michelson morley experiment questions

In 1887, Albert A. Michelson and Edward W. Morley tried to measure the speed of the ether . The concept of the ether was made in analogy with other types of media in which different types of waves are able to propagate; sound waves can, for example, propagate in air or other materials. The result of the Michelson-Morley experiment was that the speed of the Earth through the ether (or the speed of the ether wind) was zero. Therefore, this experiment also showed that there is no need for any ether at all, and it appeared that the speed of light in vacuum was independent of the speed of the observer! Michelson and Morley repeated their experiment many times up until 1929, but always with the same results and conclusions. Michelson won the Nobel Prize in Physics in 1907.

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• Michelson Morley Experiment

Waves of Light and Sound

Physics is the science of every physical phenomenon we come across in our daily life. From the very beginning, we have learnt about the light and sound that we experience easily. Scientists through various experiments and observations have established the fact that light and sound are electromagnetic waves that travel in waves. Sound waves require a medium to travel while light waves do not need any medium. It can move as effectively as in air as well as in gasses. You must all be familiar with the waves that we see on the water surface when a stone or any object is thrown into it.

At the end of the 19th century, some scientists were curious to know and hypothesised that light, as a transmitting wave, requires a medium as well to travel and it can't travel in a vaccum They suggested the presence of a very special matter called aether in outer space with some distinct characteristics that don't create any drag force against any object moving through it, be it a physical object or light. Since then various experiments have been conducted by many scientists to prove this fact but no one has ever succeeded.

The Experiment of Michelson Morley

Michelson Morley was the pioneer in this field of study. His prediction was based on the fact that sound and light being similar kinds of waves travel at different speeds. He strongly believed that the light waves also travel at different speeds in ether relative to that in a vacuum. And any medium having a density will change the direction of light passing through it due to the phenomenon of refraction. He had also developed an interferometer to experiment on the arriving light beams and prove his theory.

What is the Michelson Morley Experiment?

Sound waves require some medium through which these waves can travel. Maxwell in 1864 showed that light is an electromagnetic wave and hence was supposed that there is an ether that propagates light rays. By observing how light propagates through the ether, one can determine an absolute reference frame. Hence, the Michelson Morley experiment was accomplished to detect ether that was assumed to be the carrier of light waves. The purpose of the Michelson and Morley experiment was to detect the velocity of the Earth to ether. The procedure was based on the optical device named interferometer that compares the path lengths for light rays travelling in perpendicular directions.  

Describe Michelson Morley Experiment

According to Michelson’s experiment theory, the light should travel at different speeds through ether. The speed at which light moves depends on the relative motion through space. Michelson Morley designed an interferometer to spot minute differences in the arrival time of light beams. Out of all these beams, one can take a long time to reach the sensor while travelling through ether.  

The experiment compared the speed of light to notice the relative motion of Earth through ether. However, the conclusion of the Michelson Morley experiment comes out to be negative. It means that they found no difference between the speed of light while travelling through ether. Michelson Morley interferometer sent white light for the actual observations and yellow light from a sodium flame through a half-transparent mirror. The mirror was used to split the coming light beam into two separate beams travelling perpendicular to each other. After leaving this mirror, beams moved out to the long arms end where they faced back reflection into the middle. These two beams then recombine to produce a pattern of constructive and destructive interference. 

The Procedure of Michelson Morley Experiment

Michelson claimed that if the speed of light was constant concerning the ether medium through which the Earth moves, then that motion can be detected. It can be sensed by comparing the speed of light perpendicular to and in the direction of the Earth’s motion. The details of Michelson experiment set-up are:

The beam of light gets incident to a half-silvered glass plate. This plate acts as a beam splitter, which splits the light beam into two coherent beams. One beam transmits, and the other reflects. The beam transmitted strikes the mirror, say, M 1 , and gets reflected. The beam reflected strikes the mirror, say, M 2 , which again gets reflected. The returned beams reach the telescope, which is used for interference patterns produced by these two rays. 

The separation between the plate and two mirrors is the same, which refers to the arm’s length. The light reflected from two mirrors interfere with the mirror. 

Now, from the Michelson Morley experiment notes, it can be noticed that the apparatus and light both are moving in the same direction. Thus, the relative velocity will be c - v. After reflection, the apparatus, and light both move in the opposite direction. Hence, in this case, relative velocity will become c + v. 

Let Us Calculate the Time Taken by the Transmitted Ray to Travel to the Mirror:

\[T_1 = \frac{L}{c - v}\]

\[T_2 = \frac{L}{c + v}\]

\[T_l = T_1 + T_2\]

\[T_l = \frac{L}{c - v} + \frac{L}{c + v}\]

\[T_l = \frac{(L \times (c + v)) + (L \times (c - v))}{c^2 - v^2} \]

\[T_l = \frac{Lc + Lv + Lc - Lv}{c^2 - v^2} \]

\[T_l = \frac{2Lc}{c^2 - v^2} \]

\[T_l = L \begin{bmatrix} \frac{2c}{c^2 - v^2} \end{bmatrix} \]

\[T_l = \frac{L}{c^2} \begin{bmatrix} \frac{2c}{1 -  \frac{v^2}{c^2}} \end{bmatrix} \]

\[T_l = \frac{2L}{c} \begin{bmatrix} 1 -  \frac{v^2}{c^2} \end{bmatrix}^{-1} \]

Applying Binomial Theorem on the above equation and neglecting higher power terms gives:

\[T_l = \frac{2L}{c} \begin{bmatrix} 1 +  \frac{c^2}{v^2} \end{bmatrix} \]

Now, time taken by the reflected ray to travel to mirror:

\[T_t  = \frac{L}{\begin{bmatrix} c^2  - v^2 \end{bmatrix}^{\frac{1}{2}}} + \frac{L}{\begin{bmatrix} c^2  + v^2 \end{bmatrix}^{\frac{1}{2}}} \]

\[T_t  = \frac{2Lc}{\begin{bmatrix} c^2  - v^2 \end{bmatrix}^{\frac{1}{2}}}\]

\[T_t = \frac{2Lc}{\begin{bmatrix} c^2  - v^2 \end{bmatrix}^{\frac{1}{2}}}\]

\[T_t = \frac{L}{c^2} \begin{bmatrix} \frac{2c}{1 -  \frac{v^2}{c^2}} \end{bmatrix} ^{\frac{1}{2}} \]

\[T_t = \frac{2L}{c} \begin{bmatrix} \frac{1}{1 -  \frac{v^2}{c^2}} \end{bmatrix}^{\frac{1}{2}} \]

\[T_t = \frac{2L}{c} \begin{bmatrix} 1 -  \frac{v^2}{c^2} \end{bmatrix}^{\frac{-1}{2}} \]

Similarly, applying Binomial Theorem:

\[T_t = \frac{2L}{c} \begin{bmatrix} 1 +  \frac{v^2}{2c^2} \end{bmatrix}^{\frac{1}{2}} \]

Michelson Morley experiment derivation indicates the time difference between two rays:

\[\Delta t = T_l - T_t\]

Using the values of T l and T t :

\[\Delta t = \frac{2L}{c} \begin{bmatrix} 1 + \frac{v^2}{c^2} - 1 - \frac{v^2}{2c^2} \end{bmatrix}\]

\[\Delta t = \frac{l}{c} \times \begin{bmatrix} \frac{v^2}{c^2} \end{bmatrix} \]

After the first attempt, the apparatus is rotated clockwise to 90-degree so that two mirrors can exchange their position. Now the time difference between two mirrors can be given by:

\[\Delta t’ = - \frac{l}{c} \times \begin{bmatrix} \frac{v^2}{c^2} \end{bmatrix} \]

Due to the rotation of apparatus, there is a delay in time, which is given by:

\[ \Delta t - \Delta t’ = \frac{2L}{c}  \times \begin{bmatrix} \frac{v^2}{c^2} \end{bmatrix} \]

This time delay causes the fringe pattern to move. Let N denote the total amount of fringe shift, which can be calculated as:

\[N = \frac{\Delta \delta}{2 \pi}\]

\[N = \frac{2L}{\lambda}  \times \begin{bmatrix} \frac{v^2}{c^2} \end{bmatrix} \]

The major objective of the Michael Morley experiment was to verify the ether hypothesis. The experiment has been repeated several times but there was no particular conclusion of the Michelson-Morley experiment.

FAQs on Michelson Morley Experiment

1. What is Michelson Morley Interferometer?

Michelson designed a device named interferometer that consists of a half-silvered mirror oriented at 45-degree angles to the light beam. When light passes, it gets split into two equal parts. One of these beams gets reflected in a movable mirror, and another one transmits to the fixed mirror. This mirror shows the same effect on the returning beams, that is, split them into two beams. As a result, two beams reach the screen, and interference patterns are observed by changing the position of the mirror. This interferometer was used by Michelson and Morley in their experiment to compare the path length of light beams.

2. What is interferometry?

When two electromagnetic waves of the same nature are produced from different sources and superimposed then there is an interference of the waves. These interferences show certain special characteristics and tell a lot about its origin and source. Scientists also study these interferences to determine some unknown information occurring on a subtle and tiny level. The device that is used to analyse these interferences is called Interferometers. It has got some wide industrial use in determining the microscopic displacements inside delicate objects. The technique used by these instruments is known as interferometry. 

3. What is refraction?

All the properties of light have been studied in detail in the subject of natural physics. One of the most interesting characteristics of light is it can travel through some special type of matter which is transparent material such as glass and water. It can also travel partially in some particular type of material known as translucent materials. But the peculiarity of light that is observed is it changes its direction while it travels in from one medium of transparent material to another. It also mostly depends on the density of the material. This phenomenon of light is known as refraction.

4. What do we mean by aether?

Since ancient times various scholars and researchers have postulated the presence of a medium in space for the propagation of light. Later when it was found that light is an electromagnetic wave or radiation then this hypothesis gained more support. Scholars of that time suggested this by observing the waves travelling on the surface of the water. In later days of the 17th century, Robert Boyle again revived this theory citing the various other phenomena occurring in space such as magnetism and irregular movement of celestial bodies. He termed the word aether to describe the tiny particles that he believed is present in space.

5. Is the ether hypothesis of Michael Morley proved?

The hypothesis of the presence of aether in space is an age-old concept that was later adopted by some in the European scientific community. After Robert Boyle revived it Michael Morley tried to prove it physically by performing an experiment. Though he was not successful, many scientists have tried to prove it by experimenting with the hypothesis in other methods. But to our dismay, no one has yet been able to prove this concept and it still remains discarded by the mainstream scientific community of the world.

6. Why Does Michael Morley's Experiment Show a Negative Result?

The negative result of the Michael Morley experiment was given by two explanations, namely, ether theory and light velocity hypothesis. According to Ether Drag theory, the moving bodies drag the surrounding ether with them. Hence, no conclusion came from this experiment to claim if there is any relative motion between Earth and ether. The other was the Light Velocity hypothesis. It says that the velocity of light coming from a moving source is the vector sum of the velocity of light and source light. However, this hypothesis was also rejected after inspecting some evidence. Moreover, Einstein claimed that the motion through the ether medium is a pointless concept, and hence the experiment failed.

Michelson-Morley Experiment Questions

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• Celestial Bodies

Michelson Morley Experiment

We know a medium is absolutely necessary for any transmission in science. The medium of transmission plays an important role in efficient channeling. Waves like sound waves use air for transmission. Then, how is the light transmitted?

Let us know more about the Michelson Morley Experiment in detail to know about light transmission and velocity of the earth.

Michelson Morley Experiment was performed by two eminent scientists Albert A. Michelson and Edward W. Morley in the year 1887 to explain and demonstrate the presence of luminiferous ether.

What Is Luminiferous Ether or Aether?

Luminiferous Ether is the theoretical substance that acts as the medium for the transmission of electromagnetic waves like light rays and X-rays. Ether was assumed to be a transmission medium for the propagation of light.

Luminiferous ether was believed to be a theoretical medium in the 19th century. These substances were assumed to be frictionless, weightless and transparent substances. When the special theory of relativity was developed, the concept of luminiferous ether lost significance gradually.

Michelson Morley Experiment compared the speed of light in perpendicular directions in an attempt to detect the relative motion of matter through the stationary luminiferous aether. But this experiment yielded no results to prove a significant difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles.

The Michelson Morley Experiment was one of the failed experiments that stands as proof against the existence of the luminiferous ether concept.

Michelson and Morley tried to explain that Earth moved around the sun on its orbit, and the flow of substances like ether across the Earth’s surface could produce a detectable “ether wind”.

They tried to demonstrate the concept that the speed of the light would depend on the magnitude of the ether wind and on the direction of the beam with respect to it when the light is emitted from a source on Earth. Ether was assumed to be stationary. The idea of the experiment was to measure the speed of light in different directions in order to measure the speed of the ether relative to Earth, thus establishing its existence.

Interferometer

To measure the velocity of the Earth with the help of ether and to measure the changing pattern of the light, Albert Michelson developed a device called an interferometer.

The interferometer features the following components

• beam splitter
• beam splitter reference mirror
• coherent light source
• movable mirror

Pictorial representation of the interferometer is as shown in the figure below.

The interferometer features a half-transparent mirror that is oriented at an angle of 45°. This mirror is used to divide the light beam into two equal parts. One part of the divided beam is transmitted towards a fixed mirror and part of the divided beam is reflected in a movable mirror. The half-transparent mirror has the same effect on the returning beams, splitting them into two beams. Thus, when two diminished light beams reach the screen, a constructive and destructive wave interference pattern is observed based on the length of the arms of the device.

The speed of light was measured in the experiment by analyzing the interference fringes pattern that resulted when the light had passed through the two perpendicular arms of the interferometer. Michelson and Morley observed that light traveled faster along an arm which was oriented in the same direction as the ether. The light traveled at a slower pace in the arm oriented in the opposite direction.

As shown in the figure above, the interferometer featured perpendicular arms. The split light would travel at the same speed in both arms and therefore arrive simultaneously at the screen if the instrument were motionless with respect to the ether.

When the orientation of the interferometer is changed, the crests and troughs of the light waves produced in the two arms would interfere slightly out of synchronization.

The two scientists Michelson and Morley were expecting light to have different speeds when they travel in different directions, but they found no significantly distinguishing fringes that specified a different speed in any orientation or at any position of the Earth.

Lorentz in 1895, concluded that the Michelson Morley experiment produced the null result. Einstein wrote that If the Michelson–Morley experiment had not brought us into serious embarrassment, no one would have regarded the relativity theory as a (halfway) redemption.

When the Michelson Morley experiment was performed with increasing sophistication, the existence of ether and velocity of earth could not be proved.

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Frequently Asked Questions on Michelson Morley Experiment

Name the device used in michelson morley experiment..

Interferometer.

What is an interferometer?

It is a device used to measure the changing pattern of the light.

What is Luminiferous Ether?

It is the theoretical substance that acts as the medium for the transmission of electromagnetic waves.

Name the scientists who performed the experiment.

Albert A. Michelson and Edward W. Morley.

Which theory superseded the Michelson Morley Experiment?

Special theory of relativity.

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Michelson Morley Experiment Questions

Collegedunia Team

Content Curator

The Michelson-Morley experiment attempted to measure the relative speed of the Earth and luminiferous aether, a hypothesized substance filling space that was considered to carry light waves. 

• American physicists Albert A. Michelson and Edward W. Morley conducted the Michelson-Morley experiment between April and July 1887.
• In order to discover the relative motion of matter in the luminiferous aether ("aether wind"), the experiment compared the speed of light in perpendicular directions.
• Michelson and Morley discovered no significant variance between the speed of light in the direction of passage through the supposed aether and the speed at right angles. 
• This conclusion is widely regarded as the first significant evidence against various aether ideas, as well as the start of a line of study that eventually led to special relativity , which rules out motion against an aether.

Very Short Answers Questions [1 Mark Questions]

Ques. Which of the following was one of the conclusions of the Michaelson Morley experiment?

• Light propagates at different speeds in different directions
• All laws of physics remain invariant in all inertial frames
• The velocity of light in free space is constant
• Ether has no observable properties

Ans. The correct answer is d. Ether has no observable properties

Explanation: The aim of the Michaelson Morley experiment was to determine the time difference from which the relative velocity of ether and the earth might be inferred. However, no change was noticed. As a result, it was demonstrated that ether has no observable properties and that the velocity of light is constant in all directions.

Ques. The result of the Michaelson Morley experiment was as expected.

Ans. The correct answer is b. False

Explanation: When the Michaelson Morley experiment was carried out, it was expected that light would travel at various speeds in different directions as seen from Earth. However, the outcome showed different.

Ques. The device used in the Michaelson Morley experiment was

• Plain Grating
• Interferometer

Ans. The correct answer is d. Interferometer

Explanation: To measure the fringe shift that happens when light is transmitted in multiple directions, an interferometer was used in the Michaelson Morley experiment. It is a device used to measure the interference characteristics of light waves.

Ques. The fringes of equal inclination produced by using the Michelson Interferometer are called as

• Haidinger’s Fringes
• Michelson’s Fringes
• Equi-inclination Fringes
• Morley’s Fringes

Ans. The correct answer is a. Haidinger’s Fringes

Explanation: The Michelson Interferometer is used to obtain fringes of equal inclination. These are known as Haidinger's fringes. The fringes are all concentric circles.

Ques. How much shift was expected in the Michelson-Morley experiment?

Ans. The correct answer is d. 0.04

Explanation: Michelson created a unique instrument with significantly greater precision than any previous device. It was known as the Michelson Interferometer. A fringe shift of 0.04 was predicted using a light of wavelength 600 nm.

Short Answers Questions [2 Marks Questions]

Ques. What are interferometers?

Ans. Interferometers are devices used to measure the interference characteristics of light waves. It provides extremely exact and precise measurements. It was utilized in the Michaelson Morley experiment for this reason, to measure the fringe shift that happens when light is transmitted in multiple directions.

Ques. Who developed the interferometer?

Ans. Albert Michelson created an interferometer to calculate the speed of the Earth using ether and to determine the shifting pattern of light.

Ques. What are the components of an interferometer?

Ans. The followings are the components of an interferometer

• Movable mirror
• Coherent light source
• Beam splitter
• Beam splitter reference mirror

Ques. What was the aim of the Hoek experiment?

Ans. The Hoek experiment was performed to detect interferometric fringe changes caused by speed differences of opposingly moving light waves in water (at rest). Similar testing produced negative results.

Long Answers Questions [3 Marks Questions]

Ques. Give a brief about the Michelson–Morley experiment.

Ans. The Michelson–Morley experiment was a controlled experiment designed to identify the presence of aether, a hypothetical material filling in space that was thought to be the carrier of electromagnetic waves (visible light, radio waves, and so on). 

• Albert Michelson and Edward Morley conducted this experiment between April and July 1887.
•  In November 1887, the study article was published.

Ques. What is meant by aether in physics?

Ans. Aether, sometimes known as luminiferous ether, is a hypothesized universal substance proposed in the nineteenth century as a supporting medium for the propagation of electromagnetic waves or waves (e.g., X-rays and light), similar to how sound waves travel through elastic media such as air.

Ques. What was the exact experimental result of the Michelson–Morley experiment?

Ans. The Michelson–Morley experiment was conducted by Morley and Michelson, two physicists, who expected the light to move at various speeds while moving in different directions, but they found no significant distinguishing fringes that indicated a distinct velocity in any orientation or position of the Earth.

Very Long Answers Questions [5 Marks Questions]

Ques. What were the main assumptions about aether before the Michelson–Morley experiment?

Ans. The Earth rotates around the Sun at a speed of around 30 km/s. Because the Earth is always in motion, two main possibilities were assumed: 

• According to Augustin-Jean Fresnel (1818), the aether is immobile and only partially pulled by the Earth.
• Sir George Stokes (1844) proposed that this ether is totally pulled by the Earth and hence shares its movement at the Earth's surface.

Later, James Clerk Maxwell understood light's electromagnetic nature and developed what is now known as Maxwell's equations. However, such mathematical connections were still characterized as explaining the travel of waves through an unknown ether (aether). Finally, the scientific world preferred Augustin-Jean Fresnel's notion of a stationary aether (nearly) because it looked to be supported by the Fizeau experiment and the aberration of light from stars (1851).

Ques. Give a brief about the comparison conducted by the Michelson–Morley experiment.

Ans. In order to determine the relative mobility of substances through the immovable luminiferous aether, the Michelson-Morley experiment measured the speed of light in perpendicular directions. 

• Morley and Michelson found no substantial difference between the speed of light in the motion's direction through the imagined aether (ether) and the speed at right angles in their experiment. 
• The ultimate finding is widely regarded as the first conclusive proof against the aether idea. 
• It also started a fresh line of inquiry that led to the contemporary idea of relativity (which rules out the possibility of an immobile aether).

Ques. Which are the other experiments similar to the Michelson–Morley experiment?

Ans. Michelson-Morley experiments have been attempted several times, with various levels of success. 

• Experiments like this were carried out between 1902 and 1905, as well as a series of experiments carried out in the 1920s. 
• Experiments using optical resonators have proved the lack of any form of aether wind at levels ranging from 10 to 17. 
• Michelson-Morley-type tests, together with the Kennedy-Thorndike and Ives-Stilwell experiments, are the fundamental tests of special relativity.

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Questions on the Michelson Morley Experiment

• Thread starter OneAverageGuy
• Start date Mar 11, 2021
• Tags Experiment Michelson Michelson morley
• Mar 14, 2021

cianfa72 said: Consider the no dragging ether hypothesis (as I understand it the ether should not be dragged by the Earth in its motion around the Sun). Suppose the speed of light depends on the motion of the source. Since we know velocity is relative, with respect to what should the speed of light have a variable value? Thanks.

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• Mar 15, 2021

Ibix said: I don't think an ether hypothesis (light is a wave, with a fixed speed with respect to the ether) and a speed of light that depends on its source (light acts like machine gun bullets, with a fixed speed with respect to its source) are compatible. You have to pick one or the other (or relativity).

cianfa72 said: Thus, as far as I can understand, the second postulate of relativity --- namely from Wikipedia: as measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body actually rules out both the ether and the ballistic hypothesis

• Mar 17, 2021

Ibix said: You can't rule out anything by postulate. But it does say that relativity theory is incompatible with both ether theory (excepting Lorentz' version) and ballistic theory, yes. You then have to make predictions with the theories and do experiments to determine which one matches and which ones are ruled out.

Sounds interesting. Which "suspect sources" are these?  

vanhees71 said: Sounds interesting. Which "suspect sources" are these?

Grasshopper said: the math is identical, and so are the physical predictions

Grasshopper said: you can’t get GR from Lorentz theory

PeterDonis said: Yes, that's correct. You can't get GR from standard SR either, so I'm not sure what the point of that particular criticism is. The usual criticism of LET is Occam's razor.

A very illuminating exercise to think about the Doppler effect of sound in special relativity. Sound of course needs a fluid as a medium and then of course there's a preferred reference frame, namely the rest frame of the fluid (let's assume for simplicity that the fluid is at rest wrt. an inertial frame). Thus the frequency of the sound depends on both the velocity of the observer and the source of sound relative to the rest frame of the fluid. Now specialize the formulae to a wave with phase velocity being the speed of light (in vacuo), of course particularly an em. wave in vacuo. You'll see that for this case the frequency observed by any observer only depends on the relative velocity between observer and source. The conclusion is that with a "limiting speed", i.e., a Minkowski space-time you cannot observe a preferred reference frame for electromagnetism (aka "the ether rest frame" a la Lorentz or Poincare). That's why indeed Occam's razor should be applied to simply "kill the ether".  

• Mar 8, 2023

In the Michelson-Morrey experiment, the magnitude of the optical path time difference ∆ t (∆ t ' after 90 degrees of rotation) determines the observable interference fringes and the number of fringes in the experiment. Now the key problem is to substitute the actual parameters into the specific situation indicated by the calculation, ∆ t =3.67 × 10 -16 s; ∆ t’ = -3.67 × 10 -16 s, the size of the two is the same, and the sign is opposite, and they will correspond to the same interference fringe. That is to say, after the experimental device is rotated 90 degrees, it is reasonable that the interference fringe does not change, which has nothing to do with the problem of "ether" or "speed of light", that is, the "zero" structure of the experiment cannot explain any problem, and therefore no physical conclusions or judgments can be drawn. In the Michelson-Morrey experiment, the difference between the two optical path time differences before and after rotation is subtracted to obtain ∆=∆ t - ∆ t ' ≈ ( l 1 + l 2 ) v 2 /c 3 =2 × 3.67 × 10 -16 s, there is no observable experimental result corresponding to this mathematical operation in the experiment, because the interference fringe is not positive or negative.  

mzh62 said: there is no observable experimental result corresponding to this mathematical operation in the experiment, because the interference fringe is not positive or negative.

• Mar 9, 2023

See the diagram here: https://www.physicsforums.com/threa...michelson-interferometer.1044816/post-6791684  

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The Michelson-Morley Experiment

     Michael Fowler, UVa

The Nature of Light

As a result of Michelson’s efforts in 1879, the speed of light was known to be 186,350 miles per second with a likely error of around 30 miles per second.  This measurement, made by timing a flash of light travelling between mirrors in Annapolis, agreed well with less direct measurements based on astronomical observations.  Still, this did not really clarify the nature of light.  Two hundred years earlier, Newton had suggested that light consists of tiny particles generated in a hot object, which spray out at very high speed, bounce off other objects, and are detected by our eyes.  Newton’s arch-enemy Robert Hooke, on the other hand, thought that light must be a kind of wave motion , like sound.  To appreciate his point of view, let us briefly review the nature of sound.

The Wavelike Nature of Sound

Actually, sound was already quite well understood by the ancient Greeks.  The essential point they had realized is that sound is generated by a vibrating material object, such as a bell, a string or a drumhead.  Their explanation was that the vibrating drumhead, for example, alternately pushes and pulls on the air directly above it, sending out waves of compression and decompression (known as rarefaction), like the expanding circles of ripples from a disturbance on the surface of a pond.  On reaching the ear, these waves push and pull on the eardrum with the same frequency (that is to say, the same number of pushes per second) as the original source was vibrating at, and nerves transmit from the ear to the brain both the intensity (loudness) and frequency (pitch) of the sound.

There are a couple of special properties of sound waves (actually any waves) worth mentioning at this point.  The first is called interference .  This is most simply demonstrated with water waves.  If you put two fingers in a tub of water, just touching the surface a foot or so apart, and vibrate them at the same rate to get two expanding circles of ripples, you will notice that where the ripples overlap there are quite complicated patterns of waves formed.  The essential point is that at those places where the wave-crests from the two sources arrive at the same time, the waves will work together and the water will be very disturbed, but at points where the crest from one source arrives at the same time as the wave trough from the other source, the waves will cancel each other out, and the water will hardly move.  You can hear this effect for sound waves by playing a constant note through stereo speakers.  As you move around a room, you will hear quite large variations in the intensity of sound.  Of course, reflections from walls complicate the pattern.  This large variation in volume is not very noticeable when the stereo is playing music, because music is made up of many frequencies, and they change all the time.  The different frequencies, or notes, have their quiet spots in the room in different places.  The other point that should be mentioned is that high frequency tweeter-like sound is much more directional than low frequency woofer-like sound.  It really doesn’t matter where in the room you put a low-frequency woofer—the sound seems to be all around you anyway.  On the other hand, it is quite difficult to get a speaker to spread the high notes in all directions.  If you listen to a cheap speaker, the high notes are loudest if the speaker is pointing right at you.  A lot of effort has gone into designing tweeters, which are small speakers especially designed to broadcast high notes over a wide angle of directions.

Is Light a Wave?

Bearing in mind the above minireview of the properties of waves, let us now reconsider the question of whether light consists of a stream of particles or is some kind of wave.  The strongest argument for a particle picture is that light travels in straight lines.  You can hear around a corner, at least to some extent, but you certainly can’t see.  Furthermore, no wave-like interference effects are very evident for light.  Finally, it was long known, as we have mentioned, that sound waves were compressional waves in air.  If light is a wave, just what is waving?  It clearly isn’t just air, because light reaches us from the sun, and indeed from stars, and we know the air doesn’t stretch that far, or the planets would long ago have been slowed down by air resistance.

Despite all these objections, it was established around 1800 that light is in fact some kind of wave.  The reason this fact had gone undetected for so long was that the wavelength is really short, about one fifty-thousandth of an inch.  In contrast, the shortest wavelength sound detectable by humans has a wavelength of about half an inch.  The fact that light travels in straight lines is in accord with observations on sound that the higher the frequency (and shorter the wavelength) the greater the tendency to go in straight lines.  Similarly, the interference patterns mentioned above for sound waves or ripples on a pond vary over distances of the same sort of size as the wavelengths involved.  Patterns like that would not normally be noticeable for light because they would be on such a tiny scale.  In fact, it turns out, there are ways to see interference effects with light.  A familiar example is the many colors often visible in a soap bubble.  These come about because looking at a soap bubble you see light reflected from both sides of a very thin film of water—a thickness that turns out to be comparable to the wavelength of light.  The light reflected from the lower layer has to go a little further to reach your eye, so that light wave must wave an extra time or two before getting to your eye compared with the light reflected from the top layer.  What you actually see is the sum of the light reflected from the top layer and that reflected from the bottom layer.  Thinking of this now as the sum of two sets of waves, the light will be bright if the crests of the two waves arrive together, dim if the crests of waves reflected from the top layer arrive simultaneously with the troughs of waves reflected from the bottom layer.  Which of these two possibilities actually occurs for reflection from a particular bit of the soap film depends on just how much further the light reflected from the lower surface has to travel to reach your eye compared with light from the upper surface, and that depends on the angle of reflection and the thickness of the film.  Suppose now we shine white light on the bubble.  White light is made up of all the colors of the rainbow, and these different colors have different wavelengths, so we see colors reflected, because for a particular film, at a particular angle, some colors will be reflected brightly (the crests will arrive together), some dimly, and we will see the ones that win.

If Light is a Wave, What is Waving?

Having established that light is a wave, though, we still haven’t answered one of the major objections raised above.  Just what is waving?  We discussed sound waves as waves of compression in air.  Actually, that is only one case—sound will also travel through liquids, like water, and solids, like a steel bar.  It is found experimentally that, other things being equal, sound travels faster through a medium that is harder to compress: the material just springs back faster and the wave moves through more rapidly.  For media of equal springiness, the sound goes faster through the less heavy medium, essentially because the same amount of springiness can push things along faster in a lighter material.  So when a sound wave passes, the material—air, water or solid—waves as it goes through.  Taking this as a hint, it was natural to suppose that light must be just waves in some mysterious material, which was called the aether , surrounding and permeating everything.  This aether must also fill all of space, out to the stars, because we can see them, so the medium must be there to carry the light.  (We could never hear an explosion on the moon, however loud, because there is no air to carry the sound to us.)  Let us think a bit about what properties this aether must have.  Since light travels so fast, it must be very light, and very hard to compress.  Yet, as mentioned above, it must allow solid bodies to pass through it freely, without aether resistance, or the planets would be slowing down.  Thus we can picture it as a kind of ghostly wind blowing through the earth.  But how can we prove any of this? Can we detect it?

Detecting the Aether Wind: the Michelson-Morley Experiment

Detecting the aether wind was the next challenge Michelson set himself after his triumph in measuring the speed of light so accurately.  Naturally, something that allows solid bodies to pass through it freely is a little hard to get a grip on.  But Michelson realized that, just as the speed of sound is relative to the air, so the speed of light must be relative to the aether.  This must mean, if you could measure the speed of light accurately enough, you could measure the speed of light travelling upwind, and compare it with the speed of light travelling downwind, and the difference of the two measurements should be twice the windspeed.  Unfortunately, it wasn’t that easy.  All the recent accurate measurements had used light travelling to a distant mirror and coming back, so if there was an aether wind along the direction between the mirrors, it would have opposite effects on the two parts of the measurement, leaving a very small overall effect.  There was no technically feasible way to do a one-way determination of the speed of light.

At this point, Michelson had a very clever idea for detecting the aether wind.  As he explained to his children (according to his daughter), it was based on the following puzzle:

Suppose we have a river of width w (say, 100 feet), and two swimmers who both swim at the same speed v feet per second (say, 5 feet per second).  The river is flowing at a steady rate, say 3 feet per second.  The swimmers race in the following way: they both start at the same point on one bank.  One swims directly across the river to the closest point on the opposite bank, then turns around and swims back.  The other stays on one side of the river, swimming upstream a distance (measured along the bank) exactly equal to the width of the river, then swims back to the start.  Who wins?

Let’s consider first the swimmer going upstream and back.  Going 100 feet upstream, the speed relative to the bank is only 2 feet per second, so that takes 50 seconds.  Coming back, the speed is 8 feet per second, so it takes 12.5 seconds, for a total time of 62.5 seconds.

The swimmer going across the flow is trickier.  It won’t do simply to aim directly for the opposite bank-the flow will carry the swimmer downstream.  To succeed in going directly across, the swimmer must actually aim upstream at the correct angle (of course, a real swimmer would do this automatically).  Thus, the swimmer is going at 5 feet per second, at an angle, relative to the river, and being carried downstream at a rate of 3 feet per second.  If the angle is correctly chosen so that the net movement is directly across, in one second the swimmer must have moved four feet across:  the distances covered in one second will form a 3,4,5 triangle.  So, at a crossing rate of 4 feet per second, the swimmer gets across in 25 seconds, and back in the same time, for a total time of 50 seconds.  The cross-stream swimmer wins.  This turns out to true whatever their swimming speed.  (Of course, the race is only possible if they can swim faster than the current!)

Michelson’s great idea was to construct an exactly similar race for pulses of light, with the aether wind playing the part of the river.  The scheme of the experiment is as follows: a pulse of light is directed at an angle of 45 degrees at a half-silvered, half transparent mirror, so that half the pulse goes on through the glass, half is reflected.  These two half-pulses are the two swimmers.  They both go on to distant mirrors which reflect them back to the half-silvered mirror.  At this point, they are again half reflected and half transmitted, but a telescope is placed behind the half-silvered mirror as shown in the figure so that half of each half-pulse will arrive in this telescope.  Now, if there is an aether wind blowing, someone looking through the telescope should see the halves of the two half-pulses to arrive at slightly different times, since one would have gone more upstream and back, one more across stream in general.  To maximize the effect, the whole apparatus, including the distant mirrors, was placed on a large turntable so it could be swung around.

An animated applet of the experiment is available here –it makes the account above a lot clearer!

Let us think about what kind of time delay we expect to find between the arrival of the two half-pulses of light.  Taking the speed of light to be c miles per second relative to the aether, and the aether to be flowing at v miles per second through the laboratory, to go a distance w miles upstream will take w /( c - v ) seconds, then to come back will take w /( c + v ) seconds.  The total roundtrip time upstream and downstream is the sum of these, which works out to be 2 wc /( c ²- v ²), which can also be written (2 w / c )×1/(1- v ²/ c ²).  Now, we can safely assume the speed of the aether is much less than the speed of light, otherwise it would have been noticed long ago, for example in timing of eclipses of Jupiter’s satellites.  This means v ²/ c ² is a very small number, and we can use some handy mathematical facts to make the algebra a bit easier.  First, if x is very small compared to 1, 1/(1- x ) is very close to 1+ x .  (You can check it with your calculator.)  Another fact we shall need in a minute is that for small x , the square root of 1+ x is very close to 1+ x /2.  

Putting all this together, the upstream--downstream roundtrip time

Now, what about the cross-stream time?  The actual cross-stream speed must be figured out as in the example above using a right-angled triangle, with the hypoteneuse equal to the speed c , the shortest side the aether flow speed v , and the other side the cross-stream speed we need to find the time to get across.  From Pythagoras’ theorem, then, the cross-stream speed is the square root of ( c ²- v ²).  

Since this will be the same both ways, the roundtrip cross-stream time will be

This can be written in the form

Therefore the across-stream roundtrip time, assuming the aether velocity is much less than that of light, is

Looking at the two roundtrip times at the ends of the two paragraphs above, we see that they differ by an amount (2 w / c ) × v ²/2 c ².  Now, 2 w / c is just the time the light would take if there were no aether wind at all, say, a few millionths of a second.  If we take the aether windspeed to be equal to the earth’s speed in orbit, for example, v / c is about 1/10,000, so v ²/ c ² is about 1/100,000,000.  This means the time delay between the pulses reflected from the different mirrors reaching the telescope is about one-hundred-millionth of a few millionths of a second.  It seems completely hopeless that such a short time delay could be detected.  However, this turns out not to be the case, and Michelson was the first to figure out how to do it.  The trick is to use the interference properties of the lightwaves.  Instead of sending pulses of light, as we discussed above, Michelson sent in a steady beam of light of a single color.  This can be visualized as a sequence of ingoing waves, with a wavelength one fifty-thousandth of an inch or so.  Now this sequence of waves is split into two, and reflected as previously described.  One set of waves goes upstream and downstream, the other goes across stream and back.  Finally, they come together into the telescope and the eye.  If the one that took longer is half a wavelength behind, its troughs will be on top of the crests of the first wave, they will cancel, and nothing will be seen.  If the delay is less than that, there will still be some dimming.  However, slight errors in the placement of the mirrors would have the same effect.  This is one reason why the apparatus is built to be rotated.  On turning it through 90 degrees, the upstream-downstream and the cross-stream waves change places.  Now the other one should be behind.  Thus, if there is an aether wind, if you watch through the telescope while you rotate the turntable, you should expect to see variations in the brightness of the incoming light.

To magnify the time difference between the two paths, in the actual experiment the light was reflected backwards and forwards several times, like a several lap race.

Michelson calculated that an aether windspeed of only one or two miles a second would have observable effects in this experiment, so if the aether windspeed was comparable to the earth’s speed in orbit around the sun, it would be easy to see.  In fact, nothing was observed.  The light intensity did not vary at all.  Some time later, the experiment was redesigned so that an aether wind caused by the earth’s daily rotation could be detected.  Again, nothing was seen.  Finally, Michelson wondered if the aether was somehow getting stuck to the earth, like the air in a below-decks cabin on a ship, so he redid the experiment on top of a high mountain in California.  Again, no aether wind was observed.  It was difficult to believe that the aether in the immediate vicinity of the earth was stuck to it and moving with it, because light rays from stars would deflect as they went from the moving faraway aether to the local stuck aether.

The only possible conclusion from this series of very difficult experiments was that the whole concept of an all-pervading aether was wrong from the start.  Michelson was very reluctant to think along these lines.  In fact, new theoretical insight into the nature of light had arisen in the 1860’s from the brilliant theoretical work of Maxwell, who had written down a set of equations describing how electric and magnetic fields can give rise to each other.  He had discovered that his equations predicted there could be waves made up of electric and magnetic fields, and the speed of these waves, deduced from experiments on how these fields link together, would be 186,300 miles per second.   This is, of course, the speed of light, so it is natural to assume that light is made up of fast-varying electric and magnetic fields.  But this leads to a big problem: Maxwell’s equations predict a definite speed for light, and it is the speed found by measurements.  But what is the speed to be measured relative to?  The whole point of bringing in the aether was to give a picture for light resembling the one we understand for sound, compressional waves in a medium.  The speed of sound through air is measured relative to air.  If the wind is blowing towards you from the source of sound, you will hear the sound sooner.  If there isn’t an aether, though, this analogy doesn’t hold up.  So what does light travel at 186,300 miles per second relative to?

There is another obvious possibility, which is called the emitter theory: the light travels at 186,300 miles per second relative to the source of the light.  The analogy here is between light emitted by a source and bullets emitted by a machine gun.  The bullets come out at a definite speed (called the muzzle velocity) relative to the barrel of the gun.  If the gun is mounted on the front of a tank, which is moving forward, and the gun is pointing forward, then relative to the ground the bullets are moving faster than they would if shot from a tank at rest.  The simplest way to test the emitter theory of light, then, is to measure the speed of light emitted in the forward direction by a flashlight moving in the forward direction, and see if it exceeds the known speed of light by an amount equal to the speed of the flashlight.  Actually, this kind of direct test of the emitter theory only became experimentally feasible in the nineteen-sixties.  It is now possible to produce particles, called neutral pions, which decay each one in a little explosion, emitting a flash of light.  It is also possible to have these pions moving forward at 185,000 miles per second when they self destruct, and to catch the light emitted in the forward direction, and clock its speed.  It is found that, despite the expected boost from being emitted by a very fast source, the light from the little explosions is going forward at the usual speed of 186,300 miles per second.  In the last century, the emitter theory was rejected because it was thought the appearance of certain astronomical phenomena, such as double stars, where two stars rotate around each other, would be affected.  Those arguments have since been criticized, but the pion test is unambiguous.  The definitive experiment was carried out by Alvager et al., Physics Letters 12 , 260 (1964).

Einstein’s Answer

The results of the various experiments discussed above seem to leave us really stuck.  Apparently light is not like sound, with a definite speed relative to some underlying medium.  However, it is also not like bullets, with a definite speed relative to the source of the light.  Yet when we measure its speed we always get the same result.  How can all these facts be interpreted in a simple consistent way?  We shall show how Einstein answered this question in the next lecture.

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Michelson-Morley Experiment Why 90-degree rotation [duplicate]

Why the apparatus is rotated by 90 degree? If it is not rotated, there is still path difference between two lights. So why it is rotated?

• special-relativity
• speed-of-light
• interference

• 1 $\begingroup$ Please can you provide a reference which states that the apparatus must be rotated? $\endgroup$ –  sammy gerbil Commented Apr 3, 2018 at 17:47

3 Answers 3

Superfrankie, You were right about the first part. It doesn’t matter what direction the arms of the experiment go as long as they are the same length. For many experiments like gravitational waves it’s better to cover the full 90°. That way when you rotate experiment you will have a full range or a full contrast to compare the two readings.

I believe there was no such rotation by 90 degrees of the experimental setup, relative to the floor at least. The aim of the experiment was to measure the influence of moving through the hypothetical Aether, a substance which was hypothesized to be the medium in which light-waves travel.

The original measurement took place at two different times in the year, in which the Earth would be moving in different directions with respect to this elusive Aether. This movement of the medium should then be measurable in the speed of light, in the framework of Galilean relativity. In the end, they weren't able to find any such difference, concluding that light is not traveling in such an Aether material!

Check out the Wikipedia, especially the diagram! https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment

• $\begingroup$ The first picture on that page shows the experiment sitting on a mercury trough. The purpose of that trough was to allow the experiment to be easily rotated. $\endgroup$ –  BowlOfRed Commented Apr 3, 2018 at 15:55

Simply to account for the case where they might be measuring perpendicular to the flow of the postulated ether, which was assumed to be the medium that the light "waves" were "oscillating in.

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