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The Truth of the Experiments of Invariable Speed of Light in Special Relativity
Article in Applied Physics Research · October 2023
DOI: 10.5539/apr.v15n2p116

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The Truth of the Experiments of Invariable Speed of Light in Special Relativity
Mei Xiaochun (ycwlyjs@yeah.net)
Department of Pure Mathematics and Theoretical Physics, Institute of Initiative Physics in Fuzhou, China
Abstract It is pointed out that the most experiments on the invariant speed of light in special relativity proves the round-trip invariant speed of light, not one-way invariant. This paper makes a distinction between them. The Michelson-Morley experiment and the experiment of high-energy particles emitting photons and so on are the round-trip experiment of light’s speed, showing that the average speed of light is a constant. But the Sagnac effect experiment, the Michelson-Gale's experiment that the earth's rotation effects the speed of light, and the satellite signal propagation between China and Japan are the one-way experiments of light’s speed, showing that the speed of light is variable, satisfying the Galilean velocity addition rule. The orbit shape changes of binary stars and the phenomenon of charm stars cannot be observed due to that the calculated observing directions are different from the practical observing direction for the observers on the Earth. The Fizeau water flow experiment and the Sagnac experiment are combined to prove that the rotation of optical fiber would affects the speed of light. The problem that the Sagnac effect is independent of the refractive index of optical fiber is explained well. It is proved that the Sagnac effect formula derived from special relativity is consistent with that derived from classical mechanics when
the optical fiber’s refractive index n  2 . When n  1 , there is no the Sagnac effect according to
special relativity. While according to classical mechanics, there is the Sagnac effect. The original
experiment of Sagnac effect in 1913 was carried out in atmosphere with n  1 . Therefore, the original
Sagnac experiment became a judgment experiment. It certainly jugated that the velocity of light satisfied the Galilean addition rule rather than the Lorentz transformation formula.
Key Words: Special relativity, Invariable principle of light’s speed, Galilean velocity addition rule, Lorentz velocity transformation, Michelson-Morley experiment, Michelson-Gale experiment, Sagnac experiment, Fizeau water flowing experiment.
1 Introduce
It is well known that the most important experimental basis for Einstein's special relativity is the Michelson-Morley experiment (M-M experiment). In order to explain the zero result of the experiment, Lorentz proposed the famous Lorentz coordinate transformation. Then Einstein put forward the principle of special relativity and the invariable principle of light’s speed in 1905, establishing special relativity.
However, the authors published two papers in Applied Physics Research in 2023, to prove that the Michelson-Morley experiment was invalid and denied the legitimacy of the Lorentz transformation formula. The most important theoretical and experimental basis of Einstein's special relativity are falsified (Mei Xioachun, Yuan Canlun, 2023). ———————————— The paper was published in Applied Physics Research, 2023, Vol. 15, No. 2, https://doi.org/10.5539/apr.v15n2p116 . Some additions are made in this this version.
1

It is pointed out in the first paper that the calculation of the M-M experiment was wrong. Michelson fixed the light source on the absolutely stationary reference frame of the universe (or the ether reference frame) in the calculation of the M-M experiment. However, in the actual experiments, the light source was fixed on the earth motion reference frame and moved and rotated with the interferometer, leading to the invalidity of the M-M experiment’s experiment.
If the light source is fixed on the moving reference frame of the earth and the Galilean velocity transformation formula is adopted, the zero result of the M-M experiment can be explained and the Lorentz transformation formula is unnecessary at all.
If Michelson had done his calculation correctly in early years, there would have been neither the first dark cloud in the history of physics, no Einstein's special relativity, and there would be no later general relativity!
The second paper proves that the mass velocity formula of special relativity cannot be derived by using the Lorentz velocity transformation formula, and therefore Einstein's famous mass-energy relationship cannot be obtained. All deductions of the mass velocity formula in special relativity are cobbled together artificially and meaningless. The mass-velocity formula can only be regarded as an empirical formula, not be deduced theoretically.
Therefore, the most important two equations of Einstein's special relativistic dynamics, the massvelocity formula and the mass-energy formula actually have nothing to do with relativity. If they are correct, Einstein's special relativity is wrong.
This paper goes on to discuss the experiments of special relativity on the invariable speed of light, as well as the experiments that special relativity cannot explain. According to the observation facts of cosmic microwave background radiation, the absolute rest reference frame of the universe is introduced, and the
speed of light in the absolute rest reference frame of the universe is defined as the light’s speed c in
vacuum. When measured on the earth's surface, one-way speed of light is related to the Earth's moving speed, which is not a constant, satisfying the Galilean addition rule of velocities. But the round-trip speed of light has nothing to do with the earth's motion speed and is still an invariant.
In this paper, a dozen typical experiments of invariable speed of light done by physicists in the past hundred years are analyzed.they are divided into four types.
The first type of experiment proves that the round-trip speed of light is constant, that is, the light has a round trip motion during the measurement, and the result shows that the average speed of light is a constant, rather than that the one-way speed of light is a constant. Such experiments include the Michelson-Morley experiment and the experiment on the speed of light radiated by high-energy particles.
The second type of experiment do not actually measures the speed of light, but the second-order Doppler effect, that is, the effect of the time delay factor of relativity on the frequency of light. They are the Cedarhole experiment, the Cialdea experiment, and the Mossbauer experiment. Since the Lorentz transformation formula does not exist, this kind of experiment results in the second-order effects do not actually exist.
The third type of experiment is the observation of visual deformations of binary stars orbits and phantom stars. It is pointed out in this paper that although the observations of vision orbital deformation of binary stars and the phantom star are the problem of one-way speed of light, they are not observable because the observation angle calculated theoretically is different from the actual observation angle on the Earth, so they can not be regarded as the evidence of constant speed of light.
The fourth type of experiment includes the Sagnac effect experiment, the Michelson-Gail experiment,
2

and the Sino-Japanese satellite signal propagation experiment, which show that the speed of light in vacuum is not a constant. It is pointed out that these three experiments are true one-way experiments of light’s, which prove that the principle of the constant speed of light in vacuum of special relativity is not valid.
In this paper, the derivations of Saganac effect formula based on the variable speed of light in classical mechanics and the invariable speed of light in special relativity are discussed in detail. The derivation of special relativity is proved is wrong. The reason is that according to the derivation method of special relativity, the initial interference point of the two beams propagating along the opposite method is different from the interference point after the fiber moves a circle in the stationary reference frame, resulting in invalid calculation result. The derivation of special relativity also leads to the result of the Galilean velocity transformation, which is obviously contradictory.
The Fizeau flow experiment is also connected with the Sagnac effect experiment, and it is proved that the rotation of fiber medium will affect the speed of light. A history left problem that the change of interference fringe of light in the Sagnac effect has nothing to do with the refractive index of fiber is explained.
According to the current theory, the Sagnac effect experiment is a non-inertial system, which cannot be explained by special relativity so that general relativity is needed. Based on Lorentz velocity transformation formula, the Sagnac effect formula of special relativity in optical fiber medium is derived in this paper. It is proved that the result is the same with that derived from classical mechanics when the
Fizeau effect is considered and the refractive index of fiber is n  2 , general relativity is unnecessary. However, when n  2 , the calculation results of classical mechanics and special relativity are
different. We can distinguish them through experiments. Especially , when n  1 , there is no the Sagnac
effect according to special relativity. While according to classical mechanics, there is the Sagnac effect. The
original Sagnac effect experiment in 1913 was performed in air with n  1 and the optical loop formed by
several mirrors. So, the original Sagnac experiment becomes a judgment experiment to prove that the speed of light satisfies the Galilean addition rule rather than the Lorentz transformation formula.
In 1925, Michelson and Gale carried out an experiment on the effect of the Earth’s rotation on the speed of light (the M-G experiment) in the suburbs of Chicago, USA. The experiment measured the Earth's rotational angular speed, or the tangential motion speed of the Earth's surface. The results of the experiment, contrary to the Michelson-Morley experiment, proved that the rotation speed of the earth could be measured, and the speed of light was not constant on the earth’s surface. But because it was contrary to special relativity, the existing textbooks and literature do not mention this experiment.
It is pointed out in this paper that the M-G experiment is actually an amplified Saganc effect experiment which also measures the one-way variable speed of light. The result is fundamentally different from the M-M experiment.
The M-M experiment is compared with the Sagnac effect experiment. It is pointed out that the M-M experiment is a round-trip experiment, showing that the average speed of light is a constant. However, the Sagnac effect is a one-way experiment, showing the variable speed of light. In the experiment, two beams of light moving in opposite directions travel a complete circle and return to the starting point for interference. Before returning to the starting point, the direction of circular motion does not change.
This perfectly explains why the basic principle and the measurement method of two experiments are the same, but the M-M experiment has no the change of interfere fringes, while the Sagnac experiment has the change of interfere fringes.
3

Therefore, this paper further proves that physics requires neither the Lorentz coordinate transformation formula nor the Einstein's principle of invariable speed of light.

2 The propagation speed of light

2.1 The images of invariable speed of light in special relativity

The most basic formula of special relativity is the Lorentz coordinate transformation, which has a
perfect symmetry. As shown in Fig.1, the reference frame K is assumed to be stationary in vacuum, and the reference frame K moves along the x  axis to the right side at a uniform speed V relative to the reference frame K . Suppose that at the initial moment t0  0 , when the origins O and O of two
reference frames coincide, a light wave is emitted from the origins of coordinate system with the
propagation speed c . For the reference frame K , the Lorentz coordinate transformation formula is

x  x Vt 1V 2 / c2

y  y

z  z

t  t Vx / c2 1V 2 / c2

（1）

But for the reference frame K , the Lorentz coordinate transformation formula is

x  x Vt 1V 2 / c2

y  y'

z  z'

t  t Vx / c2 1V 2 / c2

（2）

The Lorentz speed transformation formula is

u



1

u V  uV /

c

2

or

u



1

u   uV

V / c2

（3）

According to Eq.(3), for the both reference frame, the speed of light is a constant c , or the speed of light
has nothing to do with the speed of light source.
For an observer at rest in the reference frame K , the wave front of light wave arrives at the spherical surface with radius R  ct at arbitrary moment t as shown in Fig.1. At this time, the origin O of the reference frame K moves to the position O . Thus, according the observer at rest in K , the wave front of light observed by the observer in K is not a spherical surface.

K

K'

z

z'

V

R

x

O O'

x'

K

K'

z

z'

R’

x

O O'

x'

y y'

y y'

Fig.1 Image 1 of invariable speed of light. Fig.2 Image 2 of invariable speed of light.

However, for the observer at rest in K , the situation is just opposite. The wave front of light arrives at the spherical surface with radius R  ct at time t as shown in Fig.2. At this time, the origin O of K moves to the position O . Thus, according the observer in K , the wave front of light observed by the

4

observer in K is not a spherical surface.

This picture of special relativity is very grotesque and completely at odds with human common sense

and basic logic. In order to explain this picture, Einstein had to propose the hypothesis of simultaneous
relativity, which declared that what appeared simultaneously to an observer in the reference frame K (the

wave front is a spherical surface) did not appear simultaneously to another observer in the reference frame
K (the wave front is not a spherical surface). The viewpoint of other observer in the reference frame K was opposite. He thought that the wave
front of light was a sphere surface, but the observer in the reference frame K thought that the wave front

of light was not a spherical surface.

It is proved in the author's paper that Lorentz coordinate transformation is not only unnecessary but

also impossible (Mei Xiaochun, Yuan Canlun, 2023), the images in Fig.1 and Fig.2 cannot be correct.

In fact, as Qi Ji had pointed out that if the speed of light in Eqs.(1), (2) and (3) were replaced by the
speed cw of water wave or sound wave, there were the similar Lorentz transformation formula of water
wave and sound wave with (Qi Ji, 1993）

x  x Vt 1V 2 / cw2

y  y

z  z

t  t Vx / cw2 1V 2 / cw2

（4）

x  x Vt 1V 2 / cw2

y  y'

z  z'

t  t Vx / cw2 1V 2 / cw2

As well as the Lorentz velocity transformation formula for water wave or sound wave

（5）

u



1

u V  uV /

cw2

or

u



u V 1 uV / cw2

（6）

Where V is the velocity of the source of water wave or sound wave. It can also be concluded from
Eqs.(4) ~ (6) that the velocities of water wave and sound wave are also invariable and limiting velocities. The speed of an object cannot exceed the speed of water wave and sound wave, as well as there are the time delay and the length contraction related to water wave and sound wave. The relativity theories of water wave and sound wave can also be established. It is obvious that all of these are absurd.

2.2 The speed of light in the absolutely stationary reference frame of the universe

We know that sound waves and water waves need a medium for propagation. According to modern physics, light is considered to have wave-particle duality. According to classical electromagnetic theory, light is electromagnetic wave, but it can travel through vacuum without the involvement of medium. In physical history, the ether was considered to exist as a medium through which light traveled. The existence of the ether, however, cannot be verified experimentally and would cause serious problems in physics.
The ether theory was abandoned since Einstein proposed special relativity, but this did not mean that the absolutely stationary reference frame did not exist. The cosmic microwave background radiation (CMB) was discovered in the 1960s. After that, it has been observed to deviate from the black-body radiation spectrum. Because CMB is measured on the Earth's reference frame, based on the deviations from the black-body spectrum, physicists calculates that the reference frames of the sun or the Earth are moving in
the direction of right longitude 1h.5  0h.4 and declination 0.02  70 in the celestial reference frame at a speed of about 390Km / s (Tan Zhansheng, 2007). This velocity can be regarded as the absolute motion

5

velocity of the solar or the Earth reference frame relative to the absolute stationary reference frame of the universe (or the cosmic absolute reference frame).
It is known that the propagation speed of light in vacuum is a constant c. The refractive index of
atmosphere on the earth surface is 1.0003, and the light’s vacuum refractive index n  1 . The motion of light in the cosmic reference frame is equivalent to the motion of light in vacuum with n  1 . In the
non-vacuum condition, the speed of light is less than c. We need to discuss the motion of light in various non-vacuum media. Especially in the Fizeau flow experiment and the Sagnac effect, it is necessary to consider the influence of the motion state of medium on the speed of light.

2.3 The relationship between the speed of light and the speed of observer

According to the light speed invariant principle of special relativity, the propagation speed of light is not only independent of the speed of light source, but also independent of the speed of observer. In fact, Eq.(3) does not consider whether V is the speed of light source or the speed of observer. According to special relativity, it is indistinguishable for both situations that a light source is stationary and an observer is moving, or an observer is stationary and a light source is moving.
In classical physics, however, these two cases are different. There are two ways to observe the velocity of a wave. One is that the observer is stationary and the wave source is moving. The other is that the wave source is moving and the observer is stationary. In these two cases, the wave propagation speed may be different. For example, when the observer is at rest, the speeds of water and sound waves are independent of the speeds of wave sources. If the source is stationary and the observer is moving, the observed propagation speed of wave is related to the speed of observer.
In fact, the speed of light is related to whether the essence of light is a particle or a wave. If light is essentially a particle, then according to the theory of light emission, the speed of light is related to the speed of light source. No matter what the essence of light is, this paper mainly points out that the speed of light must be related to the speed of an observer. The assertion of special relativity that the speed of light is independent of the speed of an observer is impossible to hold.
3. The round-trip invariant speed experiment of light
3.1 The invariable round-trip speed and the variable one-way trip speed of light

According to the current understanding of special relativity, the constant speed of light has been fully

verified in experiments. However, as Zhang Yuanzhong pointed out (Zhang Yuanzhong, 1994), what these

experiments tested were the round-trip speed of light, rather than the one-way trip speed. Whether or not

the speed of light is a constant in one-way trip is still an unsolved problem.

The reason is that for the measurement the one-way speed of light, we first have to calibrate two

clocks at different places. However, calibrating clocks requires light signals, which requires knowing the

speed of light in advance, so it gets stuck in a logical loop. If we measure the round -trip speed of light, in

principle we only need a clock and a mirror to realize it. However, because the speed of light is so fast, it is

difficult to make a one-way measurement of light’s speed within the limited distance on the Earth's surface.

As absolute

discussed reference

above frame,

and the

shown in Fig.3, assuming
speed of light measured in

that the source of light is fixed on the cosmic absolute reference frame

the is

cco.sTmhice

Earth's reference frame the velocity of light is

cis .moving

at

a

velocity

V . When observed in the Earth's motion reference frame,

6

c



θ

V

Fig.3 The light’s velocities in the cosmic absolute reference

frame and the earth’s moving reference frame.

According angle between

cto

the and

Galileo's addition rule V is  , we have

of

velocity,

there

is

a

relation

c



c

 V

.

Suppose

that

the

c2  c2  2cV cos V 2

（7）

When   0 , we have c  c V  c .When    , we have c  c V  c . So the speed of light

measured on the Earth's surface is not a constant, but superimposed by the speed of the Earth's reference

frame.

As measured on the Earth's surface, the speed of light is c  299792500 100s / m , and physics defines the speed of light in vacuum as c  299792458m / s . This value does not take into account the

absolute velocity of the Earth in the cosmic absolute reference frame, so the true vacuum speed of light

needs to be corrected according to Eq.(7).

Regard V
when the light’s

be the velocity source is at rest,

oanf dligcht’sbseotuhreceverleolactiitvyewtohetnhethEealritghh’st’ssusrofuarccee,

c be the light’s velocity
is moving. The around-trip

speed of light is to equal to take  and    in Eq.(7). Due to c  V , we can write Eq.(7) as

c ~ c1  c

1

1 c

V

cos



V2 c2



c1

1 2c

V

cos

 

（8）

and

c ~ c2  c

1

1 c

V

cos



V2 c2



c1

21c V

cos

 

（9）

The average value of two measurements is

c1  c2  c

(10)

2

The measurement of round-trip speed of light cancels out the effect of the Earth's speed and gives a fixed value of c  299792500 100m / s .
3.2 The M-M experiment

The authors have proved that Michelson's calculation on the M-M experiment was wrong (Mei Xiaochun, Yuan Canlun, 2023). He fixed the light source on the cosmic reference frame. However, in the practical experiments, the light source was always fixed on the motion reference frame of the Earth rotating with the Michelson's interferometer, resulting in the failure to explain the zero result of the M-M experiment.

7

The M-M experiment is obviously a round-trip experiment of light, in which the light source is fixed on the interference in the Earth laboratory. Two beams of light are sent from the center point of the spectroscope, travel some distance, are reflected by the mirrors and then return to the center point of the spectroscope in the opposite directions. This is equivalent to measuring the time for light to travel at an average speed. The result is equivalent to that the speed of light is a constant so that no change of interference fringes is founded.
According to the authors' calculations (Mei Xiaochun, Yuan Canlun, 2023), for the observer at rest in
the cosmic absolute reference frame, the Galilean velocity addition rule c  c  V is considered. Here c is the speed of light measured by the Earth observers when the light source is stationary in the Earth lab, c is the light’s speed measured in the cosmic absolute reference frame. If the arm length of the interferometer is l , and the light propagates along the transverse arm of the interferometer, the time in the round-trip of light is t1  2l / c .
When light travels along the longitudinal arm of interferometer, it is calculated that time in the
round-trip of light is t2  2l / c , so we have t1  t2 . When the interferometer is rotated 90 degrees, there is no shift of interference fringe. Although the Earth's motion speed V is taken into account in the
calculation, it does not appear in the final time difference formula, which indicates that the M-M experiment precisely reveals that the round-trip speed of light does not change, and the average speed of
light is c .
The paper also proves that if the Galileo's principle of relativity holds, it is impossible for an observer on the Earth's reference frame to observe the Earth's moving velocity in the cosmic stationary reference frame through the Michelson experiment. Because of the existence of the cosmic absolute reference frame, the relativity principle is also invalid. An observer at rest on the Earth's reference frame should also consider himself moving absolutely in the cosmic absolute reference frame. The calculation result on the cosmic absolute reference frame is also the observation result on the earth reference frame. The M-M experiment on the Earth’s surface is unable to find the shift of interference fringe.
3.3 The speeds of photons radiated by high-energy particles
In the processes that high-energy charged particles traveled at high speeds and slowed down by bombarding the nucleus of medium, leading to Bremsstrahlung radiation (D. Luckey, J. W. Weil, 1952),
electron annihilation (D. Sadch, 1963), and particle  0 decay emitting photons (T. A., Fillippas, J. G. Fox, 1964), the measurements indicated that the speed of  rays were independent of the speed of particles.
It was analyzed that this kind of experiments measured the round-trip speed of light , and did not prove that the one-way speed of light was a constant (Zhang Yuanzhong, 1994). For example, in the Sadch experiment (D. Sadch, 1963) and the T. Alvager’s experiment (T. Alvager, et., 1964), the path of ray and the path of detector device formed a closed loop, and what finally measured was the average speed of photon in the closed loop, and did not prove that the one-way speed of light was invariable.
In addition, we need to understand the mechanism of bremsstrahlung. The essence of bremsstrahlung is that the high-speed electrons in the nuclear electric field are rapidly decelerated by a force of positive charge, resulting in the release of energy. So, the speed of electron at the moment of radiation has actually been greatly reduced and can actually be considered to be moving at a low speed. The superposition of moving electron’s speed can be ignored.
In the same way, when two electrons annihilate and particles decay to produce a ray, the speed of its mass center are very low, otherwise it would be impossible to radiate high-energy photons according to the conservation of energy, so we can ignore the effect of particle’s speed on the speed of ray.
8

3.4 The Cedarholm experiment, the Ciladea experiment and the Mossberg experiment did not measure the speed of light actually
The Cedarhole’s experiment measures the ether drift velocity by measuring the flight of molecular beams in the ammonia cavity (T. Alvager, et., 1958). In the Ciladea’s experiment, two lasers were mounted on opposite sides of a rotating table to measure the drift speed of the ether (R. Cialden, 1972). The Mossbauer’s experiment measured the velocity of the Earth's reference system with respect to the ether by placing ray and ray absorber at the center and the edge of the rotor (D. C. Champeney, P. B. Moon,1961; 1972). The results of these three experiments are close to zero, which proves that the ether drift velocity is negligible.
These experiments do not actually measure the speed of light, but rather the second-order Doppler effect, i.e., the effect of time delay factor of relativity on the frequency of light (Zhang Yunazhong, 1995). The experiments indicated that the second-order effects caused by the Lorentz transformation formula were so small that they could actually be considered non-existent by taking into account the experimental errors.
4. The problems of the visible orbital deformation of binary stars and the charm stars
4.1 The main reason that the visible orbit deformations of binary stars and the charm stars are not observable
The visible orbital deformation of binary star and the charm star are the problem of one-way speed of light. It is proved below that because the angle of calculation is different from the angle of observation, they are not observable and cannot be taken as the evidences that the speed of light is unrelated to the speed of light source.
As shown in Fig.4, assume that the binary stars S1 and S2 move around their center in circle with a speed V . If the speed of light is related to the speed of light source, according to the Galilean speed addition formula, the speed of light emitted from the star S1 is c V , and the speed of light emitted from the star S2 is c V relative to the observer on the x  y plane.
Fig.4 The calculated observing direction and practically observing direction are different resulting in non-observable of orbital shape’s change of binary stars.
9

According to the calculations ( W. de Sitter, 1913; W. Zurhellen, 1914), the orbit of binary star will no longer be a circle but an ellipse to the observer, and an elliptical orbit would be severely deformed. However, the actual observations show that the eccentricity of binary star’s orbit was very small, and the phenomenon that the circular motion becomes the elliptical motion had not been founded, indicating that the speed of light had nothing to do with the speed of binary stars.
The reason why the visual orbit deformation of binary stars cannot be observed is actually very simple,
for it is just a problem of visual angle. For an observer viewed in the direction of the x and y axis, the
speed of light is related to the speeds of binary stars. But what observed in these two directions are only the
side of circular orbit along which stars move up and down along the x or y axis or a straight line. It is
hard for the distant observers to consider them as a binary system, which are ignored in astronomical observations.
In fact, an observer on the Earth would need to place a telescope in the direction of the z axis as
shown in Fig.4 to observe the front side of circular orbits of a binary system. Since the light from the binary
star along the direction of z axis is perpendicular to the directions of moving speed of binary star, there is no speed superposition. The speed of light observed by the earth observer is still c rather than c  V , so
no deformation of binary orbit can be observed.
4.2 The concrete calculation for the charm stars
As for the problem of charm stars in binary orbit, Bergman's “book Introduction to Relativity” simply mentioned that if the speed of light was related to the velocity of light’s source, there would be charm stars. Landsberg's book “Optics” explained this phenomena, but it was not detailed enough. Until 1957, Zhao Daming and Yin Shimin published an paper in Physics Bulletin in Chinese, giving a detailed calculation of charm star problem (Zhao Daming, Yin Shiming, 1957). It is briefly cited below to prove that the calculation of charm star was also based on the observation directions of the x and y axes as shown in Fig.4, and the calculation of visual deformation of binary star orbit is the same.
Fig. 5 The schematic picture of calculating charm star.
As shown in Fig.5, assume that one of binary stars S1 is moving around the center of a circular orbit,
the orbit radius is R , the circular speed is V , the angular speed is  , and the distance between the
circular center O and an observer E is L . The star starts from the point A, and the time it takes to reach
any point B in the circle is  . So, when a star stats from the point A, reaches the point B and then omits a
beam of light, when the light arrives at E, the time it takes is (Zhao Daming, Yin Shiming, 1957)
10

t





L  R cos c V sin





L(1 R cos c(1V sin

/ L) / c)

(11)

Due to V / c  1, Eq.(11) can be approximately written as

t







L c

1



R L

cos



 

1

V c

sin



 







L c

1

R L

cos



V c

sin 



R L

V c

sin



cos

 

(12)

Because the binary stars are far from the observer with R / L  1 and R / L  V / c ，the second and
fourth items in the bracket of Eq.(12) can be ignored, we get

t







L c



LV c2

sin 

(13)

Plotting t and  gave that the multiple different  satisfied an identical t , meaning that when viewed
at E, the lights of multiple stars were observed at different circular points at the same time, and the charm
star appeared. For example, for binary star GeM , L  44.6 light years, V  3.19104 m / s , according to
Eq(13), there were three charm stars. The problem is that what the observers see at the direction of E is only the linear orbits of stars, rather
than the elliptical orbits, so observers may not actually consider them as binary star systems. If observed at
the direction of the z axis, the speed of light emitted by binary stars was still c , not c  V , there were
no charm stars.

4.3 The other explanations

The extinction method of light proposed by Erval and Oseen could also explain why the orbital deformation of binary stars were imperceptible (J. G. Fox, 1962). According to the theory, when the light emitted by a moving light source at a distance in the universe entered the stationary refracting medium, it would be absorbed and re-emitted by the medium, resulting in the erasure of information related to the moving speed of light source, and it is impossible to observe the visual deformation of binary star orbit caused by the moving speed of light source.
Tang Keyun also proposed a method to explain the binary orbit problem (Tang Keyun, 2016). He thought that de sitter's argument for the constant speed of light in the binary star orbits was a mathematical ideal that did not exist in nature. The natural reason for many observed binary stars with quasi-Kepleran orbits was not that the speed of light did not change, but that the binary stars constantly emitted photons. A large number of photons came from the right period and moved toward the telescope at the right speed at any given time, to replace those that were more seriously out of the Kepleran's orbit. This ensured that the binary stars image was always in a quasi-Keplerian orbit during light’s propagation.
So, we can interpret the observation problem of binary orbits in a variety of ways. There is no need to assume that the speed of light is independent of the speed of light’s source.

5 The experiments of one-way light proves that light’s speed is variable

5.1 The time difference experiment of satellite signal transmission between China and

11

Japan is one-way speed of light
As shown in Fig.6, suppose that the reference frame K is at rest and the reference frame K  is moving in a uniform speed V . There are two light’s sources fixed at two points x1 and x2 in K  with a distance l   x2  x1 between them. At time t1 , the light’s source at point x1 emits a beam of light. At time t2 , the light arrives at point x2 . The light’s source at point x2 emits a light at time t2 , and the light arrives at point x1 at time t1 .
According to the principle of relativity, the observer in K  thinks that himself is in stationary state, so the time for the light to spend traveling from x1 to x2 is the same as that the light traveling from x2 to x1 . Let t12  t2  t1 and t21  t1 t2 ，we have t1 2  t2 1  l / c .

Fig. 6 The time difference of two-way light signals.

On the other hand, relative to the observer in K , two light sources are in moving. Suppose that the

coordinates of two light sources are x1 and x2 at arbitrary moment, the distance between them is l  x2  x1 .

Because the propagation direction of light emitted from point x1 is the same as the motion direction of light

source, the time spent for a light traveling from x1 to x2 is

t1 2



l

 Vt1 2 c

or

 t1 2



c

l V

（14）

Because the propagation direction of light emitted from point x2 is opposite to the motion direction of light source, the time taken for a beam of light traveling from x2 to x1 is

t21



l

 Vt21 c

or

t21



c

l V

（15）

Therefore, we have t1 2  t2 1 . That is to say, observed in the stationary reference frame K , the
time taken for two beams of light to reach each other's luminous position is different. Light’s velocity
satisfies the Galileo addition rule c V . However, according to the invariable principle of light’s speed in special relativity, observed in K , light’s speed is still c ，rather than c V . So observed in K , we still have t12  t21 . Thus, in the case
shown in Figure 6, does the time difference exist?
In cooperation with China's Shanxi Astronomical Observatory (CSAO) and Japan's Institute of Integrated Communications Research (CRL), the bidirectional satellite time comparison experiment (TWSTT) was conducted on October 31, 1998 to realize the synchronization of two countries' standard time. Because the signals passed through the same path with the same time, the influence of path factor on time synchronization could be decreased to the maximum loudness.
After several months of testing, the result was that the time difference between two places was 95ns, which was attributed to the Sagnac effect (Li Huanxin, Song Jinan , Li Zhigang, Liang Shuangyou, 2000). In the experiment, the accuracy of TWSTT clock was 0.2~0.2ns, and the measurement accuracy of time difference was 1~2ns.

12

Therefore, it is necessary to discuss the Saganc effect, which is also the focus of this paper, trying to reveal the essence of the Saganc experiment which shows the one way variable speed of light.
5.2 The Sagnac effect experiment in vacuum.
I) The calculation of Newtonian mechanics in stationary reference frame Since Sagnak completed this experiment in 1913, more than 110 years have passed, but special relativity can not really explain it, and it has to be attributed to the general relativistic effect.The textbooks of special relativity did not mention this effect, but it cannot avoid for special relativity. The so-called Sagnac effect actually only changes the linear motion of light in Figure 6 into a loop motion. This loop can be either round, square or any other shape. The original Sagnac effect experiments
were done in air, the refractive index of air to the light is n  1 , and the circuit of light were constructed
with four mirrors, as shown in Figure 7. A half lens A and three mirrors B, C and D were used to form an optical loop. The light was divided into two beams through the half-lens A, and after traveling in opposite directions, it interferes back at A. The whole optical path system rotates continuously, and the change of the interference fringe is observed at the eyepiece.
Fig.7 The original experiment diagram of Sagnac effect In order to compare the calculation method of Newtonian theory with the calculation method of special relativity, we use the hollow circular fiber as the loop of light.
Fig. 8 The calculation diagram of Newton mechanical for the Sagnac effect of hollow fiber loop The Sagnac effect is calculated under the conditions that the speed of light is variable and satisfies the Galilean velocity addition rule, and the speed of light is a constant and satisfies the Lorentz transformation
13

rule, to prove that it is impossible to explain the experiment according based on special relativity.

Figure 8 shows a diagram of Sagnac effect of a circular hollow fiber, which is also the basic schematic
diagram of a fiber optic gyroscope. Let the fiber with radius R is rotated at an angular speed  around the center of the circle, and the tangential speed of rotation is V  R . It's the perimete is l  2 R , the circular area of the fiber is S . A is a light source, A is a device that allows observation of the

interference fringes, which are fixed to the same position in the optical fiber.
At the initial time, when the points A and A of fiber coincides with the point B on the ground

reference frame, two beams of light are emitted from the light source and move in opposite directions. According

to the Galilean velocity addition rule of classical mechanics, when observed on the reference frame of stationary
ground, the propagation speeds of the light are c  c  V respectively. When the fiber rotates one circle and the point A and A coincides with the point B of the ground stationary reference frame again, the times

experienced by the two lights are

t1



c

l V

t2



c

l V

By considering c  V  R ，the time difference is

t

 t2

 t1



2lV c2 V 2



4S c2

（16） （17）

Let L  ct be optical path difference. If the wavelength of light used in the experiment is  , the

number of stripes shift is

N



L 



4S c

（18）

Observed in position A , the optical fiber rotation will produce N interference fringe movement, that is

the Sagnac effect. It can be seen that according to classical physics, there is no problem in explaining the

Sagnac effect. In fact, the Sagnac effect has been used to make laser navigators, which are widely used in

the aerospace industry.

II) The calculation of Newtonian mechanics on the rotating reference frame

By transforming to the optical fiber motion reference frame, assuming that the observer rotates with the optical fiber. According to Newtonian mechanics, acceleration is absolute, rotation is absolute motion, and the observer must think of himself as rotating with the fiber. Just as an observer on the Earth thinks he is moving with the Earth at about 1 meter per second, or with the Earth around the sun at about 30 kilometers per second. So the speed of light traveling in both directions in a hollow fiber is still
c  c  V . When the fiber is rotating, the change of interference fringe is observed on the interference
screen. In fact, because the change of interference fringe is an absolute effect, it will not changed due to the relative motion of observer.

III) The calculation of special relativity on the stationary reference frame

The calculation formula for the Sagnac effect can also be derived from the constant speed of light
according to special relativity shown in Fig.9. Assuming that when the A and A point of the hollow fiber coincides with the point B on the ground reference frame, the light source emits two beam lights in
opposite directions. According to the principle of constant speed of light, the speed of light has nothing to
do with the rotation speed of light source. When the light source and the viewing screen turn more than one
circle and move to the point B , the light propagating counterclockwise also propagates to the point B

14

at moment t1 . There is a relation below

l Vt1  ct1

（19）

Assuming that the light propagating clockwise propagates to the point B at moment t2 , there are also

l Vt2  ct2

（20）

We also obtain Eq.(16). That is to say, we can obtain the calculation formula of Sagnac effect based according to special relativity.

Fig. 9 The calculation diagram of special relativity for the Sagnac effect of hollow fiber loop
However, the derivation of special relativity is wrong due to following four reasons.
1. Fig.9 means that when the light propagating counterclockwise to the point B , the light propagating clockwise also propagates to the point B at the same time，so we have t1  t2 .There is no
time difference, there is no interference fringe change.
2. It can be obtain l / t1  c  c V1 and l / t2  c  c V from Eqs.(19) and (20), which are
the Galilean velocity addition formula. It means that the Galilean velofcity addition formula of Newtonian mechanics is derived from the constant speed of light in special relativity. The result is paradoxical and absurd.
3. According to Fig.9, the initial interference image occurs at the point B . After the fiber rotates one circle, the interference image occurs at the point B . Since the interference image is not observed at the
same spatial point, it is impossible to determine the cause of the interference image. 4. According to the explanation of special relativity, the change of interference fringes is caused by
that the interference screen of the fiber moves to a different position, rather than by the rotating speed of fiber, which is inconsistent with the experimental facts.
Therefore, on the stationary reference frame, the derivation of special relativity for the Sagnac effect does not hold, although the resulting formula is the same as that of Newtonian mechanics, but the physical picture is completely different.
IV) Special relativity can not explain Sagnac effect on the rotating reference frame
According to special relativity, motion is relative. An observer on a rotating reference frame thinks that he is at rest with the fiber, while an observer on the ground is in motion. Since the speed of light does not change, two lights which travel in opposite directions from point A for a circle and return to the point A expends the same time, so there is no Sagnac effect. Therefore, the Sagnac effect cannot be explained by
15

special relativity in the rotating reference frame. General relativity textbooks agree that since the rotating reference frame is non-inertial, special relativity does not apply, so the Sagnac effect needs to be explained by general relativity.
It is shown in Section 5.9 that the Sagnac effect is still not explained by general relativity, so this experiment cannot be explained by either special or general relativity.

5.3 The Sagnac effect in the media of optical fiber

The Sagnac effect in the media of optical fiber is discussed below. When light travels in a solid fiber
with n  1 , the speed of light is c  c / n when the optical fiber is at rest. When the fiber rotates, according to the Galilean velocity addition rule, the speeds of light become c  c / n  V . When the optical fiber rotates one circle and the point A and A coincides with the point B of the stationary

reference frame again, the time experienced by the two lights are

t1



c

/

l n V

t2



c

/

l n V

Due to c / n  V  R , the time difference is

（21）

t

 t2

 t1



c2

2lV / n2 V 2



4n2S c2

（22）

Let L  ct is the difference of light’s path, if light’s wave length is  , the number of fringe shift is

N



L 



4n 2 S c

（23）

Observing at the point A ，N fringe shifts will be found when the optical fiber rotates. This is the Sagnac effect of rotating fiber. It has been used in the manufacture of laser navigation instruments and has been widely used in the aerospace industry.

5.4 The real physical meaning of the Fizeau experiment of flowing water

According to the existing theories, the Fizeau's flowing water experiment indicated the dragging effect of flowing water on the ether (Zhang Yongli,1980). According to the view of this paper, the essence of Fizeau's flowing water experiment is to reveal the influence of the velocity of moving medium on the propagation velocity of light.

S3 A

S1 B

G PC T

D S1

Fig.10 The Fizeau's flowing water experiment

As shown in Fig.10, G is the light source, Si is the reflector, and T is the eyepiece. The pipe is
filled with water, and the arrow indicates the direction of flowing water. The light from the source is
divided into two beams by a spectroscope P , one traveling in the same direction as the flowing water, and

16

the other traveling in the opposite direction of flowing water. Two beams of light traveling the same

distance meet at the eyepiece, creating interference fringes.

As a general understanding, if water is not dragged by the ether, both beams of light travel at the same

speed through water, whether the water is flowing or not. When water changes from a stationary state to a

flowing state, the interference fringes do not move when viewed through an eyepiece. If the ether is

dragged by the flowing water, the result is different.
Assume that the speed of water is V , the drag speed of water pulled by the ether is kV , k is the drag coefficient. When k  1 , it is partial drag. When k  1 , it is full drag. The total length of tubes A  B and C  D is 2l . The refractive index of water is n . The speed of light in water is c / n . When

the propagation direction of light is the same as the direction of flowing water, the time for a beam of light

propagates through the water pipe is

t1



c

/

2l n

kV

（24）

When the propagation direction of light is opposite to the direction of flowing water, the time for light

propagates through the water pipe is

t2



c

/

2l n  kV

（25）

When two lights arrive at the eyepiece, the time difference is

t

 t2

 t1



2l c / n  kV

 2l c / n  kV



c2

4lkV / n2  k 2V 2

（26）

Due to V / c  1 and k  1 , the term k 2V 2 in the denominator of Eq.(26) can be omitted, we get

t



4ln2kV c2

（27）

Let light’s wave length be  , the optical path difference be L  ct , the number of interference fringe’s change is

N



L 



4ln2kV c

（28）

In the Fizeau's original experiment, l  1.5m , V  7m / s ,   5.893107 m , the refractive index of water is n 1.333 . The number of interference fringe’s change was N  0.19 , relative to k  0.46 . Michelson and Morley repeated the experiment after Fizeau, and the result was k  0.434  0.02 . The conclusion was that the ether was partially dragged in the flowing water.
Long before Fizeau made his experiment, Fresnel had considered the action of material to drag the ether and summed that light’s speed in the moving material was (Zhang Yongli,1980).

c



c n

V

1 

1 n2

 

（29）

It corresponds to takes the drag coefficient as

k

1

1 n2

(30)

Einstein’s special relativity denied the existence of the ether. It was thought that light could travel

17

through vacuum. The idea that the ether was dragged by flowing water makes no sense. Eq.(29) can also be

derived by taking c  c / n in the Lorentz velocity transformation formula (Zhang Yongli,1980). Therefore,

the result of Fizeau's flowing water experiment was also considered as the effect of special relativity.

According to the author, the Fizeau's flowing water experiment reveals the influence of medium’s

moving speed on the speed of light, instead of the ether being dragged by the flowing water. When the

medium is at rest, the speed of light moving through the medium is c  c / n . When the medium is moving

at speed V , viewed in the stationary reference frame, the speed of light becomes

c  c  kV n

（31）

Where k is the drag coefficient of common medium. In the following, we use this viewpoint to explain that

the shift of reference fringes in the Sagnac experiment is independent of the refractive index of fiber

medium.

5.5 The interpretation that the Sagnac effect is independent of refractive index of fiber

Suppose the radius of optical fiber ring is R , the length is l  2 R , and the rotational linear speed is

V  R . Considering Eq.(30), when the propagation direction of light is consistent with the rotation

direction of optical fiber, the time taken by the light to move around the optical fiber ring is

t1



c

/

n

l 

kR

（32）

Where k is the drag coefficient of optical fiber. When the propagation direction of light is opposite to the

rotation direction of optical fiber, the time taken by the light to move around the optical fiber ring is

t2



c

/

n

l  k R

Due to c  V and c / n  R(1 k) , the time difference is

（33）

t



t2



t1



c

/

n

l 

kR



c

/

n

l 

kR



2l Rk 

 4Sn2k

(c / n)2  k2 2R2

c2

（34）

If the time difference is unrelated to the refractive index of fiber, let

n2k 1

k



1 n2

（35）

Eq.(30) becomes unrelated to the refractive index of optical fiber with

t



4S c2

N



4S c

（36）

The drag coefficient k of optical fiber shown in (31) is generally different from the Fresnel formula as
shown in Eq.(30).
For the common optical fiber with n  1.4 ~ 1.6 , taking n  1.414 and n2  2 , according to Eq.(35), we have k  0.5 . According to Eq.(30), we also have k  11/ n2  0.5 . Both are almost the
same. This explains that the Sagnac effect is independent of the refractive index of fiber.

5.6 The calculation of special relativity for the Sagnac effect

18

It is proved below that the Sagnac effect of rotating optical fibers can also be calculated by using the Lorentz velocity transformation of special relativity, without considering general relativity. The problem is that the calculation result of special relativity is not the same as that of classical mechanics. Especially in the case of refractive index n  1 , according to special relativity, there is no change of the interference fringes. According to classical mechanics, there is the change of interference fringes.
As previously known, for hollow fibers, the calculation method of special relativity in Fig.9 is wrong. Therefore, for the case of medium fiber, we should use the Lorentz velocity transformation to replace the Galileo velocity addition formula on the basis of Fig.8 to derive the special relativistic calculation formula of the Saganc effect.
When the optical fiber is at rest, the speed that light travels in the optical fiber is c  c / n . When the optical fiber rotates at tangential speed V  R , the speed of light source rotating with the optical fiber is also V relative to the stationary reference frame. According to the Lorentz velocity transformation
formula, observed in a stationary reference frame, the speeds of light propagating in two opposite directions become

c



c V 1 cV /

c2

（37）

When the optical fiber rotates one circle and the points A and A coincides with the point B on
the stationary reference frame again, the time experienced by the two lights are

t



l c



l(1 cV / c2) c V

（38）

t



l c



l(1 cV / c2) c V

The time difference for two lights is

t



t

 t



l

1 cV /

 

c V

c2



1 cV / c V

c2

  

（39）

    2lV 1 c2 / c2 2lVn2 11/ n2





c2 (1V 2 / c2 ) c2 (1V 2n2 / c2 )

（40）

Due to nV  c , we have

  2lVn2 11/ n2

t 

c2



4Sn2 c2

1

1 n2

 

（41）

Eq.(41) is different from Eq.(34) which is deduced from classical method. If the time difference of fiber gyroscope is independent of the refractive index of fiber, we have

n2

1

1 n2

 



1

or

1



1 n2



1 n2

（42）

From Eq.(42), we obtain n  2 .Therefore, according to special relativity, we can still derive the Sagnac
effect of fiber gyroscope. Comparing with Eq.(34) of classical mechanics, the calculation result Eq.(42) of special relativity corresponds to let

19

k



1

1 n2

（43）

That is to say, according to special relativity, the drag coefficient of fiber medium is represent by the
Fresnel formula (30). For the common optical fiber, n  1.4 ~ 1.6 . Taking n  2  1.414 , we have k  k  0.5 . So, the results based on both classical mechanics and special relativity are the same. General relativity is unnecessary. But in general situations, if the refractive index of fiber n  2 , it is possible to
determine whether classical mechanics is correct or special relativity is correct through optical fiber
gyroscope.
We consider the original Sagnac experiment in 1913 carried out in the air with n  1 , the result is
completely different. According to classical mechanics, the Saganc effect exists. According to special
relativity, there is no Sagnac effect. We can then make a decision that the speed of light satisfies the
Galilean additional rule rather than the Lorentz transformation formula.

5.7 The original Sagnac experiment in 1913 was a judgment experiment

As shown in Fig.7, the original Sagnac experiment was carried out in air. The experiment used three mirrors B, C, D and a spectroscope A to form an optical loop. The light is divided into two beams through spectroscope A, travel in opposite directions, and come back to A. The optical path system rotates continuously. The change of interference fringes is observed at the eyepiece
Since the refractive index of air to light is n  1 , substituting it in Eq.(41) according to special relativity, we get t  0 . There is no shifts of interference fringes and has no Sagnac effect after the rotation of the optical path system. But according to classical mechanics, taking n  1 in Eq.(23), we have t  0 . The shifts of interference fringes exists. The result proves that the velocity of light satisfies the
Galilean addition formula, rather than the Lorentz addition formula. The principle of constant speed of light are not valid.
The original Sagnac effect experiment is simpler and the experimental result is very clear. It makes a direct comparison between the Galilean velocity addition rule and the Lorentz velocity transformation rule to get a completely certain result. It directly decides that the speed of light is related to the speed of light’s source, satisfying the Galilean addition rule rather than the Lorentz transformation rule.
5.8 Comparison between M-M experiment and Sagnac effect experiment in air

Both the M-M experiment and the original Sagnac effect experiment were carried out in air. The experimental principles were exactly the same, but the results were completely opposite. In the M-M experiment the shift of interference fringes can be observed, but in the Sagnac effect experiment, it can be observed. These completely opposite results were confusing.
The reason is that the M-M experiment actually measures the time difference of light passing through round-trip path, while the original Sagnac effect measures the time difference of light passing through a one-way path. In the M-M experiment, two beams of light are emitted from the center point of spectroscope, travel some distances, and are reflected by the mirrors, and then return to the center point of spectroscope in the opposite direction. It is equivalent to measure the time when light travels at the average speed. The result is equivalent to that the speed of light is a constant, without producing the change of interference fringes.
In the original Sagnac effect experiment, as shown in Fig.5, both beams of light travel a complete

20

loop, back to the starting point to intervene. Two beams of light traveling in opposite directions are always moving in the same direction of the rotation direction of the optical loop, or always moving in the opposite
direction of optical loop’s rotation until they return to the point A . The mirrors have not reversed the travel
direction of light from the rotation direction of light loop. This is equivalent to the measurement of one-way speed of light, showing that the one-way speed of light is not a constant, related to the rotating speed of fiber loop.
These two opposite examples just show that the so-called constant speed of light is actually the round-trip average speed. The one-way speed of light is not a constant.
5.9 The Michelson-Gale experiment is an amplified Sagnac experiment
In order to measure the rotation speed of the Earth, Michelson and Gale completed an experiment called "The Effect of the Earth’s rotation on the velocity of light" in 1925 (A. A. Michelson, H. G. Gale,1925). The experiment detected the Earth's angular velocity, or the rotation speed of the Earth's surface. It actually indicted that the speed of light is not isotropic on the Earth's surface, or the speed of light is variable. Since this result is contradictory to the M-M experiment and negates special relativity, it has been neglected in current relativity literature and textbooks.
Fig.11 The schematic picture of the M-G experiment. The principle of the M-G experiment is shown in Fig.11. It is basically the same as Fig.7 except there is a small loop marked by ABCD to calibrate the experimental parameters. Because the circuit area of ABCD is very small, the formed interference fringes can be neglected. Light from the source passed the spectroscope and separated into two opposite-direction beams and trivial along AEFD circuit, go back to the starting point of interference and is measured. The length of AFED loop is 2010 feet and the wide is 1113 feet. The light propagated in the pipe. The air in the pipe was pumped out to make the light’s propagation and the interference fringes stable. Obviously, the M-G experiment is an amplification of the Sagnac effect experiment carried out in air. The difference is only that the M-G experiment device is fixed and the changes of light’s speed is through the rotation of the Earth. But the Sagnac experiment changes the speed of light by rotating the instrument itself. Because there is no reverse of light propagation direction, the M-G experiment measures the one-way speed of light instead of the round-trip speed. Due to the superposition of the Earth’s rotation speed, two beams of light traveling in opposite directions at different speeds. Therefore, the M-G experiment is different from the M-M experiment. It is inevitable to detect the rotation speed of the earth. The formula for the calculation of the number of interference fringes in the M-G experiment is basically the same as that for the Sagnac effect (A. A. Michelson, H. G. Gale.1925)
21

N



4S sin c

（44）

Where  was the Earth's rotational angle speed,  was the Earth's latitude. The experiment was o
carried out outside Chicago to took   41036 . The wave length of sodium light was   5700  50 A . According to Eq. (44), the calculation value was N  0.236  0.002. In the experiments, 13 measurements had been made, and the average results were N  0.230  0.05 in good agreement with the theoretical
calculation. Measuring the angular speed of the Earth's rotation was equal to measure the tangential rotation speed
of the earth's surface. As shown in the Sagnac experiment, the speed of light and the rotation speed of the Earth meet the speed addition rule of Galileo.

5.10 Using general relativity cannot explain the Sagnac effect

Since the constant vacuum speed of light in special relativity cannot explain the Sagnac effect, some

people believe that the optical fiber rotating around the center of a circle are not an inertial system, and the special relativity principle does not apply. But the Sagnac effect can still be explained by considering

general relativity.

This is a common practice of special relativity, and when problems arise that cannot be explained,

physicists habitually push them to general relativity. From the above discussion, it can be seen that the

calculation result of special relativity in optical fiber medium is similar to that of classical mechanics,

general relativity is not needed at all.

In fact, general relativity itself has serious problems. If special relativity does not work, general

relativity cannot work too. In view of the importance of the Sagnac effect, we need to discuss this issue

seriously.

To explain the Sagnac effect, the Schwarzschild metric of the spherically symmetric gravitational field

of general relativity is considered. Under the approximate condition  / r 1 , the Schwarzschild metric

can be approximately written as ( Fei Baojun, 2007)

  ds 2  c 2 1   dt 2  1    dr 2  r 2 d 2  r 2 sin  2 d 2

 r

 r

（45）

By introducing the coordinate transformation

t   t r   r        t

（46）

Represented by the rectangular coordinates, they are
t  t x  xcos t  ysin t y  x sin t  y cos t

z  z

（47）

Substituting them in Eq.(45), it becomes the metric of gravitational field of the earth's rotating reference

frame

ds2



c2

1 

 r

(  c2

r)

dt

2



1  

 r

 



2(



r)



drdt



dr2



r2d

2



r2

sin



2d

2

 

（48）

Based on Eq.(48), the time difference shown in Eqs.(16) and (17) can be obtained ( Fei Baojun, 2007) . However, this method has following problems.

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1. It is well known that the method of the M-M experiment is identical in principle to the Saganac experiment. The Michelson interferometer in the M-M experiment is always in rotating, which is actually a non-inertial system. If the explanation of the Saganc effect requires general relativity, the M-M experiment also needs to take general relativity into account. However, according to current theory, the M-M experiments do not need to take general relativistic effects into account. If general relativity is taken into account, it will cause the interpretation of the M-M experiment to fail, so the Sagnac effect does not need to take general relativity into account too.
2. Eqs.(46) and (47) are the Galilean transformations of Newtonian mechanics, not the transformations of special relativity. So, this explanation for the Sagna effect is still Newtonian one, not real relativistic one. Since the Sagnac effect can be naturally induced by the Galilean coordinate transformation, there is no need to do so. Adding the Galilean coordinate transformation of Newtonian mechanics to the Schwarzschild metric to explain the Sagnac effect makes no sense.
3. Eq.(45) is the metric of the equivalent gravitational field of the rotating fiber, that is, the observer considers himself stationary in the gravitational field to observe the effect caused by space bending, rather than observing on the rotating reference frame. The coordinate transformation of Eq.(47), however, transfers the observer to a stationary reference frame in which the circular fiber rotates at an angular speed
 . So it indicates back to the calculation model of special relativity shown in Fig.7, the calculations of
general relativity are completely redundant and meaningless. 4. Because of the spherical symmetry of Eq.(45), two beams of light propagate along the
circumference of a concentric symmetric gravitational field in opposite directions, the gravitational field has the same effect on the speed of two beams of light. When two beams of light travel in opposite directions for a circle and meet again, it must take the same amount of time, not cause the change of interference fringes.
5. The strict solution of the gravitational field equation of a rotating sphere is the Kerr metric (Liu Liao, Zhao Zheng), not the static Schwarzschild metric. The Kerr metric is completely different from Eq. (45) and cannot be used to explain the Sagnac effect.
In short, it is impossible to explain the Sagnac effect according to the Lorentz velocity transformation and the principle of invariable speed of light of special relativity, combined with general relativity. The existence of the Sagnac effect proves that Einstein's principle of invariant speed of light is not valid.
6 Conclusions
So far, physical experiments have only proved that the speed of light is a constant in the round-trip processes, not in one-way processes. This paper makes a distinction between them. It is pointed out that the M-M experiment, the speed measurement of photons emitted by high-energy particles and so on are the round-trip experiment of light’s speed, showing that the average speed of light is a constant.
However, the Sagnac effect experiment, the M-G experiment and the experiment that the satellite signal propagates between China and Japan, are the experiments of one-way speed of light. They indicate that the speed of light is variable, satisfying the Galilean velocity addition rule, rather than the Lorentz transformation ruler.
The change of the binary orbit’s sharp and the phenomenon of charm stars cannot be observed due to that the calculated observation direction are different from the practical observing direction of the earth observers.
23

In this paper, the Sagnac effect is discussed in detail. It is proved that the calculation of the Sagnac effect in vacuum by special relativity and general relativity is wrong. The Saganc effect can not be explained by special relativity and general relativity.
The Fizeau’s following water experiment and the Sagnac effect experiment are connected. It is proved that the rotation of optical fiber medium affects the propagation speed of light. Thus, the problem that the change of interference fringe has nothing to do with the refractive index of optical fiber in the Sagnac effect is explained.
Based on the Lorentz velocity transformation formula, the Sagnac effect formula of fiber gyroscope of special relativity is derived. It is proved that the result derived from special relativity is the same with the result derived from classical mechanics after considering the Fizeau effect of optical fiber rotation when the refractive index of fiber is n  2 .
However, in general case, the calculation results of special relativity are different from those of classical
mechanics. Especially, when n  1 in the air, there is no Sagnac effect according to special relativity, but
there is the Sagnac effect according to classical mechanics. The original Sagnac effect experiment was
carried out in the air with n  1 , which just proved that Lorentz velocity transformation formula was
invalid. The speed of light was related to the speed of light source, satisfying the Galilean speed addition rule, rather than the Lorentz transformation formula.
Finally, by comparing the M-M experiment with the original Sagnac effect experiment in the air, it is pointed out that the round-trip speed of light is involved in the M-M experiment but the one-way speed of light is involved in the Sagnac effect. It perfectly explains why these two experiments have exactly the same principle and the same measurement method, but lead to completely different results. The truth of the so-called constant speed of light in the experiments of special relativity is reveled.
The conclusion of this paper is that all problems of theory and experiment about light’s speed in special relativity can be reasonably explained from the perspective of classical physics. Physics requires neither the Lorentz coordinate transformation nor the Einstein's principle of invariable speed of light.
Acknowledgement：The authors thank Dr. Zhang Chongan, Dr. Liu Zhibo and Dr. Liu Demin for their discussions and assistance in the experiments of invariant round-trip speed of light, the Michelson-Gail experiment and the Sagnac experiment.
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