MATHEMATICS & NATURE
Mathematics, Physics, Mechanics & Astronomy
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Mathematics & Nature–Free Media of Eternal Truth, China, 2021 https://orcid.org/0000-0002-3644-5170
.
Article
.
Physics
Dongfang Com Quantum Equations of LIGO Signal
X. D. Dongfang
Orient Research Base of Mathematics and Physics,
Wutong Mountain National Forest Park, Shenzhen, China
The signal waveform with monotonic frequency change detected by LIGO is implying the discrete
law of macroscopic quantization. Here, I accurately analyzed the observation data of GW150914 signal
and proved that the Livingston waveform of positive and negative strain reversal was 7.324218ms
ahead of Hanford waveform. Then, the time of the positive and negative strain peaks of the main
vibration part is corrected by using the superposition waveform, and the numerical results of the
discrete frequency of GW150914 signal are calculated. Finally, a numerical analysis method using
the minimum digit rational number solution of the characteristic Diophantine equation system was
introduced to fit the quantized Lagrange frequency change rate and frequency jump rate of the
GW150914 signal, providing a quantitative basis for inferring accurate information of the wave source.
Keywords: LIGO Signal; Lagrange change rate; Jump change rate; Dongfang’s Com Quantum
Equations;
PACS number(s): 03.65.-w—Quantum mechanics; 03.65.Ta—Foundations of quantum mechanics;
04.30.-w—Gravitational waves; 04.60.-m—Quantum gravity; 02.60.-x—Numerical approximation and
analysis
1 Introduction
Can macro quantum theory and micro quantum theo-
ry be unified in the same logical framework? The answer
to this question is yes. There is an important basic fact
that any discrete physical quantity defined to describe a
quantum process presents the law of quantization. In the
micro field, the establishment and development of quan-
tum mechanics
[1-5]
based on the Rydberg formula
[6]
of
the hydrogen spectrum is successful, although quantum
mechanics also hides some logical paradoxes
[21, 28]
that
need to be solved urgently. In the macro field, quantum
gravity has not achieved satisfactory results, which may
be due to the lack of experimental basis, so the theo-
ry deviates far from reality. LIGO’s so-called detection
of the gravitational wave of the merger of ancient spiral
binaries
[8-13]
seems to fill the experimental gap in the s-
tudy of macro quantization law. Here, the GW150914
signal wave
[8]
with accurate data report is re analyzed.
Firstly, the exact relationship between Hanford wavefor-
m and Livingston waveform is clarified, and then the
correct sup erposition waveform is obtained. Then, the
time of wide peak or uncertain peak is corrected by using
the superposition waveform within the error range, and
the frequency distribution of positive and negative strain
peak of GW150914 signal wave is calculated. Referring
to the Blanchet frequency equation
[14]
of gravitational
wave in general relativity
[15-19]
, the Lagrange frequen-
cy change rate
[21]
and frequency jump change rate with
quantization meaning are defined. We introduce a nu-
merical analysis method for the minimum digit rational
number solution of the characteristic Diophantine equa-
tion system, and use the numerical results of frequency
distribution to fit the two types of quantized frequency
change rates with high accuracy for GW150914 signals.
2 Superposition waveform of GW150914
signal
Making a high-precision scale or screen ruler to mea-
sure the vibration peak time interval of the vibration
curve, and calculate the high-precision period and fre-
quency distribution of the signal wave, so that the Han-
ford waveform and Livingston waveform of GW150914
signal can be accurately superimposed. The period-
s and frequencies mentioned here refer to the intrinsic
periods and frequencies with observational effects. The
time of measuring Hanford strain peak of GW150914
signal with screen ruler can reach the accuracy of 10
6
s.
This method is especially suitable for analyzing vibra-
tion curves of unknown original function and unpub-
lished detailed observation data. However, time accura-
cy of recording GW150914 signal wave by LIGO is 10
9
s,
which is three orders of magnitude higher than that of
a screen ruler. Therefore, we extracted the waveform
data of LIGO Open Science Center database
[20]
, and re-
drawn Hanford waveform and Livingston waveform by
computer science drawing software.
As shown in Figures 1 and Figures 2. By reading the
time of positive and negative strain peaks and compar-
Citation: Dongfang, X. D. Dongfang Com Quantum Equations of LIGO Signal. Mathematics & Nature 1, 202106 (2021).
2 X. D. Dongfang Dongfang Com Quantum Equations of LIGO Signal
ing the total time or frequency distribution of the equal
number of positive and negative main strain peaks, the
rough relationship between the two waveform phases can
be found. Then the exact time of several positive and
negative strain peaks is extracted from LIGO raw data,
and the main vibration peaks of the two waveforms are
overlapped to the maximum extent by moving one wave-
form point by point, thus the exact relationship between
the two waveforms is determined.
The Hanford waveform is shown in Figure 1. Seven
Hanford main positive strain peaks appear in turn at the
time 0.3398s, 0.3624s, 0.3842s, 0.4021s, 0.4122s, 0.4146s
and 0.4282s respectively. From this, one can obtain
the intrinsic frequency distribution of the positive strain
peaks of Hanford waveform as follows, F
+
H
= { 44.2478Hz,
45.8716Hz, 55.8659Hz, 80.0Hz, 116.2791Hz, 200.0Hz},
and the time interval between the first and seventh Han-
ford positive peaks is
t
+
H
= 0.4282s 0.3398s = 0.0884s
On the other hand, time readings of seven Hanford
main negative strain peaks are 0.3496s, 0.3743s, 0.3932s,
0.4078s, 0.4194s, 0.4259s and 0.4301s respectively. From
this, the intrinsic frequency distribution of the nega-
tive strain peaks of the Hanford waveform is calculat-
ed as follows, F
H
={40.4858Hz, 52.9101Hz, 80.2069Hz,
153.8462Hz, 238.0952Hz }, and the time interval between
the first and seventh Hanford negative strains is
t
H
= 0.4301s 0.3496s = 0.0805s
Signal GW150914 Hanford
0.25
0.30
0.35
0.40
0.45
-1.0
-0.5
0.0
0.5
1.0
Strain H10
-21
L
Figure 1 Hanford vibration curve of the GW150914 signal wave
The Livingston waveform is shown in Figure 2. Sev-
en Livingston main positive strain peaks appear in
turn at the time 0.3453s, 0.3671s, 0.3857s, 0.3998s,
0.4122s, 0.4188s and 0.4231s respectively. From this,
the intrinsic frequency distribution of the positive s-
train peaks of Livingston waveform is calculated to
be, F
+
L
={45.8716Hz, 53.7634Hz, 70.9220Hz, 80.6452Hz,
151.5152Hz, 232.5581Hz }, and the time interval between
the first and seventh Livingston positive peaks is
t
+
L
= 0.4231s 0.3453s = 0.0778s
For another, time readings of seven Livingston neg-
ative strain peaks are 0.3302s, 0.3535s, 0.3762s,
0.3936s, 0.4071s, 0.4156s and 0.4208s respectively.
From this, one can obtain the intrinsic frequency
distribution of the Livingston negative strain peak-
s, F
L
={42.9185Hz, 44.0529Hz, 57.4713Hz, 74.0741Hz,
117.6471Hz, 192.3077Hz }, and the time interval between
the first and seventh Livingston negative strain peaks is
t
L
= 0.4208s 0.3302s = 0.0906s
Signal GW150914 Livingston
0.25
0.30
0.35
0.40
0.45
-0.5
0.0
0.5
1.0
Strain H10
-21
L
Figure 2 Livingston vibration curve of the GW150914 signal
wave
By comparing the total time of seven positive and
negative strain peaks of the Hanford waveform and the
Livingston waveform, and comparing the frequency dis-
tribution of the positive and negative strain of the two
waveforms, it is not difficult to find the following ap-
proximate relationships,
t
+
H
t
L
, t
H
t
+
L
, F
+
H
F
L
, F
H
F
+
L
Considering the experimental error, it can be deduced
that the Livingston waveform is opposite to the Han-
ford waveform. In fact, the same number of positive and
negative strain peaks seen in Figures 1 and 2 is also suf-
ficient to detect the relationship between the two wave-
forms. In view of the above, the Livingston waveform
is flipped up and down in the same coordinate system,
and then gradually shifted, so that its main vibration
curve can overlap with the main vibration curve of the
Hanford waveform. The final confirmation result is that
the main vibration curves of Livingston waveform with
inversion of positive strains and negative strains as well
as delay of 7.324218ms are coincident with the main vi-
bration curves of Hanford waveform.
It is well known that the signals in Hanford and Liv-
ingston observatories are phase-shifted by π can be in-
terpreted as that is due to the fact that the Michelson
interferometers have a relative rotation of nearly π/2 and
then the signals will have the π phase difference.
Mathematics & Nature (2021) Vol. 1 3
3 Frequency distribution of GW150914 sig-
nal
Signal GW150914 Livingston
Signal GW150914 Hanford
0.25
0.30
0.35
0.40
0.45
-1.0
-0.5
0.0
0.5
1.0
Strain H10
-21
L
Figure 3 Synchronous superposition of Livingston and Hanford
vibration curves of the GW150914 signal wave: the main vibration
part of the Livingston waveform of positive and negative strain in-
version and delay of 7.324218ms coincides with the main vibration
part of the Hanford waveform
The superposition waveform of the Livingston wave-
form and the Hanford waveform is shown in Figure 3,
and the frequency of the main vibration part increases
monotonously. There are several strain peaks that de-
viate from the monotonic variation law, and the reason
may be caused by noise or the screening templates of the
extracted signals. In fact, each strain can be distorted to
varying degrees, because the record data or the filtered
data are not continuous. According to the character-
istics of frequency monotonic increase, the time of the
distortion strain peak is corrected within the error range,
and the corrected values are obtained by the characteris-
tic equation approximation with the highest credibility,
which will be intro duced in detail later. Here we only
focus on the numerical analysis of the frequency distri-
bution of GW150914 signal wave. The time of several
strain peaks in the high frequency region is LIGO origi-
nal record time, and the original accuracy of 10
9
s and
10
9
Hz are naturally retained in the correction process.
In the Figure 3, the positive and negative strain peaks
are numbered in reverse time order, and the right-most
vertical line corresponds to the number 1. The t
n
val-
ues in Table 1 is the modified time of the main positive
and negative strain peaks of the GW150914 superposi-
tion waveform. Here n is positive integer of the inverse
time series distribution, that is, quantum number.
The formulas for calculating the periods and frequen-
cies of positive and negative strain peaks are T
n
=
t
n
t
n+1
and f
n
= T
1
n
respectively. The results of
the calculations are listed in Table 1. It is known that
the period and frequency of the strain peaks represent
the period and frequency of the signal wave. There are
6 frequencies for the positive strain from 36.55320819Hz
to 197.3975904Hz, and the negative strain has seven fre-
quencies from 35.37953557Hz to 230.7600891Hz. Com-
pared with the spectral law of atomic hydrogen
[23, 24]
, in
theory, the frequency of the GW150914 signal wave is
a decreasing function of quantum numbers. The max-
imum frequency of the positive and negative strains of
the GW150914 signal wave corresponds to the minimum
quantum number of 1, so the values in the table are in-
verse timing numb ers.
Table 1 Positive and negative strain peak times of the GW150914 signal wave and its frequency distribution
n
Positive strain Negative strain
t
n
T
n
f
n
t
n
T
n
f
n
1 0.428222656 0.005065918 197.3975904 0.430297903 0.004333505 230.7600891
2 0.423156738 0.008573092 116.6440307 0.425964398 0.007333624 136.3582345
3 0.414583646 0.012607488 79.31794085 0.418630774 0.010784741 92.72359945
4 0.401976158 0.017110162 58.44479852 0.407846033 0.014636434 68.32265222
5 0.384865996 0.022037889 45.37639637 0.393209599 0.018851727 53.04553744
6 0.362828106 0.027357380 36.55320819 0.374357872 0.023402144 42.73112738
7 0.335470727 0.350955728 0.028264927 35.37953557
8 0.322690801
4 Lagrange frequency change rate
The vibration curve of GW15091414 signal wave
accords with the characteristics of standard gravity
waveform
[25-27]
of general relativity. The equation de-
scribing the frequency distribution and the variation of
gravitational waves in general relativity is Blanchet fre-
quency equation
[14]
. However, the definition of frequency
and frequency change rate in Blanchet frequency equa-
tion comes from the derivative of the phase of the vi-
bration function to time, which belongs to the formal
frequency that cannot be observed directly. It needs the
intrinsic definition of observational effect to describe the
frequency and frequency change rate of the signal wave
with frequency change. In various intrinsic definition-
s of frequency change rate, Lagrange frequency change
rate and jump change rate are relatively simple in nu-
merical processing. Now we discuss the Lagrange fre-
quency change rate of GW150914 signal wave. Because
of the inverse temporal arrangement of quantum num-
bers, the Lagrange frequency change rate is defined as
[
˙
f
n
= (f
n1
f
n+1
) (T
n
+ T
n1
)
1
, that is
4 X. D. Dongfang Dongfang Com Quantum Equations of LIGO Signal
Table 2 Observed and theoretical values of Lagrange frequency change rate of the GW150914 signal wave and the ratio of Lagrange
frequency change rate to frequency square.
n
Positive strain Negative strain Theory values
f
n
˙
f
n
˙
f
n
f
2
n
f
n
˙
f
n
˙
f
n
f
2
n
˙
f
n
f
2
n
1 197.3975904 230.7600891 1.219696970
2 116.6440307 8657.494220 0.636307692 136.3582345 11831.23042 0.636307692 0.636307692
3 79.31794085 2747.763841 0.436753649 92.72359945 3755.061951 0.436753649 0.436753649
4 58.44479852 1142.134177 0.334368530 68.32265222 1560.827218 0.334368530 0.334368530
5 45.37639637 559.1999942 0.271585859 53.04553744 764.1961764 0.271585859 0.271585859
6 36.55320819 42.73112738 418.0919129 0.228972362 0.228972362
7 35.37953557 0.198077922
˙
f
n
=
(f
n1
f
n+1
) f
n
f
n1
f
n
+ f
n1
(1)
Table 2 lists the numerical results of the Lagrange
frequency variation rate of the GW150914 signal wave,
and gives the numerical results of the frequency charac-
teristic relation
˙
f
n
f
2
n
of the positive and negative strain
peaks corresponding to the quantum number n, which
is convenient for fitting the law of signal wave frequency
change. The frequency distribution of the positive and
negative strains of the GW150914 signal wave is differ-
ent, but their Lagrange frequency change rates have the
same regularity for the same quantum values,
˙
f
±
2
= 0.636307692
f
±
2
2
˙
f
±
3
= 0.436753649
f
±
3
2
˙
f
±
4
= 0.334368530
f
±
4
2
˙
f
±
5
= 0.271585859
f
±
5
2
˙
f
6
= 0.228972362
f
6
2
(2)
From this, we can infer that the Lagrange frequency
change rate of the GW150914 signal wave obeys a com
quantum law which needs to be accurately described
by quantum numbers, which means that there are com
quantization formulas for the frequency of GW150914
signal wave and other forms of frequency change rate.
Approximate equation of high precision correspond-
ing to relation (2) can be fitted by numerical calculation.
According to the relation (2), it is further deduced that
the frequency f
n
of the GW150914 signal wave is a de-
creasing function of the quantum number n. Therefore,
the square of frequency f
2
n
and the Lagrange change rate
of frequency f
2
n
are all functions of the quantum number
n. According to the relation between frequency change
rate of oscillation function and frequency square
[28]
, it is
assumed that
˙
f
n
f
2
n
= λ (n) [η (n)]
1
, where λ (n) and
η (n) are undetermined functions. The Laurent series
expansion of two undetermined functions is as follows,
λ (n) = n
p
i=0
a
i
n
i
, η (n) = n
s
i=0
b
i
n
i
, where a
i
and b
i
are b oth undetermined coefficient, p and s are
rational numbers. If the above two series are truncat-
ed into polynomials,
˙
f
n
f
2
n
= λ (n) [η (n)]
1
is reduced
to an approximate rational formula. Taking advantage
of the
˙
f
n
f
2
n
values of 5 negative strains on the right
of the relation (2), we can only fit a lower power ratio-
nal formula with only 5 irreducible coefficients. But like
the fitting of a curve function, if the quantity is known
to be too small, the resulting function often can only
represent a small range of an implicated curve. In or-
der to obtain a high-precision approximate quantization
equation for the domain of quantum numbers, the ra-
tional method is first to use the solution of the system
of Diophantine Equations to fit the lower power ratio-
nal formula with fewer parameters, then use the low-
er power rational formula to calculate the
˙
f
n
f
2
n
values
of several larger quantum numbers, and then combine
5 known
˙
f
n
f
2
n
values to fit the higher power rational
formula with more undetermined parameters. If the nu-
merical results of the lower power rational formula and
the higher power rational formula are consistent in the
error range, then the result of the fitting is reliable.
From Table 2, it can be found that the frequency of
GW150914 signal wave is a monotone decreasing func-
tion of the quantum number. The first five terms of
the Laurent series are preserved, and the approximate
characteristic relation of frequency is obtained.
˙
f
n
f
2
n
=
a
0
+ a
1
n
1
+ a
2
n
2
+ a
3
n
3
+ a
4
n
4
n
sp
(b
0
+ b
1
n
1
+ b
2
n
2
+ b
3
n
3
+ b
4
n
4
)
which contains a total of 9 discrete undetermined coef-
ficients from a to i. Its rationality can be explained by
fitting com quantum equation at last. Euler considered
that nature pursues its diverse ends by the most effi-
cient and economical means, and that hidden simplic-
ities underlie apparent chaos of phenomena
[29]
. Based
on this philosophy, we use the observation data of the
GW150914 signal wave to fit the approximate equation,
and take s p = 1 to find the most concise form. The
reduced form is as follows
λ (n)
η (n)
=
a + bn + cn
2
+ dn
3
+ en
4
n (f + gn + hn
2
+ in
3
+ n
4
)
=
˙
f
n
f
2
n
Mathematics & Nature (2021) Vol. 1 5
where the quantum number n > 1. For the GW150914
signal wave, the
˙
f
n
f
2
n
values of the negative strain on
the right side of (2) are represented by the fractions.
Substituting them into above formula reads the follow-
ing linear Diophantine Equations,
a + 2b + 2
2
c + 2
3
d + 2
4
e
2 (f + 2g + 2
2
h + 2
3
i + 2
4
)
= 0.636307692 =
1034
1625
a + 3b + 3
2
c + 3
3
d + 3
4
e
3 (f + 3g + 3
2
h + 3
3
i + 3
4
)
= 0.436753649 =
1975
4522
a + 4b + 4
2
c + 4
3
d + 4
4
e
4 (f + 4g + 4
2
h + 4
3
i + 4
4
)
= 0.334368530 =
323
966
a + 5b + 5
2
c + 5
3
d + 5
4
e
5 (f + 5g + 5
2
h + 5
3
i + 5
4
)
= 0.271585859 =
26887
99000
a + 6b + 6
2
c + 6
3
d + 6
4
e
6 (f + 6g + 6
2
h + 6
3
i + 6
4
)
= 0.228972362 =
2676
11687
We need to find the the minimum digit rational number
solution set of the above Diophantine equations. But
solving such Diophantine equations
[30-37]
seems to lead
to a pure mathematical problem. Here, we can give the
result that the test is true: a = 63/16, b = 447/32,
c
= 69/4,
d
= 69/8,
e
= 3/2,
f
= 105/32,
g
= 389/32,
h = 227/16 and i = 13/2. Thus, a simplified approx-
imate com quantization equation for the Lagrange fre-
quency change rate of the GW150914 signal wave is ob-
tained,
˙
f
n
=
3 (n + 2) (4n + 3)
4n
2
+ 12n + 7
n (n + 3) (2n + 1) (4n + 5) (4n + 7)
f
2
n
(3)
where n > 1. The theoretical values of the last column
in Table 2 are calculated on the basis of this equation.
It is very difficult to find the reduced rational formula
of
˙
f
n
f
2
n
with high precision. Due to the power increase
of rational expressions, it is not only difficult to find
high-precision approximate rational numbers, but also
more difficult to find the minimum digit rational num-
ber solution of the Diophantine equation system. By
further modifying the strain time of the GW150914 sig-
nal wave, we obtain the following high power simple com
quantized equation of
˙
f
n
f
2
n
,
˙
f
n
=
(n + 2) (4n + 3)
6n
3
+ 24n
2
+ 28n + 9
n (n + 1) (n + 3) (2n + 3) (8n
2
+ 16n + 5)
f
2
n
(4)
where n > 1. Formally, there are differences between
high power equation (3) and high power equation (4),
but their calculation results are consistent in the er-
ror range. This means that there is no need to further
fit other higher power approximation rational function-
s. On the other hand, from a mathematical point of
view, comparing the low-power approximation obtained
by numerical analysis with the first-order expansion of
the exact theoretical equation, it is also sufficient to
prove whether the theory conforms to the experimental
observation results.
5 Jump change rate of frequency
Lagrange frequency change rate has the meaning of
an average change rate, which is easy to accept to de-
scribe the change rate of discrete frequency. Howev-
er, the calculation of Lagrange frequency change rate is
rather troublesome, and the com quantization equation
obtained is also complicated. The definition of jump
change rate of discrete quantity is concise, and the re-
sults of describing the frequency variation of signal waves
should also be concise. Now we discuss the jump change
rate of discrete frequency of the GW150914 signal wave,
its definition is
ˆ
f
n
= (f
n
f
n+1
) T
1
n
, expressed in fre-
quency as follows
ˆ
f
n
=
1
f
n+1
f
n
f
2
n
(5)
According to the frequency distribution of positive
and negative strain peaks of the GW150914 signal wave
given in Table 1, the corresponding frequency’s jump
change rate can be calculated. The results are listed in
Table 3.
The definition formula of frequency’s jump change
rate (5) shows that
ˆ
f
n
f
2
n
= 1 f
n+1
f
1
n
is a func-
tion of quantum number n, so the result of its approxi-
mate expansion is also a characteristic rational formula
of n. Similar to the steps of fitting equation (3), we try
to use the simplest rational formula about n, and sub-
stitute the numerical results of
ˆ
f
n
f
2
n
of positive and
negative strains in the above table into rational formu-
la in turn to get a system of characteristic Diophantine
Equation. Then, the coefficients are determined by the
minimum digit rational number solution of the system
of the characteristic Diophantine Equation, and the fre-
quency’s jump change rate equation of com quantization
of the GW150914 signal wave is found,
ˆ
f
n
=
6 (n + 2)
(n + 3) (4n + 7)
f
2
n
(6)
The theoretical values of
ˆ
f
n
f
2
n
in Table 3 are written
out by the equation (6). The time distribution of posi-
tive and negative strain peaks of the GW150914 signal
wave is corrected by this equation, which is within the
allowable error range. This is also the most reliable cor-
rection method at present.
The modified values of the time of the positive and
negative strain peaks are different, and the fitting form
of the frequency’s jump change rate equation is differen-
t. The com quantization frequency’s jump change rate
corresponding to equation (4) is as follows.
ˆ
f
n
=
2
24n
2
+ 96n + 95
(n + 3) (32n
2
+ 120n + 111)
f
2
n
(7)
The frequency’s jump change rate equation (6) or (7)
of GW150914 signal wave is very concise, because the
6 X. D. Dongfang Dongfang Com Quantum Equations of LIGO Signal
definition of the jump change rate is concise. It is most
convenient to describe the law of frequency variation of
signal wave with concise definition of jump change rate
in mathematical form. Equation (6) or (7) is also quan-
tized. The approximate expansion of the exact equation
for the frequency jump change rate of signal wave de-
rived theoretically should be consistent with (6) or (7).
Equations (3), (4), (6) and (7) are named Dongfang’s
com quantum equations of LIGO signal, to commemo-
rate these unique discoveries that have been strangled
since 2016, and also to warn people who pursue truth in
the future. Mainstream scholars do not really advocate
truth, but personal fame and wealth are their lifelong
goal. When great discoveries cannot be taken as their
own, mainstream scholars will completely tear up the
veil of beautifying their self-image and expose their true
colors. Therefore, if you firmly believe in the suprema-
cy of truth, there should be no illusion that the new
truth will be respected by the sanctimonious academic
community.
Table 3 Observed and theoretical values of the jump change rate and the ratio of the jump change rate to the square of the frequency
of the GW150914 signal wave.
n
Positive strain Negative strain Theory values
f
n
ˆ
f
n
ˆ
f
n
f
2
n
f
n
ˆ
f
n
ˆ
f
n
f
2
n
ˆ
f
n
f
2
n
1 197.3975904 15940.5581 0.409090909 230.7600891 21784.18038 0.409090909 0.409090909
2 116.6440307 4353.86557 0.32 136.3582345 5949.941798 0.32 0.32
3 79.31794085 1655.614669 0.263157895 92.72359945 2262.543657 0.263157895 0.263157895
4 58.44479852 763.7801306 0.223602484 68.32265222 1043.773 0.223602484 0.223602484
5 45.37639637 400.3644841 0.194444444 53.04553744 547.133425 0.194444444 0.194444444
6 36.55320819 42.73112738 314.1418061 0.172043011 0.172043011
7 35.37953557 0.154285714
6 Conclusions and comments
In this paper, the numerical method of the minimum
digit rational number solution of Diophantine charac-
teristic equation is introduced to analyze and obtain the
precise com quantization law of GW150914 signal wave,
but it is not possible to judge whether GW150914 signal
wave is the gravitational wave of the merging of spiral
binaries. This is because there are many similar signals
with monotonously increasing frequency on the ground,
and there is still a lack of accurate exp erimental data.
We cannot fit the com quantization law of these sim-
ilar signals and compare it with the com quantization
law of GW150914 signal. The precise coquantization
law of GW150914 signal is very attractive, and correct
processing of it may promote the revolution of physi-
cal theory. In 1888, Johannes Rydberg modified the
Balmer formula to propose a universal empirical formula
for the spectral lines of hydrogen atoms which led to the
birth of Bohr’s quantum theory. On this basis, quantum
mechanics, quantum electrodynamics and quantum field
theory have developed successively. The Rydberg formu-
la is the result of numerical analysis. Similar to the Ryd-
berg formula of hydrogen atomic spectrum, whether the
GW150914 signal published by LIGO belongs to natu-
ral signal or the signal of artificial simulation device, the
fitted com quantum equation (3) or (4) of the Lagrange
frequency change rate of GW150914 signal wave and the
jump change rate equation (6) or (7) of GW150914 sig-
nal wave frequency, it will be an imp ortant beginning
to reveal the law of com quantum theory contained in
macro motion. They are not only the quantitative basis
for testing the accuracy of the gravitational wave theory
of spiral binary stars, but also the experimental basis for
establishing and developing a com quantum theory that
uniformly describes the macro and micro quantization
law.
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