The Michelson Interferometer: a Cognition Machine

What have the discovery of the constancy of the speed of light, the first measurement of gravitational waves and the chemical analysis of gases, liquids and solids got in common? The Michelson interferometer plays a major role in all of these. Let’s take a closer look at the history and applications of this “cognition machine”.

Up until the beginning of the 20th century people assumed that light propagated through a medium called “the luminiferous aether”, which filled the entire cosmos. Light and all other electromagnetic waves were seen as mechanical vibrations of this aether. However, nobody managed to postulate a theory of aether which was complete and consistent.

Constancy of the speed of light

In 1881 Albert A. Michelson attempted to determine the speed of the Earth’s motion relative to the aether. He continued his work on this subject in 1887 with E. Morley. The interferometer he used in the 1881 experiment (Figure 1) consists of a light source, a small telescope and two interferometer arms arranged at right angles to one another. The light from the light source (front left in Figure 1) is split by a half-silvered mirror which is positioned at the crossover point of the arms. From there the split light travels along the two arms. At the end of the arms the light is reflected by a mirror positioned there and reflected back to the half-silvered mirror where it causes interference. Interference fringes form and these can be observed through the telescope (front right in Figure 1). The smallest change in the light paths leads to a shift in position of these interference fringes.

Interferometer
Figure 1: An interferometer like the one Michelson used in 1881 in Potsdam; Source: https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Michelsonnachbau.jpg/1280px-Michelsonnachbau.jpg

Michelson positioned one arm of the interferometer in the direction of the maximum speed of the location relative to the presumed aether, with the other being at a right angle and therefore at minimum speed. He then determined the position of the interference fringes. After this he turned the setup by 90° and determined the position of the interference fringes again. If the aether was at rest or was being partially dragged along by the Earth’s motion then this should result in different speeds of light in the two arms and cause a shift in position of the interference fringes.

Within the measurement uncertainty, which was very high at the beginning but improved later as the setups became increasingly more sensitive, it was not possible to determine a significant difference in the speeds of the light. This seemed to indicate that the aether was being dragged along completely by the Earth’s motion. However, this was contradicted by another observation: The aberration of light from the stars is caused by the finite speed of light and the speed of the Earth’s motion. It results in the apparent change in location of the stars over the course of the year. If the aether dragging was complete, there would be no such aberration.

There were several attempts made to improve and save the aether theory until, in 1905, Albert Einstein overturned the idea of “aether” altogether. Light and other electromagnetic waves do not need a carrier medium for their propagation. Based on the constancy of the speed of light and the equivalence of the physical laws in both systems at rest and in constant motion, Einstein formulated the Special Theory of Relativity. The constancy of the speed of light, proved by the Michelson interferometer, therefore led to a revolution in physics which completely changed our understanding of space and time, mass and energy.

Gravitational waves

Newton’s law of gravitation from 1687 describes the attraction between masses but does not contain any dependence on time. Gravity therefore appears to have an immediate effect over any distance. If, for example, the sun would suddenly split into two parts (a completely unrealistic scenario) we would immediately register the change in gravity on Earth. As light takes a little over eight minutes to reach Earth from the sun we would immediately detect the change in gravity resulting from the splitting of the sun but only see this phenomenon after eight minutes had passed. Newton himself was very critically aware of the unrealistic consequence of his law of gravitation, as can be seen from his letters.

In his Theory of General Relativity in 1915 Einstein described gravity as a curvature of spacetime: Space and time are influenced by large masses. As one of the first results from his equations, Einstein deduced the occurrence of gravitational waves. These are elongations and compressions of space which move at the speed of light, caused by accelerated (large) masses. According to Einstein, we would see the splitting of the sun after eight minutes and only then feel the gravitational effect.

Gravitational waves are extremely difficult to measure. Under earthly conditions these elongations and compressions are in the order of one thousandths of a proton diameter. Einstein believed it would never be possible to measure these gravitational waves but he was wrong. R. Hulse and J. Taylor received the Nobel Prize in Physics in 1993 for the indirect proof of gravitational waves from radioastronomical measurements.

Wave Observatory
Figure 2: Principle of a Laser Interferometer Gravitational-Wave Observatory (LIGO); Source: http://learner.org/courses/physics/visual/visual.html?shortname=ligo_interfermometer

Since the late 1950s attempts have been made to measure gravitational waves directly. This remained without success until 2015. Direct proof was finally obtained on September 14, 2015, nearly 100 years after Einstein’s discovery and during the trial operation of the two improved American LIGO detectors (also known as Laser Interferometer Gravitational-Wave Observatories, LIGO). Once again, Michelson interferometers were the key to success. Their arms are four kilometers long at the LIGO detectors. However, built-in optical resonators – shown in Figure 2 as light storage arms and formed by the mirrored test masses – result in an effective arm length of several hundred kilometers. This is achieved because the light is reflected back and forth many times between the mirrored test masses before it returns to the beam splitter and causes interference.

On September 14, 2015, the gravitational waves arising from the last few tenths of a second of the merging of two black holes were measured. Black holes are cosmic objects with such a high mass density that due to their extreme gravity they swallow up everything that comes too close. Not even light can escape them, which is why they are “black”. One of these black holes had 29 solar masses, the other 36 solar masses. They fused to become a black hole with 62 solar masses. The difference of three solar masses was radiated off as gravitational wave energy. This event took place 1.3 billion light years away and the gravitational waves therefore traveled approximately this many years until they reached Earth and were measured [1].

Infrared spectroscopy

In chemical analysis, infrared spectroscopy is one of the most important analysis methods. Here, light is shone through or at the sample and the transmitted or reflected light spectra are analyzed. Absorbed spectral components of the infrared light give insight into the composition of the sample. The Alcolyzer® from Anton Paar, for example, uses an optical lattice for the spectral analysis of the infrared light for the determination of alcohol in beverages. This works well because only a relatively narrow spectral range is required. Broadband spectrometers typically use a Michelson interferometer instead of an optical lattice. They are then called Fourier transform spectrometers or FTIR spectrometers after the mathematical method which is applied to reconstruct the infrared spectrum.

With a movable mirror in one arm of the Michelson interferometer, the spectral characteristics of the broadband infrared light radiated from the source are changed. The interference at the beam splitter results in some spectral components of the light directed onto the sample being completely filtered out, some components being diminished and other components being let through unchanged. With each position of the movable mirror the spectral composition of the infrared light changes in a specific way. The detector measures the intensity of the light collected after the sample. The resulting intensity curve as a function of the mirror position is converted into the infrared spectrum of the sample using the Fourier transform. This infrared spectrum can be used to determine the composition of the sample.

Summary

The Michelson interferometer is an outstanding tool for gaining new insights in physics. It is also used in many thousands of laboratories in the development of new materials or to simply prove that a milk sample corresponds to the information on the packaging. Wherever it is used it leads to new insights and therefore deserves the title “cognition machine”.

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[1] Abbott, B. P., et al.: Observation of Gravitational Waves from a Binary Black Hole Merger, Physical Review Letters, February 11, 2016. https://dcc.ligo.org/public/0122/P150914/014/LIGO-P150914%3ADetection_of_GW150914.pdf

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