Michelson-Gale-Pearson experiment
Encyclopedia
The Michelson–Gale–Pearson experiment (1925) is a modified version of the Michelson-Morley experiment
and the Sagnac-Interferometer
. It measured the Sagnac effect
due to Earth's rotation, and thus tests the theories of special relativity
and luminiferous ether along the rotating frame of Earth
.
in 1904 and then executed in 1925, was to find out whether the rotation of the Earth has an effect on the propagation of light in the vicinity of the Earth.
The Michelson-Gale experiment was a very large ring interferometer, (a perimeter of 1.9 kilometer), large enough to detect the angular velocity of the Earth. Like the original Michelson-Morley experiment, the Michelson-Gale-Pearson version compared the light from a single source (carbon arc) after travelling in two directions. The major change was to replace the two "arms" of the original MM version with two rectangle
s, one much larger than the other. Light
was sent into the rectangles, reflecting off mirror
s at the corners, and returned to the starting point. Light exiting the two rectangles was compared on a screen just as the light returning from the two arms would be in a standard MM experiment. The expected fringe shift in accordance with the stationary aether and special relativity was given by Michelson as:
where
is the displacement in fringes, 
the area in square kilometers, 
the latitude (41° 46'), 
the speed of light, 
the angular velocity of Earth, 
the effective wave-length used. In other words, this experiment was aimed to detect the Sagnac effect
due to Earth's rotation.
As it was already pointed out by Michelson in 1904, a positive result in such experiments contradicts the hypothesis of complete aether drag
. On the other hand, the stationary ether concept is in agreement with this result, yet it contradicts (with the exception of Lorentz's ether
) the Michelson-Morley experiment. Thus special relativity is the only theory which explains both experiments. The experiment is consistent with relativity for the same reason as all other Sagnac type experiments (see Sagnac effect
). That is, rotation is absolute in special relativity, because there is no inertial frame of reference in which the whole device is at rest during the complete process of rotation, thus the light paths of the two rays are different in all of those frames, consequently a positive result must occur. It's also possible to define rotating frames in special relativity (Born coordinates
), yet in those frames the speed of light is not constant in extended areas any more, thus also in this view a positive result must occur. Today, Sagnac type effects due to Earth's rotation are routinely incorporated into GPS.
Michelson-Morley experiment
The Michelson–Morley experiment was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University in Cleveland, Ohio. Its results are generally considered to be the first strong evidence against the theory of a luminiferous ether and in favor of special...
and the Sagnac-Interferometer
Sagnac effect
The Sagnac effect , named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in...
. It measured the Sagnac effect
Sagnac effect
The Sagnac effect , named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in...
due to Earth's rotation, and thus tests the theories of special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
and luminiferous ether along the rotating frame of Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
.
Experiment
The aim, as it was first proposed by Albert Abraham MichelsonAlbert Abraham Michelson
Albert Abraham Michelson was an American physicist known for his work on the measurement of the speed of light and especially for the Michelson-Morley experiment. In 1907 he received the Nobel Prize in Physics...
in 1904 and then executed in 1925, was to find out whether the rotation of the Earth has an effect on the propagation of light in the vicinity of the Earth.
The Michelson-Gale experiment was a very large ring interferometer, (a perimeter of 1.9 kilometer), large enough to detect the angular velocity of the Earth. Like the original Michelson-Morley experiment, the Michelson-Gale-Pearson version compared the light from a single source (carbon arc) after travelling in two directions. The major change was to replace the two "arms" of the original MM version with two rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...
s, one much larger than the other. Light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
was sent into the rectangles, reflecting off mirror
Mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...
s at the corners, and returned to the starting point. Light exiting the two rectangles was compared on a screen just as the light returning from the two arms would be in a standard MM experiment. The expected fringe shift in accordance with the stationary aether and special relativity was given by Michelson as:
where
is the displacement in fringes, the area in square kilometers, the latitude (41° 46'), the speed of light, the angular velocity of Earth, the effective wave-length used. In other words, this experiment was aimed to detect the Sagnac effectSagnac effect
The Sagnac effect , named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in...
due to Earth's rotation.
Result
The outcome of the experiment was that the angular velocity of the Earth as measured by astronomy was confirmed to within measuring accuracy. The ring interferometer of the Michelson-Gale experiment was not calibrated by comparison with an outside reference (which was not possible, because the setup was fixed to the Earth). From its design it could be deduced where the central interference fringe ought to be if there would be zero shift. The measured shift was 230 parts in 1000, with an accuracy of 5 parts in 1000. The predicted shift was 237 parts in 1000. According to Michelson/Gale, the experiment is compatible with both the idea of a stationary ether and special relativity.As it was already pointed out by Michelson in 1904, a positive result in such experiments contradicts the hypothesis of complete aether drag
Aether drag hypothesis
In the 19th century, the theory of the luminiferous aether as the hypothetical medium for the propagation of light was widely discussed. An important part of this discussion was the question concerning the state of motion of Earth with respect to this medium. The aether drag hypothesis dealt with...
. On the other hand, the stationary ether concept is in agreement with this result, yet it contradicts (with the exception of Lorentz's ether
Lorentz ether theory
What is now often called Lorentz Ether theory has its roots in Hendrik Lorentz's "Theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century....
) the Michelson-Morley experiment. Thus special relativity is the only theory which explains both experiments. The experiment is consistent with relativity for the same reason as all other Sagnac type experiments (see Sagnac effect
Sagnac effect
The Sagnac effect , named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in...
). That is, rotation is absolute in special relativity, because there is no inertial frame of reference in which the whole device is at rest during the complete process of rotation, thus the light paths of the two rays are different in all of those frames, consequently a positive result must occur. It's also possible to define rotating frames in special relativity (Born coordinates
Born coordinates
In relativistic physics, the Born coordinate chart is a coordinate chart for Minkowski spacetime, the flat spacetime of special relativity. It is often used to analyze the physical experience of observers who ride on a ring or disk rigidly rotating at relativistic speeds...
), yet in those frames the speed of light is not constant in extended areas any more, thus also in this view a positive result must occur. Today, Sagnac type effects due to Earth's rotation are routinely incorporated into GPS.