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Physics

MATHEMATICS AND NATURE
Mathematics, Physics, Mechanics & Astronomy
July 2021 Vol. 1 No. 1: 006 DOI: 10.13140/RG.2.2.25660.16000
Com Quantum Laws of LIGO Signal ∗
X. D. Dongfang 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, observation data of gw150914 signal are analyzed accurately, and it is proved that Livingston waveform of positive and negative strain reversal is 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, the numerical analysis method of the minimum solution of characteristic Diophantine equations is introduced to ﬁt the Lagrange frequency change rate and frequency jump change rate of GW150914 signal with quantization signiﬁcance, which provides a quantitative basis for inferring the accurate information of the wave source.
Keywords: LIGO Signal; Lagrange change rate; Jump change rate; Com quantum law.
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 theory 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 quantum mechanics[1-5] based on the Rydberg formula[6] of the hydrogen spectrum is successful, although quantum mechanics also hides some logical paradoxes[22] 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 theory 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 study of macro quantization law. Here, the GW150914 signal wave[14] with accurate data report is re analyzed. Firstly, the exact relationship between Hanford waveform and Livingston waveform is clariﬁed, and then the correct superposition 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

∗The academic circles over publicize the diﬃcult process of LIGO exploring the signal and extracting the signal according to the predetermined target, which not only exposes the essence that such so-called scientiﬁc experiments are more like secret children’s play, but also makes readers’ attention far deviate from the important theme of how to use scientiﬁc methods to test whether LIGO signal is the gravitational wave generated in the process of spiral binary star merger, so as to blindly believe in science ﬁction news. What exact law should gravitational waves obey? Since LIGO gives the so-called observation data of gw150914 signal, as long as the accurate law obeyed by gw150914 signal is analyzed and compared with the accurate law of gravitational wave, an irrefutable scientiﬁc conclusion can be obtained. In fact, the gw150914 signal does not follow the relativistic Blanchet frequency equation of gravitational waves that LIGO likes to talk about (please refer to the paper: relativistic equation failure for LIGO signals). It has a unique law and seems to be a signal on the earth. However, further analysis shows that it has some speciﬁc diﬀerences from such signals on the earth. The comprehensive conclusion from multiple perspectives shows that the key operators of LIGO secretly extract data of the motion process of the simulation device to confuse the public and thus forge gw150914 gravitational wave, which is very likely. This paper accurately ﬁts the com quantum law obeyed by gw150914 signal frequency. However, almost all famous mainstream academic journals unanimously refuse to publish such papers on the accurate analysis of the precise law of LIGO signal, and continue to publish more science ﬁction stories without experimental data analysis to further maintain lies. The author now oﬀers a reward of 1 million yuan to reward scholars who strictly deduce the accurate co quantization law of gw150914 signal in theory rather than guessing through hypothesis. People who pursue truth all over the world unite to prevent the further spread of mainstream academic corruption that ignores academic morality, only seeks fame and wealth, cooperates in fraud and stiﬂes truth. This reward is valid before the author publishes the core principles of COM quantum theory and is limited to the author’s lifetime.
Citation: Dongfang, X. D. Com Quantum Laws of LIGO Signal. Mathematics & Nature, 1, 006 (2021).

⃝c Mathematics & Nature–Free Media of Eternal Truth, China, 2021

https://orcid.org/0000-0002-3644-5170

X. D. Dongfang Mathematics & Nature July (2021) Vol. 1 No. 1

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to the Blanchet frequency equation[15] of gravitational wave in general relativity[16-20], the Lagrange frequency change rate[22] and frequency jump change rate with quantization meaning are deﬁned. We introduce the numerical analysis method of the minimum solution of the characteristic Diophantine equations, and use the numerical results of frequency distribution to ﬁt two kinds of quantized frequency change rates of GW150914 signal with high accuracy.
2 Superposition waveform of GW150914 signal

this, the intrinsic frequency distribution of the negative strain peaks of the Hanford waveform is calculated as follows, FH−={ 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

1.0

Signal GW150914 Hanford

0.5

Strain 10 21

Making a high-precision scale or screen ruler to measure the vibration peak time interval of the vibration curve, and calculate the high-precision period and frequency distribution of the signal wave, so that the Hanford waveform and Livingston waveform of GW150914 signal can be accurately superimposed. The periods 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 10−6s. This method is especially suitable for analyzing vibration curves of unknown original function and unpublished detailed observation data. However, time accuracy of recording GW150914 signal wave by LIGO is 10−9s, 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[21], and redrawn 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 comparing 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 waveform 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, FH+= { 44.2478Hz, 45.8716Hz, 55.8659Hz, 80.0Hz, 116.2791Hz, 200.0Hz }, and the time interval between the ﬁrst and seventh Hanford 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

Strain 10 21

0.0

0.5

1.0 0.25
Figure 1

0.30

0.35

0.40

0.45

Time s

Hanford vibration curve of the GW150914 signal wave

1.0 Signal GW150914 Livingston
0.5

0.0

0.5

0.25
Figure 2 wave

0.30

0.35

0.40

0.45

Time s
Livingston vibration curve of the GW150914 signal

The Livingston waveform is shown in Figure 2. Seven 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 strain peaks of Livingston waveform is calculated to be, FL+={ 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 negative 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 peaks, FL−={ 42.9185Hz, 44.0529Hz, 57.4713Hz, 74.0741Hz,

X. D. Dongfang Mathematics & Nature July (2021) Vol. 1 No. 1

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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
By comparing the total time of seven positive and negative strain peaks of the Hanford waveform and the Livingston waveform, and comparing the frequency distribution of the positive and negative strain of the two waveforms, it is not diﬃcult to ﬁnd the following approximate relationships,
∆t+H ≈ ∆t−L , ∆t−H ≈ ∆t+L , FH+ ≈ FL−, FH− ≈ FL+
Considering the experimental error, it can be deduced that the Livingston waveform is opposite to the Hanford waveform. In fact, the same number of positive and negative strain peaks seen in Figures 1 and 2 is also sufﬁcient to detect the relationship between the two waveforms. 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 vibration curves of Hanford waveform.
It is well known that the signals in Hanford and Livingston observatories are phase-shifted by π can be interpreted 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.
3 Frequency distribution of GW150914 signal
The superposition waveform of the Livingston waveform 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 deviate from the monotonic variation law, and the reason

Strain 10 21

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 characteristics 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 characteristic equation approximation with the highest credibility, which will be introduced in detail later. Here we only focus on the numerical analysis of the frequency distribution of GW150914 signal wave. The time of several strain peaks in the high frequency region is LIGO original record time, and the original accuracy of 10−9s and 10−9Hz 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 tn values in Table 1 is the modiﬁed time of the main positive and negative strain peaks of the GW150914 superposition waveform. Here n is positive integer of the inverse time series distribution, that is, quantum number.

Signal GW150914 Livingston

1.0

Signal GW150914 Hanford

0.5

0.0

0.5

1.0

0.25

0.30

0.35

0.40

0.45

Time s
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 inversion and delay of 7.324218ms coincides with the main vibration part of the Hanford waveform

Table 1 Positive and negative strain peak times of the GW150914 signal wave and its frequency distribution

Positive strain

n

tn

Tn

fn

Negative strain

tn

Tn

fn

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

The formulas for calculating the periods and frequen-
cies of positive and negative strain peaks are Tn = tn − tn+1 and fn = Tn−1 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

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6 frequencies for the positive strain from 36.55320819Hz to 197.3975904Hz, and the negative strain has seven frequencies from 35.37953557Hz to 230.7600891Hz. Compared 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 maximum 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 inverse timing numbers.
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 describing the frequency distribution and the variation of gravitational waves in general relativity is Blanchet fre-

quency equation[15]. However, the deﬁnition of frequency and frequency change rate in Blanchet frequency equation comes from the derivative of the phase of the vibration 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 deﬁnitions of frequency change rate, Lagrange frequency change rate and jump change rate are relatively simple in numerical processing. Now we discuss the Lagrange frequency change rate of GW150914 signal wave. Because of the inverse temporal arrangement of quantum numbers, the Lagrange frequency change rate is deﬁned as [f˙n = (fn−1 − fn+1) (Tn + Tn−1)−1, that is

f˙n

=

(fn−1 − fn+1) fnfn−1 fn + fn−1

(1)

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.

Positive strain

n fn

f˙n

f˙nfn−2

1 197.3975904

Negative strain

fn

f˙n

230.7600891

f˙nfn−2

Theory values f˙nfn−2
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

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 characteristic relation f˙nfn−2 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 diﬀerent, but their Lagrange frequency change rates have the same regularity for the same quantum values,

f˙2± = 0.636307692(f2±)2

f˙3± = 0.436753649(f3±)2

f˙4± = 0.334368530(f4±)2

(2)

f˙5± = 0.271585859(f5±)2

f˙6− = 0.228972362(f6−)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 fn of the GW150914 signal wave is a de-
creasing function of the quantum number n. Therefore, the square of frequency fn2 and the Lagrange change rate of frequency fn2 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˙nfn−2 = 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) = np ∑∞ ain−i, η (n) = ns ∑∞ bin−i, where ai

i=0

i=0

and bi are both undetermined coeﬃcient, p and s are

rational numbers. If the above two series are truncat-

ed into polynomials, f˙nfn−2 = λ (n) [η (n)]−1 is reduced

to an approximate rational formula. Taking advantage

of the f˙nfn−2 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

X. D. Dongfang Mathematics & Nature July (2021) Vol. 1 No. 1

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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 lower power rational formula to calculate the f˙nfn−2 values
of several larger quantum numbers, and then combine 5 known f˙nfn−2 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 fn2

=

(

)

a0 + a1n−1 + a2n−2 + a3n−3 + a4n−4

ns−p (b0 + b1n−1 + b2n−2 + b3n−3 + b4n−4)

which contains a total of 9 discrete undetermined coefﬁcients 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 eﬃcient and economical means, and that hidden simplicities 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 + cn2 + dn3 + en4 n (f + gn + hn2 + in3 + n4)

=

f˙n fn2

where the quantum number n 1. For the GW150914 signal wave, the f˙nfn−2 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 + 22c + 23d + 24e

1034

2 (f + 2g + 22h + 23i + 24) = 0.636307692 = 1625

a + 3b + 32c + 33d + 34e

1975

3 (f + 3g + 32h + 33i + 34) = 0.436753649 = 4522

a + 4b + 42c + 43d + 44e

323

4 (f + 4g + 42h + 43i + 44) = 0.334368530 = 966

a + 5b + 52c + 53d + 54e

26887

5 (f + 5g + 52h + 53i + 54) = 0.271585859 = 99000

a + 6b + 62c + 63d + 64e

2676

6 (f + 6g + 62h + 63i + 64) = 0.228972362 = 11687

We need to ﬁnd the minimum rational 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 approximate com quantiza-

tion equation for the Lagrange frequency change rate of

the GW150914 signal wave is obtained,

(

)

f˙n

=

3 (n + 2) n (n + 3)

(4n + 3) (2n + 1)

4n2 + 12n + 7 (4n + 5) (4n + 7)

fn2

(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˙nfn−2 with high precision. Because the power
of the rational formula is increased, not only is it diﬃ-

cult to ﬁnd the approximate rational number with high

precision, but also the diﬃculty of ﬁnding the minimal

solution of indeterminate equations is increased. By fur-

ther modifying the strain time of the GW150914 signal

wave, we obtain the following high power simple com quantized equation of f˙nfn−2,

(

)

f˙n

=

(n + 2) (4n + 3) n (n + 1) (n + 3)

6n3 + 24n2 + 28n + 9 (2n + 3) (8n2 + 16n + 5)

fn2

(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 describe the change rate of discrete frequency. However, 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 results 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 fˆn = (fn − fn+1) Tn−1, expressed in frequency as follows

(

)

fˆn =

1 − fn+1 fn

fn2

(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.

X. D. Dongfang Mathematics & Nature July (2021) Vol. 1 No. 1

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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.

Positive strain

n fn

fˆn

fˆnfn−2

Negative strain

Theory values

fn

fˆn

fˆnfn−2

fˆnfn−2

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

The deﬁnition formula of frequency’s jump change rate (5) shows that fˆnfn−2 = 1 − fn+1fn−1 is a function
of quantum number n, so the result of its approximate

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 substitute the numerical results of fˆnfn−2 of positive and negative
strains in the above table into rational formula in turn

to get a system of characteristic Diophantine Equation.

Then, the coeﬃcients are determined by the minimum

solution of the system of the characteristic Diophantine

Equation, and the frequency’s jump change rate equa-

tion of com quantization of the GW150914 signal wave

is found,

fˆn

=

(n

6 (n + 2) + 3) (4n +

7) fn2

(6)

The theoretical values of fˆnfn−2 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.

(

)

fˆn

=

2 24n2 + 96n + 95 (n + 3) (32n2 + 120n +

111) fn2

(7)

The frequency’s jump change rate equation (6) or (7)

of GW150914 signal wave is very concise, because the 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 quantized. The approximate expansion of the exact equation for the frequency jump change rate of signal wave derived theoretically should be consistent with (6) or (7).
6 Conclusions and comments
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 formula is the result of numerical analysis. Similar to the Rydberg formula of hydrogen atomic spectrum, whether the gw150914 signal published by LIGO belongs to natural 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 signal wave frequency, it will be an important 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.

1 Oldenberg, O. BOHR’S THEORY OF THE HYDROGEN ATOM. School Science & Mathematics 38. 6, 692–696 (1938).
2 Schr¨odinger, E. An undulatory theory of the mechanics of atoms and molecules. Physical Review 28, 1049 (1926).
3 Dirac, P. A. M. Quantum Mechanics and a Preliminary Investigation of the Hydrogen Atom. Proceedings of the Royal Society of London110.755(1926):561-579.
4 Dirac, P. A. M. The principles of quantum mechanics. 70-72 (Clarendon Press Oxford, 1958).
5 Greiner, Walter. Relativistic Quantum Mechanics. Wave E-

quations. Beijing World Publishing Corporation, 2003. 6 Bohr, N. Rydberg’s discovery of the spectral laws, Lund U-
niversity. (1954). 7 Dongfang, X. D. The Morbid Equation of Quantum Numbers.
Mathematics & Nature, 1, 002 (2021). 8 Abbott, B. P. et al. Observation of Gravitational Waves from
a Binary Black Hole Merger. Physical Review Letters 116, 061102 (2016). 9 Abbott, B. et al. Localization and broadband follow-up of the gravitational-wave transient GW150914. The Astrophysical journal letters 826, L13 (2016).

X. D. Dongfang Mathematics & Nature July (2021) Vol. 1 No. 1

006-7

10 Abbott, B. P. et al. GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence. Physical Review Letters 116, 241103 (2016).
11 Abbott, B. P. et al. GW170104: Observation of a 50-SolarMass Binary Black Hole Coalescence at Redshift 0.2. Physical Review Letters 118, 221101 (2017).
12 Abbott, B. P. et al. GW170814: a three-detector observation of gravitational waves from a binary black hole coalescence. Physical review letters 119, 141101 (2017).
13 Abbott, B. P. et al. GW170817: observation of gravitational waves from a binary neutron star inspiral. Physical Review Letters 119, 161101 (2017).
14 Abbott, B. et al. Localization and broadband follow-up of the gravitational-wave transient GW150914. The Astrophysical journal letters 826, L13 (2016).
15 Blanchet, L., Damour, T., Iyer, B. R., Will, C. M. & Wiseman, A. G. Gravitational-radiation damping of compact binary systems to second post-Newtonian order. Physical Review Letters 74, 3515-3518 (1995).
16 Einstein, Albert. Die Feldgleichungen der Gravitation. Sitzung der physikalische-mathematischen Klasse. 25, 844847(1915).
17 Einstein, A. The foundation of the general theory of relativity. 2, 109-164 (1952).
18 Einstein, A. N¨aherungsweise integration der feldgleichungen der gravitation. (Wiley Online Library, 1916).
19 Einstein, A. & Rosen, N. On gravitational waves. Journal of the Franklin Institute 223, 43-54 (1937).
20 Miller, M. C. Gravitational waves: Dawn of a new astronomy. Nature (2016).
21 LIGO, Gravitational-Wave Strain Data, https://losc.ligo.org/events/GW150914/.
22 Dongfang, X. D. On the Relativity of the Speed of Light. Mathematics & Nature, 1, 001 (2021).
23 Bohr, N. On the constitution of atoms and molecules. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 26, 857-875 (1913).
24 Schr¨odinger, E. An undulatory theory of the mechanics of

atoms and molecules. Physical Review 28, 1049 (1926). 25 Baker J. G. et al. Gravitational-wave extraction from an in-
spiraling conﬁguration of merging black holes. Physical Review Letters. 2006 Mar 22;96(11):111102. 26 Damour T, Nagar A, Hannam M, Husa S, Bru¨gmann B. Accurate eﬀective-one-body waveforms of inspiralling and coalescing black-hole binaries. Physical Review D. 2008 Aug 18;78(4):044039. 27 Iyer BR. Gravitational waveforms for binary black holes. International Journal of Modern Physics D. 2011 Sep;20(10):2081-6. 28 Dongfang X. D. Mathematical Basis of Com Quantum Theory (this page has been damaged by others and will be repaired as soon as possible), Researchgate, 2019. 29 Simmons, G. F. Diﬀerential equations with applications and historical notes. (CRC Press, 2016). 30 Henk, M. & Weismantel, R. On minimal solutions of linear Diophantine equations. Beitrage Zur Algebra Und Geometrie 41, 49-55 (1970). 31 Israilov, M. I. Determination of the number of solutions of linear Diophantine equations and its applications in the theory of invariant cubature formulas. Plant Signaling & Behavior 22, 339-341 (1981). 32 Borosh, I., Flahive, M. & Treybig, B. Small solutions of linear Diophantine equations. Discrete Mathematics 58, 215-220 (1986). 33 Contejean, E. & Devie, H. An eﬃcient incremental algorithm for solving systems of linear Diophantine equations. Information and computation 113, 143-172 (1994). 34 Lazebnik, F. On systems of linear Diophantine equations. Mathematics Magazine 69, 261-266 (1996). 35 Dickson, L. E. History of the Theory of Numbers: Diophantine Analysis. (1966). 36 Hua, L. G. Introduction to number theory. Sci. Press, Beijing, China. pp, 301-333 (1979). 37 Rosen, K. H. Elementary number theory and its applications. (Addison-Wesley, 1993).