The Speed of Light series consist of five parts. Quick access links are here.
Part 1 | Earliest Ideas
Part 2 | The Eclipses of Io
Part 3 | Chopping Light Beams
Part 4 | Done With Mirrors
Part 5 | Michelson and Morley
This final post highlights the work done by Albert Michelson and Edward Morley of the United States to measure c in various directions, and at different times of the year, as the Earth revolved in its orbit around the Sun. They wanted to answer the question of whether light needed a medium upon which to travel.
Waves are common phenomenon. They can be observed with a Slinky™, ropes, water, flags, earthquakes, as sound, even as crowd movements at a stadium. All of these examples involve some sort of medium upon, or through which, the wave motion propagates.
Should not the same be true of light waves and the various other electro-magnetic waves? Does light travel through an exceedingly thin and rigid medium? Is there a Luminiferous Aether permeating all of space which allows the travel of light but does not impede the motions of all other objects?
This question was posed during the speed of light measurement attempts carried out in the 19th century. The measurements of c were made to increasing accuracy by the likes of Albert Michelson and others. Their instruments always had some sources of error which did not allow them to discern whether the Earth’s motion through the aether of space made a difference in their value obtained. A more sensitive and accurate instrument was needed. Michelson made that instrument, the interferometer, and ultimately won the 1907 Nobel Prize for his work.
Tell Me More About Relative Motion
Consider this simple situation of a motorized boat in a river. You are observing the speed of the boat from the shore as it performs various movements in the flowing river. The river current is 2 mph. The boat speedometer is set to 6 mph. If the boat goes downstream with the current of the river, you would see it pass by going 2 + 6 = 8 mph relative to the shore.
The boat turns around and goes upstream with the same speedometer setting of 6 mph. This time you see it pass by going slower 6 – 2 = 4 mph.
Next, the boat turns to aim directly across the river. The speedometer is still set to 6 mph. The current is still 2 mph. Because of the sideways current, the boat goes off at an angle. The speed is found using the Pythagorean Theorem. It is the square root of 2 squared + 6 squared = 6.3 mph.
This simple exercise is meant to show that the speed of something through a medium depends upon the directions of the motions relative to the observer. In this case, speed is affected by the motion of the medium of the river. It was believed by many scientists in the middle 1800s that the speed of light value should be dependent upon which direction the Earth was moving through the aether medium in space. What was needed in order to show that it was true was an instrument with sufficient accuracy and sensitivity. None had been made until Michelson made the interferometer and tested it in 1881.
What Is Earth’s Motion Through The Aether?
As passengers on spaceship Earth, we are moving in several different ways through space. Here is a partial list in increasing values of speed. For reference, the speed of light is about 671,000,000 mph.
- Earth’s rotation causes objects near the equator to be traveling east nearly 1000 mph.
- Earth’s revolution around the Sun causes a speed of nearly 70,000 mph.
- The Sun carries Earth and the other planets with it around the Milky Way galaxy at nearly 500,000 mph.
- The Milky Way galaxy is moving through space at nearly 1,300,000 mph.
With a sufficiently sensitive apparatus, there ought to be a way to measure such huge relative motions of Earth through the aether of space.
The Michelson Interferometer
Michelson developed a prototype of his instrument prior to 1881. The principle was simple. Send light waves from a source at the left (a) through a half-silvered mirror (b). Part of it goes forward to another mirror and back (c). The other part goes at 90˚ to another mirror and back (d). The waves re-combine and pass to a viewer (e). This is a drawing of the interferometer from Michelson’s paper in the American Journal of Science, 1881, 22: 120-129. The distances to the flat mirrors on each arm were 1.2oo meters. The interferometer was placed on a heavy stone in the basement to stop vibrations. By choosing the time of day carefully, one of the arms would lie along the same direction as the motion of the Earth as it rounded the Sun in orbit. The other arm would lie perpendicular to the motion of the Earth.
This video by Leonid Kostrykin illustrates the motions of the waves to the mirrors and back.
If the crests of waves in one direction meet and re-combine with the crests from the 90˚direction, they will add to each other, reinforcing and showing a bright fringe of light. Light waves are exceedingly short. Any tiny change in the time of travel for either of the two directions can cause a crest to return when a trough from the other direction returns. A crest and a trough superimposed will cancel and show a dark fringe. Here is a brief video of how those fringes can appear by using a specific wavelength of green light. Notice the bright and dark fringes.
If an aether existed, light waves going over and back perpendicular to the motion of the Earth would take the same amount of time through the aether. The waves going along the same direction as the Earth would take longer going to the mirror and less time coming back. That would alter the total time for their round trip making it slightly more time than the other path.
Six hours later, the arms of the interferometer would have moved due to the 90˚ rotation of the Earth. The light waves traversing the arms would now be in different situations as before. Time of travel should be affected slightly. The observer at the small scope (e) on the nearside should see a shift in the light and dark fringes of light during the course of the 6 hours. The interferometer was capable of showing those fringe shifts if they did occur. However, the fringe shifts were so small as to be inconclusive. They definitely were not obvious and suggested that the aether idea might be wrong. The instrument needed to be more sensitive.
The Improved Interferometer
Several years later at what is now Case Western Reserve University in Cleveland, Ohio, Michelson was joined in this effort by Edward Morley. They redesigned the interferometer to make it 10x more sensitive. They added several sets of mirrors at the ends of the two arms of the instrument. This caused the light waves to travel greater distances before rejoining and going to the viewer. This drawing is from their 1887 paper which is discussed in Wikipedia. The light source of sodium yellow wavelength is at (a). The half-silvered mirror splits the light at (b) into the two 90˚paths to several mirrors at (d – e) and (d’ – e’). The waves rejoined at (b) and were viewed through a telescope (f).
The entire apparatus was sitting on a large stone slab in the basement of the building. The slab was floating in a tub containing liquid mercury. It could be rotated with nearly no effort and no vibration to watch for the shift in the light and dark fringes.
Results of the Experiment
The light fringes were watched as the instrument was slowly turned. They were observed at different times of day and at different seasons of the year. The instrument was even taken to a mountain top to see if that made a difference. They always got a null result. No fringe shifts were observed. The experiment offered no supportive evidence for the existence of an aether for light to travel upon. The speed of light was not affected by any changes in the direction of the waves. The aether apparently did not exist.
Albert Einstein, at the age of 16 in 1895, pondered the question of whether one could tell if they were moving or not by measuring the speed of light. He continued to study this question for another 10 years. At the young age of 26, while working in a Swiss patent office, he published his answer in June 1905. The paper was titled On the Electro-Dynamics of Moving Bodies. Here is the English translation. Today, we often refer to this work by Einstein as his Special Theory of Relativity.
“… light is always propagated in empty space with a definite velocity c which is independent of the state of [relative] motion of the emitting body …. The introduction of a `luminiferous ether’ will be superfluous inasmuch as the view here to be developed will not require an `absolutely stationary space’ provided with special properties.” — Annalen Physik 17 (1905).
In other words, the speed of light measured by all observers is the same regardless of their motion. And, the laws of physics are the same in all frames of reference that are not accelerating. He went on to say that those things being constant and unchanging meant that other quantities once assumed to be constants are actually not. The rate of passage of time depends upon the speed of the object. The length of an object is shortened by the fact that it moves rapidly. And, the mass of an object increases if it moves rapidly. These quantities we intuitively accept as constant are variables. That is a discussion to be left for a post another time.