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The study is dedicated to modern topic: the analysis of conditions that lead to distortion of the time and space coordinates which results from the general theory of relativity. The main goal of this research is to prove the hypothesis regarding distortion of time and space using nuclear fusion mode...
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| description | The study is dedicated to modern topic: the analysis of conditions that lead to distortion of the time and space coordinates which results from the general theory of relativity. The main goal of this research is to prove the hypothesis regarding distortion of time and space using nuclear fusion model. For this purpose the simulation instrument is used to imitate a moving proton that hits an electron of a hydrogen atom. The methodology of simulation is based upon calculation of the probabilities of elastic scattering and charge exchange of a proton with a target electron. The distortion is modeled by the functions that relate time and space logarithmically for distorted time and exponentially for distorted space. Such geometry construction is described by the Schrödinger equation using the electron wave function. Then the probability of charge exchange is calculated as the squared coefficient of this wave function in the negative side of the geometry that is divided by the sum of the squared coefficients of all the terms of the equation. Thus, the calculation result shows that the calculated probability of the charge exchange is high when the time and space are not distorted. However, when time and space are distorted it decreases, and the probability of elastic scattering is growing. The achieved result also indicates that the discrete energy levels of electrons in hydrogen atoms shift when the distortion of time and space occurs in the nuclear fusion. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2022.1.03 |
| first_indexed | 2025-07-17T10:27:51Z |
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| fulltext |
Y. Matsuki, P.I. Bidyuk, 2022
Системні дослідження та інформаційні технології, 2022, № 1 37
TIДC
ПРОГРЕСИВНІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ,
ВИСОКОПРОДУКТИВНІ КОМП’ЮТЕРНІ
СИСТЕМИ
UDC 519.004.942
DOI: 10.20535/SRIT.2308-8893.2022.1.03
THE PROOF OF HYPOTHESIS REGARDING DISTORTION
OF TIME AND SPACE USING THE NUCLEAR FUSION MODEL
Y. MATSUKI, P.I. BIDYUK
Abstract. The study is dedicated to modern topic: the analysis of conditions
that lead to distortion of the time and space coordinates which results from
the general theory of relativity. The main goal of this research is to prove
the hypothesis regarding distortion of time and space using nuclear fusion
model. For this purpose the simulation instrument is used to imitate a mov-
ing proton that hits an electron of a hydrogen atom. The methodology of
simulation is based upon calculation of the probabilities of elastic scattering
and charge exchange of a proton with a target electron. The distortion is
modeled by the functions that relate time and space logarithmically for dis-
torted time and exponentially for distorted space. Such geometry construc-
tion is described by the Schrödinger equation using the electron wave func-
tion. Then the probability of charge exchange is calculated as the squared
coefficient of this wave function in the negative side of the geometry that is
divided by the sum of the squared coefficients of all the terms of the equa-
tion. Thus, the calculation result shows that the calculated probability of the
charge exchange is high when the time and space are not distorted. How-
ever, when time and space are distorted it decreases, and the probability of
elastic scattering is growing. The achieved result also indicates that the dis-
crete energy levels of electrons in hydrogen atoms shift when the distortion
of time and space occurs in the nuclear fusion.
Keywords: general theory of relativity, nuclear fusion, distortion of time and space,
charge exchange.
INTRODUCTION
In our previous research [2–8], we have found that a rotating ultra-heavy mass
that distorts time and space produces anti-gravity. Anti-gravity is another gravity
that holds the opposite sign, + or –, of the physical properties (energy intensity
and angular momentum) from those of normal gravity. Then we predicted that
anti-gravity should expand the size of the Universe. In addition, we developed the
concept of the flying craft having a disk-shaped body for interstellar travel. The
explicit images of the ultra-heavy mass that distorts time and space are a black
hole and a nuclear fusion reactor as they continue producing heavier nuclei by
fusing the lighter nuclei such as hydrogen, deuteron and tritium. By our previous
research we have so far completed the numeric simulation of a rotating ultra-
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 1 38
heavy mass by applying the general theory of relativity with the mathematics of
the 4-dimensional tensors. However, the distortion of time and space is still an
unproven hypothesis.
A research question remains: whether the nuclear fusion relates to the distor-
tion of time and space, or not. To answer this question, we used an approximation
method. First, we have prepared an input dataset that simulates the infinite
4-dimensional time and space, by replacing them with the finite discrete values.
Then we set a geometrical placement of an electron in the field of two fixed pro-
tons with a separation in two-dimensional coordinates. With this setting, we cal-
culated the probabilities of the proton’s elastic scattering and its charge exchange
by the approximation method of quantum mechanics [9, pp. 95–97]. The prob-
ability of charge exchange leads to the fusion of the proton and the hydrogen-
atom. Also, we simulated the distortion of time and space by the same method of
our previous research [2–8], which was based on the general theory of relativity
[1 pp. 32–36]. Finally, by comparing the calculated probabilities with and without
the distortion of time and space, we examined the relation between nuclear fusion
and the distortion of time and space.
METHOD
Probabilities of charge exchange and elastic scattering by a moving proton
We have simulated a fusion of two hydrogen-atoms. But, to simplify the simula-
tion, we calculated the probabilities of moving proton’s charge exchange and its
elastic scattering with a target electron of a hydrogen atom. (Note: the moving
proton is called incident proton.) The reference [9, p. 95] sets a system of an elec-
tron in the field of fixed two protons. According to the reference, we set the fol-
lowing linear operator that is called Hamiltonian, considering the proton and the
hydrogen atom as two interacting quantum mechanical system:
22 11
2
1
1
2
1
1
2
1
Rr MR
+
R+rRr
=H
. (1)
It is an operator that forms Schrödinger’s equation shown below with wave
functions, ),( Rr , and )(RX . It consists of five components. First, 2
2
1
r , is
for the kinetic energy of electron where electron’s mass is 1 in atomic units, and
where
2
r is an operator that makes
2
),(
r
Rr
, and ),( Rr is a wave function
of electron’s coordinate r and proton’s coordinate R . Second; 21
RM
is for
the kinetic energy of the moving proton and 2
R is an operator that makes
2
)(
R
RX
, where )(RX is a wave function of the proton coordinate R . M is
the mass of the proton. (Note: )(RXM R is the momentum p of a proton, and
Mp 2/2 is the kinetic energy of a proton; then
M
RXR
2)]([
is the total kinetic
energy of two protons.) The other three terms of (1) are for the potential energies:
The proof of hypothesis regarding distortion of time and space using the nuclear fusion model
Системні дослідження та інформаційні технології, 2022, № 1 39
1) potential energy of hydrogen atom with the target electron in its initial po-
sition
Rr
2
1
1
;
2) potential energy of hydrogen atom with its electron after charge exchange
R+r
2
1
1
;
3) potential energy of hydrogen’s proton
R
+
1
.
The potential energy of the target electron 1) induces the proton’s elastic
scattering, and the potential energy of the target electron 2) induces its charge ex-
change with the incident proton. The proton’s potential energy 3) induces both
elastic scattering and charge exchange of the slowly moving incident proton.
Because the proton is moving slower than the hydrogen atom’s electron,
21
RM
, is called the slow subsystem 2H of the Hamiltonian, and
R
+
R+rRr
r
1
2
1
1
2
1
1
2
1 2
, is called the fast subsystem 1H of the Hamil-
tonian. Then (1) becomes as follows:
21 HHH .
Here 1H plays the role of potential energy while 2H plays the role of ki-
netic energy in the Hamiltonian (1). Then the following Schrödinger’s equation
gives the solution of the problem:
)(),(φ
11
2
1
1
2
1
1
2
1
)(),(φ 22 RXRr
MR
+
R+rRr
RXRrH nRrn
)(),(φ)(),(φ)( 21 RXRrERXRrHH nnn .
Henceforward we focus on the potential energy 1H of Schrödinger’s
equation:
)(),(φ
1
2
1
1
2
1
1
2
1
)(),(φ 2
1 RXRr
R
+
R+rRr
RXRrH nrn
)(),(φ)(),(φ1 RXRrRXRrH nnn , (2)
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 1 40
where ),( Rrn )(RX is the solution known as a wave function and n is the ei-
genvalue of the potential energy. The wave functions are continuous, but the
equation (2) leads to the discrete eigenvalues that define the energy states of the
hydrogen atom as the suffix n gives discrete numbers, 0, 1, 2…, that define the
discrete energy states of the hydrogen atom with an electron. Hence, the hydro-
gen-atom has a discrete energy spectrum in its atomic structure, while the slowly
moving proton has a continuous energy spectrum.
Then the coefficients of the Schrödinger equation are calculated as solution
of the problem of an electron in the field of two fixed protons with separation
(distance) of R , as shown in Fig. 1 in a flat yx coordinate system. Here, r
gives the distance between the origin O of the coordinates and an electron, which
is indicated in the plane polar coordinates. Here, R)2/1( , and R)2/1( are the
locations of two protons on the x-axis; and, Rr )2/1( is the length of the vector
between the proton located at R)2/1( and the electron, and Rr )2/1( is the
length of the vector between the proton located at R)2/1( and the electron, in-
dicated in plane polar coordinates.
The Hamiltonian (1) is symmetric )( rr with respect to interchange of
the incident particle (a slowly moving proton) and target particle (an electron of
the hydrogen-atom). Here, the interchange of the particles means that the proton’s
charge changes to –. Then symmetric and anti-symmetric functions ),( RrS
n
and ),( Rra
n are introduced. When the nucleons are far apart, the electron will be
localized near one or the other proton, therefore we have:
R+r±RrRr, Q
n
Q
nR
aS
n 2
1
2
1
2
1
)(
00
. , (3)
where
R+r±Rr Q
n
Q
n 2
1
2
1
2
1
00
are hydrogen-atom’s wave functions
[8, p. 96].
The initial condition of the simulation is that the electron is attached to the
proton at 2/R of x-coordinates. It means that the wave function of the electron
is initially:
Fig. 1. Coordinates of two protons and an electron (modified from [9], p. 89, Fig. 21)
y
x
e
r
0
The proof of hypothesis regarding distortion of time and space using the nuclear fusion model
Системні дослідження та інформаційні технології, 2022, № 1 41
Rr= Q
n 2
1
0
. (4)
Here, )2/1( RrQ
n means that Q
n is a function of Rr 2/1 , that is the
initial position of the electron, which is located at a distance from the coordinate
R2/1 to the electron e in the upper-right hand of Fig. 1. Here n0 means the elec-
tron’s initial state among its n energy states (4).
The uncertainty principle of quantum mechanics doesn’t determine the exact
position of an electron in a hydrogen-atom, but it only calculates the probability
of the electron’s position as the squared coefficients of Schrödinger’s equation (2)
that describes the system of the proton and the hydrogen-atom. Then in (2), the
coefficient of )2/1( Rr is for the proton’s elastic scattering, and the coeffi-
cient of )2/1( Rr is for the charge exchange (the capture of the proton by the
hydrogen-atom). In this simulation, an electron’s position is somewhere between
two symmetrically placed hydrogen atoms, while their protons’ positions are
fixed at the R2/1 , and R2/1 on the x-axis. Then these two protons are set in
Fig. 1 to calculate the coefficients of a slowly moving proton and a hydrogen-
atom of Schrödinger equation (2).
First, the position of the electron is at R2/1 of x-coordinates in Fig. 1. It
means the elastic scattering of the slowly moving proton because the electron of
Fig. 1 stays at the electron’s initial position with the hydrogen-atom’s proton that
is fixed at R2/1 . On the other hand, the move of the position of the hydrogen-
atom’s electron from R2/1 to R2/1 means the charge exchange (the hydro-
gen-atom’s electron changes its sign from + to –) by the interaction between the
slowly moving proton and the hydrogen-atom’s electron [9, p. 84].
Therefore, the coefficient of ),(φ
2
1
1
Rr
Rr
n
of (2) gives the amplitude of
the elastic scattering of the proton; and, the coefficient of ),(φ
2
1
1
Rr
R+r
n
gives the amplitude of the charge exchange. The coefficient of 2/R gives the
amplitude of both of the elastic scattering and the charge exchange to be made by
the hydrogen atom’s proton.
INPUT DATA FOR THE NUMERIC SIMULATION
If time and space are distorted (dependent on each other), the electron’s plane po-
lar coordinate r must be dependent on time. However, it contradicts the uncer-
tainty principle of quantum mechanics because the location of the electron cannot
be determined at any time by the principle. Then for the purpose of our numeric
simulation, we compromise this contradiction by defining the kinetic energy as a
constant term. The hydrogen-atom’s electron may change its position from its
initial position at R2/1 of x-coordinates, to the position of the charge exchange,
R2/1 , but the simulation doesn’t calculate when it occurs, but only the
probabilities of the occurrence.
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 1 42
Then we assigned 24 discrete values for the coordinates of r and R as
shown in Fig. 2.
In our simulation, symmetric and anti-symmetric functions ),( RrS
n and
),( Rra
n are substituted by the symmetric geometry of two hydrogen atoms as the
mirror images on the both-sides of the origin O , as shown in Fig. 3. We assign
the value of R by the empirically measured radius, 25 pico-meters, of hydrogen-
atom [10]. Because two hydrogen-atoms are placed next to each other in Fig. 3,
we assign 50 to the value of R . If charge exchange happens, the electron’s plane
polar coordinate, r , changes its position from the initial position, 2/R of x-
coordinates, to the position of the charge exchange, R2/1 . Then the relation
between r and R is as follows:
2
2
2
x+
R
=r
, (5)
where x is the distance from the origin O toward R2/1 and toward R2/1 , and
the origin O is at 0 on the x-axis, R2/1 is at -12 on the x-axis; and, R2/1 is
at +12 on the x-axis. The electron is initially attached to the proton at R2/1 of
x-coordinates (5); and then it will be attached to the proton at R2/1 of
x-coordinates after the charge exchange.
R
r
x – axis
R
,
r
Fig. 2. Coordinates r and R without the distortion of time and space
x
yElectron’s porition after charge exchange Electron’s initial position
Fig. 3. Position of the electron and its coordinate r
The proof of hypothesis regarding distortion of time and space using the nuclear fusion model
Системні дослідження та інформаційні технології, 2022, № 1 43
As stated by (3), the nucleons are far apart; therefore, the electron will be lo-
calized near one or the other proton. However, it doesn’t mean that R in this simu-
lation should be far apart to infinity, but it only justifies the wave functions of
hydrogen-atom that distinguish the initial state of the wave function
RrQ
n 2
1
0
and the wave function
RrQ
n 2
1
0
after the charge exchange.
Then we set sine curves as the wave functions ),( Rrn of (2). And we set
two frequencies, 1w and 2w as shown in Fig. 4, for simulating the lower energy
state (the lower frequency) and the higher energy state (the higher frequency) of
the electron of the hydrogen atom. These sine curves are the functions of r and
R , which ),( Rrn require.
If r and R are dependent on t, r becomes distorted distance ρ, while t be-
comes distorted time as shown in Fig. 5 and Fig. 6. In Fig. 2 shown above, r
and R are distance without the distortion. However, in Fig. 5 and Fig. 6, τ and ρ are
time and distance showing the interaction with each other. They are calculated by:
)(rf+t= ; (6)
)(rg+t= , (7)
where, f(r) and g(r) are given functions of r [9 p. 34]. We set them as shown be-
low, logarithmic distortion, and with exponential distortion:
rrf log)( ,
rerg )( .
Fig. 4. Sine curves with lower frequency w1 and the higher frequency w2
sin w1
x – axis
sin w2
si
n
e
x – axis
di
st
or
te
d
r
Fig. 5. Distorted coordinates of the electron’s position (ρ) with interaction of time and space
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 1 44
We assume that logarithmic distortion for distorted time (6) and exponential
distortion for distorted space (7). We think that distorted time should not vary ex-
ponentially, because distorted time coordinates should give the basis (less variable
than exponential) of the 4-dimensional time and space even if they interact with
space.
To calculate (6) and (7), we assigned a time coordinate t on the x-axis from
+12 to -12, as the electron’s initial position is at +12. According to (7), R is also
affected by t, but it doesn’t change as much as r does as shown in Fig. 6.
For the distorted r and the distorted R , we used the same wave function
(sine curve) as shown in Fig. 4.
ALGORITHM OF THE SIMULATION
The probability of charge exchange was calculated by the equation shown below:
)(),(φ
2
1
)(),(φ 2
1 RXRr=RXRrH nrn
)(
1
)(),(φ
)2/1(
1
)(),(φ
)2/1(
1
21 RX
R
+RXRr
Rr
CRXRr
Rr
C nn
. (8)
For this numeric simulation, we defined that )(),(φ
2
1 2 RXRrnr
)(
1
RX
R
is a constant term (let’s put it as T), and it is not affected by the geometry
for the potential energy of the system in Fig. 1. Then we can use the matrix algebra
shown below to calculate the coefficients, 1C and 2C . Also, we don’t need )(RX
henceforward, because (8) becomes independent from R . Then (8) becomes
),(φ
)2/1(
1
),(φ
)2/1(
1
),(φ 211 Rr
Rr
CRr
Rr
CTRrH nnn
w
Rr
Cw
Rr
CT= sin
)2/1(
1
sin
)2/1(
1
21 . (9)
x – axis
di
st
or
te
d
r
Fig. 6. Distorted coordinates of the proton’s position (R) with interaction of time and space
The proof of hypothesis regarding distortion of time and space using the nuclear fusion model
Системні дослідження та інформаційні технології, 2022, № 1 45
When the reference [9] was published in 1969, a personal power computer of
today was not available; therefore, it further described the algorithm in mathe-
matical forms with calculus. Also, it suggested that the squared module of the
coefficient 2C of nRr )])2/1(/(1[ gave the probability of charge exchange
[9, p. 86]. In this research we used a personal computer to calculate the coeffi-
cients, 1C and 2C , with the matrix algebra shown below.
First, we set a two-column matrix X,
21sin
)2/1(
1
sin
)2/1(
1
XXw
Rr
w
R+r
=X
,
and a two-row vector made of two coefficients, 1C and 2C :
2
1
C
C
=c ;
now, (9) becomes as follows:
cXT=RrH n ),(φ1 )( 2211 XCXCT .
Then we set the boundary conditions to solve the problem:
0
)],(φ[ 2
1 =
C
RrH
n
n
.
For example, in case of 1n , we have:
0)(),(φ2
)],(φ[
11
1
2
1
XRrH
C
RrH
n
n .
Then
0),(φ =RrHX' n ,
where X is a transpose matrix of X .
On the other hand,
cXT=RrH n ),(φ ;
therefore,
0)( =cXTX' .
Then, we can write:
TX'=XcX' .
Therefore, the coefficients are calculated by the equation:
TX'XX'=c 1)( ,
where 1)( XX is the inverse matrix of XX . In this simulation, we set T as
a 25 row-vector of unity (one), therefore the calculated coefficients are not abso-
lute probabilities, but relative probabilities to the unity T . We think that it is suf-
ficient to assign unity to T , because the goal of this simulation is to calculate the
probabilities by means of relative squared modules of the coefficients. The calcu-
lated coefficients are proportional to the eigenvalues of the hydrogen atom.
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 1 46
RESULT
Fig. 7 and Fig. 8 show the calculated probabilities of the charge exchange and the
elastic scattering of the slowly moving proton to the target electron. The prob-
abilities shown in these figures are the calculated results that don’t take distorted
time and space. Table 1 shows the calculated values of these figures. The prob-
ability of the proton’s elastic scattering is calculated by the squared coefficient 1C
divided by the sum of the squared coefficients of 1C and 2C , and the probability
of the proton’s charge exchange is calculated by squared 2C divided by the sum
of the squared coefficients of 1C and 2C .
T a b l e 1 . Calculated probability without the distortion of time and space
Parameter
C1 for
elastic scattering
C2 for
charge exchange
W1 11,,225522··1100––22 -6,220··1100––11
Coefficient
W2 77,,773333··1100––33 -6,068··1100––11
W1 1,568··1100––44 3,868··1100––11
Squared coefficient
W2 5,979··1100––55 3,682··1100––11
W1 4,051··1100––44 9,996··1100––11
Probability
W2 1,624··1100––44 9,998··1100––11
Note: The probability is a squared coefficient divided by the sum of squared coef-
ficients
Fig. 7. Calculated probabilities of elastic scattering and change exchange with sin w1
(without the distortion of time and space)
0,000E+00
2,000E-01
4,000E-01
6,000E-01
8,000E-01
1,000E+00
1,200E+00
Probability
Proton’s charge exchange Proton’s elastic scattering
Fig. 8. Calculated probabilities of elastic scattering and change exchange with sin w2
(without the distortion of time and space)
0,000E+00
2,000E-01
4,000E-01
6,000E-01
8,000E-01
1,000E+00
1,200E+00
Probability
Proton’s charge exchange Proton’s elastic scattering
The proof of hypothesis regarding distortion of time and space using the nuclear fusion model
Системні дослідження та інформаційні технології, 2022, № 1 47
Fig. 9, Fig. 10 and Table 2 show the result of the simulation with the dis-
torted time τ and distorted distance ρ. The probability of the charge exchange is
lower than the probability without distortion shown in Fig. 7, Fig. 8 and Table 1.
Instead, the probability of elastic scattering appears and reaches the same prob-
ability of charge exchange. It is also noted that the values of the coefficients of
the equation shift from those without distortion of time and space. It means that
the eigenvalues of Schrödinger equation (2) shift, i.e., the discrete energy states of
the hydrogen atom also shift.
T a b l e 2 . Calculated probability with the distortion of time and space
Parameter
C1 for
elastic scattering
C2 for
charge exchange
W1 1,597··11002277 1,597··11002277
Coefficient
W2 2,050··11002277 2,050··11002277
W1 2,550··11005544 2,550··11005544
Squared coefficient
W2 4,204··11005544 4,204··11005544
W1 5,000··1100––11 5,000··1100––11
Probability
W2 5,000··1100––11 5,000··1100––11
Note: The probability is a squared coefficient divided by sum of the squared coefficients.
CONCLUSIONS AND RECOMMENDATIONS
The result of the simulation shows that the proton is captured by the hydrogen
atom by the charge exchange at the beginning of nuclear fusion when the mass is
Fig. 9. Calculated probabilities of elastic scattering and change exchange with the
distortion of time and space (sin w1)
0,000E+00
1,000E-01
2,000E-01
3,000E-01
4,000E-01
5,000E-01
6,000E-01
Probability
Proton’s charge exchange Proton’s elastic scattering
Fig. 10. Calculated probabilities of elastic scattering and change exchange with the
distortion of time and space (sin w2)
0,000E+00
1,000E-01
2,000E-01
3,000E-01
4,000E-01
5,000E-01
6,000E-01
Probability
Proton’s charge exchange Proton’s elastic scattering
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 1 48
not yet heavy and when time and space are still independent. However, as the fu-
sion process proceeds and time and space are interacted, the elastic scattering of
the proton appears. It means that the nuclear fusion reaches saturation at some
point of the process with the distorted time and space.
The experiment of nuclear fusion may verify the distortion of time and
space. In our numeric simulation, the coefficient of the charge exchange differs
between the cases with and without the distortion. It means that the discrete en-
ergy states of the electron in the hydrogen atom should also vary because the so-
lution of discrete eigenvalues of Schrödinger equation (2) shifts from the case
without the distortion to the case with the distortion. (The wave functions such as
sine curves are continuous, but the equation (2) leads to the discrete eigenvalues
that define the energy states of the hydrogen atom). Also, if the increased proton’s
elastic scattering is observed in the experiment, it verifies the distortion of time
and space.
Therefore, if a laboratory experiment of nuclear fusion detects the shift of
electron’s energy states of the hydrogen atom and/or increase of the proton’s elas-
tic scattering, it will confirm the distortion of time and space in nuclear fusion.
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Black Hole, using Curvature Tensors”, System Research&Information Technology,
no. 1, pp. 54–67, 2020. doi: 10.20535/SRIT.2308.8893.2020.1.05.
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ity”, System Research & Information Technology, no. 3, pp. 124–137, 2020. doi:
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tion of the general theory of relativity. LAP LAMBERT Academic Publishing, Oc-
tober 2021, 84 p.
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https://aip.scitation.org/ doi.org/10.1063/1.1725697
Received 05.01.2022
The proof of hypothesis regarding distortion of time and space using the nuclear fusion model
Системні дослідження та інформаційні технології, 2022, № 1 49
INFORMATION ON THE ARTICLE
Yoshio Matsuki, ORCID: 0000-0002-5917-8263, National University of Kyiv-Mohyla
Academy, Ukraine, e-mail: matsuki@wdc.org.ua
Petro I. Bidyuk, ORCID: 0000-0002-7421-3565, Institute for Applied System Analysis
of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Insti-
tute”, Ukraine, e-mail: pbidyuke_00@ukr.net
ДОВЕДЕННЯ ГІПОТЕЗИ СТОСОВНО ВІДХИЛЕННЯ ЧАСУ І ПРОСТОРУ
НА ОСНОВІ МОДЕЛІ ЯДЕРНОГО СИНТЕЗУ / Й. Мацукі, П.І. Бідюк
Анотація. Дослідження присвячено сучасній тематиці: аналізу умов, які при-
зводять до спотворення координат часу і простору, — явища, що є наслідком
загальної теорії відносності, тобто коли час і простір стають взаємозалежними.
Для аналізу використано інструментарій імітаційного моделювання з метою
імітації руху протона, який вдаряє електрон атома водню. Методологія моде-
лювання ґрунтується на обчисленні ймовірностей пружного розсіювання і
обміну зарядами протона та цільового електрона. Таке спотворення
моделюється функціями, які зв’язують логарифмічно координати часу і про-
стору у випадку спотворення часу і експоненційно у випадку спотворення
простору. Геометрію цієї взаємодії описано рівнянням Шредінгера з викори-
станням хвильової функції електрона. Імовірність обміну зарядом обчислено
діленням квадрата коефіцієнта хвильової функції на суму квадратів
коефіцієнтів усіх членів рівняння. Результати розрахунків показують:
імовірність обміну зарядом висока, якщо час і простір не мають відхилень, але
коли час і простір спотворюються, вона зменшується і збільшується
ймовірність пружного розсіювання. Отриманий результат свідчить про те, що
дискретні рівні енергії електронів атомів водню зміщуються у випадку, коли у
процесі ядерного синтезу виникає спотворення часу і простору.
Ключові слова: загальна теорія відносності, ядерний синтез, спотворення ча-
су і простору, обмін зарядами.
ДОКАЗАТЕЛЬСТВО ГИПОТЕЗЫ ОБ ИСКАЖЕНИИ ВРЕМЕНИ И
ПРОСТРАНСТВА НА ОСНОВЕ МОДЕЛИ ЯДЕРНОГО СИНТЕЗА / Й. Мацу-
ки, П.И. Бидюк
Аннотация. Исследование посвящено современной тематике: анализу усло-
вий, которые приводят к искажению координат времени и пространства — яв-
ления, что является следствием общей теории относительности, т.е. когда вре-
мя и пространство стают взаимно зависимыми. Для анализа использовано
инструментарий имитационного моделирования с целью имитации движения
протона, который ударяет электрон атома водорода. Методология моделиро-
вания основывается на вычислении вероятностей упругого рассеяния и обмена
зарядами протона и целевого электрона. Такое искажение моделируется функ-
циями, которые связывают логарифмически координаты времени и простран-
ства в случае искажения времени и экспоненциально в случае искажения про-
странства. Геометрия этого взаимодействия описана уравнением Шредингера
с использованием волновой функции электрона. Вероятность обмена зарядом
вычислена делением квадрата коэффициента волновой функции на сумму
квадратов коэффициентов всех членов уравнения. Результаты расчетов пока-
зывают, что вероятность обмена зарядом высока, если время и пространство не
имеют отклонений, а если время и пространство искажаются, то она уменьша-
ется и увеличивается вероятность упругого рассеяния. Полученный результат
свидетельствует о том, что дискретные уровни энергии электронов атомов во-
дорода смещаются в случае, когда в процессе ядерного синтеза возникает ис-
кажение времени и пространства.
Ключевые слова: общая теория относительности, ядерный синтез, искажение
времени и пространства, перезарядка.
|
| id | journaliasakpiua-article-259048 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:27:51Z |
| publishDate | 2022 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/65/d7954937d66c839bc19ef9182f414c65.pdf |
| spelling | journaliasakpiua-article-2590482022-06-21T10:27:50Z The proof of hypothesis regarding distortion of time and space using the nuclear fusion model Доказательство гипотезы об искажении времени и пространства на основе модели ядерного синтеза Доведення гіпотези стосовно відхилення часу і простору на основі моделі ядерного синтезу Matsuki, Yoshio Bidyuk, Petro загальна теорія відносності ядерний синтез спотворення часу і простору обмін зарядами общая теория относительности ядерный синтез искажение времени и пространства перезарядка general theory of relativity nuclear fusion distortion of time and space charge exchange The study is dedicated to modern topic: the analysis of conditions that lead to distortion of the time and space coordinates which results from the general theory of relativity. The main goal of this research is to prove the hypothesis regarding distortion of time and space using nuclear fusion model. For this purpose the simulation instrument is used to imitate a moving proton that hits an electron of a hydrogen atom. The methodology of simulation is based upon calculation of the probabilities of elastic scattering and charge exchange of a proton with a target electron. The distortion is modeled by the functions that relate time and space logarithmically for distorted time and exponentially for distorted space. Such geometry construction is described by the Schrödinger equation using the electron wave function. Then the probability of charge exchange is calculated as the squared coefficient of this wave function in the negative side of the geometry that is divided by the sum of the squared coefficients of all the terms of the equation. Thus, the calculation result shows that the calculated probability of the charge exchange is high when the time and space are not distorted. However, when time and space are distorted it decreases, and the probability of elastic scattering is growing. The achieved result also indicates that the discrete energy levels of electrons in hydrogen atoms shift when the distortion of time and space occurs in the nuclear fusion. Исследование посвящено современной тематике: анализу условий, которые приводят к искажению координат времени и пространства — явления, что является следствием общей теории относительности, т.е. когда время и пространство стают взаимно зависимыми. Для анализа использовано инструментарий имитационного моделирования с целью имитации движения протона, который ударяет электрон атома водорода. Методология моделирования основывается на вычислении вероятностей упругого рассеяния и обмена зарядами протона и целевого электрона. Такое искажение моделируется функциями, которые связывают логарифмически координаты времени и пространства в случае искажения времени и экспоненциально в случае искажения пространства. Геометрия этого взаимодействия описана уравнением Шредингера с использованием волновой функции электрона. Вероятность обмена зарядом вычислена делением квадрата коэффициента волновой функции на сумму квадратов коэффициентов всех членов уравнения. Результаты расчетов показывают, что вероятность обмена зарядом высока, если время и пространство не имеют отклонений, а если время и пространство искажаются, то она уменьшается и увеличивается вероятность упругого рассеяния. Полученный результат свидетельствует о том, что дискретные уровни энергии электронов атомов водорода смещаются в случае, когда в процессе ядерного синтеза возникает искажение времени и пространства. Дослідження присвячено сучасній тематиці: аналізу умов, які призводять до спотворення координат часу і простору, — явища, що є наслідком загальної теорії відносності, тобто коли час і простір стають взаємозалежними. Для аналізу використано інструментарій імітаційного моделювання з метою імітації руху протона, який вдаряє електрон атома водню. Методологія моделювання ґрунтується на обчисленні ймовірностей пружного розсіювання і обміну зарядами протона та цільового електрона. Таке спотворення моделюється функціями, які зв’язують логарифмічно координати часу і простору у випадку спотворення часу і експоненційно у випадку спотворення простору. Геометрію цієї взаємодії описано рівнянням Шредінгера з використанням хвильової функції електрона. Імовірність обміну зарядом обчислено діленням квадрата коефіцієнта хвильової функції на суму квадратів коефіцієнтів усіх членів рівняння. Результати розрахунків показують: імовірність обміну зарядом висока, якщо час і простір не мають відхилень, але коли час і простір спотворюються, вона зменшується і збільшується ймовірність пружного розсіювання. Отриманий результат свідчить про те, що дискретні рівні енергії електронів атомів водню зміщуються у випадку, коли у процесі ядерного синтезу виникає спотворення часу і простору. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2022-04-25 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/259048 10.20535/SRIT.2308-8893.2022.1.03 System research and information technologies; No. 1 (2022); 37-49 Системные исследования и информационные технологии; № 1 (2022); 37-49 Системні дослідження та інформаційні технології; № 1 (2022); 37-49 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/259048/255749 |
| spellingShingle | загальна теорія відносності ядерний синтез спотворення часу і простору обмін зарядами Matsuki, Yoshio Bidyuk, Petro Доведення гіпотези стосовно відхилення часу і простору на основі моделі ядерного синтезу |
| title | Доведення гіпотези стосовно відхилення часу і простору на основі моделі ядерного синтезу |
| title_alt | The proof of hypothesis regarding distortion of time and space using the nuclear fusion model Доказательство гипотезы об искажении времени и пространства на основе модели ядерного синтеза |
| title_full | Доведення гіпотези стосовно відхилення часу і простору на основі моделі ядерного синтезу |
| title_fullStr | Доведення гіпотези стосовно відхилення часу і простору на основі моделі ядерного синтезу |
| title_full_unstemmed | Доведення гіпотези стосовно відхилення часу і простору на основі моделі ядерного синтезу |
| title_short | Доведення гіпотези стосовно відхилення часу і простору на основі моделі ядерного синтезу |
| title_sort | доведення гіпотези стосовно відхилення часу і простору на основі моделі ядерного синтезу |
| topic | загальна теорія відносності ядерний синтез спотворення часу і простору обмін зарядами |
| topic_facet | загальна теорія відносності ядерний синтез спотворення часу і простору обмін зарядами общая теория относительности ядерный синтез искажение времени и пространства перезарядка general theory of relativity nuclear fusion distortion of time and space charge exchange |
| url | https://journal.iasa.kpi.ua/article/view/259048 |
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