Real analysis of the famous blunder “Michelson-Morley experiment”

Abstract

This page is an excerpt from the published article in the Journal of Modern and Applied Physics The complete set of proofs for the invalidity of the special theory of relativity

The famous “Michelson-Morley” experiment has been carried out to determine the change in the speed of light due to the motion of the Earth in its orbit around the Sun. Based on the known speed of the Earth (approximately 30 km/s), Michelson has expected that the displacement of the interference fringes will be different at night and during the day (when the directions of the “ether headwind”, caused by the movement of the Earth in its orbit around the Sun, are opposite), … and will correspond to the calculations made. However, the result has been unexpected – no displacement was observed at all. The problem has two reasons.
The first reason is that the speed of light in vacuum depends on the intensity of the gravitational field. The speed of electromagnetic radiation in vacuum is constant in regions with uniform intensity of the gravitational field (like “near the Earth’s surface). However, it is different in regions with different intensities of the gravitational field, which was proven by the experiments. The intensity of the gravitational field near the Earth’s surface is dominated by the mass of the Earth and remains the same at any point in the Earth’s orbit. Therefore, the speed of electromagnetic radiation (of the light) in vacuum remains a local constant in the time-spatial domain “near the Earth’s surface” during the travel of the Earth around the Sun, during the travel of the Sun’s system in the Galaxy… and during the travel through the warped space of the Universe. However, the measured speed of electromagnetic radiation (of the light) in the frame of reference related to the Earth’s surface differs from the speed of light in vacuum because of the rotation of the Earth around its axis. It means that the speed of light is not the same in all inertial frames of reference. This fact is proven by all the experiments related to the behavior of the speed of light, but cannot be ascertained by experiments using Michelson’s type interferometer.
That is why, the second reason for the unexpected result of the Michelson-Morley experiment is the inappropriate conceptual design, embedded in the construction of the interferometer used. The difference in the speed of light between the two light beams, traveling in two opposite directions on the same arm, is completely compensated if the “two-way light beam interferometer” is used. That is why, the existing difference in the speed of light due to the rotation of the Earth around its axis in the direction “East-West” and “West-East” (in the reference system related to the Earth’s surface), cannot be ascertained. However, that difference is observed in the experiments analyzed above – the experiments “One-way measurement of the speed of light”, and the experiment “Michelson-Gale-Pearson.

Content:

3. The First Michelson’s Experiment

4. The well-known “renowned” Michelson-Morley Experiment

5. Discussion

6. Conclusion

1. Introduction

The theories of light at that time

Historically, in the seventeenth century, two rival theories of the nature of light were proposed – the wave theory and the corpuscular theory.

The Dutch astronomer Huygens proposed the wave theory of light – the first mathematical theory of light. The known mechanical waves propagate through a material medium (solid, liquid, or gas) at a wave speed that depends on the elastic and inertial properties of that medium. The propagation of mechanical waves is the propagation of vibrations of matter particles belonging to a material propagation medium; vibrations (oscillations) of any material particle of the propagation medium around a stationary point in the frame of reference related to the propagation medium of the mechanical wave. The propagating of the mechanical wave is the propagating of vibrations to the adjacent particles. Two basic types of wave motion for mechanical waves are known: transverse waves and longitudinal waves. For Huygens, the light is a longitudinal wave (like sound waves in air) and propagates through a medium called “ether”, or “aether”. The ether must fill all the space and be weightless and invisible (in fact, as the space itself).

In 1690 Newton proposed the corpuscular theory of light. For him, the light was emitted from a source in small particles, propagating radially from the source, and this view was accepted for over a hundred years.

The quantum theory put forward by Max Planck in 1900 combined the wave theory and the particle theory and showed that light can sometimes behave like a particle and sometimes like a wave.

After the development of Maxwell’s theory of electromagnetism, the questions about the speed of light and what medium supports the transmission of electromagnetic waves arose again. For James Clerk Maxwell and other scientists of that time, the answer was based on the supposition of Christiaan Huygens that light travels in a hypothetical medium called “luminiferous aether” – the space-filling substance thought to be necessary as a transmission medium for the spreading of the electromagnetic radiation.

However, the “luminiferous aether” turns out to be the space itself. In the published article in the Journal of Modern and Applied Physics “Dark matter”, “Dark energy”, and other problems in physics today” is substantiated that the “empty of matter space” (the vacuum) is actually compressed energy (“energy soup”). The electromagnetic radiation (the light) is a stream of tiny particles of energy (quanta) that propagate in this “energy soup” radially from the emitting source.

Vectors, scalars, vector projection, and scalar projection (reminding)

Vector (Euclidean vector), in physics, is a quantity that has both magnitude (size, length) and direction. It is represented as an arrow, whose length is proportional to the quantity’s magnitude. However, the vector has no position. It means that the vector is not altered if it moves parallel to itself.

Scalar is a quantity that has a magnitude but not a direction, as the speed of light in vacuum.

For example, velocity and acceleration (with magnitude and direction) are vector quantities, while speed (the magnitude of velocity), time, temperature, length, and mass are scalars. In English, in physics, the term “velocity” often is used, when we mean the vector with its direction; and the term “speed” is used, when we mean only the scalar magnitude of the vector.

Vector projection of a vector “A” on (or onto) а coordinate axis, or on a nonzero vector “B” (also known as the vector component or vector resolution of “A” in the direction of “B”) is the orthogonal projection of “A” on a straight line parallel to “B”. It is a vector parallel to “B”.

Scalar projection of a vector on a coordinate axis (with direction), or on another nonzero vector, is a scalar, equal to the length of the orthogonal projection of the vector on the axis, and with a negative sign if the projection has an opposite direction with respect to the axis (or vector) direction. In Cartesian coordinates, the components of the vector are the scalar projections on the coordinate axes.

In other words, some of the scalars in physics have two directions, that correspond to the signs “plus” and “minus”, while a vector can have infinite directions. The scalar projection of the vector on another vector can be recorded as

, where θ is the angle between the two vectors.

Note: In order to be more precise, we will use the term “velocity”, when we mean the vector (with its direction); and we will use the term “speed”, when we mean the scalar magnitude |V| of the vector.

2. About the theories of light and the velocity of light. Experiments – expectations and results

The Earth rotates around its axis, moves in its orbit around the Sun, and together with the Solar System moves around the center of our Milky Way galaxy.

The expectations of the scientists at the end of the 19th century.

The expectations of scientists have been that if the hypothesis of the “stationary ether” is correct, the velocity vector of the created “ether wind” at Earth’s motion, at any time, must be equal to the sum (vector addition) but in the opposite direction of the following three vectors:

(1) The velocity vector of motion of the entire Solar System as it whirls around the center of our Galaxy at approximately 220 km/s (if we measure the speed by means of the units of time and length defined on the Earth’s surface); plus

(2) The velocity vector of the Earth’s motion in orbit around the Sun (which is approximately 30 km/s); plus

(3) The vector of the linear velocity of the Earth’s surface at the location of the experiment (due to the Earth’s rotation around its axis). The linear speed of the Earth’s surface at any point on the equatorial line is approximately 0.46 km/s, but it is equal to zero at the points at the intersection of the axis of rotation with the Earth’s surface, which coincide with the northern and southern geographic poles.

Fig. 7.1 below is an illustration of the expected “ether wind” that occurs during the motion of the Earth through a hypothetical medium called luminiferous ether. The figure depicts the Sun, the Earth, and the Earth’s orbit. The three types of dotted lines depict the three components of the supposed “ether wind”, which have opposite directions to the aforementioned three vectors. The figure does not correspond to the scale (the radius of the Sun is approximately 109 times larger than the radius of the Earth, and the difference between the velocities of movement of the Earth and of the Solar System is much greater).

The expectations of scientists have been that the “ether wind” will affect the velocity of a light beam (increase or decrease the speed of light):

•  On the one hand, if the experiment is carried out at a fixed location on the surface of the rotating Earth, then the part of the vector “ether wind” created by the motion of the Earth in its orbit around the Sun should have to vary in magnitude and direction over time (e.g. at night and during the day).

•  On the other hand, the experimenter can point the light beam in different directions. Thus, the effect of the generalized ether wind vector (vector addition) on the speed of the light beam was expected to be different. In this way, the “ether wind” will have a different effect on the speed of the light beam since the scalar projection of the generalized vector “ether wind” on the trajectory of the light beam will be different.

We can call the vector projection of the velocity vector “ether wind” onto the vector of the light beam velocity – “ether headwind” (see below Fig. 7.2).

Therefore, according to expectations, the resulting speed of light would be different, depending on the direction of the light beam, and would be different at night and during the day when the direction of the “ether headwind”, caused by the movement of the Earth in its orbit around the Sun, is opposite. The difference in the speed of light for different seasons of the year (at various points of the trajectory of the Earth in its orbit around the Sun), was expected to be an indication of the velocity of motion of the Solar System in the stationary luminiferous ether.

Therefore, if the hypothesis of the existence of the “stationary ether” is true, the “ether wind” created by the Earth’s motion through the stationary ether should increase or decrease the speed of the light beam (depending on the direction and magnitude of the “ether headwind”).

But now let us reveal the “defect” of the fatal for the physics of the 20th century Michelson-Morley experiment, whose erroneous explanation of the result (that the speed of light is constant for all reference frameworks) continues to be supported by modern physics.

3. First Michelson’s Experiment

Albert Michelson designed an experimental construction, later known as the Michelson interferometer, (see Fig. 7.4 below), and made his first experiment in 1881 in order 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”.

The Michelson interferometer

The experimental construction of the interferometer designed by Michelson, illustrated below in Fig. 7.3, uses two-way light beam propagation (in the straight direction and in the opposite direction/the reflected beam) in exactly the same path.

The interferometer consists of a monochromatic light source (with an accurate frequency), a semi-silvered mirror separating the monochromatic light beam from the source along the two mutually perpendicular arms, two mirrors (A and B) reflecting the coherent light beams in opposite directions, and a detector depicting the interference fringes after reuniting the two light beams. All apparatuses are horizontal (i.e. at the same gravitational potential.

According to Michelson, if the “stationary luminiferous ether” exists, the motion of the Earth through the ether would result in an effect of the “ether wind” on the speed of the light beam. Above, we have called the projection of the three-component vector sum “ether wind” on the direction of the light beam “ether headwind” (see Fig. 7.2).

Michelson’s expectations.

According to Michelson, if the “stationary luminiferous ether” exists, the motion of the Earth through the ether would result in an effect of the “ether wind” on the speed of a light beam. Above, we have called the projection of the three-component vector sum “ether wind” in the direction of the light beam: “ether headwind” (see Fig. 7.2).

In other words, Michelson expected the speed of the light beam to be different:

•  First, depending on the direction of the arms on which the light beams spread;

•  Second, the speed of the light beam (in the case of a fixed direction in relation to the Earth’s surface) was expected to be different at night and during the day when the direction of the “ether headwind” caused by the Earth’s motion in its orbit around the Sun was opposite to the direction of the fixed light beam (see below Fig. 7.4).

On this basis, Michelson performed his first experiment in 1881 with an interferometer constructed by him (Fig. 7.4). Michelson used a monochromatic light beam split (for the two coherent light beams to be perfectly the same) on two arms in two mutually perpendicular directions. The two light beams propagate along two mutually perpendicular arms, and each beam is reflected in the opposite direction by a mirror. After reuniting the two reflected beams at the place of splitting, Michelson expected to ascertain the following:

The displacement of interference lines which is consistent with the expected difference in the speeds of the two light beams, caused by the “ether wind” due to the movement of the Earth in its orbit around the Sun.

Subsequently, the construction of the “Michelson-Morley” experiment was improved; the light beams are reflected repeatedly, but the same idea is used again – the usage of two coherent light beams in two directions, from the splitter of the monochromatic beam to the mirrors and backward. The fact that the same beam is used in opposite directions (one reflected) on the same arm, means that each of them travels exactly the same distance – from the monochromatic beam splitter to the mirror (the straight beam), and back (the reflected beam). This, however, means that if the speeds of the two opposite light beams, moving in opposite directions is changed by the “ether wind”, the change will be opposite, and the difference will be completely compensated because the paths of the two beams (the straight and the reflected) are perfectly the same! This is the reason why the difference in the speeds of the light beams on each of the arms caused by the rotation of the Earth on its axis cannot be observed!

Thus, on the basis of the speed of the Earth in its orbit around the Sun, which is approximately 30 km/s, the expectation of Michelson was that the displacement of the interference fringes (the bright or dark bands caused by beams of light that are in phase or out of phase relative to each other) will be different at night and during the day and will correspond to the calculations made. However, the speed of light in vacuum (the speed of light in the frame of reference related to the stationary space) always remains unchanged (constant) because the intensity of the gravitational field on the Earth’s surface remains constant during the travel of the Earth in its orbit around the Sun and during the travel of the Solar System in the Galaxy! That is the reason that the difference in the speed of light that can be registered is only that, which is caused by the rotation of the Earth around its axis (as a consequence of the linear velocity of the movement of the surface of the Earth in the stationary space).

The yellow arrows show (Fig. 7.4) the direction of motion of the Earth’s surface, where the interferometer is located. According to the presented image, the direction of motion of the Earth’s surface during the day is in the direction of the hypothetical “ether wind”, and at night – opposite to the “ether wind” direction. The figure depicts a glimpse of the trajectory at which the Earth moves clockwise.

Note: The experiments were carried out at short intervals of time (the “Michelson-Morley experiment” was carried out from July 8 to July 12). This means that the Earth was located approximately in the same place on its trajectory around the Sun. That is why the difference in the speed of light due to the “ether wind” at different points in the Earth’s trajectory around the Sun (which is an indication of the velocity of motion of the Solar System in the Milky Way with approximately 220 km/s – see Fig. 7.1), was not calculated by Michelson..

As stated, the predicted change in the direction of the “ether wind” during the day and at night in relation to the fixed arms of the interferometer to the Earth’s surface, should have led to different changes in the speeds of the two light beams, which should have been registered as different displacements of the interference fringes. Using a wavelength of approximately 600 nm, Michelson expected that there would have been a displacement of the interfering fringes, for which he made accurate calculations. The expected difference in the displacement of interference fringes during the day and at night was sought in different directions between the two perpendicular arms of the interferometer.

However, the expected displacement of the interference bands was not ascertained.

The results reported by Michelson:

“The small displacements -0.004 and -0.015 are simply errors of experiment.” (Michelson, 1881).

Michelson’s conclusion was as follows:

“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).

4. The well-known “renowned” Michelson-Morley Experiment

The famous Michelson–Morley experiment was performed in 1887. In collaboration with Edward Morley, Albert Michelson, constructed a new improved interferometer. As in the first experiment, the improved interferometer used two-way paths of two light beams on two perpendicular arms. However, by using multiple mirrors, the light path length of the two light beams was approximately 10 times longer. The light was repeatedly reflected back and forth along the arms of the interferometer, increasing the total light path length of each beam to 11 m. Thus, according to the intention, there was more than enough accuracy to detect the ether-hypothetical effect of the Earth’s motion. At a path length of 11 m, the expected displacement should have been approximately 0.4 of the distance between the fringes. To eliminate thermal and vibration effects, Michelson and Morley’s interferometric apparatus was assembled on the top of a large block of sandstone, approximately a foot thick, which was then floated in a pool of mercury.

The results.

The results of the experiment were entirely unexpected and inexplicable; again, the effect of the motion of the Earth around the Sun through the hypothetical ether on the speed of light was practically zero at any time of day or night at all times of the year at different points in the Earth’s orbit. The reported results were given by Michelson:

“It seems fair to conclude that if there is any displacement due to the relative motion of the earth and the luminiferous ether, this cannot be much greater than 0.01 of the distance between the fringes.” (Michelson & Morley, 1887).

Although the experiments were repeated many times with even greater precision, they produced the same negative results.

5. Discussion

As grounded above, the speed of light in vacuum is a local constant and depends on the intensity of the gravitational field in the time-spatial domain. The speed of light in vacuum “on the surface of the Earth” is determined by the Earth’s gravity and remains constant in the motion of the Earth in its orbit around the Sun and with the Solar system in the galaxy, because the intensity of the gravitational field near the Earth’s surface is constant and is determined above all by the mass of the Earth.

However, the measured speed of light in different frames of reference is different in the local region “near the Earth’s surface”. In the one-way measurement of the speed of light between two points at the same latitude:

•  the measured speed of light in the “West to East” direction in the reference system related to the Earth’s surface is (c-V);

•  the measured speed of light in the “East to West” direction in the reference system related to the Earth’s surface is (c+V);

, where c is the local constant “speed of light in vacuum, and V is the linear velocity of the Earth’s surface at the respective latitude.

The proofs presented above in the analyses of the “One-way measurement of the speed of light” and “Michelson-Gale-Pearson”, clearly ascertain the effect of the Earth’s rotation around its axis on the speed of light, measured on the Earth’s surface. The measurements of Marmet in 2000 and of Kelly in 2005 also indisputably ascertained the difference in the measured speed of light in the frame of reference related to the moving Earth’s surface in the stationary space. These examples demonstrate the validity of the Galilean transformation (which is an undisputable fact in our local physical reality).

However, in the “Michelson–Morley” experiment, no effect on the speed of light was found as a result of the Earth’s rotation around its axis. The reason lies in the inappropriate conceptual design embedded in the construction of the interferometer. When the “two-way measurement of the speed of light” is used, the average speed of the two light beams is measured, propagating in two exactly opposite directions on exactly the same path. Therefore, the change in the speeds of the two light beams in the two opposite directions, for each arm of the interferometer is completely compensated! If the resultant speed of the light beam in the direction “from the semi-silvered mirror to the reflecting mirror (either mirror A or mirror B)” is (c+V), then the speed of the light beam in the opposite direction will be exactly (c-V), where c is the speed of light in vacuum and V is the scalar projection of the linear velocity of Earth’s surface on the arm of the interferometer (i.e. on the direction of light beam propagation). The path of the light beam in both directions for each arm is absolutely equal and the direction and the length of the arm are irrelevant, because, at any value of V, the differences in the speeds will be completely compensated for each other. Thus, the resulting average speed (measured for the two directions of the light beam in any arm) will always be equal to the constant speed of light in vacuum on the Earth’s surface:

This means that the interference fringes will never be displaced, because the average speed of each light beam in both directions of any arm will always be exactly equal to c (the speed of light in vacuum) – regardless of the length of the arm, regardless of the arm’s direction!

Therefore, in the “one-way measurement of light speed experiments” and the “Michelson-Gail-Pearson experiment”, the change in the speed of light as a result of the Earth’s rotation in the reference system related to the surface of the Earth can be registered. However, when Michelson’s type interferometer is used (“interferometer using two-way propagation of light beams on exactly the same path”) – this is impossible!
The above mentioned conclusion is given in the paper (Sharlanov, 2016):

“Actually, if an “ether wind” (caused by the motion of the earth through the stationary luminiferous ether) even exists – the difference in the speed of light between the two light beams, traveling in two opposite directions on the same arm, is completely compensated. This is true for any arm in any direction! In other words, if the projection of the velocity of the “ether wind” in the direction of one of the light beams is (+V), then the projection of the velocity of the “ether wind” in the direction of the reflected light beam (traveling in opposite), will be exactly (-V).” (Sharlanov, 2016).

Therefore, the poorly designed “Michelson–Morley experiment” can be classified as an enormous fallacy, given what it means to physics “more than a hundred years of delusion”.

Over the past 100 years, many variants of the Michelson-Morley experiment have been carried out by many scientists from different famous universities and institutes of relativity and cosmology, with increasing sophistication and increasing accuracy. However, the result cannot be other – the difference in the speeds of light between the two light beams, traveling in two opposite directions on the same arm, is completely compensated if the construction of an “interferometer using two-way propagation of light beams” is used.

An example of this continuing and nowadays delusion is also a publication in “Physical Review Letters” and reported in “Physics World” (the membership magazine of the Institute of Physics, one of the largest physical societies in the world) – “Michelson-Morley experiment is best yet” accessed in September 2009:  https://physicsworld.com/a/michelson-morley-experiment-is-best-yet/.

6. Conclusion

The “Michelson-Morley experiment” is actually the primary root cause of the great delusion that “the speed of light is the same in all inertial frames of reference”, which is the core of the special theory of relativity published in 1905 by Albert Einstein.

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” was applied and actually reveals the essence of the special theory of relativity!

Moreover, to be complete the set of proofs of the invalidity of the special theory of relativity, the factual analyses of the three types of so-called “fundamental tests of the special theory of relativity” are presented too (see the link).