SELF

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S.B. Karavashkin and O.N. Karavashkina

3. Model of the source and boundary moving with equal velocities relatively the elastic line

In case of moving source and boundary, the scheme will considerably change, as well as the solution for this model. To build the model, introduce two reference frames; one of them will be constrained with the elastic line, and another (dotted) - with the moving system of the source and boundary. We will premise the distance h between the source and boundary to be constant, and the initial location of the source relatively the undotted frame we will denote asx₀ (see Fig. 3).

Fig. 3. The excitation propagation in the model with a moving source and the boundary at which the wave is reflected

The same as in previous problem, we will premise the harmonic external affection (2); and we will be interesting in the shape of wave in the line between the source and boundary in the moving frame, i.e. in the frame of source of excitation. We also will premise that as far as the wave propagates in the material elastic line, its propagation velocity in the frame related to this line is constant and equal to c.

Besides, in this problem we will not take into account the relativistic space-time metric transformation. We need not it, as we are able to transmit the measure of both time and space from the stationary frame to that moving, without any distortion.

We have described the transmission of the time measure in [2]. According to the technique stated there, the time interval is transmitted by way of metrological check of own periodic processes in moving frame with the far source of periodic signals, when the moving observer crossed the normal to the source. It is important that with this technique the matter is not the simultaneity of events but just the transmission of time measure. As we will see from the below consideration, this is quite sufficient. So, even if the periodicity of processes in material devices changed under the large velocity of moving frame, we always can retain the very etalon of time, using this technique of check, which is the evidence: relativistic transformations of particular material instruments for time measurement are independent of temporal measure of material space on the whole. To transmit an exact space measure, we can use some other technique, something like that which relativists use to determine the simultaneity in two mutually moving frames. Particularly, L. Marder describes that technique so: "The question is always asked: 'Is Lorentz' reduction real?' The doubt usually arises because the length of moving bodies is determined arbitrarily to that extent to which the taken definition of simultaneity (for example, Einsteinian which we use) is arbitrary. However, we can definitely answer, this phenomenon is real, as one and the same procedure of length measurement will give different results in accordance with classical (Newtonian) theory and Relativity. This is clear from the following example. Let two similar parallel rods AB and A'B' move with the speed V in reciprocally opposite directions, so that they fly by each other... When A passed A', the located here observer S notes their position. In the same way the place where B and B' met with the observer at S is noted. Then at leisure we can measure in the frame S the distance between these two points. Relativity predicts that the result of measurement will be equal to the value given by classical theory multiplied by

[3, chapter 2, section 7].

Approaching this experiment in the view of possibility to transmit non-transformed etalons from one frame to another, let us some refine the relativistic scheme. Let the etalon be located in the stationary frame and equipped by two lasers fixed at the ends of etalon, whose beams are perpendicular to the motion of moving frame and mutually parallel (Fig. 4).

Fig. 4. Transmission of length measure between mutually moving inertial reference frames

We will also some better equip the moving observer. We will provide him with a quite long drum whose rotation axis is directed along the motion of moving frame. Its cylinder is covered with photo-sensitive layer. As it is already understood, the measurement will go as follows. When the measure and drum coincide, laser beams will draw on the photo-sensitive layer two spirals; by the distance between then we will be able to determine the size of moving measure from the viewpoint of stationary frame. As we can see from this description, the time necessary for light beams to cover the distance between the measure and drum is equal, and both beams pass the same distance. The shift velocity of these beams relatively moving frame is the same. Photo-sensitive layer registers both beams independently and simultaneously. So nothing to say of any length change. But if we are able to transmit the measure without transformation, we can say of physical processes in the substance moving with the near-light velocity, not of change of space measure, and the more not of constant velocity of light in all reference frames.

We can use this technique also to measure the time intervals. We will need for it one laser beam modulated by the frequency of tact pulses. Knowing the rotation speed of drum and registering the intervals between dark bends on photo-sensitive emulsion, the moving observer can determine both the speed of his motion relatively the stationary frame and time interval which also will be transmitted without any distortion - of course, in limits of experimental error.

As it follows from this, we are able to synchronise completely the measures of time and length, and when we need not in our calculations to indicate the events simultaneity, in both systems the measures of space and time will be always equal and can be compared. Of course, this does not exclude the relativistic transformation of material bodies, but it evidences, the transformation has no concern to measures, only to particular objects, and can have effect only on metrologically unsupported measurements. But when analysing physical phenomena, we have to exclude those particular techniques and distortions which can be added by some physical processes in particular relative measurement; we have to rely only on techniques that are sufficiently metrologically supported.