Aether drag hypothesis
Encyclopedia
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 the question whether the luminiferous aether is dragged by or entrained within moving matter. According to the first variant no relative motion exists between Earth and aether; according to the second one, relative motion exists and thus the speed of light
should depend on the speed of this motion ("aether wind"), which should be measurable by instruments at rest on Earth's surface. Specific aether models were invented by Augustin-Jean Fresnel
who in 1818 proposed that the aether is partially entrained by matter. The other one was proposed by George Stokes in 1845, in which the aether is completely entrained within or in the vicinity of matter.
While Fresnel's almost stationary theory was apparently confirmed by the Fizeau experiment
(1851), Stokes' theory was apparently confirmed by the Michelson-Morley experiment
(1881, 1887). This contradictory situation was resolved by the works of Hendrik Antoon Lorentz (1895, 1904) whose Lorentz ether theory
banished any form of aether dragging, and finally with the work of Albert Einstein
(1905) whose theory of special relativity
doesn't contain the aether as a mechanical medium at all.
realised that variations in the refractive index of a substance predicted by the corpuscular theory would provide a useful method for measuring the velocity of light. These predictions arose because the refractive index
of a substance such as glass depends on the ratio of the velocities of light in air and in the glass. Arago attempted to measure the extent to which corpuscles of light would be refracted by a glass prism at the front of a telescope. He expected that there would be a range of different angles of refraction due to the variety of different velocities of the stars and the motion of the earth at different times of the day and year. Contrary to this expectation he found that that there was no difference in refraction between stars, between times of day or between seasons. All Arago observed was ordinary stellar aberration.
In 1818 Augustin Jean Fresnel examined Arago's results using a wave theory of light. He realised that even if light were transmitted as waves the refractive index of the glass-air interface should have varied as the glass moved through the aether to strike the incoming waves at different velocities when the earth rotated and the seasons changed. Fresnel proposed that the glass prism would carry some of the aether along with it so that "..the aether is in excess inside the prism".
He realised that the velocity of propagation of waves depends on the density of the medium so proposed that the velocity of light in the prism would need to be adjusted by an amount of 'drag'. The velocity of light
in the glass without any adjustment is given by:
The drag adjustment
is given by:
Where
is the aether density in the environment, 
is the aether density in the glass and 
is the velocity of the prism with respect to the aether.
The factor
can be written as 
because the refractive index, n, would be dependent on the density of the aether. This is known as the Fresnel drag coefficient. The velocity of light in the glass is then given by:
This correction was successful in explaining the null result of Arago's experiment. It introduces the concept of a largely stationary aether that is dragged by substances such as glass but not by air. Its success favoured the wave theory of light over the previous corpuscular theory.
(and its repetitions). With the aid of this coefficient also the negative result of all aether drift experiments sensible enough to detect first order effects (such as the experiments of Arago, Fizeau, Hoek, Mascart) can be explained. The notion of an (almost) stationary aether is also consistent with stellar aberration. However, this theory is considered to be refuted for the following reasons:
To rescue the hypotheses of a stationary aether, George Francis Fitzgerald and Hendrik Antoon Lorentz introduced length contraction
, that is, all bodies contract in the line of motion by the factor
. In addition, in Lorentz's theory (which is nowadays called Lorentz ether theory
) the Galilean transformation
was replaced by the Lorentz transformation
. Also Fresnel's dragging coefficient is reproduced, that is, in Lorentz's theory it is a modification of the propagation of light waves, not the result of any aether entrainment.
However, the accumulation of hypotheses to rescue the stationary aether concept was considered to be very artificial. So it was Albert Einstein
, who recognized that it is only required to assume the principle of relativity
and the constancy of the speed of light in all inertial frames of references, in order to develop the theory of special relativity
and to derive the complete Lorentz transformation. All this was done without using the stationary aether concept.
As shown by Max von Laue
(1907), special relativity predicts the result of the Fizeau experiment from the velocity addition theorem without any need for an aether. If
is the velocity of light relative to the Fizeau apparatus and 
is the velocity of light relative to the water and 
is the velocity of the water:
which, if v/c is small can be expanded using the binomial expansion to become:
This is identical to Fresnel's equation.
Heinrich Rudolf Hertz
(1890) incorporated Stoke's aether dragging model within his elaboration of Maxwell's theory of electromagnetism, to bring it into accord with the Galilean principle of relativity
. That is, if it is assumed that the aether is at rest within matter in one reference frame, the Galilean transformation
gives the result that matter and (entrained) aether travel with the same speed in another frame of reference.
Stokes already in 1845 introduced some Ad hoc hypothesis
it bring his theory into accord with experimental results. To reproduce Fresnel's dragging coefficient (and therefore to explain the Fizeau experiment), he argued that although the aether is completely dragged by matter, it has a different velocity within matter which would lead to the same expression as Fresnel's. And to explain aberration, Stokes assumed that the aether is completely irrotational, i.e. that the elements of the aether do not rotate, which would give the correct law of aberration. Against the latter hypotheses Lorentz argued that, given that the aether is incompressible as in Stokes' theory, and if the aether has the same normal component of velocity as the earth, it would not have the same tangential component of velocity, so all conditions posed by Stokes cannot be fulfilled at the same time. Because of the extreme nature of the additional assumptions of Stokes, his explanations as to the Fresnel-coefficient and the aberration of light were not considered as viable alternatives to the theories of Lorentz and Einstein.
and Wilhelm Wien
(1900). They assumed that aether dragging is proportional to the gravitational mass. That is, the aether is completely dragged by the earth, and only partially dragged by smaller objects on earth. And to save Stokes's explanation of aberration, Max Planck
(1899) argued in a letter to Lorentz, that the aether might not be incompressible, but condensed by gravitation in the vicinity of earth, and this would give the conditions needed for the theory of Stokes ("Stokes-Planck theory"). When compared with the experiments above, this model can explain the positive results of the experiments of Fizeau and Sagnac, because the small mass of those instruments can only partially (or not at all) drag the aether, and for the same reason it explains the negative result of Lodge's experiments. It is also compatible with Hammar's and Michelson-Morley experiment, as the aether is completely dragged by the large mass of earth.
However, this theory was directly refuted by the Michelson–Gale–Pearson experiment (1925). The great difference of this experiment against the usual Sagnac experiments is the fact that the rotation of earth itself was measured. If the aether is completely dragged by the Earth's gravitational mass, a negative result has to be expected - but the result was positive. And from a theoretical side it was noted by Lorentz, that the Stokes-Planck hypothesis requires that the speed of light is not affected by a density increase of 50000 times of the aether. So Lorentz and Planck himself rejected this hypothesis as improbable.
and Quantum mechanics
), the aether as a "material substance" with a "state of motion" plays no role anymore. So questions concerning a possible "aether drag" are not considered meaningful anymore by the scientific community. What in fact exists, is frame-dragging
as predicted by general relativity
, that is, rotating masses distort the spacetime metric
, causing a precession
of the orbit of nearby particles. But this effect is magnitudes of orders weaker than any "aether drag" discussed in this article.
Luminiferous 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....
as the hypothetical medium
Medium
- Communication :* Medium , storage and/or transmission tools used to store and deliver information or data* Transmission medium, in physics and telecommunications, any material substance which can propagate waves or energy...
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 the question whether the luminiferous aether is dragged by or entrained within moving matter. According to the first variant no relative motion exists between Earth and aether; according to the second one, relative motion exists and thus 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...
should depend on the speed of this motion ("aether wind"), which should be measurable by instruments at rest on Earth's surface. Specific aether models were invented by Augustin-Jean Fresnel
Augustin-Jean Fresnel
Augustin-Jean Fresnel , was a French engineer who contributed significantly to the establishment of the theory of wave optics. Fresnel studied the behaviour of light both theoretically and experimentally....
who in 1818 proposed that the aether is partially entrained by matter. The other one was proposed by George Stokes in 1845, in which the aether is completely entrained within or in the vicinity of matter.
While Fresnel's almost stationary theory was apparently confirmed by the Fizeau experiment
Fizeau experiment
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...
(1851), Stokes' theory was apparently confirmed by the Michelson-Morley experiment
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...
(1881, 1887). This contradictory situation was resolved by the works of Hendrik Antoon Lorentz (1895, 1904) whose Lorentz ether theory
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....
banished any form of aether dragging, and finally with the work of 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...
(1905) whose theory 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...
doesn't contain the aether as a mechanical medium at all.
Partial aether dragging
In 1810 François AragoFrançois Arago
François Jean Dominique Arago , known simply as François Arago , was a French mathematician, physicist, astronomer and politician.-Early life and work:...
realised that variations in the refractive index of a substance predicted by the corpuscular theory would provide a useful method for measuring the velocity of light. These predictions arose because the refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
of a substance such as glass depends on the ratio of the velocities of light in air and in the glass. Arago attempted to measure the extent to which corpuscles of light would be refracted by a glass prism at the front of a telescope. He expected that there would be a range of different angles of refraction due to the variety of different velocities of the stars and the motion of the earth at different times of the day and year. Contrary to this expectation he found that that there was no difference in refraction between stars, between times of day or between seasons. All Arago observed was ordinary stellar aberration.
In 1818 Augustin Jean Fresnel examined Arago's results using a wave theory of light. He realised that even if light were transmitted as waves the refractive index of the glass-air interface should have varied as the glass moved through the aether to strike the incoming waves at different velocities when the earth rotated and the seasons changed. Fresnel proposed that the glass prism would carry some of the aether along with it so that "..the aether is in excess inside the prism".
He realised that the velocity of propagation of waves depends on the density of the medium so proposed that the velocity of light in the prism would need to be adjusted by an amount of 'drag'. The velocity of light
in the glass without any adjustment is given by:The drag adjustment
is given by:Where
is the aether density in the environment, is the aether density in the glass and is the velocity of the prism with respect to the aether.The factor
can be written as because the refractive index, n, would be dependent on the density of the aether. This is known as the Fresnel drag coefficient. The velocity of light in the glass is then given by:This correction was successful in explaining the null result of Arago's experiment. It introduces the concept of a largely stationary aether that is dragged by substances such as glass but not by air. Its success favoured the wave theory of light over the previous corpuscular theory.
Problems of partial aether dragging
Fresnel's dragging coefficient was confirmed by the Fizeau experimentFizeau experiment
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...
(and its repetitions). With the aid of this coefficient also the negative result of all aether drift experiments sensible enough to detect first order effects (such as the experiments of Arago, Fizeau, Hoek, Mascart) can be explained. The notion of an (almost) stationary aether is also consistent with stellar aberration. However, this theory is considered to be refuted for the following reasons:
- It was already known in the 19th century, that partial aether dragging requires the relative velocity of aether and matter to be different for light of different colours - which is evidently not the case.
- Fresnel's theory of an (almost) stationary aether predicts positive results by experiments which are sensible enough to detect second order effects. However, those experiments as the Michelson-Morley experimentMichelson-Morley experimentThe 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 Trouton-Noble experimentTrouton-Noble experimentThe Trouton–Noble experiment attempted to detect motion of the Earth through the luminiferous aether, and was conducted in 1901–1903 by Frederick Thomas Trouton and H. R. Noble...
, gave negative results and are therefore direct refutations of Fresnel's aether.
To rescue the hypotheses of a stationary aether, George Francis Fitzgerald and Hendrik Antoon Lorentz introduced length contraction
Length contraction
In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer...
, that is, all bodies contract in the line of motion by the factor
. In addition, in Lorentz's theory (which is nowadays called Lorentz ether theoryLorentz 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 Galilean transformation
Galilean transformation
The Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. This is the passive transformation point of view...
was replaced by 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...
. Also Fresnel's dragging coefficient is reproduced, that is, in Lorentz's theory it is a modification of the propagation of light waves, not the result of any aether entrainment.
However, the accumulation of hypotheses to rescue the stationary aether concept was considered to be very artificial. So it was 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...
, who recognized that it is only required to assume the principle of relativity
Principle of relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....
and the constancy of the speed of light in all inertial frames of references, in order to develop the theory 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 to derive the complete Lorentz transformation. All this was done without using the stationary aether concept.
As shown by 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), special relativity predicts the result of the Fizeau experiment from the velocity addition theorem without any need for an aether. If
is the velocity of light relative to the Fizeau apparatus and is the velocity of light relative to the water and is the velocity of the water:which, if v/c is small can be expanded using the binomial expansion to become:
This is identical to Fresnel's equation.
Complete aether dragging
For George Stokes (1845) the model of an aether which is only partially dragged by matter was unnatural. So Stokes assumed that the aether is completely dragged by and in the vicinity of matter.Heinrich Rudolf Hertz
Heinrich Rudolf Hertz
Heinrich Rudolf Hertz was a German physicist who clarified and expanded the electromagnetic theory of light that had been put forth by Maxwell...
(1890) incorporated Stoke's aether dragging model within his elaboration of Maxwell's theory of electromagnetism, to bring it into accord with the Galilean principle of relativity
Principle of relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....
. That is, if it is assumed that the aether is at rest within matter in one reference frame, the Galilean transformation
Galilean transformation
The Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. This is the passive transformation point of view...
gives the result that matter and (entrained) aether travel with the same speed in another frame of reference.
Problems of complete aether dragging
Complete aether dragging can explain the negative outcome of all aether drift experiments (like the Michelson-Morley experiment). However, this theory is considered to be wrong for the following reasons:- The Fizeau experimentFizeau experimentThe 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...
(1851) indicated only a partial entrainment of light. - The Sagnac effectSagnac effectThe 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...
shows that two rays of light, emanated from the same light source in different directions on a rotating platform, require different times to come back to the light source. However, if the aether is completely dragged by the platform this effect should not occur at all. - Oliver Lodge conducted experiments in the 1890s, seeking evidence that the propagation of light is influenced by being in the proximity of large rotating masses, and found no such influence.
- In the "Hammar experiment", conducted by Gustaf Wilhelm Hammar in 1935, a Michelson-Morley type interferometer was used, and massive lead blocks were installed on both sides of only one leg of the interferometer. This arrangement should cause different amounts of aether drag and therefore produce a positive result. However, the result was again negative.
- It is inconsistent with the phenomenon of stellar aberration. In stellar aberration the position of a star when viewed with a telescope swings each side of a central position by about 20.5 seconds of arc every six months. This amount of swing is the amount expected when considering the speed of earth's travel in its orbit. In 1871 AiryGeorge Biddell AirySir George Biddell Airy PRS KCB was an English mathematician and astronomer, Astronomer Royal from 1835 to 1881...
demonstrated that stellar aberration occurs even when a telescope is filled with water. It seems that if the aether drag hypothesis were true then stellar aberration would not occur because the light would be travelling in the aether which would be moving along with the telescope. Consider a bucket on a train about to enter a tunnel, and a drop of water drips from the tunnel entrance into the bucket at the very center. The drop will not hit the center at the bottom of the bucket. The bucket is analogous to the tube of a telescope, the drop is a photon and the train is the earth. If aether is dragged then the droplet would be traveling with the train when it is dropped and would hit the center of bucket at the bottom. The amount of stellar aberration,
, is given by:
-
So: 
- The speed at which the earth goes round the sun, v = 30 km/s, and the speed of light is c = 299,792,458 m/s which gives
= 20.5 seconds of arc every six months. This amount of aberration is observed and this contradicts the complete aether drag hypothesis.
Stokes already in 1845 introduced some Ad hoc hypothesis
Ad hoc hypothesis
In science and philosophy, an ad hoc hypothesis is a hypothesis added to a theory in order to save it from being falsified. Ad hoc hypothesizing is compensating for anomalies not anticipated by the theory in its unmodified form....
it bring his theory into accord with experimental results. To reproduce Fresnel's dragging coefficient (and therefore to explain the Fizeau experiment), he argued that although the aether is completely dragged by matter, it has a different velocity within matter which would lead to the same expression as Fresnel's. And to explain aberration, Stokes assumed that the aether is completely irrotational, i.e. that the elements of the aether do not rotate, which would give the correct law of aberration. Against the latter hypotheses Lorentz argued that, given that the aether is incompressible as in Stokes' theory, and if the aether has the same normal component of velocity as the earth, it would not have the same tangential component of velocity, so all conditions posed by Stokes cannot be fulfilled at the same time. Because of the extreme nature of the additional assumptions of Stokes, his explanations as to the Fresnel-coefficient and the aberration of light were not considered as viable alternatives to the theories of Lorentz and Einstein.
Gravitational aether drag
Another version of Stokes' model was proposed by Theodor des CoudresTheodor des Coudres
Theodor des Coudres was a German physicist.Theodor des Coudres was the son of Julius des Coudres and his wife Anna Henrietta Rosenstock...
and Wilhelm Wien
Wilhelm Wien
Wilhelm Carl Werner Otto Fritz Franz Wien was a German physicist who, in 1893, used theories about heat and electromagnetism to deduce Wien's displacement law, which calculates the emission of a blackbody at any temperature from the emission at any one reference temperature.He also formulated an...
(1900). They assumed that aether dragging is proportional to the gravitational mass. That is, the aether is completely dragged by the earth, and only partially dragged by smaller objects on earth. And to save Stokes's explanation of aberration, Max Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...
(1899) argued in a letter to Lorentz, that the aether might not be incompressible, but condensed by gravitation in the vicinity of earth, and this would give the conditions needed for the theory of Stokes ("Stokes-Planck theory"). When compared with the experiments above, this model can explain the positive results of the experiments of Fizeau and Sagnac, because the small mass of those instruments can only partially (or not at all) drag the aether, and for the same reason it explains the negative result of Lodge's experiments. It is also compatible with Hammar's and Michelson-Morley experiment, as the aether is completely dragged by the large mass of earth.
However, this theory was directly refuted by the Michelson–Gale–Pearson experiment (1925). The great difference of this experiment against the usual Sagnac experiments is the fact that the rotation of earth itself was measured. If the aether is completely dragged by the Earth's gravitational mass, a negative result has to be expected - but the result was positive. And from a theoretical side it was noted by Lorentz, that the Stokes-Planck hypothesis requires that the speed of light is not affected by a density increase of 50000 times of the aether. So Lorentz and Planck himself rejected this hypothesis as improbable.
Summary
In modern physics (which is based on the theory of relativityTheory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
and Quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
), the aether as a "material substance" with a "state of motion" plays no role anymore. So questions concerning a possible "aether drag" are not considered meaningful anymore by the scientific community. What in fact exists, is frame-dragging
Frame-dragging
Einstein's general theory of relativity predicts that non-static, stationary mass-energy distributions affect spacetime in a peculiar way giving rise to a phenomenon usually known as frame-dragging...
as predicted by general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, that is, rotating masses distort the spacetime metric
Metric tensor (general relativity)
In general relativity, the metric tensor is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational field familiar from Newtonian gravitation...
, causing a precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
of the orbit of nearby particles. But this effect is magnitudes of orders weaker than any "aether drag" discussed in this article.
See also
- 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...
- Tests of special relativity
- Tests of general relativityTests of general relativityAt its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's...