We shall begin with some general remarks. For the sake of justice it is necessary to note, that the principle of relativity has never been verified to a maximum experimental accuracy even for the mechanical phenomena. If we believe in the absence of all-penetrating ether, then similar properties can be attributed to the gravitational field. How the observer on the Earth wouldn't be moving (in the rectilinear uniform motion or in circular motion over the Earth surface), the gravity force will change in magnitude or in direction, which can be detected from the comparison of quantitative regularities in the experiments. Therefore, the declared hypothetical experiments could be performed only in the absence of gravitation or in the case of strictly symmetrical distribution of the whole Universe relative to the observation point. But in the presence of moving bodies such a strict "compensation" of gravitation could take place at a single point only. In all real cases one can observe the absolute changes of the state (velocity, acceleration, etc.) relative to the point of space the investigated object passes through at the given instant. Besides, it can be admitted that the rigorous notion of inertial systems must be broadened in an experimental sight and extended to "near-inertial systems", i.e. to the systems which cannot be distinguished from rigorously inertial systems within the existing accuracy throughout the experiment. Otherwise this notion would be lost for practical applications and would be found useless for physics. For example, it is clear that all "relativistic" experiments were made indiscriminately on the non-inertial Earth (its non-inertiality can be easily proved by the Foucault pendulum); and if we should approach in the absolute rigorous manner, the explanation of these experiments by the relativity principle of SRT cannot be even taken into consideration (unlimited rigor gives up for lost any section of physics).
Make some more general comment. The erroneousness of the relativity theory is in no way related with the presence or absence of all effects the SRT tries to describe and speculate on this (as well as the refusal of crystal spheres does not abolish the really observed planet motion). Two questions must clearly be separated: 1) whether there exists some phenomenon as such or not? and 2) whether some theory, which ascribes an explanation of this phenomenon to "own" achievements, is valid or not? By the "reasons", which are claimed in SRT, no extraordinary effects can simply exist (the combination of statements and conclusions of the SRT is mutually exclusive, that is logically contradictory). If, nevertheless, some effect is still observed, then it is necessary to search for another real reason (explanation, interpretation) for it. Each theory contains a series of "if"'s, which should be verified experimentally. For example, whether the running of some processes in the object can change, when its velocity really (!) changes? It can, in principle. For example, the first "if" is as follows: the ether exists; the second "if" is as follows: some process depends on the velocity relative to this ether. But in this case the relative velocity of two observation systems will be pure at anything. So, if the first and second system are moving to opposite sides at the same velocity relative to the ether, then similar processes in these systems will proceed similarly. If, however, the third system moves to the same side as the first one, but at velocity relative to the ether, then, in spite of the same relative velocity , the processes in the third and first systems will differ. In the given case the principle of relativity itself (and, the more so as, SRT) is violated. Such a situation is also possible, in principle, but should be verified in the course of experiments only (it is yet be made by nobody with a required accuracy).
One more remark concerning the experimental results. The scattering of data in each of experiments on measuring the speed of light is high, as a rule. And the small tolerances declared in SRT are obtained only after some certain statistical processing (that is, after fitting under desirable results). This has already resulted in discomfiture: the most probable value of the speed of light, declared by relativists, had been twice changed with obvious escaping the limits of declared tolerances (see ).
Note that the light dispersion was discovered long ago in the open space . The dispersion of in vacuum was suggested in paper  (this hypothesis will be considered in Appendixes). The example can be mentioned, where the radiation lines have appeared in 2 months after detecting the X-ray flash , which can also have relation to light dispersion in vacuum.
The classical law of addition of velocities has relation to the translational motion of bodies only. If, however, there exists also the oscillational motion, then, generally, no definite words can be said about the total velocity (even for non-relativistic velocities). For example, the velocity of hammer impact against a tuning fork has no relation to the velocity of propagating waves. Consider one more example. Let a long rod be moving over the surface of water perpendicular to its length at velocity , and the point-like source excites the waves in front of a rod. Then these waves will pass some part of the path in water, which rests relative to the rod, at velocity , and another part of a path - in water, which rests relative to the shore. As a result, the wave velocity will lie between and (and will be, generally speaking, a function of the distance to a source). The next example. The local speed of sound relative to the airplane in airplane's saloon with holes will depend on the velocity of a steady airflow inside airplane's saloon (some analog of Fresnel's entrainment coefficient).
Rather strange is a typical "increase of accuracy" at statistical data
processing in SRT. This means that the data are artificially selected and
those dependencies are analyzed, which certainly meet the given theory. First,
the most probable values of various physical quantities can be completely
unbound causally with each other even in separate acts of interaction (recall
the distinction between the true value and the mean, most probable or
effective value in a particular process of measurement). Second, for
essentially nonlinear expressions from the equality of mean (or effective)
values it is rather difficult to extract the declared relations for true
(instantaneous, or causally bound) quantities. Such an analysis of the data
(allegedly confirming SRT) is met nowhere (in this case the theory of
fluctuations must be used, you know). Third, the attention should be
paid to the following mathematical facts:
1) the statistical averaging of a periodic function with unknown period over the other (untrue; for example, if the atom re-emission does not taken into account) period can give a zero result or a quantity lower than true one;
2) the attempt to determine a periodic dependence by selecting an incorrectly guessed or shifted harmonics gives zero () or an underestimated quantity. Possibly, the incorrect statistical data processing is just the reason, by which, in spite of considerable deviations of each of separate measurements from a zero level, rather small oscillations of quantities are obtained in some experiments (of Michelson type) after statistical processing (recall Miller's analysis in his experiments ).
It is very "fashionable" to investigate any phenomenon by means of the fine Mossbauer effect. It is rather strange, however, to attribute the temperature effect on the resonance frequency shift in the Pound-Rebka experiments to SRT's time slowdown effect - this is a clear speculation. Though temperature variations influence, to a higher or lower extent, all physical phenomena, but the SRT time bears no relation to an obviously classical field of investigation. Otherwise, if we extrapolate the global claim of relativists quite slightly into a close field - up to melting of a specimen (where the effect itself vanishes), then - what should be declared in this case: the time has stopped its running, the time became singular, or some other delirium? Statistical analysis for the temperature Pound-Rebka experiments is also rather doubtful. It is investigated the influence of temperature and its variations on the frequency shift (but what relation has this influence to some aging?). Recall that temperature characterizes the velocity dispersion inside a sample. But how this effect could be attributed to the sample as a whole? Generally speaking, it is rather strange to associate the Doppler effect with time course or to choose some concrete frequency of a specific process as an indicator of time course. Really, let be a system consisting of a great number of atoms which are excited by help of light with a frequency . Let us choose the frequency as an indicator of time course in this sample. Returning to the basic state, atoms will radiate. Some part of atoms will absorb this radiation; and multiple absorption can also take place. As a result, other frequencies will additionally appear in the system. But, on these grounds, it is inept to believe that time is changed even for such a given atoms; to say nothing of the fact, that it is absurd to ascribe a "change in time course" to the sample as a whole and all the more to attribute a something to all reference systems, to which can be mentally associated this sample (just similar globalizations are used by SRT and GRT).
The following methodological remark concerns the terminological forgery, frequently committing by relativists (one of "methods" of the self-affirmation by deception). So, terms with a value of in the denominator (for example, , etc.) came to be called "relativistic" ones, though such the terms frequently appear in the classical case as well, and, at the least, it is necessary to compare analytical expressions for the analogical terms in the classical and relativistic cases. Such the situation of deception takes place in the case of radar observations of the Venus: the rumour was set about an alleged new (?!) confirmation of the SRT, though the pure classical formulae were used (see ).