# Analysis of the “Sagnac experiment”

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

This is an analysis of the “Sagnac experiment” conducted by the French physicist Georges Sanyac in 1912. The analysis presented is based on classical mechanics and Galilean relativity, which are indisputably valid in our local time-spatial region “on the surface of the Earth”. The experiment demonstrates that in relation to a moving system in stationary space, the speed of the light differs depending on the speed and the direction of movement of the system in the stationary space. However, the Sagnac experiment is considered a paradox, because it demonstrates that the speed of light is not the same for all frames of reference – which is not convenient for modern physics because the special theory of relativity is created on the basis of the claim “the speed of light is the same for all frames of reference”. As further proof of the authenticity of the presented analysis, the derivation of the equation, which is often used in rotation analyses is shown.

Content of the website:

1. Explanation of the experiment in accordance with
classical mechanics and Galilean relativity

1.1. Examination of the Sagnac experiment in the reference system related to the surrounding stationary space – in the “Disk-Centered Inertial coordinate system”

1.2. Examination of the Sagnac experiment in the frame of reference related to the spinning disk

2.1. Analysis of one rotation cycle of the light beam “1” that travels in the direction of the disc rotation

2.3. The results

3. Conclusion

Georges Sagnac, a French physicist, constructed a device “ring interferometer” (rotating interferometer with two light beams on a closed loop), also called the “Sagnac interferometer”. The interferometer consists of a light source, collimator (transforming light or other radiation from a point source into a parallel beam), beam-splitter (splitting the beam in two directions), photographic plate, and 4 mirrors of the interferometer, which are all mounted on a spinning disc (0.5m in diameter). In this way, they are all stationary with respect to the disc, but they are actually spinning in the stationary empty space – in the reference system related to the space itself. (Fig. 5.1).

Description of the experiment: A monochromatic light beam is split and the resulting two beams follow (reflected by the four mirrors) exactly the same path in the reference system related to the spinning disk. The trajectories of the two beams, however, are in opposite directions, which is actually the brilliant idea of the experiment of Georges Sagnac. The two recombined light beams (unified again after one full cycle), are then focused on a photographic plate, creating a fringe pattern (a series of bright and dark bands, caused by beams of light that are in phase or out of phase with one another), permitting high-accuracy measurement of the interference fringe displacement, as Georges Sagnac described in his article titled “On the proof of the reality of the luminiferous aether by the experiment with a rotating interferometer” (Sagnac, 1913).

The idea is to demonstrate the different speeds of the two light beams in the frame of reference related to the spinning disk. In this frame of reference, the speed of the beam, moving in the direction of rotation of the disk decreases, and the speed of the other beam, moving in the opposite direction of rotation of the disk increases when the speed of the disk rotation increases. The experiment demonstrated that the picture of the interference fringes (the bright or dark bands caused by the beams of light that are in phase or out of phase relative to each other) changes when the speed of rotation of the disk changes.

The results of the experiment are precisely fixed.

The observed effect: is that the displacement of the interference fringes (the bright and dark bands), changes with the change in the speed of the disk rotation.

The reported result by George Sagnac is as follows:

“The result of these measurements shows that, in ambient space, light propagates with a velocity V0, independent of the collective motion of the source of light O and the optical system. This property of space experimentally characterizes the luminiferous aether. The interferometer measures, according to the expression (according to the presented equation), the relative circulation of the luminiferous aether in the closed circuit.” (Sagnac, 1913).

It is understandable that the result of the experiment was explained a century ago by the relative circulation of the luminiferous aether in a closed circuit. According to the supposition of Christiaan Huygens (Dutch physicist), light travels in a hypothetical medium called “luminiferous aether”, a space-filling substance, thought to be necessary as a transmission medium for the propagation of electromagnetic radiation.

In fact, the conclusion is not that the space has a property that characterizes the “luminiferous aether”, but rather that:

“the “ether” turns out to be the “warped space-time of the Universe” itself.” (Sharlanov, 2011).

1. Explanation of the experiment in accordance with
classical mechanics and Galilean relativity

The Earth rotates in the surrounding stationary space with a constant angular velocity. The linear speed of the Earth’s surface, at the latitude where the experiment was carried out, is constant. The plate (the table on which the rotating disk is mounted), is fixed stationary on the Earth’s surface. Therefore, the influence of the Earth’s rotation on the speeds of the two light beams (the displacement of the interference fringes due to the Earth’s rotation), is constant.

Note: The displacement of interference fringes due to the Earth’s rotation around its axis was discussed in the analysis of the “Michelson–Gale–Pearson experiment”.

According to the experiment, however, the light source, the collimator (transforming the light beam from a point source into a parallel beam), the beam-splitter (splitting the beam in two opposite directions), the photographic plate, and the four mirrors mounted on the disk rotate all together in the stationary space at the speed of the disk. As a result, the different rotational velocities of the disc create different displacements of the interference fringes due to the influence of the disc velocity on the speeds of light beams in the frame of reference related to the spinning disk

The two frames of reference, which we are considering in the theoretical explanation of the experiment, are:

1) The first one is related to the rotating disk, where the light source, the collimator, the beam-splitter, the photographic plate, and the four mirrors are mounted.

When the observer is on the disk, all devices (the collimator, the beam splitter, the photographic plate, and the four mirrors) mounted on the disk are stationary for the observer (regardless of whether the disc is spinning or not).

2) The second one is related to the stationary space itself.

Appropriate for the explanation of the experiment is, to consider it in a “Disk-Centered Inertial coordinate system” (DCI frame).

The description of the “DCI frame of reference is as follows:

• The origin of the “DCI coordinate system” is the center of the disk. If we ignore the displacement of the interference fringes due to the Earth’s rotation (which is constant, regardless of the disk rotation), we actually accept that the origin of the “DCI coordinate system” (the center of the disk, which is a fixed point on the Earth’s surface), is stationary in relation to the surrounding space. Similarly, the North and South poles are stationary in the stationary space when the Earth rotates around its axis.

This means that the “Disk-Centered Inertial coordinate system” (DCI frame), for the present case, can be considered as a stationary frame of reference in relation to the surrounding stationary space. In other words, the observer situated in the DCI frame will see how the light source, the collimator, the beam splitter, the photographic plate, and the four mirrors of the interferometer rotate together with the disc.

Before the examination of the experiment, we can recall that every mechanical or optical experiment actually takes place in the common space of the considered frames of reference.

1.1. Examination of Sagnac experiment in the reference system related to the surrounding stationary space – in the “Disk-Centered Inertial coordinate system” (DCI frame of reference)”

In our time-spatial region “in the vicinity of the Earth’s surface”, the intensity of the gravitational field is uniform (the same). According to the abovementioned initial conditions of the experiments (which do not contradict the standpoint of contemporary physics): electromagnetic radiation propagates in vacuum (i.e. in the stationary space), at a constant speed equal to c. This speed is actually the speed of light in the stationary in relation to the space “DCI frame of reference.

However, everything mounted on the spinning disc rotates (moves) in the stationary space (which means: in relation to the “DCI frame of reference”). Therefore, in this frame of reference, the length of the path that the two light beams actually travel in space is different.

This is due to the movement of each mirror in the stationary space (at the rotation of the disk) during the travel of the light beams toward the mirrors.

The two light beams travel in opposite directions. Thus, the path length in the stationary space of one of the light beams (which travels in the opposite direction of the disk rotation) is shortened, and the path length in the stationary space of the other light beam (which travels in the direction of the disk rotation) is extended. As a result of the change in the path lengths of the two light beams (due to different velocities of the disk rotation), different displacements of the interference fringes are created.

Therefore, the conclusion of the observer, located in the stationary in relation to the space “DCI coordinate system” (where the speed of light is constant and equal to c), is that the displacement of the interference fringes is due to the change in the path lengths traveled by the two light beams, which in turn depends on the velocity of the disk rotation.

1.2. Examination of the Sagnac experiment in the frame of reference related to the spinning disk

Positioned on the spinning disk, the observer will see that all devices (the collimator, the beam splitter, the photographic plate, and the four mirrors) mounted on the disk do not move – that they are stationary. Therefore, the path lengths of the two beams (the distances between the mirrors) also do not change when the disk spins. As a result, the speeds of the two light beams in the frame of reference related to the spinning disk are different. This difference depends on the velocity of the disk rotation: the speed of the beam that travels in the direction of the disk rotation decreases to (c-V), where V is the linear speeds of the mirrors, while the speed of the other light beam, which travels opposite to the direction of the disk rotation, increases to (c+V). In fact, the “light speed anisotropy” observed in the Sagnac experiment is similar to the “light speed anisotropy” in the “One-way determination of the speed light” experiments (see the described cases “Eastward Transmission” and the “Westward Transmission”).

Therefore, the conclusion made by the observer positioned in the frame of reference related to the spinning disk is that the displacement of the interference fringes is due to the difference in the speeds between the two light beams. In turn, that difference (respectively the displacement of the interference fringes) changes with the change in the velocity of the disk rotation.

Finally, we can underline that as early as 1913, the Sagnac experiment actually proved that “the speed of light is not the same in relation to all frames of reference”. This was even before the publication of the general theory of relativity. Is it not surprising that Einstein never commented on this experiment, although certainly knew about its existence?

The Sagnac experiment is unofficially considered mystical because thus far, none of its explanations have been officially accepted. Although the Sagnac experiment proves that the speed of light is not the same in all inertial reference frames, many modern physics journals publish “scientific” explanations based on the special theory of relativity… which is based on the false claim that “the speed of light is the same in all inertial frames”. In other words, this is a classical “circular reference”! An example of a published “scientific” comparison of different explanations is that of Malykin, G.B. “The Sagnac effect: correct and incorrect explanations” (Malykin, 2000). There are other such examples in the scientific literature.

Despite all of these mystifications, although there is currently no valid scientific explanation for this phenomenon, the results of these experiments have many significant practical applications. A wide range of applications is found in space navigation, aviation (optical gyroscope), and daily Earth positioning needs, where no one has observed any “anisotropy” of the “meter” as a unit of measurement (which is a claim of the special theory of relativity).

Additional proof of the credibility of the abovementioned explanation of the Sagnac experiment is given in the next subsection. This theoretical explanation demonstrates the derivation and origin of the most commonly used equation in rotational analyses.

2. Derivation of the equation, which is often used in rotation analyses

The Sagnac effect manifests itself in a setup called a ring interferometer. It is the basis of the widely used high-sensitivity fiber-optic gyroscope that fixes changes in the spatial orientation of an object (airplane, satellite).

In general, a fiber-optic gyroscope consists of a rotating coil with a number of optical fiber turns.

Optical fibers are flexible, transparent fibers made of glass (silica) or plastic. It consists of two separate parts. The middle part of the fiber is called the core and is the fiber optic medium through which the light travels. Another layer of glass called the cladding wraps around the outside of the core. The cladding’s task is to keep the light beams inside the core. This can be done because the cladding is made of a different type of glass relative to the core; the cladding has a lower refractive index and acts as a countless small mirror. Each tiny particle of light (photon) propagates down the optical fiber by bouncing repeatedly off the cladding, as though the cladding is truly a mirror (the photon reflects in repeatedly). This phenomenon is called total internal reflection, which causes the fiber to act as a waveguide.

We will examine a simple ring interferometer (a coil with only one fiberoptic turn) mounted on a rotating disk with an angular velocity ω radian/sec (see Fig. 5.2).

Two laser beams propagate in the rotating coil: one in the direction of the coil rotation, and the other in the opposite direction of the coil rotation. When the angular velocity of the rotating coil changes at the turning of the object where it is mounted, the displacement of the interference fringes also changes.

The effect (the displacement of the fringes) is dependent on the effective area of the closed optical path. However, this is not simply the geometric area of the loop, but is enhanced by the number of turns in the coil. The equation that we derive on the basis of the aforementioned theoretical explanation of the Sagnac experiment is often used in analyses of rotation:

, where A is the area of the circle bounded by the fiber-optic coil. The optical circuit (the “fiber-optic medium”), mounted on the rotating disc rotates along with the rotation of the disc at a linear speed equal to Rω, where R is the radius of the optical circuit and ω is the angular velocity of the rotating disk. The speed of light in the stationary “empty space” between the atoms is c0 (inside the “fiber-optic medium” where the speed of light is constant for the homogeneous optical medium).

As shown, the two light beams (beam 1 and beam 2) travel in opposite directions in the same fiber optic circle. Let us analyze one cycle of each of the two beams (from the moment of splitting to the moment of directing them to the screen-detector)

Here, two factors must be considered:

•  The first is that the “empty space” inside the optical fiber(the optical medium) is stationary, although each atom ofthe optical fiber moves during rotation. Since the “empty space” has no mass, no force can accelerate the space (to set it in motion). This is a consequence of Newton’s second law of motion (F = ma). Neither the strength of the chemical bonds between atoms (in the micro-world) nor the gravitational forces (according to Newton’s law of universal gravitation in the macro-world) can force the space to move, because the space has no mass.

• The second is that at the microscopic level, the cladding of the optical fiber can be seen as a continuous series of millions of miniature mirrors in which the photons are reflected as they propagate (in the case of Sagnac’sexperiment, there are only four mirrors).

Like in Sagnac’s interferometer, each of these “elementary mirrors” shifts at a definite angle from the previous photon reflection when the optical coil is rotated – (the mirrors are moved at a certain distance during the propagation time of the photons in the stationary “micro-space” of the optical medium). Thus, in the stationary space, the path of the photons (of the light beam), moving in the direction of rotation of the optical coil is extended, and the path of the light beam, moving opposite to the rotation of the optical coil, is shortened.

2.1. Analysis of one rotation cycle of the light beam “1” that travels in the direction of the disc rotation

In the stationary (in relation to the surrounding space) Disk-Centered Inertial (DCI) coordinate frame:

After splitting, light beam “1” makes one full cycle in the direction of disk rotation, and reaches the beam-splitter again after time interval t1 to redirect to the display (screen). For the stationary in the space observer (located in the DCI-coordinate system), the distance traveled by beam “1” in the stationary space inside the optical medium is longer than the fiber optic coil circumference (2πR) with (Δ = Rωt1). This is because, during the beam travel, the point of redirection to the detector (screen), as well as the entire optical loop, moves at a distance Δ, due to disk rotation. Therefore, the distance traveled by light beam “1” in the stationary surrounding space is (2πR + Rωt1); thus for the time interval t1, (the time for one turn of the light beam “1”), the observer in the “DCI frame of reference”) records the following:

, where c0 is the speed of light inside the “fiber-optic medium” (where the speed of light is constant for the homogeneous optical medium).

•  In the frame of reference related to the rotating disk, where the fiber-optic coil is mounted:

For the observer, positioned in this frame of reference (on the rotating disk), the distance traveled by the light beam “1” is 2πR, because the fiber-optic coil does not move in this frame of reference (in relation to the rotating disc). For the same time interval t1, the speed of light beam “1” is equal to (c0 – Rω), and for the time interval t1 , (the time for one turn of the light beam “1”), the observer (in the frame of reference related to the rotating disk) will register:

, which is actually equal to t1 from the expression (10) after its transformation for deriving t1, i.e., there is no “relativistic difference in time”.

2.2. Analysis of one rotation cycle of the light beam “2”, which travels in the opposite direction to the disk rotation

•  In the stationary (in relation to the surrounding space) Disk-Centered Inertial (DCI) coordinate frame:

After splitting, the light beam “2” makes one full cycle in the opposite direction to the disk rotation and reaches the beam splitter again after the time interval t2 , to be redirected to the display (screen). Actually, the distance, traveled by beam”2” in the stationary space inside the optical fiber, is shorter than the fiber optic coil circumference (2πR) with (Δ = Rωt2). This is because, for the travel time of the beam for one cycle, the redirection point to the detector (as well as the whole optical coil) has approached, due to the rotation of the disk against the direction of movement of the beam. Therefore, the distance traveled by the light beam “2” in the stationary space (in the “DCI coordinate frame”), is (2πR – Rωt2). The Observer, in the stationary in relation to the surrounding stationary space “Disk-Centered Inertial (DCI) coordinate frame”, will register for the travel time t2 (for one turn of the light beam “2”)

, where c0 is the speed of light in the “fiber optic medium” (where the speed of light for the homogeneous optical medium is constant).

•  In the frame of reference related to the rotating disk:

For the observer, positioned in this frame of reference (on the rotating disk), the distance traveled by the light beam “2” is exactly 2πR because the fiber-optic coil does not move in relation to the rotating disc (in the observer’s frame of reference). For the same time interval t2 , the speed of light beam “2” is equal to (c0 + Rω); for the travel time for one cycle of light beam “2”, the observer in the frame of reference related to the rotating disk will register:

, which is actually equal to t2 from the expression (12) after its transformation for deriving t2 , i.e., there is no “relativistic difference in time”.

2.3. The results

On the basis of the analysis, it was found that:

1. The time t2 for one complete tour of light beam “2” is the same for both frames of reference;
2. The time t1 for one complete tour of light beam “1” is the same for both frames of reference.
3. However, the time for one complete tour of light beam “1”(which moves in the direction of the rotation of the optical coil) is more than the time for one complete tour of light beam “2” (which moves in the opposite direction of the rotation of the optical coil).

The difference between the travel times of the two beams “1” and “2” actually determines the displacement of the interference fringes, which changes with the change in the velocity of the disk rotation.
For the difference between the time for one tour of light beam “1” and the time for one tour of light beam “2”, we obtain (after subtracting equation (13) from 11):

, because

Equation (14) is actually the equation (9) we had to derive.

Therefore, the demonstrated derivation of the equation, which is often used in rotation analyses, verifies the validity of the theoretical explanation of the Sagnac experiment (in accordance with classical mechanics and Galilean relativity!

5.3. Conclusion

The moving reference system in the stationary space in the Sagnac experiment is the “spinning disc”. The moving reference system in the stationary space in “One-way measurement of the speed of light” and “Michelson-Gale-Pearson” experiments is the “rotating Earth’s surface”.

The observed effects of displacement of the interference fringes in the case of “Sagnac’s ring interferometer”, the “Michelson–Gale–Pearson experiment”, and “light speed anisotropy” (the difference in the speed depending on the direction of the light beam in the case of “One-way determination of the speed of light”) clearly demonstrated the following:

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

The speed of light in vacuum is constant in our time-spatial domain “near the Earth’s surface”, where the gravitational field intensity is constant. The speed of light is different, however, in a frame of reference that moves in the stationary space. The measured speed of the light in a moving frame of reference differs depending on the speed and the direction of motion of the frame of reference in the stationary space!

The main reason, for the accepted by modern physics false claim, that “the speed of light is the same for all inertial frames of reference” turns out to be the “Michelson-Morley experiment”, which “results” are a consequence only of the inappropriate conceptual design of the two-way-interferometer of Michelson.

The delusion, that “the speed of light is the same for all inertial frames of reference”, is the fundament of the special theory of relativity. The analysis of the article “On the Electrodynamics of Moving Bodies” shows exactly where and how the claim “the speed of light is the same for all inertial frames of reference” illogically was applied – and actually reveals the essence of the special theory of relativity!

Before examining the inappropriate conceptual design, embedded in the interferometer construction, used in the experiment “Michelson-Morley” (held in 1887), we will analyze the experiment “Michelson-Gale-Pearson” (held in 1925). The experiment “Michelson-Gale-Pearson” proves again that, in the reference system related to the moving Earth’s surface, the measured speed of light is influenced by the rotation of the Earth (by the movement of the Earth’s surface) – that the speed of light is not the same for all frames of reference.

=> to the parent webpage

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 analyses of the “Michelson-Gale-Pearson” experiment yet, it is worth reading it here!

The revealing fact that the inappropriate conceptual design, embedded in the construction of Michelson’s interferometer, however indisputably shows 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…