
RELATIVE MOTION IN THE WORLD OF SOLITONS N.Chavarga Uzhgorod National University. Pidhirna Str., 46, Uzhgorod, 88000, Ukraine tel. +38 (0312) 663726, Email: chavarga@mail.uzhgorod.ua A relativity theory, based on the supposition, that all elementary particles are soliton formations of the lightcarrying environment, is proposed. Direct and reverse transformations of space and time coordinates, and also the expression for the value of light velocity in the moving frame, are obtained. Keywords: relativity theory, solitons, ether, coordinate transformations. PACS 00.03.30.+p Thus, probably all things are of the ether origin. I. Newton 1. Introduction In our works [1, 2] it was shown that the Special Relativity Theory (SRT) does not correspond to Bohr’s principle, therefore, it cannot be a correct physical theory. There appears a natural question: what can be instead of it, what theory can give us noncontradictory explanations of the corresponding experiments results? The idea, that elementary particles are probably soliton formations of an electromagnetic field (electric and magnetic fields are, in turn, Faraday’s “ether tensions”), was expressed several times, see, for instance, [3, p.177], but all in all the attempts of making up a relativity theory on this idea were not made. Its reason probably consists in the thinking inertia and very narrow specialization in modern physics – investigators who study solitons are not highly interested in the relativity theory problems, and vice versa. The present work is a certain continuation of article [2], extended and more complete expounding of the ideas represented there, with taking into consideration the experience we acquired in various discussions. 2. Space and Time Transformations 2.1. Space Transformations In the present work we represent a special Soliton Relativity Theory (SolRT), in which one of the coordinate frames represents a lightcarrying environment with properties of a solid body, and the second moves uniformly and rectilinearly with respect to the first one. The environment consists of some elements, whose dimensions are at many orders smaller than the dimensions of the elementary particles we know. Between the environment elements (amers, etherons, Planckeons, etc.), there exists “rigid cohesion”, as well as it takes place in a solid body, but we will not assume anything concerning the interaction mechanism between them and about physical essence of these elements. The environment has elastic properties, i.e. it can be deformed at compression and shift without residual deformations. The ether’s elements themselves have the inertia property, but do not undergo gravitational interaction. In case of deviating an ether particle (group of particles) from the stationary position for some reason, the elasticity forces turn it back, but the particle deviates by inertia in the opposite direction, then it comes again to the equilibrium position, etc. Thus, in general, there occur the environment oscillations, which form the basis of electromagnetic waves. Soliton formations, including 3d solitons, capable of resting in the environment, can be one of the kinds of waves in the lightcarrying environment. All elementary particles are solitons of different kinds. The notion “inert mass of a material body”, known in physics, we will connect with the value of energy available in electromagnetic solitons. The notion of energy, in turn, we will connect with the degree and volume of environment deformations. The problem of relation between the inert and gravitating masses we will not analyze in the present work. The moving frame’s axes model moving material bodies, therefore, they are made of “hard rods” consisting of solitons. In spite of the fact that we attribute the inertia property to the environment particles, the notion of mass we do not connect directly with these elements, with their materiality. Probably one should attribute some notion of “primary mass”, “protomass” or something of this kind to the elements of the ether, but in this case, we do not assume the presence of gravitational interaction between them. It is known that for formation of solitons the environment must have the features of nonlinearity and dispersion. Perhaps one should assume that not all kinds of ether oscillations have features of solitons (for example, conventional radio waves), but photons have features of an “incomplete soliton”. We do not doubt that a single photon, emitted by a hydrogen atom and passed through a small round diaphragm at one end of the galaxy, can pass in many centuries through the same diaphragm at the other end of the galaxy without hindrance. After passing the second diaphragm, the photon may be absorbed by another hydrogen atom located there, or it may beat out an electron in the photocathode of the photo element behind the telescope ocular. It testifies us to the fact, that a photon has soliton features reflecting the limitation of oscillation process propagation in the plane perpendicular to the photon propagation direction. For a spherical wave, it is impossible, at least, due to the action of energy conservation law. It is quite possible that electromagnetic oscillations can be considered as photons only after a certain value of energy (frequency), after which they acquire the property of propagating not spherically, but at one line, i.e. when the electromagnetic oscillation appears to be captured at two coordinates, but at the same time it can propagate at the third coordinate (“needle feature” of photons, according to Einstein). It is known that up to certain energy, to 0.51 MeV, photons ignore each other – the superposition principle is carried out. Even in such radiation densities that are available in the sun crown, scattering of photons on photons is not observed [4], but in case of “front” collision of two photons with energy not less than 0.51 MeV, a great probability of formation of a couple “electronpositron” is observed. Therefore, we will assume later, that in this case, a new electromagnetic formation named a positron or electron, in reality appears to be a wave selfcaptured in all the three coordinates already, i.e. it appears to be a “full soliton”, 3dsoliton or “hard” electromagnetic particle. Such solitons have features of solid bodies – in case of collision they behave like elastic billiard balls, they do not give the environment either their motion energy (inertia law is carried out), or energy available inside them (objects appear to be stable, indestructible without corresponding partner, i.e. without antiparticle). Evidently, a “full soliton” (as a wave formation) in certain conditions must manifest not only corpuscular, but also wave features, and vice versa – a nonfull soliton must manifest corpuscular features in addition to wave ones. From these positions, the corpuscularwave dualism of microobjects not understood earlier obtains an elementary explanation within the frames of classical physics. From these positions, the uncertainty relation obtains a clear explanation with the aids of classical physics [5, 6]. It is not difficult to see that in a “hard lightcarrying environment”, most probably, no motion is possible, except wave motion, since such an environment (taking the tremendous velocity of photons’ propagation into consideration) should be at many orders “harder” than any diamond. For solitons, the notion of “ether wind” does not exist, as well as it does not exist, for example, for a traverse wave on the water surface – the wave propagates along the water surface, but the water particles oscillate chiefly up and down. Evidently, that the idea of essence of elementary particles as electromagnetic formations is not agreed with the image of elementary particles as point objects, therefore, it is automatically not agreed with the probabilistic interpretation of the meaning of the wave equation psyfunction. We represent the alternative interpretation of the psyfunction meaning in [7, 8]. Note that we have no guarantee, that in reality, the material world is the congestion of electromagnetic solitons. It is also possible that such objects do not exist in the nature at all. Moreover, our task is to use the solitons’ properties known from the literature, to propagate them to the supposed ether solitons, to make up the relativity theory on the basis of the solitons’ properties and to compare the obtained conclusions with the results of the experiments. If the calculations are well agreed with the experiment, it can serve as a serious stimulus for the investigators’ returning to the lightcarrying ether idea. All the necessary preconditions for making up the soliton relativity theory existed long ago before the present work, one had only to make one step, and only the presence of the “experimentally confirmable SRT” psychologically did not allow doing it. The dislocation, whose longitudinal dimensions depend on its propagation velocity, is one of the kinds of soliton formation. That is what A.T.Filippov writes in this relation: “…in general case, all longitudinal (at the axis corresponding to the motion direction) dimensions of the dislocation decrease, i.e. , where V is the dislocation velocity, V_{0} is the sound propagation velocity. The dependence of the moving dislocation energy on the velocity is given by the formula . Both the formula for the dislocation and the formula for the energy are analogous to the corresponding formulae of the special relativity theory. With taking everything, which we got to know about dislocations, into consideration, one can say that a dislocation is similar to an elementary particle. At the end of this impressing analogy, there are also “antiparticles” – antidislocations. …it is not excessive to emphasize that this analogy is purely mathematical. In the relativity theory, the written formulae have quite another physical meaning. Besides, for real dislocations they are carried out only approximately” [3, p. 165]. A bit later we will be able to make sure that Filippov was not on a step, but on half a step from making up soliton relativity theory. After assumption that all hard elementary particles are electromagnetic solitons of the lightcarrying environment, it is logical to assume then, that they change their longitudinal dimensions in accordance with the abovementioned formula for dislocations, however, as V_{0} we will understand the light velocity C, since the “ether sound” is, most probably, the electromagnetic oscillations, (2.1) where l_{0} is the soliton’s dimension in the rest state with respect to the ether, l is the soliton’s dimension in the state of motion with the velocity V. Fig. 2.1. In the acceleration process, the moving solitons really change their dimensions, and preserve them decreased in case of uniform and rectilinear motion. Let us emphasize especially: all quantities belonging to this formula are measured with the aids of one coordinate frame, Fig. 2.1, – there is no collation of viewpoints to the dimension of one and the same soliton from different frames there, thus, the formula, though characterizes the moving object, does not belong to the relativity theory yet. For the convenience of writing and reading these formulae, the radical in (2.1) we will denote as G, and we will call it the “nonGalileoity coefficient”, from Galileo. (2.2) For low velocities, G?1, therefore, expression (2.2) turns into l=l_{0}, which represents the mathematical writing of one of Galileo’s relativity theory postulates – dimensions of physical bodies do not depend on their motion state. In case of velocities comparable with light velocity, G ? 0, the soliton’s longitudinal dimension tends to zero. As for the problem of possibility of threedimension solitons existence, then there appeared quite recently the information about nonlinear equations, whose solutions are 3d solitons [9]. This is a very good and timely argument in favor of the idea of material world made of electromagnetic solitons. In order to make up the space transformations of the soliton relativity theory, the coordinate axes of the moving frame should have the features of hard rods made of 3d solitons. Obviously, that if solitons, as components of rods, are shortened in accordance with (2.2), then the whole moving frame (and, certainly, the whole coordinate axis) will be shortened in the same proportion. In this case, for supporting the degree of bodies’ shortening in the state of uniform and rectilinear motion an external force is not needed – not only each soliton separately, but also the rod as a whole does not give its motion energy to the environment, therefore, the inertia law is strictly carried out. Bodies’ shortening takes place on the stage of acceleration with respect to the environment, and their length is renewed on the braking stage. Lorentz used a very similar idea for explaining the results of Michelson’s interferential experiments. Here one should especially emphasize that, when starting to study the nature, we introduced the notion of absolute space for the whole infinite Universe, and we do not introduce the notion of one’s own space in the moving frame – in the moving frame, only physical bodies and coordinate frames (as the hard bodies’ mathematical models) are shortened. In other words, we have no right to speak about its shortening up till the moment of the rethinking and redetermination of the space notion. For making up the relativity theory as the chapter of physics, one should obtain as many transformations as the independent physical essences and the corresponding notions are available. In modern physics, this question is hushed up, except, probably, Feynman [10], and one amounts to nothing more than making up space and time transformations. It is quite probable that in future, it will be possible to represent all physical notions through the properties of the physical space (ether) and time, and it will appear that such an approach was justified. For example, it will appear that the energy is the degree and volume of the environment deformation; mass is the amount of energy available in the soliton; electric charge is not a specific kind of matter, but the property of some solitons to deform their environment inside and around (causing environment condensation and rarefaction in this case); electric and magnetic fields are the type of environment deformation (compression, shift); gravitation – the residual phenomena of electric and magnetic interactions, etc. Following the tradition, in this work, we will confine ourselves to making up the transformations for space and time. For the simplicity of presentation, we will analyze only one space axis, along which one of the coordinate frames moves. ^ The moving rod is shortened. At zero moment of time, the left ends of the rods coincided. At some moment t, the right ends of the rods coincided. In order to obtain the space transformations, one should collate the measuring devices of the different frames with each other and determine the transformation coefficient. Evidently, the procedure must consist in collating the results of the length measurement for one and the same physical object; otherwise the transformations, and also the whole theory together with them, will be senseless. As an object of comparison, in the theory one can simply take the “amount of space” between some points resting in the immovable frame, for instance, A and B, Fig. 2.2, and measure it with rulers of frames K and K. The result of the measured amount of space is the quantity of marks, quantity of the length standards that can enter between points A and B. In this case, it is understood that in the rest state (before the experiment had begun) the length standard in frame K was absolutely the same as in frame K. We will proceed from the fact, that in the infinite threedimension material space each of its point is individual, that it cannot be confused with any other point of the space in any way, therefore, it should be characterized mathematically by an individual number, which repeats nowhere any more. One of the ways of such representing the space is the coordinate way. Thus, if we want to make up the space transformation (for simplicity we will confine ourselves to the singledimension case) we are to be able to answer the following question: if in the resting frame some arbitrary and resting point A has the coordinate x, then what will be the coordinate of the same point, if it is measured with the aids of the moving frame at an arbitrary time moment t? In this case, one should remember that the notion “coordinate x of point A” means the distance from a certain point in space (considered as zero, i.e. coordinate origin) to point A, and the notion “distance” itself means the quantity of length etalons on this segment. Assume that we have two equal hard rods made of 3d solitons. According to the condition of the problem, in the rest state, both the rods lengths and the marks on them coincide. For convenience of statement, the beginnings of the rods (left ends) we will consider as the origins of the coordinate frames. One of the rods we will transmit towards the negative values of x, then we will accelerate it up to the velocity V in the direction of positive values of x. The time moment, when the frames’ coordinate origins coincide, we will consider as zero, t=0. Without loss of the conclusion generality, we will consider that the right end of the immovable rod coincides with the analyzed point A, and that at some arbitrary moment t it appeared so that the right end of the moving rod also coincides with the position of point A, Fig. 2.2. The origin of frame K is now located opposite some point B in frame K. Between points B and A at the given time moment l marks are situated on axis х and l marks on axis x – these are the measurements data for the amount of space between points A and B (the measurements are fulfilled with the aids of different coordinate frames). On the other hand, the quantity l represents the data of measurements of the whole moving rod’s length (fulfilled with the aids of frame К, at the same time it is the coordinate х of point A at the moment t), and the quantity l represents the data of measurements of the same moving rod’s length, but with the aids of frame K. The quantity l_{0} represents the data of measurements of the resting rod’s length (fulfilled with the aids of frame K), at the same time it is the coordinate x of point A. The connection between l and l_{0} is shown on Fig. 2.1 and it is set by the relation (2.2) l=l_{0}G On the other hand, the quantity of marks on the rod does not depend on its motion state, therefore, numerically (concerning the quantity of marks) l=l_{0} (2.3) Since we assume that expression (2.2) concerns all types of solitons, of which the rods consist (electrons, protons, neutrons), through expression (2.3) we declare, that in the soliton world, in the moving frame, there are no instruments for correct measurement of bodies’ length, since all instruments are also made of solitons, and they change their length in the same proportion as the measured bodies. The incorrectness of similar length measurements can be illustrated by the following analogy: if the heated rod’s length is measured with a ruler heated to the same temperature and made of the same type of steel as the rod, then the result of measurements will not depend on the rod’s temperature, in spite of the fact that in reality the heated rod’s length is significantly larger than its length in a cold state. Expression (2.3) is not an equation, since 4 centimeters are not equal to 4 inches, though 4=4, however, it gives us the answer to the following question: what is the result of measuring amount of space between points A and B with the aids of the moving frame. Taking (2.2) into consideration, expression (2.3) can be written in the following way: (2.4) It is seen from the figure that l=l_{0}–Vt, therefore, (2.4) will obtain the following form: (2.5) Since in the analyzed case l simultaneously means the coordinate х of point A according to the measurements data of frame K (l =x ), and l_{0} means the coordinate x of the same point A according to the measurements data in K (l_{0}=x), expression (2.5) can be rewritten as follows: (2.6) This is just the space coordinate transformation in the soliton relativity theory. Both in the form and in the sense of its component quantities it completely coincides with Lorentz’s space transformation. We do not seek the physical meaning of the quantities belonging to (2.6), since it was unequivocally determined before deriving (2.6), as it should be in a normal physical theory. The other two dimensions of the soliton do not depend on the motion state, therefore, y=y, z=z (2.7) Thus, in equations (2.6) and (2.7) we consciously put the information about the real shortening of moving bodies, made of solitons, along axis x, and preservation of bodies’ dimensions along axes y and z. Of course, it unequivocally testifies to the nonequivalence of the coordinate frame in the soliton relativity theory. Let us draw reader’s attention to the fact, that in its derivation, we did not need to deal with the problem of time measurement in the moving frame. This fact reflects the independence of such physical essences as space and time – just in an independent way we introduced these notions for describing world pattern, therefore, we obtained the transformations as for independent quantities. In other words, we obtain the answer to the question “what is the moving body’s length, if the measurements are fulfilled with the aids of the moving frame?” without using information about the value of the measured time in the moving frame, i.e. at this stage we have no reasons for raising the hypothesis about united spacetime. All the quantities of equation (2.6) have the same meaning as in Galileo’s transformations: х is the coordinate of an arbitrary and resting point in frame K, x is the coordinate of the same point, measured with the aids of the moving frame at an arbitrary time moment, t is an arbitrary time moment. There is no causal connection between x and t – selection of coordinate x does not influence the selection of t at all, and vice versa. In case of low velocities of the frame K motion, the quantity G?1, therefore (2.6) turns into Galileo’s transformations: x'=x–Vt, i.e. concerning space transformation, the soliton relativity theory corresponds to Bohr’s principle. 
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