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==Relative motion between the Earth and aether== ===Aether drag=== {{Main|Aether drag hypothesis}} The two most important models, which were aimed to describe the relative motion of the Earth and aether, were [[Augustin-Jean Fresnel]]'s (1818) model of the (nearly) stationary aether including a partial aether drag determined by Fresnel's dragging coefficient,<ref group=A name=fresnel /> and [[George Gabriel Stokes]]' (1844)<ref group=A name=stokes /> model of complete aether drag. The latter theory was not considered as correct, since it was not compatible with the [[aberration of light]], and the auxiliary hypotheses developed to explain this problem were not convincing. Also, subsequent experiments as the [[Sagnac effect]] (1913) also showed that this model is untenable. However, the most important experiment supporting Fresnel's theory was [[Hippolyte Fizeau|Fizeau]]'s 1851 [[Fizeau experiment|experimental confirmation]] of [[Fresnel]]'s 1818 prediction that a medium with [[refractive index]] ''n'' moving with a velocity ''v'' would increase the speed of light travelling through the medium in the same direction as ''v'' from ''c''/''n'' to:<ref group=E name=Fizeau1 /><ref group=E name=michel2 /> {{block indent|<math>\frac{c}{n} + \left( 1 - \frac{1}{n^2} \right) v.</math>}} That is, movement adds only a fraction of the medium's velocity to the light (predicted by Fresnel in order to make [[Snell's law]] work in all frames of reference, consistent with stellar aberration). This was initially interpreted to mean that the medium drags the aether along, with a ''portion'' of the medium's velocity, but that understanding became very problematic after [[Wilhelm Veltmann]] demonstrated that the index ''n'' in Fresnel's formula depended upon the [[wavelength]] of light, so that the aether could not be moving at a wavelength-independent speed. This implied that there must be a separate aether for each of the infinitely many frequencies. ===Negative aether-drift experiments=== The key difficulty with Fresnel's aether hypothesis arose from the juxtaposition of the two well-established theories of Newtonian dynamics and Maxwell's electromagnetism. Under a [[Galilean transformation]] the equations of Newtonian dynamics are [[Invariant (physics)|invariant]], whereas those of electromagnetism are not. Basically this means that while physics should remain the same in non-accelerated experiments, light would not follow the same rules because it is travelling in the universal "aether frame". Some effect caused by this difference should be detectable. A simple example concerns the model on which aether was originally built: sound. The speed of propagation for mechanical waves, the [[speed of sound]], is defined by the mechanical properties of the medium. Sound travels 4.3 times faster in water than in air. This explains why a person hearing an explosion underwater and quickly surfacing can hear it again as the slower travelling sound arrives through the air. Similarly, a traveller on an [[airliner]] can still carry on a conversation with another traveller because the sound of words is travelling along with the air inside the aircraft. This effect is basic to all Newtonian dynamics, which says that everything from sound to the trajectory of a thrown baseball should all remain the same in the aircraft flying (at least at a constant speed) as if still sitting on the ground. This is the basis of the Galilean transformation, and the concept of frame of reference. But the same was not supposed to be true for light, since Maxwell's mathematics demanded a single universal speed for the propagation of light, based, not on local conditions, but on two measured properties, the [[permittivity]] and [[Permeability (electromagnetism)|permeability]] of free space, that were assumed to be the same throughout the universe. If these numbers did change, there should be noticeable effects in the sky; stars in different directions would have different colours, for instance.{{Verify source|date=June 2011}} Thus at any point there should be one special coordinate system, "at rest relative to the aether". Maxwell noted in the late 1870s that detecting motion relative to this aether should be easy enoughâlight travelling along with the motion of the Earth would have a different speed than light travelling backward, as they would both be moving against the unmoving aether. Even if the aether had an overall universal flow, changes in position during the day/night cycle, or over the span of seasons, should allow the drift to be detected. ====First-order experiments==== Although the aether is almost stationary according to Fresnel, his theory predicts a positive outcome of aether drift experiments only to ''second'' order in <math>v/c</math> because Fresnel's dragging coefficient would cause a negative outcome of all optical experiments capable of measuring effects to ''first'' order in <math>v/c</math>. This was confirmed by the following first-order experiments, all of which gave negative results. The following list is based on the description of [[Wilhelm Wien]] (1898), with changes and additional experiments according to the descriptions of [[Edmund Taylor Whittaker]] (1910) and [[Jakob Laub]] (1910):<ref group=B name=wien /><ref group=B name=whitt /><ref group=B name=laub /> * The experiment of [[François Arago]] (1810), to confirm whether refraction, and thus the aberration of light, is influenced by Earth's motion. Similar experiments were conducted by [[George Biddell Airy]] (1871) by means of a telescope filled with water, and [[Ăleuthère Mascart]] (1872).<ref group=E name=Arago /><ref group=E name=Airy /><ref group=E name=masc1 /> * The experiment of Fizeau (1860), to find whether the rotation of the polarization plane through glass columns is changed by Earth's motion. He obtained a positive result, but Lorentz could show that the results have been contradictory. [[DeWitt Bristol Brace]] (1905) and Strasser (1907) repeated the experiment with improved accuracy, and obtained negative results.<ref group=E name=Fizeau2 /><ref group=E name=Brace2 /><ref group=E name=Strasser /> * The experiment of [[Martin Hoek]] (1868). This experiment is a more precise variation of the [[Fizeau experiment]] (1851). Two light rays were sent in opposite directions â one of them traverses a path filled with resting water, the other one follows a path through air. In agreement with Fresnel's dragging coefficient, he obtained a negative result.<ref group=E name=Hoek /> * The experiment of [[Wilhelm Klinkerfues]] (1870) investigated whether an influence of Earth's motion on the absorption line of sodium exists. He obtained a positive result, but this was shown to be an experimental error, because a repetition of the experiment by [[Hermanus Haga|Haga]] (1901) gave a negative result.<ref group=E name=Klinkerfues /><ref group=E name=Haga /> * The experiment of Ketteler (1872), in which two rays of an interferometer were sent in opposite directions through two mutually inclined tubes filled with water. No change of the interference fringes occurred. Later, Mascart (1872) showed that the interference fringes of polarized light in calcite remained uninfluenced as well.<ref group=E name=Ketteler /><ref group=E name=masc2 /> * The experiment of [[Ăleuthère Mascart]] (1872) to find a change of rotation of the polarization plane in quartz. No change of rotation was found when the light rays had the direction of Earth's motion and then the opposite direction. [[Lord Rayleigh]] conducted similar experiments with improved accuracy, and obtained a negative result as well.<ref group=E name=masc1 /><ref group=E name=masc2 /><ref group=E name=Rayleigh1 /> Besides those optical experiments, also electrodynamic first-order experiments were conducted, which should have led to positive results according to Fresnel. However, [[Hendrik Antoon Lorentz]] (1895) modified Fresnel's theory and showed that those experiments can be explained by a stationary aether as well:<ref group=A name=lorb /> * The experiment of [[Wilhelm RĂśntgen]] (1888), to find whether a charged capacitor produces magnetic forces due to Earth's motion.<ref group=E name=Roentgen /> * The experiment of [[Theodor des Coudres]] (1889), to find whether the inductive effect of two wire rolls upon a third one is influenced by the direction of Earth's motion. Lorentz showed that this effect is cancelled to first order by the electrostatic charge (produced by Earth's motion) upon the conductors.<ref group=E name=Coudres /> * The experiment of KĂśnigsberger (1905). The plates of a capacitor are located in the field of a strong electromagnet. Due to Earth's motion, the plates should have become charged. No such effect was observed.<ref group=E name=Koenigsberger /> * The experiment of [[Frederick Thomas Trouton]] (1902). A capacitor was brought parallel to Earth's motion, and it was assumed that momentum is produced when the capacitor is charged. The negative result can be explained by Lorentz's theory, according to which the electromagnetic momentum compensates the momentum due to Earth's motion. Lorentz could also show, that the sensitivity of the apparatus was much too low to observe such an effect.<ref group=E name=Trouton1 /> ====Second-order experiments==== [[File:Michelson-Morley experiment conducted with white light.png|right|thumb|The MichelsonâMorley experiment compared the time for light to reflect from mirrors in two orthogonal directions.]] While the ''first''-order experiments could be explained by a modified stationary aether, more precise ''second''-order experiments were expected to give positive results. However, no such results could be found. The famous [[MichelsonâMorley experiment]] compared the source light with itself after being sent in different directions and looked for changes in phase in a manner that could be measured with extremely high accuracy. In this experiment, their goal was to determine the velocity of the Earth through the aether.<ref group=E name=michel1 /><ref group=E name=michel3 /> The publication of their result in 1887, the [[null result]], was the first clear demonstration that something was seriously wrong with the aether hypothesis (Michelson's first experiment in 1881 was not entirely conclusive). In this case the MM experiment yielded a shift of the fringing pattern of about 0.01 of a [[Fringe shift|fringe]], corresponding to a small velocity. However, it was incompatible with the expected aether wind effect due to the Earth's (seasonally varying) velocity which would have required a shift of 0.4 of a fringe, and the error was small enough that the value may have indeed been zero. Therefore, the [[null hypothesis]], the hypothesis that there was no aether wind, could not be rejected. More modern experiments have since reduced the possible value to a number very close to zero, about 10<sup>â17</sup>. {{Blockquote|It is obvious from what has gone before that it would be hopeless to attempt to solve the question of the motion of the solar system by observations of optical phenomena at the surface of the earth.|A. Michelson and E. Morley. "On the Relative Motion of the Earth and the Luminiferous Ăther". ''[[Philosophical Magazine]]'' S. 5. Vol. 24. No. 151. December 1887.<ref>{{cite web|url=http://www.aip.org/history/gap/PDF/michelson.pdf|title=Selected Papers of Great American Physicists|website=www.aip.org|access-date=30 April 2018|url-status=live|archive-url=https://web.archive.org/web/20150715063415/https://www.aip.org/history/gap/PDF/michelson.pdf|archive-date=15 July 2015}}</ref>}} A series of experiments using similar but increasingly sophisticated apparatuses all returned the null result as well. Conceptually different experiments that also attempted to detect the motion of the aether were the [[TroutonâNoble experiment]] (1903),<ref group=E name=Trouton2 /> whose objective was to detect [[Torsion (mechanics)|torsion]] effects caused by electrostatic fields, and [[Experiments of Rayleigh and Brace|the experiments of Rayleigh and Brace]] (1902, 1904),<ref group=E name=Rayleigh2 /><ref group=E name=Brace1 /> to detect [[double refraction]] in various media. However, all of them obtained a null result, like MichelsonâMorley (MM) previously did. These "aether-wind" experiments led to a flurry of efforts to "save" aether by assigning to it ever more complex properties, and only a few scientists, like [[Emil Cohn]] or [[Alfred Bucherer]], considered the possibility of the abandonment of the aether hypothesis. Of particular interest was the possibility of "aether entrainment" or "aether drag", which would lower the magnitude of the measurement, perhaps enough to explain the results of the MichelsonâMorley experiment. However, as noted earlier, aether dragging already had problems of its own, notably aberration. In addition, the interference experiments of [[Oliver Lodge|Lodge]] (1893, 1897) and [[Ludwig Zehnder]] (1895), aimed to show whether the aether is dragged by various, rotating masses, showed no aether drag.<ref group=E name=Lodge /><ref group=E name=Lodge2 /><ref group=E name=Zehnder /> A more precise measurement was made in the [[Hammar experiment]] (1935), which ran a complete MM experiment with one of the "legs" placed between two massive lead blocks.<ref group=E name=Hammar /> If the aether was dragged by mass then this experiment would have been able to detect the drag caused by the lead, but again the null result was achieved. The theory was again modified, this time to suggest that the entrainment only worked for very large masses or those masses with large magnetic fields. This too was shown to be incorrect by the [[MichelsonâGaleâPearson experiment]], which detected the Sagnac effect due to Earth's rotation (see [[Aether drag hypothesis]]). Another completely different attempt to save "absolute" aether was made in the [[LorentzâFitzGerald contraction hypothesis]], which posited that ''everything'' was affected by travel through the aether. In this theory, the reason that the MichelsonâMorley experiment "failed" was that the apparatus contracted in length in the direction of travel. That is, the light was being affected in the "natural" manner by its travel through the aether as predicted, but so was the apparatus itself, cancelling out any difference when measured. FitzGerald had inferred this hypothesis from a paper by [[Oliver Heaviside]]. Without referral to an aether, this physical interpretation of relativistic effects was [[KennedyâThorndike experiment|shared by Kennedy and Thorndike]] in 1932 as they concluded that the interferometer's arm contracts and also the frequency of its light source "very nearly" varies in the way required by relativity.<ref group=E name=kenn /><ref>They commented in a footnote: "From [the MichelsonâMorley] experiment it is not inferred that the velocity of the earth is but a few kilometers per second, but rather that the dimensions of the apparatus vary very nearly as required by relativity. From the present experiment we similarly infer that the frequency of light varies conformably to the theory."</ref> Similarly, the [[Sagnac effect]], observed by G. Sagnac in 1913, was immediately seen to be fully consistent with special relativity.<ref group=E name=Sagnac1 /><ref group=E name=Sagnac2 /> In fact, the [[MichelsonâGaleâPearson experiment]] in 1925 was proposed specifically as a test to confirm the relativity theory, although it was also recognized that such tests, which merely measure absolute rotation, are also consistent with non-relativistic theories.<ref>The confusion over this point can be seen in Sagnac's conclusion that "in the ambient space, light is propagated with a velocity V0, independent of the movement as a whole of the luminous source O and the optical system. That is a property of space which experimentally characterizes the luminiferous aether." The invariance of light speed, independent of the movement of the source, is also one of the two fundamental principles of special relativity.</ref> During the 1920s, the experiments pioneered by Michelson were repeated by [[Dayton Miller]], who publicly proclaimed positive results on several occasions, although they were not large enough to be consistent with any known aether theory. However, other researchers were unable to duplicate Miller's claimed results. Over the years the experimental accuracy of such measurements has been raised by many orders of magnitude, and no trace of any violations of Lorentz invariance has been seen. (A later re-analysis of Miller's results concluded that he had underestimated the variations due to temperature.) Since the Miller experiment and its unclear results there have been many more experimental attempts to detect the aether. Many experimenters have claimed positive results. These results have not gained much attention from mainstream science, since they contradict a large quantity of high-precision measurements, all the results of which were consistent with special relativity.<ref>Roberts, Schleif (2006); Physics FAQ: [http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Experiments_not_consistent_with_SS Experiments that Apparently are NOT Consistent with SR/GR] {{webarchive|url=https://web.archive.org/web/20091015153529/http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html |date=2009-10-15 }}</ref>
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