In the 19th century, the theory of theluminiferous aether as the hypotheticalmedium for the propagation of light waves was widely discussed. The aether hypothesis arose because physicists of that era could not conceive of light waves propagating without a physical medium in which to do so. When experiments failed to detect the hypothesized luminiferous aether, physicists conceived explanations for the experiments' failure which preserved the hypothetical aether's existence.

Theaether drag hypothesis proposed that the luminiferous aether is dragged by or entrained within moving matter. According to one version of this hypothesis, no relative motion exists between Earth and aether. According to another version, the Earth does move relative to the aether and the measuredspeed of light should depend on the speed of this motion ("aether wind"), which should be measurable by instruments at rest on Earth's surface. In 1818,Augustin-Jean Fresnel proposed that the aether is partially entrained by matter. In 1845,George Stokes proposed that the aether is completely entrained within or in the vicinity of matter.

Although Fresnel's almost-stationary theory was apparently confirmed by theFizeau experiment (1851), Stokes' theory was apparently confirmed by theMichelson–Morley experiment (1881, 1887).Hendrik Lorentz resolved this contradictory situation inhis own aether theory, which banished any form of aether dragging.Albert Einstein'sspecial theory of relativity (1905) excludes aether as a mechanical medium.^[1][2][3]

In modern physics (which is based on thetheory of relativity andquantum mechanics), the aether as a "material substance" with a "state of motion" no longer plays any role. So questions concerning a possible "aether drag" are no longer considered meaningful by the scientific community. However,frame-dragging as predicted bygeneral relativity, in which rotating masses distort thespacetime metric, causing aprecession of the orbit of nearby particles, does exist. But this effect is orders of magnitude weaker than any "aether drag" discussed in this article.

In 1810,François Arago 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 therefractive 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 there was no difference in refraction between stars, between times of day or between seasons. All Arago observed was ordinarystellar aberration.^[4]

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".^[5] He realised that the velocity of propagation of waves depends on the density of the medium and so proposed that the velocity of light in the prism would need to be adjusted by an amount of 'drag'. The velocity of light${\displaystyle v_n}$ in the glass without any adjustment is given by:

${\displaystyle v_n=\frac{c}{n}}$

The drag adjustment${\displaystyle v_d}$ is given by:

${\displaystyle v_d=v\left(1-\frac{{\rho }_e}{{\rho }_g}\right)}$

Where${\displaystyle {\rho }_e}$ is the aether density in the environment,${\displaystyle {\rho }_g}$ is the aether density in the glass and${\displaystyle v}$ is the velocity of the prism with respect to the aether.

The factor${\displaystyle \left(1-\frac{{\rho }_e}{{\rho }_g}\right)}$ can be written as${\displaystyle \left(1-\frac{1}{n^2}\right)}$ because the refractive index, n, would be dependent on the density of the aether. This is known as theFresnel drag coefficient. The velocity of light in the glass is then given by:

${\displaystyle V=\frac{c}{n}+v\left(1-\frac{1}{n^2}\right)}$

This correction was successful in explaining thenull 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.

Fresnel's dragging coefficient was directly confirmed by theFizeau experiment and its repetitions. In general, with the aid of this coefficient the negative result of all optical aether drift experiments sensitive enough to detectfirst order effects (such as theexperiments of Arago, Fizeau, Hoek, Airy, Mascart) can be explained. The notion of an (almost) stationary aether is also consistent withstellar aberration. However, this theory is considered to be refuted for the following reasons:^[1][2][3]

• It was already known in the 19th century, that partial aether dragging requires therelative 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 predictspositive results by experiments which are sensitive enough to detect second order effects. However, experiments such as theMichelson–Morley experiment and theTrouton–Noble experiment, gavenegative results within their margin of error and are therefore considered refutations of Fresnel's aether.
• In theHammar experiment, conducted byGustaf Wilhelm Hammar in 1935, acommon-path interferometer was used. 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.^[6]

ForGeorge Stokes (1845) the model of an aether which is totally unaffected or only partially affected by moving matter was unnatural and unconvincing, so he assumed that the aether is completely dragged within and in the vicinity of matter, partially dragged at larger distances, and stays at rest in free space.^{[7][8][9][10]} AlsoHeinrich Rudolf Hertz (1890) incorporated a complete aether drag model within his elaboration of Maxwell's theory of electromagnetism, to bring it into accord with the Galileanprinciple of relativity. That is, if it is assumed that the aether is at rest within matter in one reference frame, theGalilean transformation gives the result that matter and (entrained) aether travel with the same speed in another frame of reference.^[1]

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:^[1][11]

• TheFizeau experiment (1851) indicated only a partial entrainment of light.
• TheSagnac effect 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.^[12][13]

• It is inconsistent with the phenomenon ofstellar 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 1871Airy 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,${\displaystyle \alpha }$, is given by:

${\displaystyle \tan (\alpha )=\frac{v\delta t}{c\delta t}.}$ So:${\displaystyle \tan (\alpha )=\frac{v}{c}}$

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${\displaystyle \alpha }$ = 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 additional assumptions in order to bring his theory into accord with experimental results. To explain aberration, he assumed that his incompressible aether is irrotational as well, which would give, in connection with his specific model of aether drag, the correct law of aberration.^[7] To reproduce Fresnel's dragging coefficient (and therefore to explain the Fizeau experiment) he argued that the aether is completely dragged within a medium –i.e. the aether gets condensed when it enters the medium and rarefied when it leaves it again, which modifies the speed of the aether as well as that of light and leads to the same expression as Fresnel's.^[8]

Even though Stokes' aberration theory was considered viable for some time, it had to be given up because Lorentz argued in 1886, that when 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.^[14]

Another version of Stokes' model was proposed byTheodor des Coudres andWilhelm 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.^[15] 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 theMichelson–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 field, a negative result has to be expected - but the result was positive.^[11]

And from a theoretical side it was noted byHendrik Antoon Lorentz, that the Stokes-Planck hypothesis requires that the speed of light is not affected by a density increase of 50,000 times of the aether. So Lorentz and Planck himself rejected this hypothesis as improbable.^[1][16]

Since Lorentz was forced to abandon Stokes' hypothesis, he chose Fresnel's model as a starting point.^{[citation needed]} He was able to reproduce Fresnel's dragging coefficient in 1892, though in Lorentz's theory it represents a modification of the propagation of light waves, not the result of any aether entrainment. Therefore,Lorentz's aether is fully stationary or immobile. However, this leads to the same problem that already afflicted Fresnel's model: it stood in contradiction with the Michelson–Morley experiment. Therefore,George Francis FitzGerald (1889) and Lorentz (1892) introducedlength contraction, that is, all bodies contract in the line of motion by the factor${\displaystyle \sqrt{1-v^2/c^2}}$. In addition, in Lorentz's theory theGalilean transformation was replaced by theLorentz transformation.^[17]

However, the accumulation of hypotheses to rescue the stationary aether concept was considered to be very artificial. So, it wasAlbert Einstein (1905), who recognized that it is only required to assume theprinciple of relativity and the constancy of the speed of light in allinertial frames of reference, in order to develop the theory ofspecial relativity and to derive the complete Lorentz transformation. All this was done without using the stationary aether concept.^[18]

As shown byMax von Laue (1907), special relativity predicts the result of the Fizeau experiment from thevelocity addition theorem without any need for an aether. If${\displaystyle V}$ is the velocity of light relative to the Fizeau apparatus and${\displaystyle U}$ is the velocity of light relative to the water and${\displaystyle v}$ is the velocity of the water:

${\displaystyle U=\frac{c}{n}}$

${\displaystyle V=\frac{c/n+v}{1+v/nc}}$

which, if v/c is small can be expanded using the binomial expansion to become:

${\displaystyle V\approx \frac{c}{n}+v\left(1-\frac{1}{n^2}\right)}$

This is identical toFresnel equation.^[19]

Maurice Allais proposed in 1959 an aether hypothesis involving a wind velocity of about 8 km/s, much lower than the standard value of 30 km/s supported by scientists of the nineteenth century, and compatible with the Michelson–Morley and the disputed^[20]Dayton Miller experiments,^[21] as well as his own experiments.^[22][23] The controversialAllais effect is not predicted by general relativity and his experimental results have been disputed.^{[24]: 211 [25][26]}

• History of special relativity
• Tests of special relativity
• Tests of general relativity
• Frame-dragging

• Wikibooks: Special Relativity
• Resnick, Robert,Basic Concepts in Relativity and Early Quantum Theory, 1972, John Wiley and Sons Inc.

• Mathpages:Stokes’ Mistake

• Aether theories

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