Aether drag hypothesis

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. 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 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 v_n in the glass without any adjustment is given by: : v_n = \frac{c}{n} The drag adjustment v_d is given by: : v_d = v \left(1 - \frac {\rho_e}{\rho_g} \right) Where \rho_e is the aether density in the environment, \rho_g is the aether density in the glass and v is the velocity of the prism with respect to the aether. The factor \left(1 - \frac {\rho_e}{\rho_g}\right) can be written as \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: : 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. Problems of partial aether dragging Fresnel's dragging coefficient was directly confirmed by the Fizeau experiment and its repetitions. In general, with the aid of this coefficient the negative result of all optical aether drift experiments sensitive enough to detect first order effects (such as the experiments of Arago, Fizeau, Hoek, Airy, 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: ==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. 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. • 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. • 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, \alpha, is given by: ::\tan(\alpha) = \frac{v \delta t}{c \delta t}. So: \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 \alpha = 20.5 seconds of arc every six months. This amount of aberration is observed and this contradicts the complete aether drag hypothesis. Stokes' responses to those problems 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. Gravitational aether drag Another version of Stokes' model was proposed by Theodor des Coudres 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 field, a negative result has to be expected - but the result was positive. ==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 \sqrt{1-v^{2}/c^{2}}. In addition, in Lorentz's theory the Galilean transformation was replaced by the Lorentz transformation. 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. 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 V is the velocity of light relative to the Fizeau apparatus and U is the velocity of light relative to the water and v is the velocity of the water: : U = \frac {c}{n} : V = \frac {c/n + v}{1 + v/nc} which, if v/c is small can be expanded using the binomial expansion to become: : V \approx \frac {c}{n} + v \left(1 - \frac{1}{n^2} \right) This is identical to Fresnel equation.{{Citation |author =Laue, Max von|year=1907 |title=Die Mitführung des Lichtes durch bewegte Körper nach dem Relativitätsprinzip |trans-title=The Entrainment of Light by Moving Bodies in Accordance with the Principle of Relativity|journal=Annalen der Physik |volume =23|pages =989–990 |doi=10.1002/andp.19073281015 |bibcode=1907AnP...328..989L == 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 disputed Dayton Miller experiments, as well as his own experiments. The controversial Allais effect is not predicted by general relativity and his experimental results have been disputed. ==See also==