Аналіз негативного потоку гравітаційних хвиль
In this article, we made the mathematical explanation of the anti-gravitational waves, by the inspiration that we got from the observed positron in cosmic rays. Then, we analyzed the mathematical difference between positive and negative flows of gravitational waves; and we calculated the spin of the...
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| author | Matsuki, Yoshio Bidyuk, Petro I. |
| author_facet | Matsuki, Yoshio Bidyuk, Petro I. |
| author_institution_txt_mv | [
{
"author": "Yoshio Matsuki",
"institution": "The Laboratory for Econometrics and Forecasting at the World Data Center for Geoinformatics and Sustainable Development, the National Technical University of Ukraine \"Igor Sikorsky Kyiv Polytechnic Institute\", Kyiv"
},
{
"author": "Petro I. Bidyuk",
"institution": "Educational and Scientific Complex \"Institute for Applied System Analysis\" of the National Technical University of Ukraine \"Igor Sikorsky Kyiv Polytechnic Institute\", Kyiv"
}
] |
| author_sort | Matsuki, Yoshio |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
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| datestamp_date | 2020-03-02T17:05:10Z |
| description | In this article, we made the mathematical explanation of the anti-gravitational waves, by the inspiration that we got from the observed positron in cosmic rays. Then, we analyzed the mathematical difference between positive and negative flows of gravitational waves; and we calculated the spin of the negative flow of gravitational waves, which is used to stabilize the movement of the waves. In the mathematical formulas we found that positive and negative flows move in opposite directions from each other; therefore, if we see the spin (rotation) of the waves from the planet that emits the waves, the positive flow rotates anti-clockwise, while the negative flow rotates clockwise. We also investigated the possible origin of gravitational waves, and concluded that the negative flow can occur when the positive flow appears, leaving holes behind, in the gravitational field, which is trig-gered by the movements of a large mass of the planet. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2019.4.01 |
| first_indexed | 2025-07-17T10:26:33Z |
| format | Article |
| fulltext |
Y. Matsuki, P.I. Bidyuk, 2019
Системні дослідження та інформаційні технології, 2019, № 4 7
TIДC
ПРОГРЕСИВНІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ,
ВИСОКОПРОДУКТИВНІ КОМП’ЮТЕРНІ
СИСТЕМИ
UDC 519.004.942
DOI: 10.20535/SRIT.2308-8893.2019.4.01
ANALYSIS OF NEGATIVE FLOW OF GRAVITATIONAL WAVES
Y. MATSUKI, P.I. BIDYUK
Abstact. In this article, we made the mathematical explanation of the anti-
gravitational waves, by the inspiration that we got from the observed positron in
cosmic rays. Then, we analyzed the mathematical difference between positive and
negative flows of gravitational waves; and we calculated the spin of the negative
flow of gravitational waves, which is used to stabilize the movement of the waves.
In the mathematical formulas we found that positive and negative flows move in op-
posite directions from each other; therefore, if we see the spin (rotation) of the
waves from the planet that emits the waves, the positive flow rotates anti-clockwise,
while the negative flow rotates clockwise. We also investigated the possible origin
of gravitational waves, and concluded that the negative flow can occur when the
positive flow appears, leaving holes behind, in the gravitational field, which is trig-
gered by the movements of a large mass of the planet.
Keywords: Gravitational waves, antimatter, rectilinear coordinates, negative energy
flow, spin of gravitational waves.
INTRODUCTION
In our previous research [1], we calculated the energy density of gravitational
waves from Moon, assuming that it influences Earth’s global temperature. How-
ever, the result of the analysis showed that the energy density of Moon’s gravita-
tional waves toward Earth’s global temperature was negative in comparison with
that of Moon’s gravitational field.
After this result of the analysis, we held a question: Don’t gravitational
waves really exist? For answering to this question, we continued the research by
setting new tasks: (a) to compare the characteristic of gravitational waves with
that of electron and positron, where positron is the antimatter of electron, and (b)
to find the mechanism that creates negative flow (antimatter) of the gravitational
waves. Here, we set the task (b), because all the particles (waves) must have their
antimatters. So, we thought that the existence of antimatters is a prerequisite for
confirming the existence of gravitational waves.
In order to implement these two tasks, we took the following steps: (1) to in-
vestigate the findings from the observation of electron and positron in the cosmic
rays, (2) to review the theory of electron and positron in quantum mechanics, (3)
to investigate the mechanism that produces gravitational waves, (4) to make the
mathematical formula of negative flow of gravitational waves, and (5) to compare
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2019, № 4 8
the spin momentum of negative energy flow with the spin momentum of positive
energy flow. We selected the spin momentum as an indicator that is to illustrate
the characteristic of gravitational waves, which we made in our previous research
for positive flow of the waves [1].
Above (4) and (5) are our original, while we analyzed the ratio of posi-
tron/electron for the task (1) from the information that we took from [2]; and, we
took the necessary equations from Dirac [3, 4] for the tasks (2) and (3).
ANALYSIS
Observed electron and positron in cosmic rays
Fig. 1 shows the observed ratio of positron to electron in cosmic rays, with the
intensity of electromagnetic energy that was related to the creation of the posi-
tron [2]. It shows that more positrons were observed when the related electromag-
netic energy was stronger. And, then, in order to further investigate Fig. 1, we
analyzed this data with the method of the Least Squares Estimates of Classical
Regression Model.
We show the result of the analysis in Table 1 and the descriptive statistics of
the data in Table 2. The regression model is bXaY , where Y is the ratio
of positron versus electron, X is observed energy of the electromagnetic
field, and a and b are coefficients. The calculated coefficient is
54 10455,910572,5 b with 95% confidence interval, 410560,1 with
90 % confidence interval, and 410763,1 with 85% confidence interval, where
we assumed the standard normal distribution of the coefficients. This calculated
result indicates that positron (antimatter of electron) is more observed in the
higher energy of the electromagnetic field.
Fig. 1. Observed ratio of positron to electron and energy of the electromagnetic field*
Analysis of Negative Flow of Gravitational Waves …
Системні дослідження та інформаційні технології, 2019, № 4 9
*Note: Remake from [2]. This source article explains that the lower rate of posi-
tron/electron observation below 10 GeV is due to the new solar magnetic field polarity
after the year 2001.
T a b l e 1 . Summary of the least squares estimates
a 210964,6
Coefficient 410572,5
b
Standard error of Coefficient 510824,4
R2 (coefficient of determination) 0,9175
Durbin-Watson Statistic 2,341
Sum of Squared Residuals 410857,1
T a b l e 2 . Descriptive statistics
Variable Ratio of positron/electron
Electro-magnetic energy
of electron and positron (GeV)
Mean 210065,8 19,77
Standard deviation 210316,1 22,61
Minimum 210820,6 2,424
Maximum 0,1147 80,00
Skewness 1,453 1,408
Kurtosis 3,934 3,965
Valid number
of observations
14 14
Mathematical formulas of electron and positron
Paul Dirac [4] predicted that both positron and electron are balanced, therefore
they are not usually observed; but the positron appears with presence of the elec-
tromagnetic field. The equation of motion for an electron in the electromagnetic
field of hydrogen atom is:
22211100 A
c
e
pA
c
e
pA
c
e
p
0333
mcA
c
e
p m . (1)
Here, ip )3,2,1,0( i are momentum of electron, i are coefficients that
give angular momentum of electron, and iA
c
e
are electromagnetic field of hydro-
gen atom, e is electric charge of electron, c is a constant, and is the wave func-
tion of electron (1).
The equation of motion for positron is:
22211100 A
c
e
pA
c
e
pA
c
e
p
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2019, № 4 10
0333
mcA
c
e
p m .
Here, is a wave function of positron.
Equations of motion for gravitational waves and anti-gravitational waves
From the implication of the equations of motions for electron and positron, we
formulated the solutions of the equations of motions for positive flow and nega-
tive flow of gravitational waves.
For positive flow of the waves
(from [1])
For negative flow of the waves
(Our new idea)
At first, we have the solution of the equation
of motion, which is energy density of gravi-
tational waves, which move in one direction
of 3x with the speed of light:
2
12
2
2211
0
0 )(
4
1
16 uuut (2)
We think that the negative flow of energy is:
2
12
2
2211
0
0 )()}({
4
1
16 uuut (3)
Below, we show how the equations (2) and (3) are derived from the equation (8), which
will be explained in the latter part of this article:
According to Dirac [3], the necessary condition for solving the equation of motion of
the gravitational waves is 0,
gg , while
xx
g
g
2
, , where x are the
contravariant vectors that are described in the 4-dimentional curvilinear coordinates, and
g and g are fundamental tensors. Now we take rectilinear coordinates system as
approximation of curvilinear coordinates system, then the second derivatives of
0,
gg are considered to be resolved (integrated) already; and, then, and we de-
fine lug , , where u is the derivative of the function g of
xl , where
x
g
g , , and , , are the suffixes that indicate those coordinates; while, we
assume that the waves move in only one direction of the space, , , = 0, or 3, where
0 is for time, and 3 is the selected one direction. Also, we put uuuu
, where
u are contravariant two-vector tensors and u are covariant two-vector tensors, and
uu ; and, l are constants, which satisfy 0
llg . Therefore, ,g
lu , is regarded as the first integral of 0,
gg , then the equation (6), which
is shown later in the latter part of this article, becomes
ulluglug
2
1
2
1
,
then 0)
2
1
(
lugu , and )(
2
1
lululu . Meanwhile, the gen-
eral formula of the action integral is 3210det dxdxdxdxgRI , where R will be
Analysis of Negative Flow of Gravitational Waves …
Системні дослідження та інформаційні технології, 2019, № 4 11
explained later with the equation (4). LgRgR
)( ,, , where
)(
gL . Then, L for the waves moving in one direction becomes:
))((
4
1
lulululululuggL .
With the constraint, 0L , the solution of the above action integral is expressed by the
pseudo-tensors
t that lead to the spin momentum densities of the gravitational waves:
16
lluuut )
2
1
(
2
1 2 , where l is one direction, in which the waves are
moving in. Here, we consider the gravitational waves moving only in the direction of 3x ,
therefore 10 l , 021 ll , and 13 l .
Below, we calculate the spin momentum den-
sities of the positive flow of gravitational
waves in rectilinear coordinates, as approxi-
mation of curvilinear coordinates
lluuut ))2/1()(2/1(16 2 :
lulu
3
0
.
For 0 :
3
3
02
2
01
1
00
0
0
3
0
lulululululu
03
33
00
003
0
0
0 00 uguguu
uuluu )2/1()2/1( 00300 .
Here,
1000
0100
0010
0001
g , therefore
,100 g and 133 g .
Also, for contra-variant vector A and
covariant vector A ,
AgA , and
AgA therefore, for example, 00u
00
0000 ugg , 10
001110 uggu , and
03
333
0 ugu .
For 1 :
3
1
0
13
3
12
2
11
1
10
0
1 00 uululululu
0)2/1( 1130131
33
01
00 uluuugug .
For 2 :
3
2
0
23
3
32
2
21
1
12
0
1 00 uululululu
Below we calculate the spin momentum
density of the negative flow of gravita-
tional waves in rectilinear coordinates, as
approximation of curvilinear coordinates
lluuut )})2/1((){2/1(16 2 :
lulu
3
0
.
For 0 :
uuululu )2/1(0300
3
0
.
For 1 :
01301
3
0
uululu .
For 2 :
lulu
3
0
02302 uu .
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2019, № 4 12
.0)2/1( 2230232
33
02
00 uluuugug
For 3 :
3
3
0
33
3
32
2
31
1
30
0
3 00 uululululu
3330333
33
03
00 )2/1( uluuugug
u)2/1( .
Thus, uuu )2/1(0300 and
uuu )2/1(0333 .
Therefore, uuu )2/1(3300
uu ))2/1(( , and 3300 uu 032u ,
where 3003 uu . Also, 01
1
11111 lugu ,
and 02
2
22222 lugu ,
therefore 02211 uu .
Here, 100 g , 1332211 ggg ,
and 131210030201 gggggg
0323130232120 gggggg .
Then,
uut )(2/1(16
llu ))2/1( 2 becomes
2
3
0,
0
0 )2/1(()2/1(16 uuut .
Here,
11
11
00
00
2
3
0,
)2/1( uuuuuuu
02
02
01
01
33
33
22
22 22 uuuuuuuu
31
31
23
23
12
12
03
03 2222 uuuuuuuu
11
1111
1100
0000
00
2)2/1( ugguugguu
33
3333
3322
2222
22 ugguuggu
02
2200
0201
1100
01 22 ugguuggu
12
2211
1203
3300
03 22 ugguuggu
31
1133
3123
3322
23 22 ugguuggu
2
33
2
22
2
11
2
00
2)2/1( uuuuu
2
03
2
02
2
01 2)1(2)1(2)1( uuu
2
3300
2
31
2
23
2
12 ))(2/1(222 uuuuu
2
12
2
22
2
11 2uuu 2
3300 ))(2/1( uu
2
12
2
2211 2))(2/1( uuu .
Because: 02211 uu , 2211 uu ,
2
22
2
11 uu , 2
22
2
22
2
11 2uuu , 2
2211 )( uu
For 3 :
uuululu )2/1(3303
3
0
.
Thus, uuu )2/1(0300 and
uuu )2/1(0333 .
Therefore, uuu 3300 and
033300 2uuu , where 3003 uu .
Also, 01
1
11111 lugu , and 22u
02
2
222 lug , therefore 02211 uu .
Then,
lluuut )})2/1((){2/1(16 2
becomes
))(2/1(()2/1(16 2
3
0,
0
0 uuut .
Here,
))2/1((( 2
3
0,
uuu
2
33
2
22
2
11
2
00 )()()()( uuuu
2
12
2
03
2
02
2
01 2222 uuuu
22
31
2
23 )2/1(22 uuu
22
12
2
22
2
11 )2/1(2 uuuu
2
2211
2
12
2
22 ))(2/1(22 uuuu
2
12 )(2 u .
Because: 02211 uu , 2211 uu ,
Analysis of Negative Flow of Gravitational Waves …
Системні дослідження та інформаційні технології, 2019, № 4 13
2
22
2
22
2
2222 4)2()( uuuu ,
2
22
2
2211 2))(2/1( uuu .
So, 2
12
2
2211
0
0 ))(4/1(16 uuut .
And then, we assume an infinitesimal ro-
tation operator, R , in the plane of contravari-
ant vectors 21xx . If it is applied to any vec-
tor, 1A , 2A , it has the effect: 21 ARA ,
12 ARA , and 121
2 ARAAR , so
iR must have the eigenvalues 1 when ap-
plied to a vector [3]. Here, 1iR . So, the
operator R makes anti-symmetric change of
the vectors.
–A1 A1
A2
x2
x2
When we apply this infinitesimal rotation
operator, R , to AAu , the rotations
will occur as follows:
)(()()( 11111111 ARAARAAARRu
1212212112 2uuuAAAA ,
where 1221 uu .
)()()( 21212112 RAAARAAARRu
11221122 )( uuAAAA .
)()()( 22222222 RAAARAAARRu
1221121221 2)( uuuAAAA .
)()( 22112211 AAAARuuR
)()()()( 22221111 RAAARARAAARA
12212112 AAAAAAAA
022 1212 uu .
1222112211 )()( AAAAAARuuR
1221122121 44 uAAAAAAAA .
))(()( 22112211
2 uuRRuuR
)( 2211 RuRuR
12121212 22)2(2( RRuuuR
)(2)(2 11221122 uuuu
2
22
2
11 uu , 2
22
2
22
2
11 2uuu ,
2
22
2
22
2
11 2uuu ,
2
2222
2
2211 )}()({)}({ uuuu
2
22
2
22
2
2222 4)}2({)( uuuu ,
2
22
2
2211 2))(2/1( uuu . So,
0
016 t 2
12
2
2211 )()}(){4/1( uuu .
Then, we assume an infinitesimal rota-
tion operator, R , in the plane of con-
travariant vectors 21xx . If it is applied to
any vector, 1A , 2A , it has the effect:
21)( AAR , 12 )( AAR , and
121
2 )()( AARAR .
–A1 A1
x1
–A2
x2
When we apply this infinitesimal rotation
operator, R , to AAu , the rota-
tions will occur as follows: )( 11uR
)(())(()( 111111 ARAAARAAR
1212212112 2uuuAAAA ,
where 1221 uu . )()( 2112 AARuR
11221122 )( uuAAAA
)( 1122 uu . )()( 2222 AARuR
12212222 )()( AAAARAAARA
)( 21122112 uuuu
1212 2)2( uu ;
)()( 22112211 AAAARuuR
221111 )()()( ARARAAARA
21211222 )( AAAAAARAA
022)( 121212 uuAA ;
)()( 22112211 AAAARuuR
)()( 12212112 AAAAAAAA
1221 44 uAA .
))(()( 22112211
2 uuRRuuR
)22()( 12122211 uuRRuRuR
)(222 11221212 uuRuRu
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2019, № 4 14
)(4)(4 22111122 uuuu .
2211 uu is invariant because
0)( 2211 uuR as shown above, and iR has
the eigenvalues 2 when applied to
2211 uu or 12u .
Therefore, 2
12
2
2211 ))(4/1( uuu (the com-
ponents of u that contribute to the mo-
mentum density of gravitational waves) cor-
responds to spin 2 [3].
(See note* bellow.)
)(4)(2 11221122 uuuu
)(4 2211 uu . 2211 uu is invariant
because 0)( 2211 uuR as shown above,
and iR has the eigenvalues 2 when
applied to )( 2211 uu or 12u .
Therefore, 2
2211 )}(){4/1( uu 2
12 )( u
corresponds to spin 2 .
We add minus-sign to 2, in order the show
the direction of negative flow, as shown in
Fig. 2.
(Also see note* bellow to compare this
result with electron’s spin momentum.)
The geometric relation between the positive flow and negative flow of gravi-
tational waves is shown in Fig. 2.
Note*: In the equation of motion (1) for electron in the electromagnetic field of
hydrogen atom, the infinitesimal operator iR for the rotation of the electron in the plane
of 32 xx is 11 p ; and it has the eigenvalue of )2/1( ; because, the necessary
condition for solving the equation (1) is : )( 2332111 ppciim
0)(2 32231 ppic , and )(2 32231 ppic is invariant with 1i . So, ii 2 ,
then )2/1(i . Therefore, the spin momentum of electron is 1)2/1( . Here m is the
orbital angular momentum of electron in hydrogen atom, m is its time-differential of m
and 1 is the time-differential of 1 , and the suffix 1, 2, 3 represent matrices of tensors
in 3 space coordinates, c is a constant, and
0010
0001
1000
0100
1
; is Planck’s constant and
1 is a matrix
0001
0010
0100
1000
, which makes 1 by 111 c .
Negative
flow
x2
x1
x3
Positive
flow
x2
x1
x3
Fig. 2. Calculated directions of spins
Analysis of Negative Flow of Gravitational Waves …
Системні дослідження та інформаційні технології, 2019, № 4 15
Here, it is noted that, in quantum mechanics [4], rectilinear coordinates are
used, but not curvilinear coordinates; while, the rectilinear coordinates system
holds 44 combinations of vectors, the curvilinear coordinates has 34 combi-
nations of vectors.
For positron, instead of electron, i is replaced by i in the above equa-
tions.
Mechanism to create gravitational waves
The next research question is “how are both positive and negative flows of gravi-
tational waves made?” We think that the answer for positive flow of gravitational
waves is described in Einstein’s General Theory of Relativity [3]. In this theory,
Einstein used Riemann’s geometry to describe his idea of gravitational field of a
planet. The gravitational field is a tide of vectors i , where 0i , 1, 2 , 3 , and the
tide is to be made as the effect of differential, i
i
R
dt
d
2
2
, in the curvature of the
4-dimensional coordinates, where
2
1
a
R , and a is a radius of the curved sur-
face [5].
In order to further generalize the curvature of the 4-dimensional coordinates,
Einstein used Riemann tensor for setting the condition to solve the equation of
motion, 0),,,(...Riemann uuuu , where
2
2
ds
d
uu , u is the vector
eue
d
dx
u , which are tangent vectors to the center of the curvature, and
0e , 1e , 2e , 3e are basis vectors that lie in the directions of their increasing order
of the coordinates of 0x , 1x , 2x , and 3x ; also,
ex , where
dxdxgdsdd 2 , and ds is the length of the travel of particles along the
geodesics, and Riemann tensor is ),,,(,Riemann
xexw , where 0, 1, 2, 3,
and w is the gradient (deviation) of the coordinates, which means dxw .
And then, the condition for solving the equation of motion becomes
0
2
2
d
dx
d
dx
R
ds
d
.
Then, in case of
ew , Ricci tensors become ),( vuRicci
),,,(,Riemann
xexw , which is
RR . Then, in case of , Ricci
tensors become the curvature scalar, R , where
RewRicciR ),( . Mean-
while, Einstein defined the differential symmetries of Riemann tensors to describe
the gravitational field with the curvature: RgRG
2
1
; then, he assumed
0R (4)
in the empty space where only gravitational field of a planet exists.
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2019, № 4 16
Then,
0,,
R ,
where )(
2
1
,,, ggg .
In rectilinear coordinates as an approximation of curvilinear coordinates,
0
, then 0,,
R .
On the other hand,
)(
2
1
,,,, ggggR .
By interchanging and , and neglecting
to replace
curvilinear coordinates by rectilinear coordinates we have:
0)( ,,,,
gggggRgR .
Then,
0)( ,,,,
ggggg . (5)
On the other hand, the moving particle in a scalar field of potential energy V
follows d’Alambert equation 0)( ,,
VVgV . In order to describe
the gravitational waves moving in the 4-dimensional space, we replace V by vec-
tors x by a certain coordinate system in which
gx, , then d’Alambert equa-
tion becomes 0,
gggg then 0
g . Meanwhile,
)(
2
1
,,,
ggggg ,
so
0)
2
1
()(
2
1
,,,,,
gggggggggg ,
where ,,,,,,,,,, gyyyyyyyyg n
n
n
n
n
n
n
n , where and are
in symmetrical relation in the equation, therefore they are exchangeable; and,
x
xy
y
n
n )(
, , 0, 1, 2, 3, while x are located in N-dimensional physical
space of ny , n 1, 2, ….., N.
Therefore,
0
2
1
,,
ggg . (6)
Then, in order to describe the waves moving in the gravitational field, it is differ-
entiated by x once again,
,,,,,,, 2
1
2
1
2
1
ggggggggg
dx
d
Analysis of Negative Flow of Gravitational Waves …
Системні дослідження та інформаційні технології, 2019, № 4 17
0
2
1
,,
ggg . (7)
In the equation (7), 0)
2
1
( ,,,
ggg , because g is constant in rec-
tilinear coordinates system, therefore 0, g .
By interchanging and ,
0)
2
1
()
2
1
( ,,,,
gggggg . (8)
By adding (5), (7) and (8),
0,
gg . (9)
It satisfies d’Alambert equation, so it describes the waves that travel in emp-
ty space.
Note: The equation (2) is the first integral of equation (9) in rectilinear coor-
dinate system (flat space); however, here is a paradox: the gravitational waves are
predicted in the curvilinear coordinate system (curved space) where the waves
move on the curved surface of the coordinates. However, if it is in the curvilinear
coordinates, 0
for the equation (4), 0
for the equation (5), and 0)
2
1
( ,,,
ggg for the equation (7); then, we
are not able to get the equation (9), which enables us to calculate the spin momen-
tum densities with the equation (2). It means that the equation (9) is only an ap-
proximation, which is given by the condition that the waves move only in one
direction of
xl as if the waves move in the rectilinear coordinates system.
Mechanism to create negative flow of gravitational waves
On the other hand, we think that the negative flow of gravitational waves must be
described by:
0,
gg .
This means that the negative waves move backward from the direction of the
positive flow of the waves. When the positive flow moves forward, it creates vacuum
or hole in the geometric structure of the gravitational field of the equation (4).
This explanation corresponds to Dirac’s explanation about the creation of
positron [4]. And, then, we have made the following explanation: Usually, the
positive flow and the negative flow should be balanced; therefore, neither of the
positive flow nor negative flow of gravitational waves is observable. However,
when planet moves, the movement of the mass of the planet breaks the balance;
then gravitational waves of both positive flow and negative flow appear.
CONCLUSIONS AND RECOMMENDATION
In this research, we investigated a question: “Do gravitational waves really ex-
ist?” As the result of our investigation, we didn’t find the straight answer, but we
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2019, № 4 18
found that the gravitational waves must have both positive and negative flows if
they exist. So, we also investigated one more question: “How are both positive
and negative flows of gravitational waves created?”
To find the answer for this second question, we made the negative image of
the energy flow of gravitational waves, and calculated its spin momentum, and we
compared it with the spin of the positive flow. As the result, we found that the
negative flow of gravitational waves moves in one direction, spinning clockwise,
while the positive flow of gravitational waves moves in opposite direction to that
of negative flow, spinning anti-clockwise, when looking at both flows of the
waves from the producer (planet) of the waves.
Then, we found a possible explanation about the process that creates the
negative flow of gravitational waves. In the process that creates positron (antimat-
ter of electron), electron and positron are usually not observable because they are
balanced in the space. However, getting magnetic radiations, electron appears and
also positron appears as the hole from where electron goes out. Similarly, positive
flow and negative flow of gravitational waves are usually not observable, but
when the planet moves, the gravitational waves appear from the gravitational
field; and then, when positive flow appears, negative flow also appears as the
vacuum of the gravitational field, which is made by the positive flow.
A paradox still remains. The mathematical explanation of gravitational
waves is made by the curvature of the gravitational field; however, our approach,
shown in this report, used the system of rectilinear coordinates, and it is only an
approximation for very small range of the curvilinear coordinate system. There-
fore, we still need further investigation in curvature coordinate system, to find
more general explanation.
REFERENCES
1. Matsuki Y. Calculating energy density and spin momentum density of Moon’s gravi-
tational waves in rectilinear coordinates (part 4) / Y. Matsuki, P.I. Bidyuk // Sys-
tem Research & Information Technology. — 2019. — N 3. — P. 7–17.
2. Beringer J. Particle Data Group / J. Beringer et al. // Phys. Revi. D86, 010001. —
2012. — P. 306 (Figure 26.2 Differential spectrum of electrons plus positrons
multiplied by E3).
3. Dirac P.A.M. General Theory of Relativity / P.A.M. Dirac. —New York: Florida
University, A Wiley-Interscience Publication, John Wiley & Sons, 1975. —
P. 69.
4. Dirac P.A.M. The Principle of Quantum Mechanics / P.A.M. Dirac. — Fourth Edi-
tion. — Oxford: Clarendon Press, 1958. — P.312
5. Goldstein H. Classical Mechanics / H. Goldstein, C.P. Poole, J.L. Safko. — 3rd Edi-
tion. —Pearson Education, Inc., (2002). — P. 646 (especially Chapter 7.11 “In-
troduction to the general theory of relativity”, P. 324–328).
6. Matsuki Y. Empirical Investigation on Influence of Moon’s Gravitational-Field to
Earth’s Global Temperature (Part-3) / Y. Matsuki, P.I. Bidyuk // System Re-
search & Information Technology. — 2019. — N 2. — P. 18–24.
Received 02.09.2019
From the Editorial Board: the article corresponds completely to submitted manu-
script.
|
| id | journaliasakpiua-article-188193 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:26:33Z |
| publishDate | 2019 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/9c/5f5d14865d51b3e5823ee4f048090e9c.pdf |
| spelling | journaliasakpiua-article-1881932020-03-02T17:05:10Z Analysis of negative flow of gravitational waves Анализ негативного потока гравитационных волн Аналіз негативного потоку гравітаційних хвиль Matsuki, Yoshio Bidyuk, Petro I. gravitational waves antimatter rectilinear coordinates negative energy flow spin of gravitational waves гравітаційні хвилі антиматерія прямолінійні координати негативний потік енергії спин гравітаційних хвиль гравитационные волны антиматерия прямолинейные координаты негативный поток энергии спин гравитационных волн In this article, we made the mathematical explanation of the anti-gravitational waves, by the inspiration that we got from the observed positron in cosmic rays. Then, we analyzed the mathematical difference between positive and negative flows of gravitational waves; and we calculated the spin of the negative flow of gravitational waves, which is used to stabilize the movement of the waves. In the mathematical formulas we found that positive and negative flows move in opposite directions from each other; therefore, if we see the spin (rotation) of the waves from the planet that emits the waves, the positive flow rotates anti-clockwise, while the negative flow rotates clockwise. We also investigated the possible origin of gravitational waves, and concluded that the negative flow can occur when the positive flow appears, leaving holes behind, in the gravitational field, which is trig-gered by the movements of a large mass of the planet. Приведено математическое объяснение антигравитационных волн, обусловленное наблюдением позитрона в космических лучах. Проанализирована математическая разница между положительными и отрицательными потоками гравитационных волн; вычислено вращение негативного потока гравитационных волн, который заключается в стабилизации движения волн. В математических формулах обнаружено, что положительные и отрицательные потоки движутся в обратном направлении друг от друга, поэтому, если спин (вращение) волн от планеты, испускающей волны, положительный поток вращается против часовой стрелки, тогда как отрицательный поток — по часовой стрелке. Исследовано возможное происхождение гравитационных волн и сделан вывод: отрицательный поток может возникать, когда появляется положительный поток, который оставляет отверстия в гравитационном поле, что инициируется движениями большой массы планеты. Подано математичне пояснення антигравітаційних хвиль, зумовлене спостереженням позитрона в космічних променях. Проаналізовано математичну різницю між позитивними та негативними потоками гравітаційних хвиль; обчислено обертання негативного потоку гравітаційних хвиль, який полягає в стабілізації руху хвиль. У математичних формулах виявлено, що позитивні та негативні потоки рухаються у зворотному один до одного напрямку, тому, якщо спін (обертання) хвиль від планети, яка випускає хвилі, позитивний потік обертається проти годинникової стрілки, тоді як негативний потік — за годинниковою стрілкою. Досліджено можливе походження гравітаційних хвиль і зроблено висновок: негативний потік може виникати, коли з'являється позитивний потік, який залишає отвори в гравітаційному полі, що ініціюється рухами великої маси планети. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2019-12-23 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/188193 10.20535/SRIT.2308-8893.2019.4.01 System research and information technologies; No. 4 (2019); 7-18 Системные исследования и информационные технологии; № 4 (2019); 7-18 Системні дослідження та інформаційні технології; № 4 (2019); 7-18 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/188193/189952 Copyright (c) 2021 System research and information technologies |
| spellingShingle | гравітаційні хвилі антиматерія прямолінійні координати негативний потік енергії спин гравітаційних хвиль Matsuki, Yoshio Bidyuk, Petro I. Аналіз негативного потоку гравітаційних хвиль |
| title | Аналіз негативного потоку гравітаційних хвиль |
| title_alt | Analysis of negative flow of gravitational waves Анализ негативного потока гравитационных волн |
| title_full | Аналіз негативного потоку гравітаційних хвиль |
| title_fullStr | Аналіз негативного потоку гравітаційних хвиль |
| title_full_unstemmed | Аналіз негативного потоку гравітаційних хвиль |
| title_short | Аналіз негативного потоку гравітаційних хвиль |
| title_sort | аналіз негативного потоку гравітаційних хвиль |
| topic | гравітаційні хвилі антиматерія прямолінійні координати негативний потік енергії спин гравітаційних хвиль |
| topic_facet | gravitational waves antimatter rectilinear coordinates negative energy flow spin of gravitational waves гравітаційні хвилі антиматерія прямолінійні координати негативний потік енергії спин гравітаційних хвиль гравитационные волны антиматерия прямолинейные координаты негативный поток энергии спин гравитационных волн |
| url | https://journal.iasa.kpi.ua/article/view/188193 |
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