Fizeau experiment
Encyclopedia
The Fizeau experiment was carried out by Hippolyte Fizeau
in 1851 to measure the relative speeds of light in moving water. Albert Einstein
later pointed out the importance of the experiment for special relativity
. See also Tests of special relativity.
. The Fresnel drag coefficient is
.
When light is transmitted through a moving medium, its speed relative to a stationary observer is:
This was confirmed by Fizeau's experiment in 1851.
In 1895, Lorentz predicted the existence of an extra term due to dispersion
:
This was confirmed by Zeeman in 1914.
(1892, 1895) that the experiment can be explained by the reaction of the moving water upon the interfering waves without the need of any aether entrainment. On this occasion, Lorentz introduced a different time coordinate for moving bodies within the aether, the so called Local time (an early form of the Lorentz transformation
for small velocities compared to the speed of light
). In 1895, Lorentz went a step further and explained the coefficient by local time alone and without mentioning any interaction of light and matter.
Within special relativity
, Lorentz's formalism was simplified with the aid of the velocity addition formula
, which was derived by Albert Einstein (1905) from the complete Lorentz transformation. Thus it was shown by Jakob Laub
and Max von Laue
(1907) that the Fresnel drag coefficient can be easily explained by that formula and so the experiment is supporting evidence for the colinear case of Einstein's velocity addition formula. Einstein later emphasized the importance of the experiment for developing and confirming the theory.
Although it is referred to as the Fizeau experiment, Fizeau was an active experimenter who carried out a wide variety of different experiments involving measuring the speed of light in different situations.
Fizeau's result was replicated by Albert Michelson and Edward Morley
(1886), and by Pieter Zeeman
(1914).
Another experiment was that of Franz Harress (1910). Contrary to Fizeau, he used a rotating device and actually confirmed Fresnel's dragging coefficient. However, he additionally found a "systematic bias" in the data, which later turned out to be the Sagnac effect
.
From the velocity composition law it follows that the speed of light observed in the laboratory, where water is flowing with speed v (in the same direction as light) is
Thus the difference in speed is (assuming v is small comparing to c, approximating to the first non-trivial correction)
Hippolyte Fizeau
Armand Hippolyte Louis Fizeau was a French physicist.-Biography:Fizeau was born in Paris. His earliest work was concerned with improvements in photographic processes. Following suggestions by François Arago, Léon Foucault and Fizeau collaborated in a series of investigations on the interference of...
in 1851 to measure the relative speeds of light in moving water. Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
later pointed out the importance of the experiment for 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...
. See also Tests of special relativity.
Fresnel drag coefficient
Fizeau's test was designed to evaluate the prediction by Augustin Fresnel that a moving dispersive medium should create a partial offset in the speed of any light moving through it, because the refractive index, n, would be dependent on the entrainment of the luminiferous aetherLuminiferous aether
In the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....
. The Fresnel drag coefficient is
.When light is transmitted through a moving medium, its speed relative to a stationary observer is:
This was confirmed by Fizeau's experiment in 1851.
In 1895, Lorentz predicted the existence of an extra term due to dispersion
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
:
This was confirmed by Zeeman in 1914.
The experiment
It was shown by Hendrik LorentzHendrik Lorentz
Hendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
(1892, 1895) that the experiment can be explained by the reaction of the moving water upon the interfering waves without the need of any aether entrainment. On this occasion, Lorentz introduced a different time coordinate for moving bodies within the aether, the so called Local time (an early form of the Lorentz transformation
Lorentz transformation
In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik...
for small velocities compared to the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
). In 1895, Lorentz went a step further and explained the coefficient by local time alone and without mentioning any interaction of light and matter.
Within 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...
, Lorentz's formalism was simplified with the aid of the velocity addition formula
Velocity-addition formula
In physics, a velocity-addition formula is an equation that relates the velocities of moving objects in different reference frames.- Galilean addition of velocities :...
, which was derived by Albert Einstein (1905) from the complete Lorentz transformation. Thus it was shown by Jakob Laub
Jakob Laub
Jakob Johann Laub was a physicist from Austria-Hungary, who is most well known for his work with Albert Einstein in the early period of special relativity.-Life:...
and Max von Laue
Max von Laue
Max Theodor Felix von Laue was a German physicist who won the Nobel Prize in Physics in 1914 for his discovery of the diffraction of X-rays by crystals...
(1907) that the Fresnel drag coefficient can be easily explained by that formula and so the experiment is supporting evidence for the colinear case of Einstein's velocity addition formula. Einstein later emphasized the importance of the experiment for developing and confirming the theory.
Although it is referred to as the Fizeau experiment, Fizeau was an active experimenter who carried out a wide variety of different experiments involving measuring the speed of light in different situations.
Fizeau's result was replicated by Albert Michelson and Edward Morley
Edward Morley
Edward Williams Morley was an American scientist famous for the Michelson–Morley experiment.-Biography:...
(1886), and by Pieter Zeeman
Pieter Zeeman
Pieter Zeeman was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Hendrik Lorentz for his discovery of the Zeeman effect.-Childhood and youth:...
(1914).
Another experiment was that of Franz Harress (1910). Contrary to Fizeau, he used a rotating device and actually confirmed Fresnel's dragging coefficient. However, he additionally found a "systematic bias" in the data, which later turned out to be 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...
.
Derivation in special relativity
The speed of light in immobile water is c/n.From the velocity composition law it follows that the speed of light observed in the laboratory, where water is flowing with speed v (in the same direction as light) is
Thus the difference in speed is (assuming v is small comparing to c, approximating to the first non-trivial correction)
See also
- Aether drag hypothesisAether drag hypothesisIn 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...
- Velocity-addition formulaVelocity-addition formulaIn physics, a velocity-addition formula is an equation that relates the velocities of moving objects in different reference frames.- Galilean addition of velocities :...
- History of special relativityHistory of special relativityThe history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others...