This webpage is a part of the published article **“The Complete Set of Proofs for the Invalidity of the Special Theory of Relativity” **in the **Journal of Modern and Applied Physics**.

**Abstract**

The Michelson-Gale-Pearson experiment is analyzed below. The given theoretical explanation of the experiment is in accordance with the classical mechanics and the theory of relativity of Galileo, which are lawful valid in our time-spatial domain “near the Earth’s surface” with a uniform, constant intensity of the gravitational field. It is shown that the equation that Michelson proves by means of this experiment (which, in the words of Michelson, is *“deduced on the hypothesis of a fixed ether”*), has been deduced based on classical mechanics and the Galilean relativity. The speed of light in vacuum (in relation to the stationary space) is constant on the surface of the Earth because the intensity of the gravitational field is practically uniform and constant. **The result of the analysis is, however, that the experiment proves that the measured velocity of light is actually different in different directions in the frame of reference related to the Earth’s surface** (as demonstrated in the analysis of the abovementioned experiments “One-way measurement of the speed of light”). However, the question remains – why Michelson did not wish to make this conclusion…

**Content of the webpage**:

**1. Introduction**

**2. Description of the used “ring-interferometer”**

**3. Results presented to the scientific community**

**5. Conclusion**

The expectation of the influence of Earth’s rotation on the velocity of light was based on the* hypothesis of a stationary ether*. According to this hypothesis, there is an invisible substance filling the space that was believed to be the necessary medium for the propagation of electromagnetic radiation (of light). Initially, the hypothesis of the stationary ether was tested on the expected change in the speed of light when the Earth moves in its orbit around the Sun. With the experiments of Michelson in the 1881 year (Michelson, 1881), and later with the experiment “Michelson-Morley”, such a change in the speed of light was not registered (Michelson & Morley, 1887). At the time, the conclusion of Michelson was:

*“The interpretation of these results is that there is no displacement of the interference bands… The result of the hypothesis of a stationary ether is thus shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous.” *(Michelson, 1881)*.*

The obvious reality is:

**1) **The medium of propagation of electromagnetic radiation) in the Universe is actually the space itself – *the space warped by matter*. The speed of light propagation in the “empty space” depends on “the energy density of the space”, and this density depends on the intensity of the gravitational field. Electromagnetic radiation is the propagation of quanta (tiny energy packets) in the medium of propagation, which turns out to be a “compressed energy” (energy soup), as was proven in the published article in the **Journal of Modern and Applied Physics** ** “Dark matter”, “Dark energy”, and other problems in physics today**“,

Not only in the 19th century but in the 21st century, it is still not realized that **the Earth does not move so simply through the space**:

**All celestial bodies (as well the Earth), are traveling through the space-time of the Universe together with the distortion (contraction) of the stationary space, warped by the body itself.**

This means that the intensity of the gravitational field on the surface of the celestial body is always constant because is dominated by the mass of the celestial body itself (e.g. Earth). This means that the speed of electromagnetic radiation in vacuum which depends on the intensity of the gravitational field is always constant on the surface of the celestial body (the Earth).

**Therefore, that is the reason why there is no variation in “the speed of light in vacuum” when the Earth moves in orbit around the Sun and together with the Solar System in the Galaxy.**

However, the speed of light in vacuum is different in regions with different intensities of the gravitational field:

The speed of light in vacuum * (c= ν.λ)* is lower in regions with stronger gravitation (near the Sun), and this fact was experimentally proven as early as 1964 by the American astronomer Irvin Shapiro (Shapiro time-delay), and was confirmed again highly accurately, using controlled transponders aboard space probes “Mariner-6” and “Mariner-7” when they were in orbit around the planet Mars.

The fact that the *speed of light in vacuum* increases in regions with weaker intensity of the gravitational field (near the border of the Solar system) is the explanation and proof of the “inexplicable” anomalies in the accelerations of the space probes “Pioneer 10”, “Pioneer 11”, “Galileo”, and “Ulysses”, which, in fact, experimentally prove the presented logic:

*“the expected travel time of the communicational electromagnetic signals between the spacecraft and the Earth (based on the universal constancy of the speed of electromagnetic radiation in vacuum everywhere in the Universe), turns out to be much greater than the real travel time. Therefore, we register backward attraction (acceleration anomaly) of the space probe to the Sun” *[Sharlanov, 2011].

**2) **Newton’s law of universal gravitation states that in the Universe, any particle or body with a mass m_{1} attracts any other particle or body (with a mass m_{2}) with a force that is directly proportional to the product of their masses (m_{1} and m_{2}), and inversely proportional to the square of the distance between their centers (r), where G is the gravitational constant:

The “empty space” does not have mass. Therefore, from Newton’s law of universal gravitation, it becomes clear that **the “empty space” is stationary **– that the vacuum is stationary.

This is undeniable because the “empty space” is without mass, and therefore gravitational forces do not attract it (the space does not rotate together with the Earth’s surface – only material bodies and molecules in the atmosphere are involved in the rotation).

The celestial bodies rotate into the surrounded stationary space and the measured speed of light in the frame of reference related to the Earth’s surface differs in directions “East-to-West” and “West-to-East” from the speed of light in vacuum and the difference is equal to the linear speed of the Earth’s surface at the latitude where the experiment is carried out.

**In a local time-spatial region** with a uniform intensity of the gravitational field, the measured velocity of light in the different reference systems is different and obeys (it is subject to) the classical mechanics and the theory of relativity of Galileo.

The experiment “Michelson-Gale-Pearson” was carried out in the local time-spatial region “*near the surface of the Earth*”, in the frame of reference related to the moving Earth’s surface. The experiment was designed to test *whether the speed of light is influenced by the Earth’s rotation*.

In this page, the reader will make sure that the result of the presented theoretical explanation of the experiment “Michelson-Gale-Pearson”, **based on the classical mechanics and** **the theory of relativity of Galileo,** **completely coincides** with the experimental result reported by Michelson and Gale. In fact, **the analysis of the experiment shows that the speed of light is not the same in all inertial frames of reference **(the * Effect of the Earth’s Rotation on the Velocity of Light *was proven)!

The idea for this test was originally given by Michelson (Michelson, 1904). According to Michelson, the experiment was undertaken at the urgent instance of Dr. L. Silberstein. In the first part of the article *“The Effect of the Earth’s Rotation on the Velocity of Light, I.”,* we can read:

*“In the Philosophical Magazine, (6) 8, 716, 1904, a plan was proposed for testing the effect of the earth’s rotation on the velocity of light.” *(Michelson, 1925).

**2.**** ****Description of the used “ring-interferometer”. Results presented to the scientific community**

**Description of the experiment.** The “Michelson-Gale-Pearson experiment” (see below *Fig. 6.1*) uses a very large rectangular ring interferometer (a perimeter of 1.9 kilometers – 612.648m x 339.24m).

The experiment was carried out in the Northern Hemisphere at а latitude (41° 46′).

A beam of light was split in half and the two beams were sent in opposite directions in an evacuated tube (vacuum conditions). Mirrors located in each corner of the rectangle reflected the two beams. When the two beams were reunited, they were out of phase. This means that the two beams did not arrive at the same time, although they passed exactly the same path in the frame of reference related to the Earth’s surface. Therefore, the light beams travel at different speeds in the frame of reference related to the Earth’s surface, and as we will see, the interference fringes displacement corresponds to the calculated theoretical value depending on the linear speed of the Earth’s surface at the latitude of the northern and southern sides of the rectangular contour… i.e., **this displacement corresponds to the theoretical value calculated according to classical mechanics and Galilean relativity**.

The theoretical rationale and the description of the experiment were presented by Michelson and Gale in two articles “*The Effect of the Earth’s Rotation on the Velocity of Light” (part I and part II)*, published in 1925 in *Astrophysical Journal *‒ (Michelson, 1925); (Michelson & Gale, 1925).

*“The expression for the difference in path between two interfering pencils, one of which travels in a clockwise, and other in a counterclockwise direction, may be deduced on the hypothesis of a fixed ether as follows”:“If l1 is the length of path at latitude Φ1 and l2 that at latitude Φ2, ν1 and ν2 the corresponding linear velocities of the earth’s rotation, and V the velocity of light, the difference in time required for the two pencils to return to the starting-point will be”:*

. *(Michelson, 1925).*

In the same article, from equation (16), Michelson deduced the formula (17) for the difference in phase of the two light beams, when returning to the starting point:

The task that Michelson actually defines, is experimentally to verify the validity of formula (17), where ** Δ **is the displacement of the fringes;

**is the area of the rectangular around which the light travels,**

lh **is the Earth’s angular velocity,**

*ω***the effective wavelength of the light employed, and**

*λ***is the speed of light in vacuum**

*V*As reported by Michelson:

*“Air was exhausted from a twelve-inch pipe line laid on the surface of the ground in the form of a rectangle 2010×1113 feet. Light from a carbon arc was divided at one corner by a thinly coated mirror into direct and reflected beams, which were reflected around the rectangle by mirrors and corners. The two beams returning to the original mirror produced interference fringes.” *(Michelson & Gale, 1925).

The experiment is similar to that of Georges Sagnac (see the analysis). The difference is that the moving frame of reference is not the spinning disk in the stationary space, but is the moving Earth’s surface in the stationary space. The source of light, the detector, and the mirrors move eastward in stationary space with linear speed at the respective local latitudes for the northern and southern sides of the rectangular contour.

The “Michelson-Gale-Pearson experiment” was carried out accurately – the precision of the experiment is undeniable:

*“The displacement of the fringes due to the earth’s rotation was measured on many different days, with complete readjustments of the mirrors, with the reflected image sometimes on the right and sometimes on the left of the transmitted image, and by different observers.” (Michelson & Gale, 1925).*

The experiment, as reported by Michelson in the second part of the article, is successful; the obtained equation (18) as a result of the experiment coincides with the theoretically deduced equation (17) in the first part of the article (Michelson, 1925) :

*“The calculated value of the displacement on the assumption of a stationary ether, as well as in accordance with relativity (Galilean!) is: *

**The immediate result of the experiment is that the effect of the Earth’s rotation on the velocity of light was confirmed!**

We can see that the reported conclusion – that the established by the experiment “calculated value” is in accordance with *“the displacement on the assumption of a stationary ether”.* However, this does not correspond to the conclusion of Michelson in 1881 (45 years earlier), that *“the result of the hypothesis of a stationary ether is thus shown to be incorrect and the necessary conclusion follows that the hypothesis is erroneous”*.

As we know, in 1881 and in 1887, Michelson attempted to determine the change in the speed of light due to the motion of the Earth in its orbit around the Sun through the “stationary ether”. These experiments are discussed in the next subpage, where the reason for this conclusion by Michelson in 1881 was presented. The explanation of all “unexpected” and “inexplicable” results of the most famous experiments related to the behavior and measurement of the speed of light is based on classical mechanics, on the theory of relativity of Galileo, and the *“Model of the physical reality in the Universe”* presented in part II of this book.

**But now let us consider the explanation of the “Michelson-Gale-Pearson experiment”, which is based on classical mechanics and Galilean relativity**:

**4.**** ****Explanation of the results of the experiment in conforming to classical mechanics and Galilean relativity **

*This subsection presents a theoretical explanation of the experimental results in accordance with classical mechanics and Galilean relativity, which are in force, (valid) in the time-spatial domain with a uniform intensity of the gravitational field (*

**“on the surface of the Earth”).**Let us examine in detail the movement of the two light beams (Fig. 6.1), taking into account that the two sides of the rectangular ring interferometer (AB and CD) are parallel to the equator. All the parts of the pipeline (with mirrors) move at linear speed corresponding to the corresponding latitudes (of the southern pipeline and northern pipeline) according to their location. Since the experiment was carried out in the Northern Hemisphere, then the linear velocity in the stationary space of mirrors A and B (located on the southern side of the rectangle) is greater than the linear velocity in the stationary space of mirrors C and D (located on the northern side).

We will examine the experiment with respect to the two reference systems: within the frame of reference related to the space itself *(Earth-Centered Inertial (ECI)* *coordinate system)*, and within *the frame of reference related to the Earth’s surface*. As was shown in *Fig. 6.1*, beam “1” travels in a clockwise direction, and beam “2” travels in a counterclockwise direction.

**4.1. Examination of the experiment in the reference system related to the stationary space (in the stationary “Earth-centered inertial system”).**

For an observer, positioned in the stationary space (in the “Earth-centered inertial (ECI) frame of reference”), each point on the Earth’s surface moves at the linear velocity corresponding to the latitude where the point is located (for a point closer to the equator, its linear speed is higher). In “ECI-frame of reference”, the measured speed of light in all directions is equal to the *“speed of light in vacuum”* and is a constant because the gravitational field intensity in the local region “in the vicinity of the Earth’s surface” is constant. However, in this frame of reference, the paths that the two beams pass (in the stationary space), are different. This is because the path in the stationary space that the two beams pass between the mirrors will be different because the mirror to which the two beams travel will move away (or approach) during the time of travel of the respective beam between the mirrors that are parallel to the equator. Moreover, the movement of the mirrors in the stationary space, which are located in the southern and northern pipes, occurs at different linear speeds.

As was mentioned, the *linear speed *of mirrors A and B in the southern pipe (closer to the equator), is greater than the *linear* *speed* of mirrors С and D in the northern pipe. It means that the path in the stationary space of light beam **2**, propagating to the East in the southern pipe, will be longer than the path of light beam **1**, propagating to the East in the northern pipe (mirror B moves faster than mirror C). Respectively, the path of light beam **1**, propagating to the West in the southern pipe will be shorter than the path of light beam **2** propagating to the West in the northern pipe (mirror A moves/ approaches faster than does mirror D).

Let us denote the path lengths of the beam paths “1” and “2” in the stationary space (in the ECI-frame of reference). According to *Figure 6.1*, (and in accordance with the direction of propagation), the path lengths of the beams “1” and “2” on the side **AB** are **|BA| _{1}** and

**|AB|**

_{2}respectively, and the path lengths of the beams “1” and “2” on the side

**CD**are

**|DC|**and

_{1}**|CD|**respectively. Therefore, due to the difference in latitude of the sides

_{2}**АВ**and

**CD**(the linear speed of mirror A and mirror B located on the south side are greater than the linear speed of mirror C and mirror D located on the north side), for the path of the two light beams in the stationary space (in the ECI-frame of reference) in direction West to East, we can write

, and for the westward travel-path of the light beams, we can write:

Therefore, the path traveled in the stationary space by the light beam “2” (which travels in a counterclockwise direction) is longer than the traveled path covered by the light beam “1” (which travels in a clockwise direction):

As a result, the two light beams are out of phase when they return to point A. The resulting phase difference will be greater, not only when the sides AB and CD are longer. When the sides AD and BC are longer, the difference between the linear speeds is greater due to the greater latitudinal difference. Therefore, the phase difference will increase when the area of the rectangle is larger (like in the Sagnac ring interferometer).

**4.2. Examination of the experiment in the frame of reference related to the Earth’s surface** **that moves/rotates in the surrounding stationary space**

Michelson (the observer/ experimenter), actually made his measurement in the frame of reference related to the Earth’s surface. The two light beams are moving in opposite directions, but travel the same total travel-path in this frame of reference. This is because the pipelines and the mirrors are stationary in this frame of reference (they are fixed on the Earth’s surface); therefore, the distances between them do not change.

However, if the observer measures the speed of light in the frame of reference related to the Earth’s surface, they will register different speeds of the light beams in the directions “from East to West” and “from West to East” (as in the experiments titled “One-way measurement of the speed of light” – see *the relevant subpage*). Moreover, the difference in the speeds of the light beams will be greater on the southern side in comparison with this difference on the northern side, due to the greater linear speed of the Earth’s surface at the southern side. As a result, the two light beams are out of phase when they return to point A.

**Let us, according to the abovementioned reasoning, make a calculation ****(according to classical mechanics)**** for the difference between the travel time of the two beams ****in the reference system related to the surface of the Earth:**

If * c* is the

*speed of light in vacuum*(the local physical constant in our

**local**time-spatial domain);

*is the northern pipeline length (latitude*

**l**_{1}*), where the linear speed of the Earth’s surface is*

**∅**_{1}*; and*

**v**_{1}*is the southern pipeline length (latitude*

**l**_{2}*), where the linear speed of the Earth’s surface is*

**∅**_{2}*, then,*

**v**_{2}*in the frame of reference related to Earth’s surface*:

*1) According to Galilean relativity: the measured speed of light in the northern pipe, in the “East to West” direction will be (c+v*

_{1}

, and that in the “West to East”

) *direction*will be**(c-v**_{1}

**)**;*2) According to Galilean relativity: the measured speed of light in the southern pipe in the “East to West” direction will be (c+v*

_{2}

**)**, and that in the “West to East”*direction*will be**(c-v**_{2}

**)**;Therefore, the time necessary for the light beam “1” (moving in the clockwise direction), to travel through the northern pipe is * l_{1}/(c-v_{1});* on the southern side, it is

*, and the total time for the two sides is:*

**l**_{2}**/(c+v**_{2}**)**The time necessary for the “2” light beam (moving in the counterclockwise direction) to travel through the northern pipe is * l_{1}/(c+v_{1})*, the time needed for the “2” light beam to travel through the southern pipe is

*, and the total time for the two sides is:*

**l**_{2}**/(c-v**_{2}**)**If we ignore the small difference between the travel-times of the two beams on side BC and on side AD (in the directions “South to Nord” and “Nord to South”), the total time-difference between the two light beams will be:

… i.e., in the frame of reference related to the Earth’s surface (where the experiment was carried out):

The equation (24), obtained from the given real explanation of the experiment (based on the classical mechanics and the relativity of Galileo), is the same as the equation (16) from the article by Michelson, which, according to him is *“deduced on the hypothesis of a fixed ether”*. (Michelson, 1925).

**5. Conclusion**

We can conclude from equation (16), mentioned in the first Michelson’s article (Michelson, 1925), which, according to his words, is *“deduced on the hypothesis of a fixed ether”*:

1. That equation (16) was derived based on classical mechanics and Galilean Relativity.

2. That the equation (16) is derived *in the frame of reference related to the Earth’s surface *(where the experimenter was located and the experiment was carried out);

3. That in our time-spatial region of constant gravity, *“the speed of the light in vacuum is constant”* is used, which is actually the speed of the light in the reference system related to the stationary space (in this case – related to the

*“Earth-Centered Inertial (ECI) coordinate system”*).

Let us track the chronology:

**1) **In his first article *“The Effect of the Earth’s Rotation on the Velocity of Light, I”* (Michelson, 1925), Michelson showed that equation (17) follows directly from equation (16). However, Michelson did not show that equation (16) is deduced on the basis of classical mechanics and Galilean relativity. He only mentioned that *“the expression for the difference in the path between the two interference pencils”*, which is the equation (16), *“may be deduced on the hypothesis of a fixed ether”*.

**2)** In the second article, it is reported that

**3) The equation **(24) that was derived in the analysis, is the time difference for reaching the starting point of the two light beams (the difference between equation (22) and equation (23)). We have seen that equation (24), which is derived in the previous subsection, based on classical mechanics and Galilean relativity,

**(16), whose derivation Michelson does not show, but mentions that**

*is exactly the same as equation**“may be deduced on the hypothesis of a fixed ether”*.

**Therefore, the “Michelson-Gale-Pearson experiment” proves the validity of our theoretical** **explanation, which was done on the basis of classical mechanics and** **Galilean relativity! **

In fact, if we look at the formulas (22) and (23), they show that, in the frame of reference related to the Earth’s surface, ** the speed of light in different directions is different** (as in the experiments

*“one-way determination of the speed of light”*). Therefore, the question can be asked:

*Why does Michelson not mention that when deriving the theoretical formulas (16) and (17), he used the fact that in relation to the Earth’s surface (in the frame of reference related to the Earth’s surface) – the measured speed of light in “West to East” direction is (V-v), and in “East to West” direction is (V+v), where V is the speed of light in vacuum, and v is the linear velocity of the Earth’s surface? This would mean that:*

**The speed of light is not the same for all inertial frames of reference!**

In fact, the result of the *“Michelson-Gale-Pearson experiment”* undeniably proves this fact!

The reason for this “failure to mention” by Michelson in 1925, is (perhaps) that he did not want to enter into conflict with the proponents of the special theory of relativity, because:

**The Nobel Prize in Physics 1907** was awarded to Albert A. Michelson

“for his optical precision instruments and the spectroscopic and metrological investigations carried out with their aid”. (Nobelprize.org)

In fact, Michelson has earned this award for
his great contribution to science. Actually, it is not his conclusion that *“the speed of light is the same in all
inertial frames of reference”* …

But let us now analyze in the next subpage the well-known *“Michelson-Morley experiment”*. The inappropriate design (to achieve the intended purpose), is the reason for the accepted (supported so far) erroneous hypothesis: *that the speed of light is the same, from the point of view of any inertial reference system that moves in an arbitrary direction and at any speed in the stationary space*. The task of the experiment was to determine *the change in the speed of light due to the motion of the Earth in its orbit around the Sun through the “stationary luminiferous ether”.* Such a dependency does not really exist, because the speed of light in vacuum depends only on the intensity of the gravitational field, and it is constant in regions with a uniform intensity of the gravitational field – i.e. **the speed of light in a vacuum **remains constant at the surface of the Earth as it moves around the Sun. **However**, there is a difference in the speed of light (in the frame of reference related to the Earth’s surface), *due to the Earth’s rotation around its axis* *in the stationary space*, but with the Michelson’s type interferometer‒ this difference cannot be ascertained (see the following “Analysis of the famous blunder “Michelson-Morley experiment”)! In fact, the inappropriate conceptual design of the construction of this interferometer is the reason for the accepted (up to now) erroneous hypothesis, that:

**“the speed of light is the same in any inertial system moving in an arbitrary direction and at an arbitrary speed in the stationary space anywhere in the Universe”**

If you haven’t read the analysis of “One-way measurement of the speed of light” yet, it is worth reading it here!

If you haven’t read the analysis of the “Sagnac experiment” yet, it is worth reading it here!

Revealing the fact that the inappropriate conceptual design, embedded in the construction of the Michelson interferometer, however indisputably shows here, that the claim *“the speed of light is the same in all inertial frames of reference”* is a great delusion and the *“Michelson-Morley experiment”* is actually ** the primary root cause for the biggest blunder in physics of the 20th century – the special theory of relativity**.

Furthermore, the analysis of the article *“On the Electrodynamics of Moving Bodies”*, where Einstein published the special theory of relativity, shows **exactly where and how** the claim *“the speed of light is the same in all inertial frames of reference”* was applied …

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