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Article
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Physics
Com Quantum Proof of LIGO Binary Mergers Failure
X. D. Dongfang
Orient Research Base of Mathematics and Physics,
Wutong Mountain National Forest Park, Shenzhen, China
LIGO claims to have detected a large number of ancient and distant binary merging gravitational
waves. However, only the frequency of GW150914 signal increases significantly and monotonously,
showing the expected characteristics of spiral double star merger, but it is highly similar to the engine
op erating frequency in the starting process of contemporary fighter. LIGO observers should know
which is more likely. Other signal waves of LIGO have no research value due to lack of detailed data.
Here, I further analyzed the frequency distribution and change law of GW150914 signal, and proved
the unreliability of its spiral double black hole merger assertion by fitting the precise recurrence rela-
tionship of the frequency of GW150914 waveform with macro quantization significance. The specific
pro cess and conclusions are as following. Firstly, the characteristic equation for effectively correcting
the amplitude time of the waveform is proposed, the specification conditions for the numerical analysis
metho d 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
recurrence equation characterizing the frequency distribution of the signal is obtained. Then, the com-
plex but clear data processing program 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 the
LIGO numerical relativistic waveform is opaque, and the conclusion is fuzzy and lacks due scientific
analysis. Then, the iconic maximum frequency of the merger event of GW150914 signal wave source
supp osed to be a spiral double star is calculated, and it is confirmed that this characteristic frequency
is missing in the GW150914 waveform. The reason why neither Hanford waveform nor Livingston
waveform has the corresponding characteristic frequency band is further analyzed, which proves that
the merger of the GW150914 spiral double black holes of LIGO is not successful, It means that the
LIGO signal is far more likely to be the signal of the start-up of modern fighter on the ground than
the gravitational wave of the merger of ancient and far away spiral binaries. Finally, an experimental
prop osal for detecting the gravitational wave of the simulated spiral double star system is proposed
to effectively test the confidence of the laser interference gravitational wave detector.
Keywords: GW150914 waveform; numerical analysis; Diophantine equations; Spiral binary black
hole; Dongfang com quantum law; frequency recurrence equation; Donfang characteristic frequency.
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.
1 Introduction
Experimental reports that can not repeat the observa-
tion results, some are illusions about similar phenomena,
and some are lies. 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 bina-
ry stars have been merged. In particular, highly similar
signals on the ground, such as those generated by the
start-up of modern fighter aircraft, can be recognized as
noise and accurately filtered out. This wonderful story
is obviously unconvincing. Therefore, it is most appro-
priate to define the so-called spiral binary stars merger
gravitational wave declared by LIGO as LIGO manufac-
turing.
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. Howev-
er, according to the theoretical waveform, the expected
waveform is extracted from the chaotic waveform, and
then the extracted waveform is used as evidence to de-
clare that the so-called experimental observation con-
firms the theoretical inference. This kind of strong twist-
Citation: Dongfang, X. D. Com Quantum Proof of LIGO Binary Mergers Failure. Mathematics & Nature 1, 202107 (2021).
2 X. D. Dongfang Com Quantum Proof of LIGO Binary Mergers Failure
ed chaotic logic is defined as modern advanced scientific
thought only because we succumbs to the academic au-
thority 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, 6]
. Extraction
of LIGO data
[7-10, 28]
completely depends on the wave-
form template of general relativity gravitational wave
theory
[11-15]
. 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 obvious-
ly not the data of real observation significance, but data
that has been seriously tampered with or even fabricat-
ed in disguise. After extracting the desired waveform
from the chaotic mixed waveform through the theoreti-
cal 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 gravitation-
al wave radiated by it increases monotonously. Gravity
theory holds that the frequency of the gravitational wave
should meet the nonlinear Blanchet equation
[16, 17]
. Al-
though 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 fre-
quency of GW150914 signal does not obey the Blanchet
frequency equation
[18]
.
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 charac-
teristic physical quantities such as the frequency or wave-
length of the gravitational wave. Formally, if we imitate
the quantum theory of the hydrogen atom
[19-25]
to es-
tablish the quantum theory of the gravitational system,
it seems that the calculation formula of the frequency or
wavelength of gravitational wave can be given. How-
ever, 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
[6, 26, 27]
, 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 gen-
erated by the merger of spiral binary black holes, its re-
liability 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 understand-
ing of the macro quantization law of variable frequency
signal. This is why we take it as the exp erimental basis
of com quantum theory.
Now, suppose that GW150914 waveform comes from
a certain frequency conversion rate movement, we fur-
ther study the frequency distribution law of GW150914
waveform. Firstly, the plausible amplitude time is ex-
tracted from the GW150914 waveform data released by
LIGO, the characteristic equation satisfied by the ampli-
tude 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 recur-
rence 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 in-
tended to the mystify waveform of com quantum theory
is provided here, and the com quantum standard wave-
form of GW150914 waveform is drawn. It is of great
significance to calculate the maximum characteristic fre-
quency of GW150914 waveform. Because if GW150914
waveform comes from the gravitational radiation of spi-
ral 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 charac-
teristic frequencies. However, the characteristic pulse is
missing in both Hanford waveform and Livingston wave-
form. It is necessary and important to find out the cause
of disappearance with theoretical and experimental sig-
nificance. In addition, considering that the experimental
observation results should be repeatable, an experimen-
tal proposal for detecting the gravitational wave simulat-
ing spiral motion in the laboratory is also proposed. The
purpose is to further confirm the confidence of the grav-
itational wave laser detector and increase the experience
of identifying the gravitational wave through repeatable
experiments.
2 Frequency recurrence equation of G-
W150914 waveform
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
Mathematics & Nature (2021) Vol. 1 3
waveform that the positive and negative strains over-
turned and the time delayed 7.324218ms. As shown
in Figure 1, the real line segment indicates the correc-
tion 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 addi-
tion to noise resulting in waveform distortion, noise may
lead to waveform distortion, and the detector may al-
so miss some real positive and negative strain peaks by
recording a signal per 6.10352 × 10
−5
s. Therefore, cor-
rection 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 x
5
and x
7
respectively, and the time for
the three wide negative strain peaks that have not been
determined is represented by t
3
, t
7
and t
8
, respective-
ly. The intrinsic period and the intrinsic frequency are
defined as T
n
= t
n
− t
n+1
and f
n
= T
−1
n
respectively,
in which the subscript n is also quantum number and
arranged in reverse chronological order.
GW150914 Livingston
GW150914 Hanford
0.25
0.30
0.35
0.40
0.45
-1.0
-0.5
0.0
0.5
1.0
TimeHtL s
Strain
Figure 1 The superposition of the Hanford and Livingston
waveforms of the GW150914 waveform
Table 1 Positive and negative strain peak times of GW150914 waveform and its frequency distribution
n Positive strain Negative strain
t
n
/s T
n
/s t
n
/s T
n
/s
1 0.428222656 0.005065918 0.430297903 0.004333505
2 0.423156738 0.008568080 0.425964398 0.425964398 − t
3
3 0.414588658 0.012597024 t
3
t
3
− 0.407859272
4 0.401991635 0.401991635 − x
5
0.407859272 0.014622451
5 x
5
x
5
− 0.362882581 0.393236822 0.018832351
6 0.362882581 0.362882581 − x
7
0.374404471 0.374404471 − t
7
7 x
7
x
7
− x
8
t
7
t
7
− t
8
8 x
8
t
8
Finding the minimum solution of the Diophantine
equation system
[29-31]
which accords with the physi-
cal meaning can determine the best approximation e-
quation of com quantum law, and the resulting La-
grange frequency change rate of the positive and neg-
ative strain from the GW150914 singal is the same. S-
tudying 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.
The GW150914 waveform belongs to the high frequen-
cy signal wave. Being similar to the Lagrange frequency
change rate, the ratio f
n+1
f
−1
n
of the adjacent frequen-
cies of the p ositive and negative vibration peaks of high
frequency signal waves is decided by the quantum num-
ber n. Because the exact function of the frequency f
n
can always be expressed to be the Laurent series on the
quantum number n, f
n
f
−1
n+1
is the ratio of the two Lau-
rent 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 f
n+1
f
−1
n
is a nonlinear
recurrence equation with no simple function solution.
[32]
.
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) f
n+1
f
−1
n
is a monotone decreasing function of quan-
tum 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
4 X. D. Dongfang Com Quantum Proof of LIGO Binary Mergers Failure
adjacent frequency is, and so there is a limit value of
lim
n→∞
f
n+1
f
−1
n
= 1, which indicates that the highest pow-
er of the numerator and the denominator of f
n+1
f
−1
n
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
two conditions is the rational formulas of the coefficients
to be determined. Here we take the following form,
f
n+1
f
n
=
kn
3
+ an
2
+ bn + c
kn
3
+ dn
2
+ en + f
=
T
n
T
n+1
(1)
where k, a, b, c, d, e, f are all undetermined constants,
pulsing the undetermined normal strain peak time x
5
and x
7
or negative strain peak time t
3
and t
7
in Table
1, there are 11 unknown parameters, and the reduced
parameters after reduction are 10.
T
+
4
T
+
5
=
0.401991635 − x
5
x
5
− 0.362882581
=
0.014622451
0.018832351
=
T
−
4
T
−
5
T
+
1
T
+
2
=
0.005065918
0.008568080
=
0.004333505
0.425964398 − t
3
=
T
−
1
T
−
2
T
+
5
T
+
6
=
x
5
− 0.362882581
0.362882581 − x
7
=
0.018832351
0.374404471 − t
7
=
T
−
4
T
−
5
1
3
k+1
2
a+1b+c
1
3
k+1
2
d+1e+f
=
0.005065918
0.008568080
=
0.004333505
0.007329336
≈
311
526
2
3
k+2
2
a+2b+c
2
3
k+2
2
d+2e+f
=
0.008568080
0.012597024
=
0.007329336
0.01077579
≈
1629
2395
3
3
k+3
2
a+3b+c
3
3
k+3
2
d+3e+f
=
0.012597024
0.017093816
=
0.01077579
0.014622451
≈
1678
2277
4
3
k+4
2
a+4b+c
4
3
k+4
2
d+4e+f
=
0.017093816
0.022015238
=
0.014622451
0.018832351
≈
5995
7721
5
3
k+5
2
a+5b+c
5
3
k+5
2
d+5e+f
=
0.022015238
0.362882581 − x
7
=
0.018832351
0.374404471 − t
7
(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
x
5
and x
7
, and the negative strain peak time t
3
and t
7
satisfy the following equations respectively,
The first equation gives x
5
= 0.384897819s and the
second equation gives t
3
= 0.4186350615s. So the
two period values to be determined are respectively
T
+
4
=0.017093816s and T
+
5
=0.022015238s, and the t-
wo undetermined negative strain periods are T
−
2
=
0.007329336s and T
−
3
=0.01077579s respectively. Sub-
stituting 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 deter-
mine 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
f =
407789722467k − 314244792483a + 271503710307b
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,
f
n+1
=
(n + 1)
32n
2
+ 136n + 143
(n + 3) (32n
2
+ 120n + 111)
f
n
(3)
According to the last equation of equation (2), it
can be solved for the positive strain peak time x
7
=
0.335554568s and the negative strain peak timet
7
=
0.351027448s, and the corresponding periods are T
+
6
=
0.027328013s and T
−
6
= 0 .023377023s, respectively.
These values are in the range of error.
The recurrence equation (3) is fitted by the frequen-
cy of GW150914 waveform. Using equation (3), com
quantum laws satisfied by the frequency change rate of
GW150914 waveform can be derived by simple algebra-
ic 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 on-
ly best approximation, and other approximations can
be fitted. The numerical results of the same quantum
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 rea-
sonable 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 ac-
cording to the characteristics of frequency distribution
and variation of the signal wave. Then the minimum so-
lution of characteristic Diophantine equation system can
be determined by numerical analysis, and then the spe-
cific 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 approx-
imate equation often requires repeated approximation.
From a practical point of view, if that the numerical cal-
culation 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
Mathematics & Nature (2021) Vol. 1 5
considered as the standard, it is completely able to ac-
cept 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 G-
W150914 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 es-
timate 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 specula-
tion out of thin air is not only untenable, but also covers
up some important truths.
The period or frequency of signal wave of change fre-
quency is a continuous function of time. It is difficult
to determine the zero point of GW150914 waveform for-
m 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 fit-
ting method and drawing procedure of the com quantum
theory standard waveform whose frequency distribution
meets the recurrence equation (3). The specific opera-
tion 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
T
n
= t
n
− t
n+1
, this time satisfies the recurrence re-
lation t
±
n
= t
±
n−1
−
f
±
n−1
−1
, which is replaced by the
equation (3) to read,
t
n
= t
n−1
−
(n + 1)
32n
2
− 8n − 1
(n − 1) (32n
2
+ 8n − 1)
(t
n−2
− t
n−1
) (4)
By Table 1, t
+
1
=0.428222656s and t
+
2
=0.423156738s
gives the positive strain peak period T
+
1
=0.005065918s
of n = 1, t
−
2
=0.425964398s and t
−
2
=0.430297903s
gives the negative strain peak period T
−
1
=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=3
k
i=3
(i + 1)
32i
2
− 8i − 1
(i − 1) (32i
2
+ 8i − 1)
T
+
1
t
−
n
= t
−
1
−
1 +
n
k=3
k
i=3
(i + 1)
32i
2
− 8i − 1
(i − 1) (32i
2
+ 8i − 1)
T
−
1
(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.
Table 2 Time and frequency distribution of positive and negative strain peaks of GW150914 waveform
n
Positive strain Negative strain
t
n
/s T
n
/s f
n
/Hz t
n
/s T
n
/s f
n
/Hz
0 0.430398110 0.002175454 459.6741012 0.4321588376 0.0018609346 537.3644033
1 0.428222656 0.005065918 197.3975891 0.430297903 0.004333505 230.7600891
2 0.423156738 0.008568058 116.7125619 0.425964398 0.007329336 136.4379995
3 0.414588680 0.012597004 79.38395511 0.418635062 0.010775789 92.80062677
4 0.401991676 0.017093789 58.50078061 0.407859272 0.014622451 68.38798934
5 0.384897887 0.022015203 45.42315599 0.393236822 0.018832351 53.10011606
6 0.362882684 0.027327971 36.59254469 0.374404471 0.023377023 42.77704585
7 0.335554713 0.0330055 30.29798064 0.351027448 0.028233724 35.41863655
8 0.302549213 0.039025938 25.62398372 0.322793724 0.033383754 29.95468968
9 0.263523275 0.045370908 22.04055515 0.289409970 0.038811400 25.76562555
10 0.218152367 0.250598570
6 X. D. Dongfang Com Quantum Proof of LIGO Binary Mergers Failure
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 the energy distribution is proportional
to the square of the strain, ε ∝ h
2
, so h ∝
√
ε ∝
√
f.
From this, h
n
∝
√
f
n
, h
n+1
∝
f
n+1
. In this way, t-
wo strains h
n+1
and h
n
with the phase difference of 2π
satisfy the relational h
n+1
=
f
n+1
f
−1
n
1/2
h
n
, that is,
h
n
=
f
n
f
−1
n−1
1/2
h
n−1
, in the form of (3). And then
from the equation (3), one gets the result
h
n
=
n
32n
2
+ 72n + 39
(n + 2) (32n
2
+ 56n + 23)
1
2
h
n−1
(6)
The equation (6) is only a semi definite quantitative e-
quation based on guesswork rather than a numerical fit-
ting 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.
Equations (5) and (6) are applied to GW150914 wave-
form. First, the time of the next several positive and
negative strain peaks is calculated by the recurrence e-
quation (5). The time of each period is divided into 400
equal parts with different time intervals. Then, correc-
tion values of 400 positive and negative strains of n = 2
are determined by the cosine function. Then, the posi-
tive and negative strains of other periods are calculated
by semi-quantitative equation (6). It is necessary to se-
lect the appropriate starting time and ending time, oth-
erwise the calculated strain distribution will be deformed
in the waveform.
In 2016, I used Excel to generate 4000 groups of G-
W150914 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 su-
perposition 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 wavefor-
m are also drawn. The com quantum theory waveform
in the high frequency band is consistent with the nu-
merical 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 fundamen-
tal 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.
Hanford waveform
Livingston waveform
Relativity Waveform
Com Quantum Waveform
0.25
0.30
0.35
0.40
0.45
-1.0
-0.5
0.0
0.5
1.0
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 pro-
cessing procedure. Drawing the com quantum waveform
of the variable frequency signal wave, including modi-
fying the strain time of GW150914 waveform to fit an
applicable waveform function within the allowable range
of error, requires determining the com quantization for-
mula of frequency distribution of variable frequency sig-
nal wave. To different variable frequency signal wave of
natural phenomena, any new effective numerical method
will prompt the discovery of new discrete laws. Scien-
tific conclusions should not be confined to qualitative
descriptions. By trying to draw a numerical relativistic
waveform of LIGO signal wave, we can infer the rea-
son why the drawing procedure of so-called numerical
relativistic waveform of GW150914 waveform is opaque.
This is because drawing the numerical waveform requires
the corresp onding numerical equation rather than the o-
riginal 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 calcula-
tion method.
Mathematics & Nature (2021) Vol. 1 7
4 Missing characteristic frequency of G-
W150914 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 bi-
nary stars will undergo three processes: inspired, merg-
er 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 monoton-
ic frequency of GW150914 waveform is most consistent
with the characteristics of the gravitational wave of the
spiral binary stars. According to the correct superpo-
sition 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 co-
incide with the Livingston vibration curve after upside-
down 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 rea-
sonable 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 gravi-
tational wave radiation of merging spiral binary stars,
the frequency of spiral binary stars’ precession increas-
es monotonously, and the frequency of the gravitation-
al 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 s-
tars must have a frequency limit, which is expressed by
f
0
. In this case, f
0
is the characteristic frequency of the
gravitational wave of spiral binaries, that is, the connec-
tion frequency between precession process and oscilla-
tion process, which corresponds to a special pulse in the
gravitational wave of spiral binaries. Whether this par-
ticular pulse exists indicates whether the spiral binaries
have finally merged.
According to the definition of Lagrange frequency
change rate
˙
f
n
= (f
n−1
− f
n+1
)/(T
n
+ T
n−1
)
[18, 27]
,
the period is expressed by the correspond-
ing frequency, and the relationship
˙
f
n
=
(f
n−1
− f
n+1
) f
n−1
f
n
(f
n−1
+ f
n
)
−1
is obtained. Al-
though
˙
f
0
has no meaning,
˙
f
1
has the corresponding cal-
culation results. So if n = 1 is taken, then
˙
f
0
is defined.
Solving the equation
˙
f
1
= (f
0
− f
2
) f
0
f
1
(f
0
+ f
1
)
−1
, the
physical meaning of the root is,
f
0
=
1
2f
1
f
1
f
2
+
˙
f
1
+
f
1
f
2
+
˙
f
1
2
+ 4f
2
1
˙
f
1
(7)
Where
˙
f
1
= 1407f
2
1
1160 is given by the Lagrange fre-
quency rate formula
[?]
of gravitational waves,
˙
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
(8)
Then the values of f
±
0
can be obtained by calculating
the frequencies of f
±
1
and f
±
2
in Table 1 respectively.
The frequencyrecurrence equation (3) can also be used
to calculate the characteristic frequency f
±
0
. The form
of equation (3) is derived from the recurrence of high fre-
quency and low frequency, which can be rewritten into
the recurrence from high frequency to low frequency,
f
n
=
(n + 3)
32n
2
+ 120n + 111
(n + 1) (32n
2
+ 136n + 143)
f
n+1
(9)
Take n = 0 to obtain the iconic maximum frequency
f
0
=
333
143
f
1
(10)
this formula is called Donfang characteristic frequency.
If the gw15091 signal source is the merging spiral double
star, the positive and negative pulse strain correspond-
ing to the maximum frequency f
0
will be radiated dur-
ing the merging process. The results calculated by the
two methods are consistent, and the calculation by equa-
tion (3) is simpler. For GW150914 waveform, because
f
+
1
= 197.3975904Hz, f
−
1
= 230.7600891Hz, Therefore,
the Dongfang characteristic frequencies of positive and
negative strains are:
f
+
0
= 459.674109113Hz
¯
f
−
0
= 537.364403289Hz
(11)
This indicates that at least the special pulse correspond-
ing to the cohesion frequency f
+
0
= 459.674109113Hz
should be radiated during the spiral binary stars merg-
ing 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 correspond-
ing to the characteristic frequency in the detection data
of GW150914 waveform. LIGO claims that Hanford de-
tector and Livingston detector synchronously detected
the GW150914 waveform within 0.25 0.47s. So the
problem is suddenly enlightened! In principle, it is im-
possible 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 da-
ta extraction is correct, and the result just proves that
the binaries of GW150914 waveform source have not re-
alized 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
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
8 X. D. Dongfang Com Quantum Proof of LIGO Binary Mergers Failure
star of GW150914 waveform later? It can be seen that
LIGO absolutely wants to create all binary star merger
events, otherwise the detector can rep eatedly 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 cos-
mic 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 merg-
er 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 do es fol-
low a new quantum law, which contains enough logical
propositions. It brings us many thought-provoking sci-
entific and ethical problems, and will also promote the
progress of physical theory and signal detection technol-
ogy.
5 Conclusions and comments
Nature is always thrilling! Human’s understanding of
nature can be constantly improved, but the ability to
understand nature is always limited. When scientific re-
searchers can’t complete their plans for a long time, they
often make up fairy tales. As everyone knows, there is
no flawless lie, people can often rack one’s brains, use all
sorts of intrigues and wiles to achieve their personal goal-
s, but after all, human beings must be in awe of nature.
The articles of the LIGO team follow the same pattern
to announce that the two expensive detectors have con-
tinuously captured the remote and ancient binary star
merger events, which is really very boring.
However, the detection of gravitational wave or simu-
lated gravitational wave will promote theoretical physics
to a new stage of development. Gravitational wave sig-
nal or simulated gravitational wave signal contains new
physical information about com quantum theory and
many scientific problems that need to be solved urgent-
ly. 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 fre-
quency 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 bina-
ry 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 bi-
nary 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 wave-
form. 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 bi-
nary black holes with GW150914 waveform source needs
further analysis and demonstration. If the GW150914
binary stars had did not merge, the detection of gravi-
tational 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 grav-
itational wave detectors.
Is there any possibility that the source of the G-
W150914 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 under-
stand the gravitational system of one billion or billions
of light years away. Any qualitative conclusions ab out
the cosmos in ancient-distant time and space eventual-
ly 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
[33-37]
, 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. S-
tudying the law of the fundamental characteristic physi-
cal quantity of gravitational waves such as the frequency
and so on, an accurate theory must not depend on un-
proven assumptions. Its correct development is bound to
be compatible with the achievements of classical physic-
s and modern physics, especially to accept the test of
formulaic exact experimental law.
Gravitational waves in general relativity are often de-
scribed 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 frequen-
Mathematics & Nature (2021) Vol. 1 9
cy motion can be achieved to obtain the corresponding
gravitational waves. Since the universal gravitational
constant G can be accurately measured in the laborato-
ry, people are bound to be able to build similar sensors
to detect gravitational waves in the laboratory. It is sug-
gested that gravitational waves of spiral systems should
be widely simulated in the laboratory. The observed re-
sults of gravitational waves in the laboratory are rep eat-
able. The repeatable experimental results can be used to
measure the confidence of gravitational waves detected
by gravitational wave laser interferometer or other sen-
sors. It is of great significance that the detection results
of gravitational waves simulating spiral systems will be
reliable experimental basis for testing different gravita-
tional theories, and finally help us reveal the truth and
falsity of the gravitational wave of the spiral black hole.
It is also a challenge to identify the signal waves when
modern high-speed locomotives start, and the mystery
will eventually be solved.
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Latest findings
Dongfang Modified Equations of Electromagnetic Wave
Systematically show the correct solution process of the initial value problem of Maxwell equations in rectangular coordinate system and cylindrical coordinate system, and clearly point out that the transverse electromagnetic wave equation described in the classical electromagnetic theory is the result of incorrect understanding and treatment of Maxwell equations: the definite solution conditions of magnetic field and electric field in the same phase that do not conform to the natural law are assumed in advance, and then the plane transverse electromagnetic wave mode is determined through the general solutions of the second-order Maxwell equations, and the conclusion violates the law of energy conservation, In particular, the mathematical process does not conform to the solving rules of differential equations. Through this simple example, I clarify my clear position: since the era of Maxwell's electromagnetic theory, theoretical physics has fallen into a strange circle in which the wrong calculation of celebrities is defined as standard methods and the assumption that celebrities cannot prove is defined as basic principles, resulting in a large number of wrong logic and wrong conclusions in physical theory, even some branches of theoretical physics are completely wrong from beginning to end, and all these errors are covered up by formal mathematical operations, the formal mathematics seriously distorts the laws of nature. However, all correctable and uncorrectable errors have not been found and recognized by mainstream physicists, and especially the pointing out of these errors has been rejected by mainstream scholars. A serious question arises: Can the future mainstream physics change this academic abnormal state?