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Physics

MATHEMATICS & NATURE
Mathematics, Physics, Mechanics & Astronomy

2021 Vol. 1 No. 1: 007 DOI: 10.13140/RG.2.2.19546.88005

LIGO’s Spiral Binary Black Holes Failed to Merge

X. D. Dongfang Wutong Mountain National Forest Park, Shenzhen, China

Frequency distribution and variation law of the GW150914 waveform, one of a large number of ancient and distant binary merging gravitational waves claimed by LIGO, are deeply studied, and the recurrence relation of frequency of GW150914 waveform with macro quantization signiﬁcance is accurately ﬁtted. Firstly, the characteristic equation for eﬀectively correcting the amplitude time of the waveform is proposed, the normative conditions of the numerical analysis method of the minimum solution of the characteristic Diophantine equations are determined, the new correction value of the amplitude time of the GW150914 waveform is given, and then the quantized recursive equation characterizing the frequency distribution of the signal is obtained. Secondly, the complex but clear data processing procedure for drawing the com quantum theory waveform is introduced, and the standard waveform of GW150914 waveform is drawn. It is pointed out that the drawing of LIGO numerical relativistic waveform is opaque, and the conclusion is vague and lacks due scientiﬁc analysis. Thirdly, the missing characteristic frequency in GW150914 waveform is conﬁrmed, and then the reason why Hanford waveform and Livingston waveform have no corresponding band of characteristic frequency is analyzed. It is proved that LIGO’s GW150914 spiral binary black holes failed to merge successfully, which shows that no matter how powerful the research team is it is diﬃcult to create astronomical events without any ﬂaws. Finally, an experimental proposal to eﬀectively test the conﬁdence of a laser interferometer gravitational wave detector is proposed to detect the gravitational wave of simulated spiral binary system.
PS: LIGO made up enough lies that the gravitational wave of the merger of spiral binaries was detected because they naively believed that as long as they teased the readers and announced that the binaries in all gravitational wave events were merged, there would be no corresponding gravitational wave in the future, and it would never be possible for anyone to discover the truth of the so-called gravitational wave of spiral binaries. However, there is no perfect lie in the world. Theoretical physicists only need to master the correct theoretical knowledge of gravity and understand the precise motion law of binary stars, and they can ﬁnd many fatal loopholes in LIGO’s lies. What is introduced here is just one of the loopholes in LIGO’s lie of detecting the gravitational wave of the merger of spiral black holes: if the story of spiral double black holes is true, it must radiate a peak corresponding to a speciﬁc frequency. LIGO is obviously very ignorant about the basic knowledge of these gravitational theories, so it is unable to carry out the necessary calculations. This unfortunate ignorance has become one of the huge loopholes in the lie of LIGO’s spiral binary gravitational wave. In fact, readers can also expose the lie of LIGO gravitational wave from other aspects, and ﬁnally ﬁnd out what kind of laboratory signal LIGO’s so-called gravitational wave signal is simulated with. Evidence to expose LIGO lies will be more wonderful one by one. However, LIGO and its cooperative institutions are likely to use the precise inferences of our paper to fabricate spikes of a speciﬁc frequency and further release false gravitational waves. Therefore, we have to keep other wonderful evidence secret for the time being, prepare for Jedi counterattack, and ﬁnally conclude for LIGO: there are many lies in the scientiﬁc community, and LIGO’s lies, although very cunning, are the most ignorant, It can only deceive those non real theoretical physics scholars, especially the news media.
Keywords: GW150914 waveform; numerical analysis; Diophantine equations; com quantum law; frequency recurrence equation.
PACS number(s): 03.65.Ta—Foundations of quantum mechanics; measurement theory; 04.30.w—Gravitational waves; 04.80.Nn Gravitational wave detectors and experiments; 02.60.-x— Numerical approximation and analysis.

Citation: Dongfang, X. D. LIGO’s Spiral Binary Black Holes Failed to Merge. Mathematics & Nature, 1, 007 (2021).

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

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

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

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1 Introduction
Imagine that the ancient and distant dense binaries merge frequently at a speciﬁc time, and the merged information happens to be transmitted to the earth and captured by LIGO according to the foresight of research institutions in recent years. There will be no such opportunity after that, because all spiral binary stars have been merged. This story is obviously unconvincing. Therefore, it is most appropriate to deﬁne the so-called spiral binary stars merger gravitational wave declared by LIGO as LIGO manufacturing.
The vibration curves depicted by LIGO are called waveforms. The monotonic increase in frequency of GW150914 waveform[1] is only qualitatively consistent with the radiation frequency of the spiral system, and many other signals such as locomotive start also have the monotonic increase in frequency. The identiﬁcation of signal wave of unknown wave source needs to compare the accurate law obeyed by physical quantities such as the frequency of the original detection data of the signal with the accurate law of physical quantities such as the radiation frequency of the model wave source. However, according to the theoretical waveform, the expected waveform is extracted from the chaotic waveform, and then the extracted waveform is used as evidence to declare that the so-called experimental observation conﬁrms the theoretical inference. This kind of strong twisted chaotic logic is deﬁned as modern advanced scientiﬁc thought only because we succumbs to the academic authority of the famous scientiﬁc research team. How long can its vitality last?
It is a serious misunderstanding of the law of nature to put general relativity above gravitational waves[2-4] and believe that there will be no gravitational waves without general relativity. Relativity itself is not an inevitable theory to describe the laws of nature[5]. Extraction of LIGO data[6-8, 27] completely depends on the waveform template of general relativity gravitational wave theory[10-14]. If the actual operation is like this and is publicized as a hard and eﬀective work, its playful color is very strong. The so-called signal wave data is obviously not the data of real observation signiﬁcance, but data that has been seriously tampered with or even fabricated in disguise. After extracting the desired waveform from the chaotic mixed waveform through the theoretical template, it is determined that it is the gravitational wave generated during the merger of ancient and distant spiral binary black holes, just like drawing a curve in the desert according to a function graph, taking photos, and then determining that the curve is the footprint of aliens. If a spiral binary exists, the frequency of the gravitational wave radiated by it increases monotonously. Gravity theory holds that the frequency of the gravitational wave should meet the nonlinear Blanchet equation[15, 16]. Although the Blanchet frequency equation has no explicit function solution and it can not be used to calculate the accurate frequency distribution law of gravitational

wave, the conclusion of numerical analysis is that the frequency of GW150914 signal does not obey the Blanchet frequency equation[25].
It can be predicted that the gravitational quantization theory represented by string theory, superstring theory and M theory combines general relativity with quantum mechanics and can not calculate the most basic characteristic physical quantities such as the frequency or wavelength of the gravitational wave. Formally, if we imitate the quantum theory of the hydrogen atom[18-24] to establish the quantum theory of the gravitational system, it seems that the calculation formula of the frequency or wavelength of gravitational wave can be given. However, in this way, the picture of matter cloud in the gravitational ﬁeld predicted by the imitation theory is not consistent with the distribution law of planets, and the derived radiation frequency formula of spiral binaries does not accord with the discrete frequency distribution and variation law of GW150914 waveform. In fact, the assumptions and principles of quantum mechanics used to describe micro motion also have their speciﬁc scope of application, even do not conform to logic[25, 26], and can not be directly used to describe the macro motion law dominated by universal gravity. If only from the perspective of the monotonic increase of the frequency of GW150914 waveform, it is claimed that this signal is a spiral binary and must be the gravitational wave generated by the merger of spiral binary black holes, its reliability is obviously far from enough. Through in-depth analysis of the frequency and amplitude distribution law of GW150914 waveform wave, it can be found that it is very likely to come from the analog device, but the com quantization laws shown by the frequency of this signal are still of research value. It will promote understanding of the macro quantization law of variable frequency signal. This is why we take it as the experimental basis of com quantum theory.
Now, suppose that GW150914 waveform comes from a certain frequency conversion rate movement, we further study the frequency distribution law of GW150914 waveform. Firstly, the plausible amplitude time is extracted from the GW150914 waveform data released by LIGO, the characteristic equation satisﬁed by the amplitude time or the corresponding frequency is found, and the speciﬁcation condition of the minimum solution of the characteristic Diophantine equations is determined. Then, the characteristic equation is used to accurately correct the wide peak or uncertain peak of GW150914 waveform, and ﬁt the com quantized frequency recurrence equation according to the minimum solution of the characteristic Diophantine equations. In order to compare with LIGO’s numerical relativistic waveform, the numerical drawing procedure of complex but not intended to the mystify waveform of com quantum theory is provided here, and the com quantum standard waveform of GW150914 waveform is drawn. It is of great signiﬁcance to calculate the maximum characteristic frequency of GW150914 waveform. Because if GW150914

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

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waveform comes from the gravitational radiation of spiral binary stars merge, then, from the precession process to the oscillation process, the binary star must radiate at least one peak pulse corresponding to one of the characteristic frequencies. However, the characteristic pulse is missing in both Hanford waveform and Livingston waveform. It is necessary and important to ﬁnd out the cause of disappearance with theoretical and experimental signiﬁcance. In addition, considering that the experimental observation results should be repeatable, an experimental proposal for detecting the gravitational wave simulating spiral motion in the laboratory is also proposed. The purpose is to further conﬁrm the conﬁdence of the gravitational wave laser detector and increase the experience of identifying the gravitational wave through repeatable experiments.
2 Frequency recurrence equation of GW150914 waveform

grange frequency change rate of the positive and negative strain from the GW150914 singal is the same. Studying the simplest com quantized oscillating function y = sin [2π (1 + 5t) t] with high frequency approximation shows that the same change law of positive and negative strain peak time is a kind of high frequency eﬀect, but when the frequency is low, the time distribution law of the positive and negative strain will show a signiﬁcant diﬀerence.

GW150914 Livingston

1.0

GW150914 Hanford

0.5

Strain

0.0

0.5

The displacement of all vibration curves of LIGO is called strain. The frequency of the main vibration part of GW150914 waveform increases monotonously, and the main vibration part of the Hanford waveform of the GW150914 waveform coincides with of the Livingston waveform that the positive and negative strains overturned and the time delayed 7.324218ms. As shown in Figure 1, the real line segment indicates the correction time of the positive and negative strain peak of the superimposed waveform, while the virtual line segment represents the time of the distorted positive and negative strain peak. With the inverse time sequence number, the last positive or negative strain peak corresponding to the maximum frequency of the monotonically increasing frequency corresponds to the smallest quantum number n = 1. Investigating the several wide peaks of the main vibration part in the superimposed waveform, in addition to noise resulting in waveform distortion, noise may lead to waveform distortion, and the detector may also miss some real positive and negative strain peaks by recording a signal per 6.10352 × 10−5s. Therefore, correction time of strain peak within the range of error has many kinds of accessibility values. Table 1 lists the time of the positive and negative strain peaks corrected by numerical approximation, and the time for the two wide positive strain peaks that have not been determined is represented by x5 and x7 respectively, and the time for the three wide negative strain peaks that have not been determined is represented by t3, t7 and t8, respectively. The intrinsic period and the intrinsic frequency are deﬁned as Tn = tn − tn+1 and fn = Tn−1 respectively, in which the subscript n is also quantum number and arranged in reverse chronological order.
Finding the minimum solution of the Diophantine equation system[28-30] which accords with the physical meaning can determine the best approximation equation of com quantum law, and the resulting La-

1.0

0.25

0.30

0.35

0.40

0.45

Figure 1

Time t s
The superposition of the Hanford and Livingston

waveforms of the GW150914 waveform

The GW150914 waveform belongs to the high frequen-

cy signal wave. Being similar to the Lagrange frequency

change rate, the ratio fn+1fn−1 of the adjacent frequencies of the positive and negative vibration peaks of high

frequency signal waves is decided by the quantum num-

ber n. Because the exact function of the frequency fn

can always be expressed to be the Laurent series on the quantum number n, fnfn−+11 is the ratio of the two Laurent series. Referring to the spectral law of hydrogen

atoms, other smaller frequencies can be determined by

using the maximum or higher frequencies. So the other

smaller frequencies can be determined by the maximum

frequency. The two series of series are truncated, and the

approximate rational formula of fn+1fn−1 is a nonlinear recurrence equation with no simple function solution.[31].

After the truncation of the series, the retained terms can

be the same or diﬀerent, but the approximate rational

formula obtained by the truncation series must conform

to the following physical meaning:

1) fn+1fn−1 is a monotone decreasing function of quantum numbern, otherwise, 0 points and singularities de-

stroy the radiation rule of binary stars, and there is a

quasi quantum number problem which can lead to a sim-

ilar black hole horizon;

2) The larger the quantum number is, the closer the

adjacent frequency is, and so there is a limit value of

lim
n→∞

fn+1fn−1

=

1,

which

indicates

that

the

highest

pow-

er of the numerator and the denominator of fn+1fn−1 are

the same, and the coeﬃcients of the highest power term

are the same.

The approximate formula of the adjacent frequency

ratio of the GW150914 signal which satisﬁes the above

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

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two conditions is the rational formulas of the coeﬃcients to be determined. Here we take the following form,

fn+1 fn

=

kn3 + an2 + bn + c kn3 + dn2 + en + f

=

Tn Tn+1

(1)

where k, a, b, c, d, e, f are all undetermined constants, pulsing the undetermined normal strain peak time x5 and x7 or negative strain peak time t3 and t7 in Table 1, there are 11 unknown parameters, and the reduced parameters after reduction are 10.

Table 1
n
1 2 3 4 5 6 7 8

Positive and negative strain peak times of GW150914 waveform and its frequency distribution

Positive strain

tn /s

Tn /s

0.428222656

0.005065918

0.423156738

0.008568080

0.414588658

0.012597024

0.401991635

0.401991635 − x5

x5

x5 − 0.362882581

0.362882581

0.362882581 − x7

x7

x7 − x8

x8

Negative strain

tn /s

Tn /s

0.430297903

0.004333505

0.425964398

0.425964398 − t3

t3 0.407859272

t3 − 0.407859272 0.014622451

0.393236822

0.018832351

0.374404471

0.374404471 − t7

t7

t7 − t8

t8

T4+ T5+

=

0.401991635 − x5 x5 − 0.362882581

=

0.014622451 0.018832351

=

T4− T5−

T1+ T2+

=

0.005065918 0.008568080

=

0.004333505 0.425964398 − t3

=

T1− T2−

T5+ T6+

=

x5 − 0.362882581 0.362882581 − x7

=

0.018832351 0.374404471 − t7

=

T4− T5−

13k+12a+1b+c 0.005065918 0.004333505 311

13 k + 12 d + 1e + f

=

=

0.008568080

0.007329336

≈ 526

23k+22a+2b+c 0.008568080 0.007329336 1629

23 k + 22 d + 2e + f

=

=

0.012597024

0.01077579 ≈ 2395

33k+32a+3b+c 0.012597024 0.01077579 1678 33k+32d+3e+f = 0.017093816 = 0.014622451 ≈ 2277

43k+42a+4b+c 0.017093816 0.014622451 5995

43 k + 42 d + 4e + f

=

0.022015238

=

≈ 0.018832351 7721

53 k + 52 a + 5b + c

0.022015238

0.018832351

53k+52d+5e+f = 0.362882581 − x7 = 0.374404471 − t7

(2)

For the same number of quantum numbers, the ratio

of the adjacent frequency or period of the positive and

negative strain peaks of the GW150914 waveform are

the same, so the undetermined normal strain peak time

x5 and x7, and the negative strain peak time t3 and t7 satisfy the following equations respectively,

The ﬁrst equation gives x5 = 0.384897819s and the
second equation gives t3 = 0.4186350615s. So the
two period values to be determined are respectively T4+=0.017093816s and T5+ =0.022015238s, and the two undetermined negative strain periods are T2− = 0.007329336s and T3− =0.01077579s respectively. Substituting the periods or frequencies corresponding to the

ﬁrst few quantum numbers into equation (1), one gets

a system of Diophantine equations for 9 irreducible un-

known parameters,

Among them, the last equation is used only to determine the strain peak time. The general solutions of the Diophantine equations composed of the ﬁrst 4 equations are expressed by a, b and k,

c = 179010775681k − 136493444161a + 117076892161b 108125168641
d = 108456318961a − 103149296b + 161348546706k 108125168641
e = 157808689202a + 109487811921b − 191625152562k 108125168641
407789722467k − 314244792483a + 271503710307b f=
108125168641

When k = 32, a = 168 and b = 279, the above new

system of Diophantine equations has the minimum pos-

itive integer solution, c = 143, d = 216, e = 471 and

f = 333. By replacing these coeﬃcients into the equa-

tion (1), the simpliﬁed formula for the com quantized

frequency recurrence equation is determined,

(

)

(n + 1) 32n2 + 136n + 143

fn+1 = (n + 3) (32n2 + 120n + 111) fn

(3)

According to the last equation of equation (2), it can be solved for the positive strain peak time x7 = 0.335554568s and the negative strain peak timet7 = 0.351027448s, and the corresponding periods are T6+ = 0.027328013s and T6− = 0.023377023s, respectively. These values are in the range of error.
The recurrence equation (3) is ﬁtted by the frequency of GW150914 waveform. Using equation (3), com quantum laws satisﬁed by the frequency change rate of GW150914 waveform can be derived by simple algebraic operation, and the derivation process is omitted here. Recurrence relation (3) is a more basic com quantum law for spiral systems. But equation (3) is not the only best approximation, and other approximations can be ﬁtted. The numerical results of the same quantum

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

007-5

number are necessarily consistent within the error range. Because the quantum law is succinct and graceful, and the binding system has obvious quantum characteristics when the quantum number is small. Therefore, it is reasonable to use the possible small natural number to ﬁt the distribution law of the discrete physical quantities as small as possible. The simplest form of undetermined characteristic recurrence equation can be conjectured according to the characteristics of frequency distribution and variation of the signal wave. Then the minimum solution of characteristic Diophantine equation system can be determined by numerical analysis, and then the speciﬁc equation can be determined, in which elimination of zero points and singularity points is the key condition for ﬁtting the equation. The ﬁtting of the best approximate equation often requires repeated approximation. From a practical point of view, if that the numerical calculation results are in conformity with the experimental observation data or the curve of the numerical equation is coincided with the curve of the function equation is considered as the standard, it is completely able to accept the reductive numerical equation for eliminating the zero points and the singularity points in the operation process.
3 Com quantum numerical theory standard waveform
Using the frequency recurrence relationship of GW150914 waveform, a standard waveform can be drawn and compared with the so-called numerical relativistic waveform of LIGO. The editor of Physical Reviews D believes that a simple quadratic ﬁtting can also well estimate the strain of GW150914 waveform, so it is not necessary to draw a standard waveform by ﬁtting the accurate law of gw150904 signal frequency. Only after practicing it in person can we know that such speculation out of thin air is not only untenable, but also covers up some important truths.
The period or frequency of signal wave of change frequency is a continuous function of time. It is diﬃcult to determine the zero point of GW150914 waveform form and other speciﬁed strain time directly. It can be seen that drawing the numerical relativistic waveform[1] needs an open, transparent and clear data processing procedure. This section introduces the numerical ﬁtting method and drawing procedure of the com quantum theory standard waveform whose frequency distribution meets the recursive equation (3). The speciﬁc operation also needs the help of Excel. Although the content is cumbersome and diﬃcult to master quickly, we will be able to experience the calculation process required to draw the numerical theory waveform, so as to reﬂect on the opacity of the so-called numerical relativistic gravity waveform in LIGO, and see through the intention that LIGO team apply colours to a drawing by irrelevant fac-

tors to describe GW150914 waveform: deliberately to

make things look mysterious so as to divert readers’ at-

tention to the greatest extent, so that if the reader does

not blindly follow the trend, he will expose his lack of

knowledge and produce a sense of inferiority.

According to equation (3), the strain time in oth-

er periods can be calculated by using the strain time

of the phase diﬀerence of 2π in the two adjacent pe-

riods. Using the deﬁnition inversion of the period

Tn = lation

tn t±n

− =

tn+1, t±n−1

−th(ifs n±t−im1)e−1s,atwishﬁiecsh

the recurrence is replaced by

rethe

equation (3) to read,

(

)

(n + 1) 32n2 − 8n − 1

tn = tn−1 − (n − 1) (32n2 + 8n − 1) (tn−2 − tn−1) (4)

By Table 1, t+1 =0.428222656s and t+2 =0.423156738s gives the positive strain peak period T1+ =0.005065918s of n = 1, t−2 =0.425964398s and t−2 =0.430297903s gives the negative strain peak period T1− =0.004333505s n = 1. From this, the diﬀerence equation of positive and

negative strain peak time is obtained as follows,

t+n

=

t+1

−

{ 1

+

∑n

[ ∏k

( (i + 1) 32i2 (i − 1) (32i2

− +

8i 8i

− −

) ]} 1 1)

T1+

t−n

=

t−1

−

{ 1

+

k=3
∑n

[i=3 ∏k

(i (i

+ −

( 1) 32i2 1) (32i2

− +

8i 8i

− −

) ]} 1 1)

T1−

k=3 i=3

(5)

The time of other positive and negative strain peaks can

be calculated by using the equation (5). Table 2 lists the

correction times for the 11 positive strain peaks and 11

negative strain peaks of the GW150914 signal, including

the corresponding frequency and period.

Referring to Planck Bohr’s hypothesis of quantum me-

chanics, if it is determined that the energy of gravitation-

al wave is an increasing function of frequency, and as-

suming that the strain of gravitational wave laser inter-

ferometer comes from the action of gravitational wave,

the amplitude of signal wave should also be an increasing

function of gravitational wave frequency. If GW150914

waveform is gravitational wave, then, should the abnor-

mal part of the main vibration in the GW150914 wave-

form be interpreted as the waveform distortion caused

by noise, or the systematic error intentionally left when

extracting the waveform, or the accidental error?

It is analogous to the representation of electromag-

netic wave energy, if the gravitational wave energy ε is

directly proportional to the frequency f , that is, ε ∝ f ,

then, because the energy of the gravitational wave is

proportional to the square of the amplitude, it is further

conjectured that to the square of

the t√he

energy strain,

dεis∝t√rihb2u,tisoonhis∝pr√opεor∝tio√nfa.l

From this, hn ∝ fn, hn+1 ∝ fn+1. In this way, t-

wo strains satisfy the

hn+1 and relational

hn with hn+1 =

t(hfenp+h1afns−e1)d1iﬀ/2ehrenn, ctehaotf

2π is,

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

007-6

hn

=

( fn

fn−−11)1/2hn−1,

in

the

form

of

(3).

And then

from the equa[tion ((3), one gets the r)esul]t 1

n 32n2 + 72n + 39

2

hn = (n + 2) (32n2 + 56n + 23) hn−1 (6)

The equation (6) is only a semi deﬁnite quantitative e-

quation based on guesswork rather than a numerical ﬁtting equation. In fact, it can not be proved to belong to a precise natural law at present. It is listed here only because the strain relationship it gives is in accordance with the traditional understanding and can be used as a reference for quantitative description.

Table 2 Time and frequency distribution of positive and negative strain peaks of GW150914 waveform

Positive strain

n

tn /s

Tn /s

fn /Hz

tn /s

Negative strain Tn /s

0

0.430398110

0.002175454

459.6741012

0.4321588376

0.0018609346

1

0.428222656

0.005065918

197.3975891

0.430297903

0.004333505

2

0.423156738

0.008568058

116.7125619

0.425964398

0.007329336

3

0.414588680

0.012597004

79.38395511

0.418635062

0.010775789

4

0.401991676

0.017093789

58.50078061

0.407859272

0.014622451

5

0.384897887

0.022015203

45.42315599

0.393236822

0.018832351

6

0.362882684

0.027327971

36.59254469

0.374404471

0.023377023

7

0.335554713

0.0330055

30.29798064

0.351027448

0.028233724

8

0.302549213

0.039025938

25.62398372

0.322793724

0.033383754

9

0.263523275

0.045370908

22.04055515

0.289409970

0.038811400

10

0.218152367

0.250598570

fn /Hz 537.3644033 230.7600891 136.4379995 92.80062677 68.38798934 53.10011606 42.77704585 35.41863655 29.95468968 25.76562555

Equations (5) and (6) are applied to GW150914 waveform. First, the time of the next several positive and negative strain peaks is calculated by the recurrence equation (5). The time of each period is divided into 400 equal parts with diﬀerent time intervals. Then, correction values of 400 positive and negative strains of n = 2 are determined by the cosine function. Then, the positive and negative strains of other periods are calculated by semi-quantitative equation (6). It is necessary to select the appropriate starting time and ending time, otherwise the calculated strain distribution will be deformed in the waveform.
In 2016, I used Excel to generate 4000 groups of GW150914 waveform time strain data. The excel ﬁle is called “Com Quantum Waveform Data of GW150914 waveform 2016”. It should be noted that more data can be generated by computer, and diﬀerent generation superposition can also be scrambled to imitate observation data. Therefore, we have reason to suspect that some unrepeatable experimental data may be forged. The com quantum theory waveform shown in Figure 2 is drawn from 4000 sets of data. In order to compare the diﬀerent waveforms of GW150914 waveform, Hanford waveform, Livingston waveform and numerical relativistic waveform are also drawn. The com quantum theory waveform in the high frequency band is consistent with the numerical relativistic waveform, while the phase diﬀerence in the low frequency band is very large. Because the numerical relativistic waveform of GW150914 waveform has no transparent drawing procedure, the fundamental reason for the diﬀerence between the two waveforms in the low frequency band cannot be found at present. LIGO’s conclusion has always been lack of scientiﬁc rea-

soning, vague and reckless.

Com Quantum Waveform

1.0

Hanford waveform

Livingston waveform

Relativity Waveform 0.5

0.0

0.5

1.0

0.25

0.30

0.35

0.40

0.45

Figure 2 The Hanford vibration curve of the GW150914 wave-

form, the Livingston vibration curve, the LIGO relativistic wave

and the standard waveform of com quantum theory..

The drawing of the com quantum waveform of the above GW150914 waveform has a clear numerical processing procedure. Drawing the com quantum waveform of the variable frequency signal wave, including modifying the strain time of GW150914 waveform to ﬁt an applicable waveform function within the allowable range of error, requires determining the com quantization formula of frequency distribution of variable frequency signal wave. To diﬀerent variable frequency signal wave of natural phenomena, any new eﬀective numerical method will prompt the discovery of new discrete laws. Scientiﬁc conclusions should not be conﬁned to qualitative descriptions. By trying to draw a numerical relativistic waveform of LIGO signal wave, we can infer the reason why the drawing procedure of so-called numerical

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relativistic waveform of GW150914 waveform is opaque. This is because drawing the numerical waveform requires the corresponding numerical equation rather than the original function of the expected waveform. In a word, the drawing of numerical theory waveform can greatly reduce the empty debate about opaque operation, and can also discover the precise rules hidden in the observed data in the process of improving the numerical calculation method.
4 Missing characteristic frequency of GW150914 waveform
The system of spiral binary stars is the simplest and most important model of the gravitational wave source. Modern gravitational theory holds that the merger of binary stars will undergo three processes: inspired, merger and ringdown. Various LIGO signal waves have been corrected to give waveforms that meet the theoretical expectations. However, from the main vibration part of various LIGO signal waves, only the strictly monotonic frequency of GW150914 waveform is most consistent with the characteristics of the gravitational wave of the spiral binary stars. According to the correct superposition curve of Hanford vibration curve and Livingston vibration curve shown in Figure 1, it is easy to ﬁnd that the Hanford vibration curve of 0.43s∼0.47s does not coincide with the Livingston vibration curve after upsidedown inversion and translation, and even some strain phases are opposite. This detail may imply important scientiﬁc reasons to be discovered. If we can’t give a reasonable explanation for these questions and arbitrarily deﬁne GW150914 waveform as the gravitational wave of spiral binary black holes, it is obviously not a scientiﬁc conclusion.
Now let’s discuss a more critical question. Even if the GW150914 waveform really comes from the gravitational wave radiation of merging spiral binary stars, the frequency of spiral binary stars’ precession increases monotonously, and the frequency of the gravitational wave radiated by the binary stars also increases monotonously in the precession process. However, the frequency of binary stars’ precession will not increase inﬁnitely, so the gravitational wave of spiral binary stars must have a frequency limit, which is expressed by f0. In this case, f0 is the characteristic frequency of the gravitational wave of spiral binaries, that is, the connection frequency between precession process and oscillation process, which corresponds to a special pulse in the gravitational wave of spiral binaries. Whether this particular pulse exists indicates whether the spiral binaries have ﬁnally merged.
According to the deﬁnition of Lagrange frequency change rate f˙n = (fn−1 − fn+1)/(Tn + Tn−1)[25, 26], the period is expressed by the corresponding frequency, and the relationship f˙n = (fn−1 − fn+1) fn−1fn (fn−1 + fn)−1 is obtained. Al-

though f˙0 has no meaning, f˙1 has the corresponding calculation results. So if n = 1 is taken, then f˙0 is deﬁned. Solving the equation f˙1 = (f0 − f2) f0f1 (f0 + f1)−1, the

physical meaning of the root is,

f0

=

1 2f1

[ f1f2

+ f˙1

√( + f1f2

+ f˙1)2

+

] 4f12f˙1

Where

f˙1

=

/ 1407f12 1160

is

given

by

the

Lagrange

fre-

quency rate formula of GW150914 waveform,

(

)

f˙n

=

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

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

fn2

Then the values of f0± can be obtained by calculating the frequencies of f1± and f2± in Table 1 respectively.
The frequency recurrence equation (3) can also be used to calculate the characteristic frequency f0±. The form of equation (3) is derived from the recurrence of

high frequency and low frequency, which can be rewrit-

ten into the recurrence from high frequency to low fre-

quency,

(

)

(n + 3) 32n2 + 120n + 111

fn = (n + 1) (32n2 + 136n + 143) fn+1

Take n = 0 and get f0 = 333f1/143. The merger of spiral binaries will inevitably radiate positive and negative
pulse strains corresponding to the maximum frequency
f0. The results calculated by the two methods are consistent, and the calculation by equation (3) is simpler. For GW150914 waveform, because f1+ = 197.3975904Hz, f1− = 230.7600891Hz, so there is,

f0+ = 459.674109113Hz f0− = 537.364403289Hz

(7)

This indicates that at least the special pulse corresponding to the cohesion frequency f0+ = 459.674109113Hz should be radiated during the spiral binary stars merging of GW150914 waveform sources.
The gravitational wave pulse corresponding to the characteristic frequency is the main sign of the merger of spiral binaries. However, there is no pulse corresponding to the characteristic frequency in the detection data of GW150914 waveform. LIGO claims that Hanford detector and Livingston detector synchronously detected the GW150914 waveform within 0.25 0.47s. So the problem is suddenly enlightened! In principle, it is impossible for the two detectors to consistently produce systematic errors, so that the special pulse marking the merger of binary stars after 0.43s disappears at the same time. So, does the data extraction template lead to the disappearance of characteristic frequency? Or the data extraction is correct, and the result just proves that the binaries of GW150914 waveform source have not realized the ﬁnal merger, and the binaries of GW150914 waveform source are still in? The new problems caused by the failure of the ﬁnal merger of binary stars are: will be the binary stars maintain a uniform circular motion

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or move away after reaching the nearest distance? What is the shape of the gravitational wave after the binary star reaches the nearest distance? Where was the binary star of GW150914 waveform later? It can be seen that LIGO absolutely wants to create all binary star merger events, otherwise the detector can repeatedly detect the subsequent situation, and all myths and stories will go through. Isn’t this the real reason why all reports of LIGO claim that binaries have completed the merger? However, if the GW150914 waveform is deﬁned as the gravitational wave of spiral binary stars, the merger of wave source binary stars has not been completed, which is completely contrary to the conclusion expected and announced by LIGO. Now let’s look forward to LIGO’s wonderful explanation.
The conclusion of human reasoning about ancient cosmic events is restricted by physical and logical tools. From GW150914 waveform to gw170817 signal, LIGO always gives highly repeated conclusions: the extracted signal wave is either the gravitational wave of the merger of binary black holes or the gravitational wave of the merger of binary neutron stars, which means that there seems to be a heyday of the merger of binary stars in the historical process of the evolution of the universe, its radiation information can be accurately captured by LIGO detector. If this is true, how to explain this special cosmic history? However, GW150914 waveform does follow a new quantum law, which contains enough logical propositions. It brings us many thought-provoking scientiﬁc and ethical problems, and will also promote the progress of physical theory and signal detection technology.
5 Conclusions and comments
Nature always beats hearts! Scientiﬁc researchers must understand especially that the human brain can complete all its functions, but it must have enough awe and respect for Nature after all. The LIGO team invariably announced that the information of the merging of one ancient binary after another was just captured by two expensive detectors, which were really very tiring.
However, the detection of gravitational wave or simulated gravitational wave will promote theoretical physics to a new stage of development. Gravitational wave signal or simulated gravitational wave signal contains new physical information about com quantum theory and many scientiﬁc problems that need to be solved urgently. Spiral binary is the simplest model of spiral system. According to the detection data of spiral binary stars, the com quantized recurrence equation of radiation frequency can be ﬁtted by the minimum solution method of characteristic Diophantine equation. From this, the quantum number corresponding to each frequency can be determined, and the characteristic frequency of binary star merging can also be calculated theoretically. The com quantum law of GW150914 waveform and the fre-

quency recurrence equation of com quantization belong to the experimental law. The characteristic frequency of spiral binary stars, which is the only sign of a binary merger, is one of the necessary corollaries of the experimental law. However, there is no radiation pulse corresponding to the characteristic frequency of binary stars merging in the observed data of GW150914 waveform. Finding out the reason, whether the signal wave extraction template fails to include the peak marking the merger of spiral binaries, or whether the binaries may not achieve the ﬁnal merger, the answer is not clear at present. As a gravitational wave, the ﬁnal result of binary black holes with GW150914 waveform source needs further analysis and demonstration. If the GW150914 binary stars had did not merge, the detection of gravitational waves for the later period of GW150914 binary black holes constitutes a decisive experiment to test the theory of gravitational waves and the conﬁdence of gravitational wave detectors.
Is there any possibility that the source of the GW150914 waveform is dense binary stars with smaller mass in the near space-time, or some other similar wave source? In fact, it is diﬃcult for humans to truly understand the gravitational system of one billion or billions of light years away. Any qualitative conclusions about the cosmos in ancient-distant time and space eventually need to be examined by by in-depth calculation. As we all know, orbit and period of planets and so on, the classical gravitation theory describes these conclusions of the gravitational system accurately, and the application of classical gravity theory to aerospace engineering has also made brilliant achievements. Including the singular conclusions[32-36], such as black hole, some conclusions of modern physics still need to be tested by extensive formulaic experimental laws and logical demonstrations. The mathematical forms of diﬀerent theories describing the same natural law may be totally diﬀerent, but for the analysis of experimental detection data, their numerical results must be consistent within the error range. Studying the law of the fundamental characteristic physical quantity of gravitational waves such as the frequency and so on, an accurate theory must not depend on unproven assumptions. Its correct development is bound to be compatible with the achievements of classical physics and modern physics, especially to accept the test of formulaic exact experimental law.
Gravitational waves in general relativity are often described as spatiotemporal ripples, which make them very mysterious. In fact, the essence of gravitational waves is the manifestation forms of gravitational ﬁeld changes caused by moving objects, so gravitational waves are ubiquitous, but it is usually diﬃcult for gravitational waves to be detected by instruments. In the laboratory, the simulation spiral motion or other variable frequency motion can be achieved to obtain the corresponding gravitational waves. Since the universal gravitational constant G can be accurately measured in the laboratory, people are bound to be able to build similar sensors

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to detect gravitational waves in the laboratory. It is suggested that gravitational waves of spiral systems should be widely simulated in the laboratory. The observed results of gravitational waves in the laboratory are repeatable. The repeatable experimental results can be used to measure the conﬁdence of gravitational waves detected

by gravitational wave laser interferometer or other sensors. It is of great signiﬁcance that the detection results of gravitational waves simulating spiral systems will be reliable experimental basis for testing diﬀerent gravitational theories.

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