In the 19th century, the theory of the luminiferous aether as the hypothetical medium 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, which preserved the hypothetical aether's existence, for the experiments' failure to detect it.

The aether 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 measured 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. 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 the Fizeau experiment (1851), Stokes' theory was apparently confirmed by the Michelson–Morley experiment (1881, 1887). Hendrik Lorentz resolved this contradictory situation in his own aether theory, which banished any form of aether dragging. Albert Einstein's special theory of relativity (1905) excludes aether as a mechanical medium.^[1][2][3]

Partial aether dragging

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 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 there was no difference in refraction between stars, between times of day or between seasons. All Arago observed was ordinary stellar 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 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 the Fresnel 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 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.

Complete aether dragging

For George 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]} Also Heinrich 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 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.^[1]

Problems of complete aether dragging

Lodge's ether machine. Light from a sensitive common path interferometer was guided between the rapidly rotating disks.

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]

• The Fizeau experiment (1851) indicated only a partial entrainment of light.
• The Sagnac 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]

Complete aether dragging is inconsistent with the phenomenon of stellar aberration. In this illustration, imagine the stars to be infinitely distant. Aberration occurs when the observer's velocity has a component that is perpendicular to the line traveled by the light incoming from the star. As seen in the animation on the left, the telescope must be tilted before the star will appear in the center of the eyepiece. As seen in the animation of the right, if the aether is dragged in the vicinity of the Earth, then the telescope must be pointed directly at the star for the star to appear in the center of the eyepiece.

• 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 Airy 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.

Lorentz and Einstein

Since Lorentz was forced to abandon Stokes' hypothesis, he chose Fresnel's model as a starting point. 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) introduced length 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 the Galilean transformation was replaced by the Lorentz transformation.^[17]

However, the accumulation of hypotheses to rescue the stationary aether concept was considered to be very artificial. So, it was Albert Einstein (1905), 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 reference, 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.^[18]

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 ${\displaystyle V}$ 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 to Fresnel equation.^[19]

Allais aether hypothesis

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 Dayton Miller experiments,^[20] as well as his own experiments regarding the controversial Allais effect unpredictable by general relativity.^[21][22] Despite advocating for the need of another theory of gravity,^[23] his hypothesis didn't gain significant traction amongst mainstream scientists.

Summary

In modern physics (which is based on the theory of relativity and quantum 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 by general relativity, in which rotating masses distort the spacetime metric, causing a precession of the orbit of nearby particles, does exist. But this effect is orders of magnitude weaker than any "aether drag" discussed in this article.

See also

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

Bibliography and references

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

External links

• Mathpages: Stokes’ Mistake