2. Background of the concept of ether
The earliest written evidences of the arrangement of matter and vacuum are known from the works of philosophers of China and Greece [4, 5]. In the middle of the first millenary B.C. Chinese philosophers put forward a hypothesis that all existent consists of two opposite in sign principles - Yin and Yang . Yin and Yang - are categories expressing the idea of the world dualism. The word Yang originally meant sunshine, or what pertains to sunshine and light, that of Yin meant the absence of sunshine, i.e., shadow or darkness. In later development the Yang and Yin came to be regarded as two cosmic principles or forces, respectively representing masculinity, activity, heat, brightness, dryness, hardness, etc., for the Yang, and feminity, passivity, cold, darkness, wetness, softness, etc., for the Yin. Through the interaction of these two primary principles, all phenomena of the universe are produced. This concept has remained dominant in Chinese cosmological speculation down to recent times. Yin and Yang determine not only an evolution, but also an arrangement of all existent in the world. An early reference to it appears already in the Kuo Yü or Discussion of the States (which was itself compiled, however, probably only in the fourth or third century B.C.)
Philosophers of Ancient Greece comprehensively dealt with universe and cosmogony problems. It was precisely they who gave the name ether to all-penetrating, imperceptible and not subject to our feelings substance. The ether model suggested by Democrite  seems to be most non-contradictory. He stated that the basis of all elementary particles was ameres- really indivisible, lacking parts. Ameres being an atom's parts possess properties that radically differ from those of the atom. While atoms have gravity, ameres do not have it. The whole aggregate of ameres moving in vacuum, according to Anaximander, is a common world medium, ether or apeiron.
Though phenomena related to electricity and magnetism were known in ancient times, the history of science rise dealing with magnetism and electricity starts with the work of the British queen Elizabeth's court doctor Hilberti published in 1600 . Hilberti noticed a lot of difference between electrical and magnet forces. A magnet stone does not need to be rubbed as glass or sulphur to trigger its magnet properties. A magnet stone attracts only those things that it can attract, while electrified things attract everything. Magnetic attraction cannot be affected by a piece of paper or canvas placed between the bodies or by submersion of these bodies into water, while electrical attraction can be easily destroyed with shields. Finally, a magnetic force tends to orient the bodies in a certain direction, while an electrical one just tends to unite them in formless groups.
Creators of the fundamentals of modern mathematics and physics considered ether to be a material medium. For instance, Descartes wrote that space is filled with matter throughout. According to Descartes, the formation of visible matter, planets, occurs from the ether vortexes. Newton stated that to think "that one body can affect another one located at some distance from it, through vacuum without any "mediator" is so absurd to me that, to my mind, not a single person having the least idea of philosophical matters, can believe it" . At the end of his life Isaac Newton explained the availability of the gravity force by the pressure of the ether medium on a material body. According to his latest views, the ether density gradient is necessary to rush bodies from the ether denser areas to less dense ones. However, to let the gravity manifest itself in the way it is observed by us, the ether should, by Newton, possess very great elasticity.
The subsequent generations of scientists continued studying the ether properties. It appeared that the focal length of an achromatic telescope should be increased if it was directed to the star that the earth is moving to . Arago concluded that the light going out from any star, in all cases of reflection and refraction behaves exactly the same way it would have behaved if the star had been at the same place it is likely to occupy as the result of aberration, and the Earth had been at rest.
Fresnel accepted the Young's suggestion that the refraction ability of transparent bodies depends on the concentration of ether in them and he began to develop a theory of interaction of ether and a substance. Here is what Whittaker writes on this point in his remarkable review of the development history of the notions of ether and electricity . "Arago has refined this supposition assuming the ether density in any body was proportional to the square of the refraction index. Thus, if C is the light velocity in the vacuum and C1 - the light velocity in a given material body that is at rest, so that m = C/C1 is the refraction index, then the ether densities r and r 1 in the interplanetary space and body will be, accordingly, correlated by the relation r 1 = m 2r .
Then Fresnel supposed that a body in motion carries a part of the ether that is in it, namely, the part that is the excess of the ether density as compared with the ether density in the vacuum, while the rest ether in this body is motionless. Thus, the density of the moving ether is equal to (r 1 - r ) or (m 2 - 1)r and the ether with the density r remains immovable. Then the velocity with which the ether centre of gravity in the body moves forward in the propagation direction is equal to [(m 2 - 1)/(m 2)]w , where w is a component of the body velocity in this direction. This component should be added to the light wave velocity in the body, ten the absolute velocity of light in the moving body will be
C1 + [(m 2 - 1)/ (m 2)]w . (1)
Hereinafter, an evident drawback emerged in the Fresnel's theory, i.e. his theory required that the relative velocity of the ether and matter should be different for the light of different colours.
Many years later Stokes put forward the same suggestion but in some other form . Assume that all the ether in the body moves simultaneously: the ether that enters the body from the front and at once thickens and the ether that leaves the body from behind where it at once rarefies. With this assumption, the ether mass r w should pass through a unit area of the plane drawn in any place inside the body at a right angle to the body movement direction in a unit of time. Consequently, the ether in the body has a velocity of drift equal to -r w /r 1 in relation to the body, then the light velocity in relation to the body will be C1 - r w /r 1, and the light absolute velocity in the moving body will be C1 + w - r w /r 1 or C1 +[(m 2 - 1)/(m 2)]w , as before. In 1851 this formula was experimentally corroborated by Fizeau who measured a shift of interference bands formed by light that had passed through a tube with running water .
The first serious attempt to describe the ether mathematically was made by MacCullagh in 1839. According to MacCullagh, the ether is a rigid medium in the world space. This medium exhibits elastic resistance to rotation deformations and is described by the antisymmetric tensor of the second rank whose members of the main diagonal are equal to zero . The successive scientists showed that MacCullagh's ether can be described by Maxwell's equations for the empty space .
MacCullagh offered the following equation of the ether medium movement:
where is an elastic shift, t is time.
As MacCullagh notes, in this equation, the dielectric permeability corresponds to the reciprocal of the constant elasticity .
In his review , Whittaker notes that specialists in mathematical physics of the time of MacCullagh as well as the next generation specialists cast doubt on his work. One can say that it was appreciated only in 40 years when other scientists drew their attention to it. But there is no doubt that MacCullagh really developed the theory according to which oscillations in a medium calculated by dynamics right laws should possess the same properties as the light oscillations. Until the end of the XIX century prominent scientists argued about the ether medium - whether it should be considered a quasi-solid body that undergoes deformations under magnetic and electrical forces, or a quasi-liquid body whose particles execute vortex motions under the influence of the same forces.
One of the most developed definitions of the ether was given by the natural science classic J. Maxwell [13 - translated from Russian]. "Ether differs from ordinary matter. When light moves through air, then it is evident that the medium in which the light is propagating is not air itself, because, first, air cannot transmit shear waves, while compression waves transmitted by it propagate million times slower than light":
"One cannot assume that the ether structure is similar to that of gas in which molecules are in the state of chaotic movement, since in such a medium, a shear oscillation over one length of the wave attenuates to the value less than a five hundredth of the initial amplitude:. But we know that a magnetic force at some area round the magnet is preserved while steel keeps its magnetism. Since we have no grounds to assume that a magnet can loose all its magnetism just as time passes, we can conclude that molecular vortexes do not require constant expenditure of work to maintain their movement:".
"Whatever problems we face in our attempts to work out a well-grounded notion of the ether structure, it is beyond any doubt that interplanetary and interstellar spaces are no empty spaces, they are filled with material substance or a body that is most extensive and, perhaps, most homogenous of those that are known to us".
Maxwell asserted it is unlikely that one can avoid the conclusion about the light consisting of lateral wave motion of the same medium that induces electrical and magnetic phenomena.
Maxwell and later Hertz tried to extend the theory of electromagnetic field to the case when weighty bodies are in motion. In the review  it is mentioned that these attempts were not a success. Neither of them took into account the motion of material particles in relation to the associated ether, so in both investigations moving bodies were considered to be just homogenous parts of the medium filling the entire space, those parts differing from one another only by particular values of electrical and magnetic constants. Evidently this assumption does not agree with Fresnel's theory that explains optical behaviour of moving transparent bodies.
Unlike Maxwell, Stokes showed in 1845 that the aberration phenomenon can be explained if one accepts the concept of noncircuital ether . "Assume that the Earth motion imparts a motion to the neighbouring ether portions. This motion can be considered as superimposed on the vibratory motion of the ether particles during the light propagation, so, in general, the orientation of the light wave fronts will change, influence will be thereby exerted on the direction in which we see a heavenly body and which initially is normal to wave fronts. But if the ether is in noncircuital motion, so that its elements do not rotate, it is easy to see that no influence will be exerted on the light direction in space, the light disturbance propagates as before along straight lines from a star and the normal to the wave front deviates from this line at a low angle u/C at any point, where u is the ether velocity component at a given point expanded perpendicularly to the light propagation line and C is the light velocity. If we assume that the ether near the Earth is at rest in relation to the Earth surface, then it may seem that a star is displaced to the Earth movement direction at the angle measured by the Earth velocity to light velocity ratio, multiplied by the sine of the angle between the Earth movement direction and the line connecting the Earth with the star. The law of aberration exactly reflects this.
One of the classical physics creators W. Thomson worked hard on designing models and mechanisms of interaction of physical bodies and fields with the ether. For instance, W Thomson noticed that the bar electromagnet that is equivalent to the current circulating in the wire wound around it, can be compared with a strait pipe immersed in an ideal liquid that flows in it at one end and out at the other so that the liquid particles move along magnetic field lines . If two such pipes are placed with homogenous ends facing each other, they are attracted, if they are placed with heterogeneous ends facing each other, they are repelled. This scheme seems attractive due to similarity of magnetic forces action to the interaction of the pipes filled with an ideal liquid.
But there is one fundamental difference that prevents considering this analogy to be rightful. For instance, a ferromagnetic particle attracted by a solenoid remains inside it. At the same time, the particle that entered the pipe with the moving ideal liquid at one end will be evacuated into the space at the other end of the pipe if only to preserve the motion inertia.
Thomson also worked out the concept of the incompressible ether medium composed of the "atoms arbitrarily red and blue" related to each other by rigid ties and located at the Bravais's lattice sites . By his concept, the ether is presumed to be quasi-rigid and to resist any rotation absolutely. Thomson's ether can be subject to shear deformation. For the ether model to meet the condition of absolute resistance to rotation, Thomson placed spinning gyroscopes on rigid ties. The gyroscopes can be represented as flows of incompressible liquid. The angular velocity of the motion in every gyroscope can be infinitely great. In this condition the spatial network of differently oriented gyroscopes will exhibit infinitely great resistance to the ether medium rotation round any axis. By Thomson's concept, the ether model constructed in such a way can transmit oscillations like natural ether.
Virtually Thomson's model does not agree with modern ideas. It is very complicated. It is difficult to imagine gyroscopes with an infinitely great angular velocity. Rather simple reasoning shows that an infinitely great velocity requires great energy. It is not quite clear how the areas of gyroscopes, in which the rotation occurs round the mutually perpendicular axes, mate. Thomson does not explain what physical mechanism executes rigid ties. At the same time, in our opinion, the concept of the ether medium consisting of "atoms" of two kinds related by rigid ties and located at the sites of a certain lattice seems to be rational.
Then Thomson concluded that the equations of light propagation are no more than the equations of shear oscillations in a solid body . By his model, magnetic induction at any point can be represented by a turn of a volumetric element of a solid body from the equilibrium position. Electrostatic force is equal to
and magnetic induction is equal to
where is elastic displacement. In conclusion Thomson replaced the elastic solid body of a usual type by the ether medium of MacCullagh type.
The ether concept received new development in the context of Michelson's experiments . At the end of the XIX century A. Michelson decided that if the ray bundle in the interferometer were sent along the equal way in parallel and normally to the Earth movement, then the travel-time difference for these rays could be obtained. He obtained interference bands between the two bundles of light that had passed along the perpendicular trajectories; but when the device was turned by 90 degrees so that the difference was opposite, the expected shift of the bands did not occur. Michelson considered this result to be the evidence for the Stokes's theory which suggests that the ether near the Earth is moving.
In 1882 P.G. Tet supposed that "had the ether been in motion in relation to the Earth, then the absolute deviations of the lines in the diffraction spectrum should have been different in various azimuths" .
Michelson and Morley's experiments continued in 1897 when Michelson tried to define experimentally whether the Earth and ether's relative movement changes with the change of the vertical height over the Earth's surface . However no result pointing to dependence of the light velocity vs. the distance to the Earth's centre was obtained. Michelson concluded that if one had to choose out of Fresnel and Stokes's theories, he should accept the latter's theory and assumed that the Earth's effect on the ether stretches for thousands of kilometres over its surface.
Meanwhile, the dilemma existing in this subject became even more acute under the effect of experimental results that pointed to the direction opposite to that of Michelson. In 1892 O. Lodge  watched the interference between two portions of the bifurcated ray of light that were made to move in the opposite directions along the closed trajectory in space bounded by two quickly rotating steel disks. The observations showed that the light velocity is not subject to the adjacent matter to the power 1/200 of the matter velocity. Continuing his investigations, Lodge heavily magnetized the moving matter (it was iron in his experiment) so that the light propagated through the moving magnetic field and electrified it in such a way as to place the beam trajectory in the moving electrostatic field. Appreciable influence upon the light velocity was exerted in no case.
H. Lorentz tried to resolve the contradictions in explaining the ether nature. He transformed Fresnel's hypothesis in such a way that in his theory a weighty body that was in motion transferred the ether excess it contained as compared with the space that is matter free . Lorentz also supposed that polarized molecules of a dielectric, like many small condensers, increased the dielectric constant and it was this (so called) increase in the dielectric constant that moved together with the moving matter. Thus, the flaw in Fresnel's theory, which required that the relative velocity of the ether and matter should be different for the light of different colours, was eliminated. Lorentz theory requires only different values of the dielectric constant for the light of different colours and the dispersion theory provides a satisfactory explanation to this requirement.
In contrast to H. Hertz hypothesis which suggested that a moving body should transfer all the ether contained in it, the validity of H. Lorentz hypothesis was subsequently corroborated by various experiments. In 1901 R. Blondlot carried the airflow through a magnetic field normally to magnetic force lines . The airflow was sent between the condenser plates that were connected by the wire in such a way that they had an equal potential. When the air moved in the magnetic field the electromotive force …'appeared in the air. According to Hertz theory, this force should generate the electric induction D of the e …' value (where e is the air dielectric permeability that is virtually equal to unit), so, according to Hertz theory, the condenser plates should be charged. According to Lorentz theory, on the other hand, the electric induction D is determined by equation
D = E + (e - 1) E',
where E is a dielectric force acting on the charge that is at rest; in this case that force is equal to zero. Thus, according to Lorentz theory, the charges on the condenser plates will have only the (e - 1)/e part of the value that they should have by Hertz theory, i.e. virtually they will be equal to zero. The result obtained by Blondlot supported Lorentz theory.
An experiment of this kind was performed by G. Wilson in 1905 . In this experiment the space between the inner and outer plates of a cylindrical condenser was filled by a dielectric - ebonite. When a certain potential difference is maintained between the plates of such a condenser, charges are induced on the plates. If the condenser is rotated round its axis in a magnetic field which force lines are parallel to this axis, then these charges will change due to additional polarization that rises in the dielectric molecules as they move in the magnetic field. According to Lorentz theory, the additional charge value is (e - 1)/e times greater than the value calculated by Hertz theory. The result of Wilson's experiment as well as that of Blondlot supported Lorentz theory.
Reconciliation of the electromagnetic theory with Fresnel's law on light propagation in moving bodies was an evident step forward. But there was a complication that interfered with the immovable ether theory: in its initial form it could not explain the negative result of Michelson and Morley's experiment. In 1892 FitzGerald speculated that when material bodies moved relative to the ether, their dimensions slightly differed . Later this hypothesis of FitzGerald was accepted by Lorentz. After that the amount of people that have accepted this idea began gradually to increase and it was accepted by physicists-theorists.
Let us consider how this hypothesis explains the result obtained by A. Michelson. If one assumes that the ether is immovable, then one of two rays, into which the initial light ray is bifurcated, directed along the Earth movement should pass its way faster than the other one directed across this movement. This difference might be fully compensated if the way coinciding with the direction of the Earth movement was shorter than that of the ray directed across the movement. It might have happened if the linear dimensions of the moving bodies had always decreased in the direction of their movement in the ratio (1 - V2/2C2) to the unit (V is the body velocity, C is the light velocity). Therein lies the meaning of FitzGerald hypothesis for reduction of bodies during their movement through the ether.
Planck came up with another proposal in 1899 . It was based on Stokes theory and implied that both conditions of Stokes theory (the ether movement should be irrotational and its velocity near the Earth surface should be equal to the Earth velocity) could be met if it was granted that the ether was compressed by Boyle's law and was subject to gravitation. Round the Earth it is compressed like the atmosphere, the light velocity does not depend on the ether thickness.
A few authors including H. Lorentz criticized Stokes theory . This criticism lied in the fact that an irrotational motion of an incompressible liquid was fully determined when the velocity normal component was specified at its border. So if we assume that the ether has the same velocity normal component as the Earth, then it would not be able to have the same velocity tangential component. Hence it follows that in a general case there is no such a motion that would meet Stokes equation. This complexity was not satisfactorily solved by any proposal put up for its solution. One of those proposals is in assumption that the Earth movement creates vortex perturbation which does not influence more stable irrotational motion despite the fact that it is emitted with the light velocity.
A radical revolution in physicists' ideas of the ether took place after the principles of A. Einstein's theory of relativity had been published. For instance, in 1905 A. Einstein wrote: "Introduction of the "luminiferous ether will appear to be excess" [24, p. 8]. In 1915 in another work he wrote: ":one should abandon the introduction of the concept of the ether which turned in a useless makeweight to the theory:" [24, p. 416]. In 1920 he wrote: ":the special theory of relativity does not require the absolute negation of the ether" [24, p. 685]. At one moment A. Einstein accepted the ether existence, at another he rejected it. The last A. Einstein's statement about the ether medium refers to 1952: "By the fact that the special theory of relativity showed physical equivalence of all inertial systems, it proved inconsistency of the resting ether hypothesis. So it was necessary to give up the idea that an electromagnetic field should be considered as the state of some material bearer" [24, p. 753].
E. Whittaker writes [8, p. 359] that the accepted principle of relativity destroyed all competing concepts of the ether. But not all known physicists appeared to agree to the ether elimination and the theory of relativity itself.
One of the outstanding physicists Paul Dirac described his understanding of vacuum in such a way : "According to these new concepts, vacuum is not emptiness that has nothing inside. It is filled with an enormous number of electrons that are in such a state with negative energy that can be considered to be some ocean. This ocean is filled with electrons without limits up to the negative energy value and so there is nothing like a bottom in this electron ocean. The phenomena we are interested in are the phenomena occurring at this ocean surface and what is taking place at depth is not observable and is of no interest. As long as the ocean is quite homogenous and its surface is flat, it is not observable. But if we take a handful of water and lift it, then the obtained homogeneity breaking will be just what is observed in the form of electrons presented in this picture as the lifted part of the water and the hole left at its place, i.e. positrons".
Another prominent scientist L. Brillouin arrived at the conclusion that ":the general theory of relativity is a brilliant example of the glorious mathematical theory built on sand and leading to an increasing pile of mathematics in cosmology (a typical example of science fiction)" . In his book "A new view on the theory of relativity" ha writes that both the theory of relativity and quantum theory appeared at the beginning of the XX century. Then a rapid development of the quantum mechanics began. Spin, Pauli-Fermi prohibition principle, de Broglie waves, Schrodinger equation and many other things were discovered. Experiments supplemented theory, the improved theory allowed prediction of new phenomena. The development of quantum mechanics demonstrated a remarkable symbiosis of theory and experiment that leads to an unlimited growth of knowledge. The situation with the theory of relativity is somewhat different. Tested only by a few experiments it remains logically contradictory. It has not brought luxuriant growth of new scientific trends that might be brought by a fruitful theory. Heavy battles with logical, philosophical and physical contradictions in the theory itself are still going on in its field.
Note that the above reasoned statements made by the world-famous scientists cannot be ignored. The latest scientific achievements, especially those in the field of radio-wave propagation including that in outer space, the discovery of the "dark matter" induce to come back to solving the ether problem.
To sum up, in the XIX century great physicists were developing two competing ether theories. One of them suggested by Descartes, Maxwell and, to a certain extent, H. Lorentz speculated that there were vortexes composed of some very small particles in the ether. Flows of these particles form magnetic fields. The motion of those particles from one charged body to another ensures electrostatic interaction. The other theory developed by MacCullagh, Thomson and Stokes was based on the assumption that ether is a quasi-solid body. Magnetic and electrical fields arise in it from deformations of a certain type.
At present the attempts to develop a non-contradictory theory of the ether medium (vacuum) are going on. As in the main preceding works of the XIX century, two theories are being mainly developed - of quasi-liquid (gas-like) and quasi-solid ether. For instance, K.P. Sinha, C. Sivaram and E.C.G. Sudarshan suggested a model of vacuum as a superfluid medium . In this paper, as well as in several preceding ones, the authors develop a concept of the luminiferous ether being a superconductive liquid consisting of united pairs of fermions and anti-fermions (as, for instance, electron-positron, neutrino - anti-neutrino etc.). This superconductive liquid is considered to be globally stable and is the basis of the universe. The imagined medium can contain tensor bosons that may possess mass or be massless. They can provide a mechanism for strong electromagnetic and gravitational interaction. According to the authors, the concept is such that the main fermion - anti-fermion interaction can result in the variety of the forces being manifested and seem to be able to provide the basis for the generalized field theory.
In the known work of V.A. Atsyukovsky a model of the gas-like ether is offered . This model is close to L. Lesage's model . Magnetic fields of this ether are formed by vortex structures. There are a number of other modern works of variable validity degree that present ether liquid or quasi-gaseous [29, 30, and 31].
A number of other works present a model of quasi-solid ether [12, 32, 33]. As a rule, these works are based, to a greater or lesser extent, on MacCullagh's model and develop it.
Below we offer and ground the least contradictory model, as we think, namely, the model of quasi-solid ether (ether medium). We suggest the solution of the second great problem - why the ether is carried (partly) by the moving physical bodies at the Earth surface but remains immovable in relation to the planet Earth that moves through space. The ether is presented as an all-penetrating medium consisting of the particles of two types that are equal but opposite in sign. The ether was demonstrated to have certain electromagnetic density and elasticity. The relations and interaction between the space, ether, physical (weighty) bodies and time are explained. The essence of the observed electromagnetic phenomena, inertia and gravitation are grounded.
Due to the fact that recently many researchers have interpreted the term "vacuum" as a synonym of "ether", we will cite Whittaker: "It seems absurd to me to retain the name "vacuum" for the category that has so many physical properties, while the historical term "ether" is excellently suitable for this purpose" .