Gravity Control by means of Modified Electromagnetic Radiation

Gravity Control by means of Modified Electromagnetic Radiation

Fran De Aquino
Maranhao State University, Physics Department, S.Luis/MA, Brazil.
Copyright © 2011 by Fran De Aquino. All Rights Reserved.



Here a new way for gravity control is proposed that uses electromagnetic radiation modified to have a smaller
wavelength. It is known that when the velocity of a radiation is reduced its wavelength is also reduced. There are
several ways to strongly reduce the velocity of an electromagnetic radiation. Here, it is shown that such a reduction
can be done simply by making the radiation cross a conductive foil.

Key words: Modified theories of gravity, Experimental studies of gravity, Electromagnetic wave propagation.
PACS: 04.50.Kd , 04.80.-y, 41.20.Jb, 75.70.-i.


It was shown that the gravitational
mass mg and inertial mass mi are correlated
by means of the following factor [1]:
( )11121
2
00 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+−=
cm
p
m
m
ii
g
where is the rest inertial mass of the
particle and is the variation in the
particle’s kinetic momentum; is the speed
of light.
0im
pΔ
c
When is produced by the
absorption of a photon with wavelength
pΔ
λ , it
is expressed by λhp =Δ . In this case, Eq.
(1) becomes
( )21121
1121
2
0
2
0
0
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎠
⎞⎜⎝
⎛+−=
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎠
⎞⎜⎝
⎛+−=
λ
λ
λ
cmh
m
m i
i
g
where cmh i00 =λ is the De Broglie
wavelength for the particle with rest inertial
mass . 0im
It is easily seen that cannot be
strongly reduced simply by using
electromagnetic waves with wavelength
gm
λ
because 0λ is very smaller than .
However, it is known that the wavelength of
a radiation can be strongly reduced simply by
strongly reducing its velocity.
m1010−
There are several ways to reduce the
velocity of an electromagnetic radiation. For
example, by making light cross an ultra cold
atomic gas, it is possible to reduce its velocity
down to 17m/s [2-7]. Here, it is shown that the
velocity of an electromagnetic radiation can
be strongly reduced simply by making the
radiation cross a conductive foil.
From Electrodynamics we know that
when an electromagnetic wave with
frequency and velocity incides on a
material with relative permittivity
f c
rε ,
relative magnetic permeability rμ and
electrical conductivity σ , its velocity is
reduced to rncv = where is the index of
refraction of the material, given by [
rn
8]
( ) ( )311
2
2 ⎟⎠
⎞⎜⎝
⎛ ++== ωεσμε rrr v
c
n
If ωεσ >> f, π2ω = , the Eq. (3) reduces to
( )4
4 0 f
n rr πε
σμ=
Thus, the wavelength of the incident
radiation becomes
( )54mod σμ
πλλ
fnn
fc
f
v
rr
====










Fig. 1 – Modified Electromagnetic Wave. The
wavelength of the electromagnetic wave can be
strongly reduced, but its frequency remains the same.
v = c v = c/nr
λ = c/f λmod = v/f = c/nr f
nr

2
Now consider a (GHz1 m3.0≅λ )
radiation incident on Aluminum foil with
and thicknessmS /1082.3 7×=σ mμξ 5.10= .
According to Eq. (5), the modified
wavelength is
( )6106.14 5mod mf −×== σμ
πλ
Consequently, the wavelength of the
radiation inside the foil will be
and not
GHz1
m5mod 106.1
−×=λ m3.0≅λ .
It is known that a radiation with
frequency f, propagating through a material
with electromagnetic characteristics ε, μ and
σ , has the amplitudes of its waves decreased
in e−1=0.37 (37%), when it passes through a
distance z, given by
( )
)7(
11
1
2
2
1 ⎟⎠
⎞⎜⎝
⎛ −+
=
ωεσεμω
z
The radiation is totally absorbed at a
distance δ≅5z [8].
In the case of the radiation
propagating through the Aluminum foil Eq.
(7), gives
GHz1
)8(57.21057.2
1 6 m
f
z μ
πμσ
=×== −
Since the thickness of the Aluminum foil is
mμξ 5.10= then, we can conclude that,
practically all the incident radiation is
absorbed by the foil.
GHz1
If the foil contains atoms/mn 3, then
the number of atoms per area unit is ξn .
Thus, if the electromagnetic radiation with
frequency incides on an area of the foil
it reaches
f S
ξnS atoms. If it incides on the total
area of the foil, , then the total number of
atoms reached by the radiation is
fS
ξfnSN = .
The number of atoms per unit of volume, ,
is given by
n
( )90
A
N
n
ρ=
where is the
Avogadro’s number ;
kmoleatomsN /1002.6 260 ×=
ρ is the matter density
of the foil (in kg/m3) and A is the atomic
mass. In the case of the Aluminum ( )kmoleAmkg 98.26,/2700 3 ==ρ the result is
( )10/1002.6 328 matomsnAl ×=
The total number of photons inciding on the
foil is 2hfPn photonstotal = , where P is the
power of the radiation flux incident on the
foil.
When an electromagnetic wave incides
on the Aluminum foil, it strikes on front
atoms, where
fN( ) atomff nSN φ≅ . Thus, the
wave incides effectively on an area
af SNS = , where 241 atomaS πφ= is the cross
section area of one Aluminum atom. After these
collisions, it carries out with the
other atoms of the foil (See Fig.2).
collisionsn











Fig. 2 – Collisions inside the foil.
foil
atom
Sa
Wave

Thus, the total number of collisions in the
volume ξS is
( )
( )11ξ
φξφ
nS
nSnSnSnNN atomatomcollisionsfcollisions
=
=−+=+=
The power density, , of the radiation on
the foil can be expressed by
D
( )12
af SN
P
S
P
D ==
The same power density as a function of the
power radiated from the antenna, is given
by
0P
( )13
4 2
0
r
P
D π=
where r is the distance between the antenna
and the foil. Comparing equations (12) and
(13), we get

3
( )14
4 02
P
r
SN
P af ⎟⎟⎠
⎞
⎜⎜⎝
⎛= π
We can express the total mean number
of collisions in each atom, , by means of
the following equation
1n
( )151 N
Nn
n collisionsphotonstotal=
Since in each collision is transferred a
momentum λh to the atom, then the total
momentum transferred to the foil will be ( ) λhNnp 1=Δ . Therefore, in accordance
with Eq. (1), we can write that

( )
( )161121
1121
2
0
2
0
1
0
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎥⎦
⎤⎢⎣
⎡+−=
=
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎥⎦
⎤⎢⎣
⎡+−=
λ
λ
λ
λ
collisionsphotonstotal
i
g
Nn
Nn
m
m

Since Eq. (11) gives ξnSNcollisions = , we get
( ) (17
2
ξnS
hf
P
Nn collisionsphotonstotal ⎟⎟⎠
⎞
⎜⎜⎝
⎛= )
Substitution of Eq. (17) into Eq. (16) yields
( ) ( )181121
2
0
2
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟⎠
⎞
⎜⎜⎝
⎛+−= λ
λξnS
hf
P
m
m
i
g
Substitution of Eq. (14) into Eq. (18) gives
( )1911
4
121
2
0
22
0
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟⎠
⎞
⎜⎜⎝
⎛
⎟⎟⎠
⎞
⎜⎜⎝
⎛+−= λ
ξ
π cm
nS
fr
PSN
m
m
i
af
i
g
Substitution of ( ) atomff nSN φ≅ and af SNS =
into Eq. (19) it reduces to
( )2011
4
121
2
2
0
2
0
2223
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟⎠
⎞
⎜⎜⎝
⎛+−= λπ
ξφ
cfmr
PSSn
m
m
i
atomaf
i
g
In the case of a 20cm square Aluminum foil,
with thickness mμξ 5.10= , we get
kgmi
3
0 101.1
−×= , ,
, ,
22104 mSf
−×= 21010 matom −≅φ
22010 mSa
−≅ 328 /1002.6 matomsnn Al ×==
Substitution of these values into Eq. (20),
gives
( )
( )
( )21111084.8121
2
22
011
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟⎠
⎞
⎜⎜⎝
⎛ ×+−= λfr
P
m
m
Ali
Alg
Thus, if the Aluminum foil is at a distance
mr 1= from the antenna, and the power
radiated from the antenna is WP 320 = , and
the frequency of the radiation is GHzf 1=
then Eq.(21) gives
( )
( )
( )221108.2121
25
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎥⎦
⎤⎢⎣
⎡ ×+−=
−
λAli
Alg
m
m
In the case of the Aluminum foil and Ghz1
radiation, Eq. (6) shows that
m5mod 106.1
−×=λ . Thus, by substitution of
λ by modλ into Eq. (22), we get the
following expression
( )
( )
( )231
0
−≅
Ali
Alg
m
m
Since gmP g
rr = then the result is
( ) ( ) ( ) ( )240 gmgmP AliAlgAl rrr −≅=
This means that, in the mentioned conditions,
the weight force of the Aluminum foil is
inverted.
It was shown [1] that there is an
additional effect of Gravitational Shielding
produced by a substance whose gravitational
mass was reduced or made negative. This
effect shows that just above the substance the
gravity acceleration will be reduced at the
same ratio
1g
01 ig mm=χ , i.e., gg 11 χ= , (
is the gravity acceleration bellow the
substance). This means that above the
Aluminum foil the gravity acceleration will
be modified according to the following
expression
g
( )
( )
( )25
0
11 gm
m
gg
Ali
Alg
⎟⎟⎠
⎞
⎜⎜⎝
⎛== χ
where the factor ( ) ( )AliAlg mm 01 =χ will be
given Eq. (21).
In order to check the theory presented
here, we propose the experimental set-up
shown in Fig. 3. The distance between the
Aluminum foil and the antenna is mr 1= .
The maximum output power of the GHz1

4
transmitter is 32W CW. A 10g body is
placed above Aluminum foil , in order to
check the Gravitational Shielding Effect. The
distance between the Aluminum foil and the
10g body is approximately 10 cm. The
alternative device to measure the weight
variations of the foil and the body (including
the negative values) uses two balances (200g
/ 0.01g) as shown in Fig .3.
In order to check the effect of a second
Gravitational Shielding above the first
one(Aluminum foil), we can remove the 10g
body, putting in its place a second Aluminum
foil, with the same characteristics of the first
one. The 10g body can be then placed at a
distance of 10cm above of the second
Aluminum foil. Obviously, it must be
connected to a third balance.
As shown in a previous paper [9] the
gravity above the second Gravitational
Shielding, in the case of 12 χχ = , is given by
( )2621122 ggg χχ ==
If a third Aluminum foil is placed above the
second one, then the gravity above this foil is
, and so on. gggg 31123233 χχχχχ ===

5





































Fig. 3 – Experimental Set-up

Coaxial
50 Ω
10g
Balances
200g / 0.01g
Aluminum foil
Nylon thread
100g 100g
Transmitter
1GHz
32W CW
1 m
1 m
Antenna
10 cm
1.0 m 2.0 m 1.0 m
PVC tube

6

References

[1] De Aquino, F. (2010) Mathematical Foundations of the
Relativistic Theory of Quantum Gravity, Pacific Journal
of Science and Technology, 11 (1), pp. 173-232.

[2] Hau, L.V., et al., (1999) Nature, 397, 594-598.

[3] Kash, M. M. et al., (1999) Phys. Rev. Lett. 82, 5229.

[4] Budiker, D. et al., (1999) Phys. Rev. Lett. 83, 1767.

[5] Liu, Ch. et al., (2001) Nature 409, 490.

[6] Dutton, Z., et al., (2001) Science 293, 663.

[7] Turukhin, A. V., et al., (2002) Phys. Rev. Lett. 88,
023602

[8] Quevedo, C. P. (1977) Eletromagnetismo, McGraw-
Hill, p. 270.

[9] De Aquino, F. (2010) Gravity Control by means
of Electromagnetic Field through Gas at Ultra-
Low Pressure, Pacific Journal of Science and
Technology, 11(2) November 2010, pp.178-
247.