the imaginary
spacetime.
wE
The electric field 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, , will be
the double of the current density expressed
by the well-known equation of Langmuir-
Child
wE
wj
( )321033.22
9
4
2
6
220
2
3
2
3
2
3
r
V
r
V
r
V
m
e
j
e
r
−×=== αεε
where 1≅rε for the air; is
the called Child’s constant;
61033.2 −×=α
r , in this case, is
the distance between the center of the charges
and the Gravitational Shieldings and
(see Fig.6) (
1wS 2wS( ) mmr 161521 107104.1 −− ×=×= ); V is the
voltage drop given by
( )33
22 00 A
Qr
rrEV Qw εε
σ ===
where is the anomalous amount of charge
in the region with area , i.e.,
Q
A
qAQQ ησσ == , η is the ratio of
proportionality, and 2102 /108.94 mCRqq
−×≅= πσ
is the normal charge density ; is
the total charge[
Cq 000,500=
24], then nq qAQ ηση ==
( qn Aq σ= is the normal amount of charge in
the area ). A
By substituting (33) into (32), we get
( )34
2
22
222
2
3
2
3
2
3
0
2
0
2 ⎟⎟⎠
⎞
⎜⎜⎝
⎛=
⎟⎟⎠
⎞
⎜⎜⎝
⎛
===
A
Q
rr
A
Qr
r
V
jjw ε
αεαα
Since 02εσQwE = and www Ej σ= , we can
write that
( )
( )351014.2
18.018.018.0
22
2
5.516
5.5
0
5.1
5.53
5.5
0
5.1
5.53
5.55.5
0
5.1
5.53
0
3
0
343
2
3
η
ε
ησα
ε
σα
ε
α
εε
ασ
×=
====
=
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
⎟⎟⎠
⎞
⎜⎜⎝
⎛==
rrAr
Q
A
Q
A
Q
r
EjE
qQ
wwww
The electric field has an oscillating
component, , with frequency, , equal to
the lowest Schumann resonance frequency
wE
1wE f
Hzf 83.71 = . Then, by using Eq. (7), that can
be rewritten in the following form [18]:
( )36110758.1121 32
43
27
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−×+−== −
f
E
m
m r
i
g
ρ
σμχ
we can write that
( )37110758.1121 3
1
2
4
1
3
27
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−×+−== −
f
E
m
m
w
wwrw
i
g
w ρ
σμχ
By substitution of Eq. (35), 1=rwμ ,
and into the
expression above, we obtain
32 /101 mkgw
−×=ρ Hzf 83.71 =
( )3811084.7121 5.510 ⎭⎬⎫⎩⎨⎧ ⎥⎦⎤⎢⎣⎡ −×+−= − ηχw
The gravity below will be
decreased by the effect of the Gravitational
Shieldings and , according to the
following expression
2wS
1wS 2wS
( )sunww gg 21χχ−
where www χχχ == 21 . Thus, we get
gravity due to the Sun is multiplied by the
factor , in such way that the gravity resultant
upon the monolith becomes .
Thus, for example, if
8χ
SunR ggg
8χ−=
525.2−=χ the result is
. Under these circumstances,
the weight of the monolith becomes of
the initial weight.
2/028.0 smg R =
3109.2 −×
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 in the
mentioned regions, and possibly can produce
a tunneling effect to the imaginary
spacetime.
wE
The electric field 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, , will be
the double of the current density expressed
by the well-known equation of Langmuir-
Child
wE
wj
( )321033.22
9
4
2
6
220
2
3
2
3
2
3
r
V
r
V
r
V
m
e
j
e
r
−×=== αεε
where 1≅rε for the air; is
the called Child’s constant;
61033.2 −×=α
r , in this case, is
the distance between the center of the charges
and the Gravitational Shieldings and
(see Fig.6) (
1wS 2wS( ) mmr 161521 107104.1 −− ×=×= ); V is the
voltage drop given by
( )33
22 00 A
Qr
rrEV Qw εε
σ ===
where is the anomalous amount of charge
in the region with area , i.e.,
Q
A
qAQQ ησσ == , η is the ratio of
proportionality, and 2102 /108.94 mCRqq
−×≅= πσ
is the normal charge density ; is
the total charge[
Cq 000,500=
24], then nq qAQ ηση ==
( qn Aq σ= is the normal amount of charge in
the area ). A
By substituting (33) into (32), we get
( )34
2
22
222
2
3
2
3
2
3
0
2
0
2 ⎟⎟⎠
⎞
⎜⎜⎝
⎛=
⎟⎟⎠
⎞
⎜⎜⎝
⎛
===
A
Q
rr
A
Qr
r
V
jjw ε
αεαα
Since 02εσQwE = and www Ej σ= , we can
write that
( )
( )351014.2
18.018.018.0
22
2
5.516
5.5
0
5.1
5.53
5.5
0
5.1
5.53
5.55.5
0
5.1
5.53
0
3
0
343
2
3
η
ε
ησα
ε
σα
ε
α
εε
ασ
×=
====
=
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
⎟⎟⎠
⎞
⎜⎜⎝
⎛==
rrAr
Q
A
Q
A
Q
r
EjE
wwww
The electric field has an oscillating
component, , with frequency, , equal to
the lowest Schumann resonance frequency
wE
1wE f
Hzf 83.71 = . Then, by using Eq. (7), that can
be rewritten in the following form [18]:
( )36110758.1121 32
43
27
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−×+−== −
f
E
m
m r
i
g
ρ
σμχ
we can write that
( )37110758.1121 3
1
2
4
1
3
27
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−×+−== −
f
E
m
m
w
wwrw
i
g
w ρ
σμχ
By substitution of Eq. (35), 1=rwμ ,
and into the
expression above, we obtain
32 /101 mkgw
−×=ρ Hzf 83.71 =
( )3811084.7121 5.510 ⎭⎬⎫⎩⎨⎧ ⎥⎦⎤⎢⎣⎡ −×+−= − ηχw
The gravity below will be
decreased by the effect of the Gravitational
Shieldings and , according to the
following expression
2wS
1wS 2wS
( )sunww gg 21χχ−
where www χχχ == 21 . Thus, we get
Page 11
11
Fig. 6 - Gravitational Shieldings 1wS and 2wS produced by strong densities of electric charge in the
upper boundary of the Earth-Ionosphere.
ground
+ + + + + + + + + + + + + + +
R
Region with much greater
concentration of electric chargesIonosphere
Upper boundary
of the
Earth-Ionosphere waveguide
r 1wS
2wS
d
Reach of the Gravitational Shielding
~10 X d
60 km
Earth-Ionosphere waveguide
sunww gg 21χχ−g g
wE
Qσ
A
qσ
Fig. 6 - Gravitational Shieldings 1wS and 2wS produced by strong densities of electric charge in the
upper boundary of the Earth-Ionosphere.
ground
+ + + + + + + + + + + + + + +
R
Region with much greater
concentration of electric chargesIonosphere
Upper boundary
of the
Earth-Ionosphere waveguide
r 1wS
2wS
d
Reach of the Gravitational Shielding
~10 X d
60 km
Earth-Ionosphere waveguide
sunww gg 21χχ−g g
wE
Qσ
A
qσ
Page 12
12
gg
g
gsun χη =⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎭⎬
⎫
⎩⎨
⎧
⎥⎦
⎤⎢⎣
⎡ −×+−− −
2
5.510 11084.71211
where
( )3911084.71211 25.510 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎭⎬
⎫
⎩⎨
⎧
⎥⎦
⎤⎢⎣
⎡ −×+−−= −
g
g sunηχ
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
to or the local gravity
im159.0+
im159.0− ( )g is
reduced to a value in the range of
to , the body performs a transition
to the imaginary spacetime. This means that,
if the value of
g159.0+
g159.0−
χ given by Eq.(39) is in the
range 159.0159.0 −<< χ , then any body
(aircrafts, ships, etc) that enters the region -
defined by the volume ( )dA 10~× below the
Gravitational Shielding , 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 , which reduces the gravitational
mass of the body (or the gravitational
shieldings, which reduce the local gravity)
does not
2wS
1wE
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 of the body, it will never
more come back to the Real Universe.
Ψ
Equation (39) shows that, in order to
obtain χ in the range of 159.0159.0 −<<χ the
value of η must be in the following range:
4.1351.127 << η
Since the normal charge density is
then it must be increased
by about 130 times in order to transform the
region , below the Gravitational
Shielding , in a gate to the imaginary
spacetime.
210 /108.9 mCq
−×≅σ
( dA 10~× )
2wS
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
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 is the length of
the object in its rest frame, then the length
, observed by an observer in relative
motion with respect to the object, is given by
0L
L
( ) ( )401 2200 cVLV
L
L −== γ
where is the relative velocity between the
observer and the moving object and the
speed of light. The function
V
c( )Vγ is known as
the Lorentz factor.
It was shown that Eq. (3) can be
written in the following form [18]:
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−
−
−=
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+−= 1
1
1
211121
22
2
00 cVcm
p
m
m
ii
g
This expression shows that
( ) ( )41
1
1
1
22
2
0
V
cVcm
p
i
γ=
−
=⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+
By substitution of Eq. (41) into Eq.(40) we
get
( ) ( )42
1
2
0
00
⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+
==
cm
p
L
V
L
L
i
γ
It was shown that, the term, cmp i0Δ , in the
equation above is equal to 2cWn r ρ , where
is the density of electromagnetic energy
absorbed by the body and the index of
refraction, given by
W
rn
( ) ⎟⎠⎞⎜⎝⎛ ++== 112 2ωεσ
με rr
r v
c
n
In the case of επσ f2>> , ( ) 28 EfW πσ= and
fcvcnr πμσ 42== [30]. Thus, in this case,
Eq. (42) can be written as follows
( )43
10758.11 432
3
27
0
E
f
L
L
r ⎟⎟⎠
⎞
⎜⎜⎝
⎛×+
=
−
ρ
σμ
gg
g
gsun χη =⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎭⎬
⎫
⎩⎨
⎧
⎥⎦
⎤⎢⎣
⎡ −×+−− −
2
5.510 11084.71211
where
( )3911084.71211 25.510 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎭⎬
⎫
⎩⎨
⎧
⎥⎦
⎤⎢⎣
⎡ −×+−−= −
g
g sunηχ
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
to or the local gravity
im159.0+
im159.0− ( )g is
reduced to a value in the range of
to , the body performs a transition
to the imaginary spacetime. This means that,
if the value of
g159.0+
g159.0−
χ given by Eq.(39) is in the
range 159.0159.0 −<< χ , then any body
(aircrafts, ships, etc) that enters the region -
defined by the volume ( )dA 10~× below the
Gravitational Shielding , 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 , which reduces the gravitational
mass of the body (or the gravitational
shieldings, which reduce the local gravity)
does not
2wS
1wE
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 of the body, it will never
more come back to the Real Universe.
Ψ
Equation (39) shows that, in order to
obtain χ in the range of 159.0159.0 −<<χ the
value of η must be in the following range:
4.1351.127 << η
Since the normal charge density is
then it must be increased
by about 130 times in order to transform the
region , below the Gravitational
Shielding , in a gate to the imaginary
spacetime.
210 /108.9 mCq
−×≅σ
( dA 10~× )
2wS
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
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 is the length of
the object in its rest frame, then the length
, observed by an observer in relative
motion with respect to the object, is given by
0L
L
( ) ( )401 2200 cVLV
L
L −== γ
where is the relative velocity between the
observer and the moving object and the
speed of light. The function
V
c( )Vγ is known as
the Lorentz factor.
It was shown that Eq. (3) can be
written in the following form [18]:
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−
−
−=
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+−= 1
1
1
211121
22
2
00 cVcm
p
m
m
ii
g
This expression shows that
( ) ( )41
1
1
1
22
2
0
V
cVcm
p
i
γ=
−
=⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+
By substitution of Eq. (41) into Eq.(40) we
get
( ) ( )42
1
2
0
00
⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+
==
cm
p
L
V
L
L
i
γ
It was shown that, the term, cmp i0Δ , in the
equation above is equal to 2cWn r ρ , where
is the density of electromagnetic energy
absorbed by the body and the index of
refraction, given by
W
rn
( ) ⎟⎠⎞⎜⎝⎛ ++== 112 2ωεσ
με rr
r v
c
n
In the case of επσ f2>> , ( ) 28 EfW πσ= and
fcvcnr πμσ 42== [30]. Thus, in this case,
Eq. (42) can be written as follows
( )43
10758.11 432
3
27
0
E
f
L
L
r ⎟⎟⎠
⎞
⎜⎜⎝
⎛×+
=
−
ρ
σμ
Page 13
13
Note that tEE m ωsin= .The average value
for 2E is equal to 221 mE because E varies
sinusoidaly ( is the maximum value
for
mE
E ). On the other hand, 2mrms EE = .
Consequently we can change 4E by ,
and the equation above can be rewritten as
follows
4
rmsE
( )44
10758.11 432
3
27
0
rms
r E
f
L
L
⎟⎟⎠
⎞
⎜⎜⎝
⎛×+
=
−
ρ
σμ
Now, consider an airplane traveling in a
region of the atmosphere. Suddenly, along a
distance of the trajectory of the airplane
arises an ELF electric field with intensity
and frequency . The
Aluminum density is and
its conductivity is .
According to Eq. (44), for the airplane the
distance is shortened by . Under
these conditions, a distance of about
3000km will become just 0.08km.
0L
15 .10~ −mVErms Hzf 1~
33 .107.2 −×= mkgρ
17 .1082.3 −×= mSσ
0L
5107.2 −×
0L
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:
( )
22
0
0
1 cV
T
VTT
−
== γ
where is the interval time measured at the
object in its rest frame (known as the proper
time);
0T
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:
2
0
022
0 1
1
⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+=
−
=
cm
p
T
cV
T
T
i
For , we can write that and cV << Vmp i0=Δ
ϕϕ 22002021 =⇒== VmgrmVm iii
where ϕ is the gravitational potential.
Then, it follows that
22
22
0
2
2
0
2
2
cc
V
cm
p
andV
m
p
ii
ϕϕ ==⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ==⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ
Consequently, the expression of T becomes
2022
0 21
1 c
T
cV
T
T
ϕ+=
−
=
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:
( )4510758.111 432
3
27
0
2
0
0 rms
r
i
E
f
T
cm
p
TT ⎟⎟⎠
⎞
⎜⎜⎝
⎛×+=⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+= − ρ
σμ
Now, consider a ship in the ocean. It is
made of steel ( 300=rμ ; ;
). When subjected to a
uniform ELF electromagnetic field, with
intensity and
frequency
16 .101.1 −×= mSσ
33 .108.7 −×= mkgρ
13 .1036.1 −×= mVErms
Hzf 1= , the ship will perform a
transition in time to a time T given by
( ) 460195574.1
10758.11
0
4
32
3
27
0
T
E
f
TT rms
r
=
=⎟⎟⎠
⎞
⎜⎜⎝
⎛×+= − ρ
σμ
( )
If shJanuaryT 0min00,19431,0 = then
the ship performs a transition in time
to shJanuaryT 0min00,19811,= . Note
that the use of ELF ( )Hzf 1= is fundamental.
It is important to note that the
electromagnetic field , besides being
uniform, must remain with the ship during
the transition to the time
rmsE
T . If it is not
uniform, each part of the ship will perform
transitions for different times in the future.
On the other hand, the field must remain with
the ship, because, if it stays at the time ,
the transition is interrupted. In order to the
electromagnetic field remains at the ship, it is
necessary that all the parts, which are
involved with the generation of the field, stay
0T
Note that tEE m ωsin= .The average value
for 2E is equal to 221 mE because E varies
sinusoidaly ( is the maximum value
for
mE
E ). On the other hand, 2mrms EE = .
Consequently we can change 4E by ,
and the equation above can be rewritten as
follows
4
rmsE
( )44
10758.11 432
3
27
0
rms
r E
f
L
L
⎟⎟⎠
⎞
⎜⎜⎝
⎛×+
=
−
ρ
σμ
Now, consider an airplane traveling in a
region of the atmosphere. Suddenly, along a
distance of the trajectory of the airplane
arises an ELF electric field with intensity
and frequency . The
Aluminum density is and
its conductivity is .
According to Eq. (44), for the airplane the
distance is shortened by . Under
these conditions, a distance of about
3000km will become just 0.08km.
0L
15 .10~ −mVErms Hzf 1~
33 .107.2 −×= mkgρ
17 .1082.3 −×= mSσ
0L
5107.2 −×
0L
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:
( )
22
0
0
1 cV
T
VTT
−
== γ
where is the interval time measured at the
object in its rest frame (known as the proper
time);
0T
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:
2
0
022
0 1
1
⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+=
−
=
cm
p
T
cV
T
T
i
For , we can write that and cV << Vmp i0=Δ
ϕϕ 22002021 =⇒== VmgrmVm iii
where ϕ is the gravitational potential.
Then, it follows that
22
22
0
2
2
0
2
2
cc
V
cm
p
andV
m
p
ii
ϕϕ ==⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ==⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ
Consequently, the expression of T becomes
2022
0 21
1 c
T
cV
T
T
ϕ+=
−
=
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:
( )4510758.111 432
3
27
0
2
0
0 rms
r
i
E
f
T
cm
p
TT ⎟⎟⎠
⎞
⎜⎜⎝
⎛×+=⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+= − ρ
σμ
Now, consider a ship in the ocean. It is
made of steel ( 300=rμ ; ;
). When subjected to a
uniform ELF electromagnetic field, with
intensity and
frequency
16 .101.1 −×= mSσ
33 .108.7 −×= mkgρ
13 .1036.1 −×= mVErms
Hzf 1= , the ship will perform a
transition in time to a time T given by
( ) 460195574.1
10758.11
0
4
32
3
27
0
T
E
f
TT rms
r
=
=⎟⎟⎠
⎞
⎜⎜⎝
⎛×+= − ρ
σμ
( )
If shJanuaryT 0min00,19431,0 = then
the ship performs a transition in time
to shJanuaryT 0min00,19811,= . Note
that the use of ELF ( )Hzf 1= is fundamental.
It is important to note that the
electromagnetic field , besides being
uniform, must remain with the ship during
the transition to the time
rmsE
T . If it is not
uniform, each part of the ship will perform
transitions for different times in the future.
On the other hand, the field must remain with
the ship, because, if it stays at the time ,
the transition is interrupted. In order to the
electromagnetic field remains at the ship, it is
necessary that all the parts, which are
involved with the generation of the field, stay
0T
Page 14
14
inside the ship. If persons are inside the ship
they will perform transitions for different
times in the future because their
conductivities and densities are different.
Since the conductivity and density of the ship
and of the persons are different, they will
perform transitions to different times. This
means that the ship and the persons must
have the same characteristics, in order to
perform transitions to the same time. Thus, in
this way is unsuitable and highly dangerous
to make transitions to the future with
persons. However, there is a way to solve
this problem. If we can control the
gravitational mass of a body, in such way
that 0ig mm χ= , and we put this body inside
a ship with gravitational mass 0ig MM ≅ ,
then the total gravitational mass of the ship
will be given by‡‡
( ) 00 iiggtotalg mMmMM χ+=+=
or
( ) ( )471
0
0
0 i
i
i
totalg
ship M
m
M
M χχ +==
Since
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+−== 1121
2
00 cM
p
M
M
ii
g
shipχ
we can write that
( )48
2
3
1
2
0
ship
i cM
p χ−=⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+
Then it follows that
( )49
2
3
1 0
2
0
0 ⎟⎟⎠
⎞
⎜⎜⎝
⎛ −=⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+= ship
i
T
cM
p
TT
χ
Substitution of Eq. (47) into Eq. (49) gives
( )50
2
1
0
0
0 ⎟⎟⎠
⎞
⎜⎜⎝
⎛ −=
i
i
M
m
TT
χ
Note that, if ( )000391148.0 ii mM−=χ , Eq.
(50) gives ( )0195574.10TT =
which is the same value given by Eq.(46).
‡‡ This idea was originally presented by the author in
the paper: The Gravitational Spacecraft [30].
Other safe way to make transitions
in the time is by means of flights with
relativistic speeds, according to predicted by
the equation:
( )51
1 22
0
cV
T
T
−±
=
With the advent of the Gravitational
Spacecrafts [30], which could reach velocities
close to the light speed, this possibility will
become very promising.
It was shown in a previous paper [18]
that by varying the gravitational mass of the
spacecraft for negative or positive we can go
respectively to the past or future.
If the gravitational mass of a particle is
positive, then t is always positive and given
by
( )521 220 cVtt −+=
This leads to the well-known relativistic
prediction that the particle goes to the future
if . However, if the gravitational
mass of the particle is negative, then t is also
negative and, therefore, given by
cV →
( )531 220 cVtt −−=
In this case, the prevision is that the particle
goes to the past if . In this way,
negative gravitational mass is the necessary
condition to the particle to go to the past.
cV →
Now, consider a parallel plate
capacitor, which has a high-dielectric strength
semiconductor between its plates, with the
following characteristics 1=rμ ; ;
. According to Eq.(45), when
the semiconductor is subjected to a uniform
ELF electromagnetic field, with intensity
14 .10 −= mSσ
33 .10 −= mkgρ
( )mmKVmVErms /1.0.10 15 −= and frequency
Hzf 1= , it should perform a transition in
time to a time T given by
( ) (5408434.1
10758.11
0
4
32
3
27
0
T
E
f
TT rms
r
=
=⎟⎟⎠
⎞
⎜⎜⎝
⎛×+= − ρ
σμ
)
However, the transition is not performed,
because the electromagnetic field is external
to the semiconductor, and obviously would
not accompany the semiconductor during the
transition. In other words, the field stays at
inside the ship. If persons are inside the ship
they will perform transitions for different
times in the future because their
conductivities and densities are different.
Since the conductivity and density of the ship
and of the persons are different, they will
perform transitions to different times. This
means that the ship and the persons must
have the same characteristics, in order to
perform transitions to the same time. Thus, in
this way is unsuitable and highly dangerous
to make transitions to the future with
persons. However, there is a way to solve
this problem. If we can control the
gravitational mass of a body, in such way
that 0ig mm χ= , and we put this body inside
a ship with gravitational mass 0ig MM ≅ ,
then the total gravitational mass of the ship
will be given by‡‡
( ) 00 iiggtotalg mMmMM χ+=+=
or
( ) ( )471
0
0
0 i
i
i
totalg
ship M
m
M
M χχ +==
Since
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+−== 1121
2
00 cM
p
M
M
ii
g
shipχ
we can write that
( )48
2
3
1
2
0
ship
i cM
p χ−=⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+
Then it follows that
( )49
2
3
1 0
2
0
0 ⎟⎟⎠
⎞
⎜⎜⎝
⎛ −=⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+= ship
i
T
cM
p
TT
χ
Substitution of Eq. (47) into Eq. (49) gives
( )50
2
1
0
0
0 ⎟⎟⎠
⎞
⎜⎜⎝
⎛ −=
i
i
M
m
TT
χ
Note that, if ( )000391148.0 ii mM−=χ , Eq.
(50) gives ( )0195574.10TT =
which is the same value given by Eq.(46).
‡‡ This idea was originally presented by the author in
the paper: The Gravitational Spacecraft [30].
Other safe way to make transitions
in the time is by means of flights with
relativistic speeds, according to predicted by
the equation:
( )51
1 22
0
cV
T
T
−±
=
With the advent of the Gravitational
Spacecrafts [30], which could reach velocities
close to the light speed, this possibility will
become very promising.
It was shown in a previous paper [18]
that by varying the gravitational mass of the
spacecraft for negative or positive we can go
respectively to the past or future.
If the gravitational mass of a particle is
positive, then t is always positive and given
by
( )521 220 cVtt −+=
This leads to the well-known relativistic
prediction that the particle goes to the future
if . However, if the gravitational
mass of the particle is negative, then t is also
negative and, therefore, given by
cV →
( )531 220 cVtt −−=
In this case, the prevision is that the particle
goes to the past if . In this way,
negative gravitational mass is the necessary
condition to the particle to go to the past.
cV →
Now, consider a parallel plate
capacitor, which has a high-dielectric strength
semiconductor between its plates, with the
following characteristics 1=rμ ; ;
. According to Eq.(45), when
the semiconductor is subjected to a uniform
ELF electromagnetic field, with intensity
14 .10 −= mSσ
33 .10 −= mkgρ
( )mmKVmVErms /1.0.10 15 −= and frequency
Hzf 1= , it should perform a transition in
time to a time T given by
( ) (5408434.1
10758.11
0
4
32
3
27
0
T
E
f
TT rms
r
=
=⎟⎟⎠
⎞
⎜⎜⎝
⎛×+= − ρ
σμ
)
However, the transition is not performed,
because the electromagnetic field is external
to the semiconductor, and obviously would
not accompany the semiconductor during the
transition. In other words, the field stays at
Page 15
15
the time , and the transition is not
performed.
0T
7. Detection of Earthquakes at the Very
Early Stage
When an earthquake occurs, energy
radiates outwards in all directions. The
energy travels through and around the earth
as three types of seismic waves called
primary, secondary, and surface waves (P-
wave, S-wave and Surface-waves). All
various types of earthquakes follow this
pattern. At a given distance from the
epicenter, first the P-waves arrive, then the
S-waves, both of which have such small
energies that they are mostly not threatening.
Finally, the surface waves arrive with all of
their damaging energies. It is predominantly
the surface waves that we would notice as the
earthquake. This knowledge, that, preceding
any destructive earthquake, there are telltales
P-waves, are used by the earthquake warning
systems to reliably initiate an alarm before
the arrival of the destructive waves.
Unfortunately, the warning time of these
earthquake warning systems is less than 60
seconds.
Earthquakes are caused by the
movement of tectonic plates. There are three
types of motion: plates moving away from
each other (at divergent boundaries); moving
towards each other (at convergent
boundaries) or sliding past one another (at
transform boundaries). When these
movements are interrupted by an obstacle
(rocks, for example), an Earthquake occurs
when the obstacle breaks (due to the sudden
release of stored energy).
The pressure P acting on the obstacle
and the corresponding reaction modifies the
gravitational mass of the matter along the
pressing surfaces, according to the following
expression [18]:
( )551
2
121 0
2
32
2
ig m
cv
P
m
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛+−= ρ
where ρ and are respectively, the density
of matter and the speed of the pressure waves
in the mentioned region.
v
Hooke’s law tells us that ,
thus Eq. (55) can be rewritten as follows
2vP ρ=
( )561
4
121 02 ig mc
P
m ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡ −+−= ρ
or
( )571
4
121
2
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡ −+−== ρχ c
P
m
m
i
g
Thus, the matter subjected to the
pressure P works as a Gravitational
Shielding. Consequently, if the gravity below
it is , then the gravity above it is⊕g ⊕gχ , in
such way that a gravimeter on the Earth
surface (See Fig.7) shall detect a gravity
anomaly gΔ given by
( ) ( )581 ⊕⊕⊕ −=−=Δ gggg χχ
Substitution of Eq. (57) into this Eq. (58)
yields
( )591
4
12
2 ⊕⎥⎥⎦
⎤
⎢⎢⎣
⎡ −+=Δ g
c
P
g ρ
Thus, when a gravity anomaly is detected,
we can evaluate, by means of Eq. (59), the
magnitude of the ratio ρP in the
compressing region. On the other hand,
several experimental observations of the time
interval between the appearing of gravity
anomaly gΔ and the breaking of the obstacle
(beginning of the Earthquake) will give us a
statistical value for the mentioned time
interval, which will warn us (earthquake
warning system) when to initiate an alarm.
Obviously, the earthquake warning time, in
this case becomes much greater than 60
seconds.
the time , and the transition is not
performed.
0T
7. Detection of Earthquakes at the Very
Early Stage
When an earthquake occurs, energy
radiates outwards in all directions. The
energy travels through and around the earth
as three types of seismic waves called
primary, secondary, and surface waves (P-
wave, S-wave and Surface-waves). All
various types of earthquakes follow this
pattern. At a given distance from the
epicenter, first the P-waves arrive, then the
S-waves, both of which have such small
energies that they are mostly not threatening.
Finally, the surface waves arrive with all of
their damaging energies. It is predominantly
the surface waves that we would notice as the
earthquake. This knowledge, that, preceding
any destructive earthquake, there are telltales
P-waves, are used by the earthquake warning
systems to reliably initiate an alarm before
the arrival of the destructive waves.
Unfortunately, the warning time of these
earthquake warning systems is less than 60
seconds.
Earthquakes are caused by the
movement of tectonic plates. There are three
types of motion: plates moving away from
each other (at divergent boundaries); moving
towards each other (at convergent
boundaries) or sliding past one another (at
transform boundaries). When these
movements are interrupted by an obstacle
(rocks, for example), an Earthquake occurs
when the obstacle breaks (due to the sudden
release of stored energy).
The pressure P acting on the obstacle
and the corresponding reaction modifies the
gravitational mass of the matter along the
pressing surfaces, according to the following
expression [18]:
( )551
2
121 0
2
32
2
ig m
cv
P
m
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛+−= ρ
where ρ and are respectively, the density
of matter and the speed of the pressure waves
in the mentioned region.
v
Hooke’s law tells us that ,
thus Eq. (55) can be rewritten as follows
2vP ρ=
( )561
4
121 02 ig mc
P
m ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡ −+−= ρ
or
( )571
4
121
2
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡ −+−== ρχ c
P
m
m
i
g
Thus, the matter subjected to the
pressure P works as a Gravitational
Shielding. Consequently, if the gravity below
it is , then the gravity above it is⊕g ⊕gχ , in
such way that a gravimeter on the Earth
surface (See Fig.7) shall detect a gravity
anomaly gΔ given by
( ) ( )581 ⊕⊕⊕ −=−=Δ gggg χχ
Substitution of Eq. (57) into this Eq. (58)
yields
( )591
4
12
2 ⊕⎥⎥⎦
⎤
⎢⎢⎣
⎡ −+=Δ g
c
P
g ρ
Thus, when a gravity anomaly is detected,
we can evaluate, by means of Eq. (59), the
magnitude of the ratio ρP in the
compressing region. On the other hand,
several experimental observations of the time
interval between the appearing of gravity
anomaly gΔ and the breaking of the obstacle
(beginning of the Earthquake) will give us a
statistical value for the mentioned time
interval, which will warn us (earthquake
warning system) when to initiate an alarm.
Obviously, the earthquake warning time, in
this case becomes much greater than 60
seconds.
Page 16
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