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This article is devoted to the key concept of modern electrodynamics—the invariance of the speed of light. The general principle of relativity is considered in detail. Some critical remarks to the relativistic invariance and to the Lorentz transformations are presented. The general invariance of Maxwell equations is discussed. Different theoretical expectations for possible results of Michelson-Morley experiment and some physical consequences are considered. Some critical remarks to the notion of the light speed and its constancy are given. The relativistic law for velocity addition, including strangeness of a noncollinear addition and a superluminal motion, is discussed. Critical analysis of two works which proof the need for existence of an invariant velocity is consequentially made.

It is known that one of the key moments of the special relativity theory (SRT) is the question of the invariance of light speed and the physical sense of such invariance. Contradictory statements about this were made still by the SRT founder A. Einstein (see, for example, [

In dealing with the question of the invariance of light speed, one cannot bypass the discussion of the concept of relativity itself, which even entered the name of the theory of SRT. Contrary to Galileo’s ideas about the isolation of the system, the SRT exchanges light pulses between systems. The notion of relativity is brought to the limit in the SRT and has lost its original physical meaning: in fact, a system with several objects (usually two) is singled out, and the rest of the real Universe is removed from consideration. If it is possible to postulate such an abstraction in SRT, then all the more you can simply postulate the independence of the processes within the selected system on the speed of the system’s motion relative to the “emptiness” remained from the whole Universe. But, even in spite of such abstraction, “real” relative values for bodies will not appear anyway. Indeed, the response of body i to an attempt to change its state is determined by local characteristics: the state of the body i and the fields at the given point of space. But the changes that have taken place with the body i will affect the other bodies j only after some intervals of time. Thus, all changes of physical values should be determined relative to a local location or local characteristics. And this is the manifestation of Newton’s absolute space. The principle of relativity (in any form) suggests the following: it is impossible to detect uniform motion of a system “not looking” beyond its limits. Previously, the role of an all-penetrating medium for the possible detection of such a movement was carried out by the ether. Note that it was not a question of detecting absolute motion, but only movement relative to the ether, that is, “not looking” outward, it was possible to compare these movements (here it means a computational possibility only, since the system of reference points and standards cannot be related to the ether). But even with the “cancellation” of the ether, according to modern ideas, there remains a “candidate” with similar properties―the gravitational field (in principle not screenable). For example, from the anisotropy of the relict radiation, with the additional hypothesis that the velocity of propagation of gravitational interactions and the speed of light is equal, the anisotropy of the gravitational field (all-pervading) can follow. Thus, the inequality of inertial systems in macro- scales can in principle be discovered “without looking” outward, even at a local point. Consequently, the declared hypothetical relativistic experiments could be done only in the absence of gravity or with a strictly symmetrical distribution of the entire universe relative to the observation point. But in the presence of moving bodies, such a strict “compensation” of gravity could only be at one point. In addition, it should be recognized in the experimental plan that the strict concept of an inertial system should be extended and expanded to “almost inertial systems,” that is, systems that are indistinguishable from strictly inertial systems within the existing accuracy throughout the entire experiment. Otherwise, this concept would be devoid of practical application and turned out to be useless for physics. For example, it is clear that all “relativistic” experiments without exception were conducted on a non-inertial Earth (the non-inertiality of the Earth is simply proved by Foucault’s pendulum), and from absolutely rigorous viewpoint, it is impossible to involve the principle of relativity of SRT (unlimited rigor “puts a cross” on any section of physics).

It is known that SRT is based on two postulates: the postulate of the light speed constancy and the principle of relativity, which is extended to electromagnetic phenomena [

It would seem that the answer to the question of the light speed constancy has already been given in the Michelson-Morley experiment studying the effect of the Earth motion on the speed of light. We also recall similar optical experiments made by Morley, Kennedy-Thorndike, Viennese experiment by Joose and others [

The main objectives of this work are as follows:

-to give a number of theoretical remarks concerning the physical meaning of relativistic invariance;

-to analyze some theoretical ideas about the Michelson-Morley experiment;

-to critically analyze the proof of the existence of an invariant velocity.

We begin with general remarks concerning the distortion of the very meaning of the invariance concept in the SRT. The wide-distributed relativistic cliche looks rather strange as if the SRT is just a new geometry, and that’s why it is allegedly consistent. There feels a clear bias toward mathematics. It must be recalled that physics is engaged in research on the causes of phenomena and specific mechanisms that directly affect the phenomenon under investigation. Of course, in order to obtain a mathematical solution, coordinate transformations are often used in physics. In essence, these are just elementary mathematical substitutions only. However, if someone claims that since the solutions are correct, then the whole Universe has really “transformed” from one area (for example, from a circle under conformal transformations) to another area, then all physicists will understand the inadequacy of such statements. It can come into mind only to the pseudo-mathematician with a sick imagination that the whole universe will contract if he does some operations with mathematical “letters”. But if some relativistic scientist says that he squeezed the entire Universe, when he went to a nearby bakery, many yes-mans will confirm this nonsense (possible, they did not read the tale “Naked King” as a child).

The existence of Lorentz transformations (published in 1900 by Larmor in the book “Ether and matter” even before the creation of the SRT) does not prove the objectivity of kinematic effects at all. First, the Lorentz transformations are not the only, but only one of many mathematical invariants of the wave equation. Prior to them, for example, the Vogt transformations were discovered, also being an invariant of the wave equation (Klein first pointed out the importance of studying group properties in 1872). Secondly, any physical principles do not follow from the mathematics itself: the invariance property is completely determined by a combination of operations and symbols in the equation. In particular, the Lorentz transformations with the speed of sound

Thus, the group properties of mathematical equations, as transformations with mathematical symbols, have absolutely nothing to do with any physical principles or postulates, that is, group properties can be found without additional physical hypotheses. For example, the Lorentz transformations, reflecting the group properties of Maxwell’s equations in the emptiness (or of the classical wave equation, including in acoustics), are absolutely not connected with the postulate of light speed constancy or with the principle of relativity introduced in the SRT.

Now let us make a remark about one of the possible mathematical derivations of the Lorentz transformations. A transformation is sought that transforms the equation of one sphere (or interval) into the equation of another sphere (respectively, of another interval). Obviously, such a transformation is not the only one for four variables. First, the separate equating

The theory of relativity is actually a “theory of visibility (only seem)”: what will we see in the experiment if the theoretical laws of electromagnetic interactions are putted in a basis of the observations (absolutization of electromagnetic phenomena). Similarly, we can raise the question of how the phenomena observed with the aid of sound, etc., will look. Of course, the finiteness of the interaction transmission rate alters the phenomena observed with the help of these interactions. But this does not prevent us from making unified extrapolations for binding to space and time (absolute classical physical concepts) for the universal description of the world, not limited by any universal hypotheses. All the kinematics of the SRT follows from the invariance of the interval

Let us analyze in more detail the “fundamental” question of the invariance of the Maxwell equations, which is widely declared in the SRT. The following four equations in the differential form are attributed to the system of fundamental equations of electrodynamics in the textbook [

However, this system of eight equations in the coordinate form is obviously insufficient to determine the 16 quantities (with all components taken into account) E, D, B, H, j and

and can add 9 more equations with three new unknown functions

The first four equations can be of independent interest only when considering fields in the void. However, the invariance of the Maxwell equations in the void with respect to the Lorentz transformations does not mean anything at all for other phenomena. First, in an empty space, we can cut off half the segment and double it-we get the same segment. Therefore, in an empty mathematical space, you can use any frame of reference, consistent geometries and conversion factors. This can be determined only by the convenience of a mathematical description. However, the presence of real physical bodies and fields in space defines natural reference points, characteristic scales and interrelations between objects. All this determines the differences between the real physical space and the empty mathematical space. Secondly, the property of certain interactions to propagate in a vacuum at the speed of light does not determine the rate of propagation of interactions in the medium. Despite the huge role of electromagnetic interactions, perturbations in media propagate with the speed of sound. Using one scalar constant c belonged to the vacuum, it is impossible to determine the velocities of sound and light in gases, liquids and solids. For example, light of not every frequency can propagate in a medium (recall about scattering, absorption, attenuation, reflection). It is not clear how the anisotropy of real solids could arise in the initially isotropic space. All these and many other properties go beyond the applicability of the Maxwell equations in vacuum. But the SRT offers cloning spherically symmetric properties of point flashes of light in a vacuum for all properties of material bodies and media. Consequently, adjusting the properties of the whole world under the invariance of Maxwell’s equations in the void is an overestimated claim of the SRT. Thirdly, splitting the uniform (in its effect) field into electric and magnetic parts is relatively arbitrary, and the invariance of these artificially splitted parts cannot be of decisive importance.

Let’s give some important remark. Maxwell’s equations themselves can acquire physical meaning only after a physical method for measuring the introduced fields is indicated. To date, such a “closing equation” is the equation of motion of charged particles under the action of the Lorentz force. Recall that at different time periods as an electromagnetic force, the Lorentz force was not the only one. Among the most famous expressions were: Ampère’s force, Weber’s force and some others. If modern electrodynamics had a self-consistent nature, then, since the fields manifest themselves by their force action, the expression for the electromagnetic force would have to be derived from Maxwell’s equations rather than being introduced artificially. Such an expression was obtained in [

Further, Maxwell’s equations are obtained by phenomenological generalization of experimental facts at low velocities (by analogy with hydrodynamics). Therefore, do not expect that they are guessed in the final form. Maxwell’s equations (or the wave equation) determine the phase velocity, while the relativity theory has a “claim” to the maximum speed of signal transmission―the group velocity. In fact, we always deal with a specific light, so this fact should be marked by some index: for example, instead of c we need to write a parametric dependence

Below, we will analyze what should be obtained in the experiments of Michelson-Morley and others from the position of the principle of relativity [

Let two particles moving parallel to each other with velocity

point O_{1} the particle velocity relative to the installation will be_{1}. No difference in the velocities of these two particles for two mutually perpendicular directions will be observed, regardless of the velocities

Let us now assume the wave nature of light. In this case, the speed of light can depend only on the properties of the medium and the internal characteristics of the propagating light itself. We will consider the etheric concept below, but for now we will rely only on the classical principle of relativity in a vacuum. If the light is a wave, then the speed of the source changes only the frequency. Thus, for a given frequency ω, the speed of light

The Towson experiment with two identical lasers also could not detect anything, since when the beams are brought into a single picture (in one direction) the frequencies become the same, and no regular beats will be observed. Thus, an attempt to seek changes in the speed of light in experiments with one fixed frequency is incorrect in its essence. The only dependence you can try to detect is

The Kennedy-Thorndike interferometer differed from Michelson’s interferometer only in that a different length of perpendicular arms was chosen at once. However, for an interference pattern, only the difference in the path of the rays relative to the wavelength of the light used (a fraction of the wavelength) is important. In addition, the accuracy of measuring the lengths of the interferometer arms (for example, the Michelson interferometer) is always less than the wavelength of the light used. Consequently, contrary to the opinion of [

The conclusion is the following: even if the result of this experiment were zero, it would not be able to distinguish Galilean invariance from Lorentz invariance. The Michelson-Morley experiment does not support the constancy of the light speed and does not disprove any classical principles. The installations with a fixed position of the source and receiver relative to a fixed installation moving as a whole in the medium are not capable to detect a change in the interference pattern (in-phase superposition of waves) with a change in orientation (rotation) of the installation. Thus, if the principle of relativity is true (even in the Galilean form!), then the result of the Michelson-Morley experiments (and also of Kennedy-Thorndike, Tomaschek, Bonch-Bruevich and Molchanov, etc.) must be strictly zero in the absence of ether under any assumptions!

If we accept the hypothesis of the existence of ether, then the speed of light will depend on the properties of this medium. Just like for sound, it does not depend on the speed of the source, but it is added up with the speed of the receiver (the buzz from the supersonic airplane is propagated at a constant speed, fixed by the medium and, as a result, the airplane is ahead of the sound). It is obvious that since light interacts both with matter (is scattered or absorbed), and with ether (propagates in it), then the interaction of ether with matter must be observed. But the relativistic interpretation of the Michelson-Morley experiment presupposed something incredible: the rigid “binding” of light to the ether, together with the total absence of interaction of the ether with the bodies (without the entrainment by the Earth, the installation). Naturally, in the case of partial entrainment of the ether, the theory becomes more complicated. However, this does not refute the ether hypothesis. Relativists also propose to act as in a joke about a drunkard under the lamp: seek not where he can find, but where it’s easier to seek.

We will not discuss experiments in which intensity was compared (this is the same as comparing average temperatures for two hospitals, including morgues), but make some remarks concerning the initial idea of interference experiment from the viewpoint of ether concepts. In fairness, it should be noted that the Michelson experiment and its analogs (despite the disputes on the installation device and the theory) always confidently gave a non-zero velocity of the ether wind taking into account possible errors [

Another point is usually hushed up. The whole set of experimental data on optics testifies to the correctness of the Huygens principle: every point to which the wave has reached is a source of secondary waves. Even in the absence of metallic screening, a thin plate of glass (or air) is sufficient for necessity to take into account the reemission of light by these locally resting elements. As a result, the actually measured speed in the ether concept should be obviously less than the speed of the Earth’s motion.

Thus, the Michelson-Morley experiment does not confirm the strict Lorentz invariance of the speed of light.

To begin with, it is necessary to determine what is meant by the speed of such an “object” as light. After all, in the experiments one talked about small variations against a background of enormous magnitude. Of course, the classical definition of speed, as the ratio of the traversed path to the elapsed time interval

However, in any case, the result is at least unambiguous, since the concept of speed in classical physics is clearly defined. And only in relativistic physics there are many “passports” for the “mysterious agent 007”-for light. Let us list them: 1) the “Great constant” c, to which is given a relativistic oath, 2) the coordinate velocity, when the relativists even cannot hide the need for sacrilegious

In the course of general physics, the relativistic law for velocity addition is usually considered in the one-dimensional case (the formula of the velocity addition was published by Larmor in “Aether and Matter” in 1900, before the creation of SRT).

Consider the following methodological remark [

where

The classical law for velocity addition relates only to the translational motion of bodies. If there is also an oscillatory motion, then in general terms nothing definite about the total velocity can be said even for nonrelativistic velocities. For example, the velocity of a malleus blow to a tuning fork has no relation to the velocity of propagating waves.

Although the question of the speed of light was stated above, we formulate more clearly the law of velocity addition for a light signal (for a purely corpuscular and purely wave model of light) using the example of one-dimensional motion. The axis is directed from the source to the receiver. Suppose, at a distance L from the receiver, the source emits a light beam of some frequency

Let us make one remark about the “extraordinariness” of the relativistic law for velocity addition, which allows us to exchange a light signal, even when the algebraic sum of the velocities is greater than c. Let’s pay attention to the obvious fact: signals for information exchange should be sent necessarily in the direction of the object, and not in the opposite direction. Therefore, there is nothing surprising in the exchange of signals in the classical case also, when, as a result of the formal addition of velocities,

It is also obvious that the physical limitation on the speed cannot be imposed by mathematics (the fact that under the radical sign there will be a negative value in some expressions). We just need to remember that all the SRT formulas were obtained using the exchange of light signals (Einstein’s synchronization method). If the body moves at once faster than light, it simply cannot be caught up with the signal sent after it. Similarly, you can introduce the synchronization with the help of sound (and there will also be singularities in the formulas), but this will not be followed by the impossibility of supersonic speeds. The speed of propaga- tion of disturbances (sound or light) in a medium is in no way connected with the speed of movement of some body through this medium.

Note the curious facts. The speed of light is deliberately chosen in SRT as the maximum speed (as an insuperable boundary). The relativistic law for velocity addition is arranged so that the total velocity is always obtained no more than the speed of light, i.e. it would be impossible “to jump into the light train”. In this case, if one of the speeds is chosen equal to c, then the final speed will also be equal to c, regardless of the direction of the second speed. That is, it would also be impossible to jump off the light train. The speed of not only light, but also of the object would always remain equal to c. However, if for the mythical world of tachyons we deliberately choose velocities greater than the speed of light, then we will still get a value less than the speed of light. At the same time, you can get exactly the same final speed even if you add two speeds, each of which is less than the speed of light:

For example, the relativistic addition of two motions with velocities

Generally speaking, the intrinsically contradictory properties of light in the SRT are simply postulated. Therefore, Fock’s assertion [

One more remark concerns experimental results. The dispersion of data in each of the experiments on measuring the light speed is usually high. And the small variations declared in the SRT are obtained only after a certain statistical processing, that is, after fitting to the desired results. This already led to confusions: the declared most probable value of the light speed was changed twice with explicit yields beyond the declared tolerances (see [

Even for a vacuum, the light speed can depend on the frequency. It is generally accepted that when particles are injected into a vacuum, various processes occur in it, such as the appearance of virtual particle-antiparticle pairs. Many interaction processes can be described using virtual pairs. In the course of light propagation, it also affects the properties of the vacuum; in particular, vacuum polarization can take place. Consequently, the reciprocal effect of a polarized vacuum on the process of light propagation must exist according to the reciprocity principle. As a result, light of a certain frequency will propagate through the vacuum―some “medium” with a certain permeability ε, determined by the propagating light itself, that is,

There are various methods for measuring the speed of light, for example: astronomical methods, interrupt method, rotating mirror method, radio geodetic method, standing wave method (resonator), method of independent measurements ofλ and ν. Currently, the latter method is the most accurate; it is this method that the Bureau of Standards measures the speed of light to within an eighth sign of accuracy. However, in this way there are fundamental difficulties [

When using the interval in the SRT pseudo-proofs, the following moment is not emphasized: a specific light is used, going from one point to another, that is, the substitution of

and even equality of intervals cannot be justified. There is a need to refer to experiment again, since this relationship is associated with some “unknown so far” Doppler law. For example, see article [

Let us consider in detail article [

The author [

How a special case can be the most general thing: is it possible in reality to guarantee a strict parallelism of velocities? Obviously not! For two velocities u and v with given modules, the case of their parallelism is a set of measure zero. And for noncollinear vectors, the result of relativistic addition already depends on the order of its application (on the order of addition of velocities)!

The value of

Mermin [

We make the following remark. It is necessary to accurately subdivide the measurable velocities (related to the measuring device located in some system) and the calculated velocities (not related to the system in which the measuring instrument is located). Obviously, in our case, the speed

Note that in mathematics there is no such general property that any function of two variables can be expressed as a function of one variable, even if it is “continuous and differentiable”. And the plausible phrases about “parametric dependence”, “fixation of a variable” and the replacement of the partial derivative in (2.10) by the total derivative (2.14) are intended to hide the obvious deception. Each can elementarily find examples when this does not work. Thus, (2.17) does not hold in the general case, to which the “proof” of Mermin allegedly claims. Since we have seen earlier that the symmetry (2.6) does not hold in the SRT, then the equality (2.18) does not work all the more so. Then the expression (2.19) and the search for the function h lose meaning. Also the value

Further, instead of (3.1), we must write other self-consistent expressions:

Expression (3.5) is correct, since it uses only classical relativity. It is obvious that (3.6) no longer corresponds to the previous definitions. But even if you forget about everything, said above, including the absence of meaning in the search for h, then the simplest solution (3.9) will be

If we allow the possibility of exotic (relativistic) transformations from the belief in the relativity principle, that is, assuming a possible dependence of a row of quantities on the relative velocity, then an additional hypothesis is the assumption of the dependence of these quantities on the modulus of the relative velocity. Then we cannot even be sure of the equality of the quantities measured when going back and forth. For example, then you can doubt that in the system of reference of the train

guments relate to the train’s motion system, that is,

Then the author postulates (this is again an additional hypothesis) that this relation will be preserved in the v-system also. We will not correct all the intermediate formulas of the analyzed article, but directly write the final expression

and the limit:

But again, from here no special functions

Further, the author notes that for a negative value of K, the law for velocity addition (5.2) can lead to the result

There is no evidence of the invariance of the light speed in a vacuum. The speed of wave propagation does not depend on the velocity of the source for any waves and at any speed of their propagation (the set among them occurs). This is just a property of wave motion, including in classical physics. The velocity

Mermin proposes to determine the value of K from expression (5.3), forgetting that in the system B only two velocities are measurable:

Generally speaking, the synchronization method using an infinitely remote source on the median perpendicular to the motion line [

We also give brief remarks to the “justification” of the relativistic law for velocity addition in [

Further, the replacement only

Finally, the dependence of mass on speed is fantasized: not the mass grows at a speed, but the effective force decreases as the speed of the body approaches the transfer rate of the interactions (to the momentum transfer rate)! In classical physics, there is also a similar decrease in effective force.

Thus, the paper [

The principle of relativity and a mathematical skew, with an exaggeration of the role of invariance in physical research, were discussed in the paper. It was analyzed in detail a “bloated soap bubble” with the invariance of the Maxwell equations. Further, the Michelson-Morley experiment was analyzed in terms of various theoretical expectations. This experiment cannot distinguish between Galilean and Lorentz invariance. The fundamental problems associated with the speed of light and with the law for velocity addition were discussed. Some pseudo- proofs of the necessity of the invariant velocity existence are critically examined.

Thus, there is no strong theoretical evidence for the necessity of the invariant velocity existence, as well as experimental confirmation of this statement, including for light.

Artekha, S.N., Chu- bykalo, A. and Espinoza, A. (2017) On the Question of the Invariance of the Light Speed. Journal of Modern Physics, 8, 1213- 1233. https://doi.org/10.4236/jmp.2017.88080