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In this figure we see the primed movable frame and non-primed stationary one. The clocks are marked as periodic structures. They have a feature - the pulse is sent from the stationary frame to that movable exactly at the point 1 and is received also at the exactly determined point 1'. Thus, the timing pulses with some timing frequency come from the stationary frame to that movable. To synchronise, we are interesting first of all in transformation of timing pulses when receiving by movable observer. Naturally, in accordance with Doppler effect, in the movable frame, the time interval will some increase if the movable frame runs from that stationary, and decrease if the movable frame runs closer to that stationary. On one hand, as Einstein thought, this is an inconvenience, as the measure of time intervals extension depends on mutual position of frames. But on the other hand, this is an invaluable advantage, as this allows the observers to be informed about interrelation of processes occurring within these frames. Actually, if the observers once have timed their clocks, the difference in periods will depend on time necessary to pass the distance 1 - 1'. But if, going on moving relatively each other, the observers repeat their experiments, they will see the time delay between the timing pulses changed. This, to the point, fully contradicts the conclusions of Einstein's mathematical formalism, though this is just the reality which you are proposing to consider in the beginning of your post. Actually, if the frames are moving in parallel and their axes x are distanced by some value d, and if there is some angle between the point of radiation of synchronised pulse and point of its receipt, we from the point of stationary observer will have the following regularity (see Fig. 2):

where t₁₂ is the time between the timing pulses emitted by the stationary frame, t'₁₂ is the time between the received timing pulses in the view of stationary observer, t'₁₂ is the variation of time interval for the moving observer, - again, from the position of stationary observer. But the moving observer will have a similar pattern, only numerical values can differ. Analysing the yielded expressions, we see that (17) and (18) contain a direct interrelation of duration of radiated and received timing pulses, and they depend on the interposition of frames at the instant of signal radiation/reception. This regularity is nonlinear. We should mark, in this case it is not important, whether the observers are aware of regularity, how the light velocity varies in passing from the stationary frame to that moving. All measurements of timing have been conducted in the stationary frame. Given the moving observer can rely only on qualitative results, not on quantitative, we have to develop the criterion of timing independent of possible transformation of light velocity and frequency in passing from one frame to another and vice versa. And we can easily establish such criterion, having plotted the regularities (18). If we take

In Fig. 3 we first of all can see that at any d the curves of relative variation of time interval go through zero point. This means, there exists an interposition at which the difference of time intervals is zero. At small distances this zero point is shifted from the position of between-frames vertical line, but at distances about 30 light seconds and more this point can be strongly fixed on the vertical between the directions of observers' motion. In addition, at large between-frames distance the derivative (denoted as a dotted line of the same colour as the curve) becomes strongly symmetrical as to the position of the vertical and has the minimum there; and that minimum coincides with the zero point of the relative difference of time intervals. Note also, we calculated the curves for quite large speed of moving observer, for whom 30 light seconds is quite small value.

On the basis of this regularity we can see more clear the technique of timing. To time, the moving observer need not to know the law of light velocity transformation. Whatever it can be, the minimum of derivative will not change its position. And at that minimum the time intervals will remain EQUAL. To register this minimum, the moving observer has only to copy with the necessary accuracy the transformation law of time interval of timing pulses received from the stationary observer and to re-calculate it relatively the zero point of relative difference. As the moving observer cannot experimentally obtain the relative difference per se, he can seek the extreme point by variation of the derivative of experimental data. At large between-frames distance the moving observer can obtain these data immediately, and at small distance he can create a probe frame, if sending it with the copy of clock far from the stationary observer. This will enable him to avoid the shift of extreme observed at small distances between the frames.

As we see, the inconvenient reference frame just enables us with any given experimental accuracy to synchronise the time in frames without any additional premises and transformations. If well-made timing, the time intervals in both frames will be equal with the given experimental accuracy quite enough for relative results of practice. Of course, the researcher will need to complete the curves to obtain the synchronous interval, but this is an usual experimental situation. As an example we can mention the calculated value of absolute zero of temperature which no one achieved, but the value has been calculated with high accuracy (-273,16^o C). And we have to pay our attention that in the region of extreme the curve of derivative is very smooth - this considerably lessens the error connected with the inexactly found point of extreme. This feature is just reflected in the fact that the sidereal time is most precise. As is known, "when observed on passage instruments and zenithal tubes, there is applied the method to register the instants when stars passing the meridian. If observed on prismatic astrolabe by Danjon, there are registered the instants of stars passing through the al mukantarath (small circle of celestial sphere parallel to the horizon) with zenithal distance of 30^o. After preliminary data, the errors characterising the accuracy of time determination with the help of these instruments are equal, accordingly, to 19, 18, 16 and 12 msec" [Citovich, A.P. Time. Physical encyclopaedia, v. 1, p. 333].

With this technique of timing, we can obtain even more accurate time, synchronising it with the average statistic intervals of pulsing of a dozen most stable cepheids. The very stability of cepheids will tell us not only that the processes in them are stable, but that we are positioned as to them in the region of extreme. So the time measured in such way will be most close to the Newton's absolute time. It follows from this that if two observers in mutually moving inertial frames synchronise their clocks not with each other, as Einstein suggested, but in accordance with Newtonian mechanics with the absolute time after the same far cepheids, they both will have a common time standard with quite good experimental accuracy. And having it, they will easily check the simultaneity of events.

And we can notice one more merit of this technique "inconvenient" for relativists. When plotting the curves of time intervals variation, the moving observer does not need to use the clock timed with the stationary observer. To measure this regularity, he will need some strongly periodic process in HIS own frame in whose units he can plot. And having it plotted, he can calculate the point of extreme and take as the standard the value of his own periodic processes that corresponds to the calculation. Well, we do not surprise taking as the unit of length 1 650 763,73 of radiation period corresponding to 2p₁₀ - 5d₅ transition of crypton-86 atom (even with hundredths!) And so in this case.

In this technique the metrological nuances can be very different. In particular, instead mechanical pendulums one can synchronise with the help of light pulsing packets generated on a device like shown in Fig. 4.

We see this device much alike one of popular constructions of Rojdestvensky's interferometer, but it has some difference. Not continuous radiation of source but synchronous pulses of large relative pulse duration is fed to the input of this generator. A part of light beam is immediately reflected from the semi-opaque mirror to the output of device, and a half of beam sequentially reflects from internal mirrors and also appears at the output, some shifted in time as to the first half. This creates packets of pair pulses which can be transmitted by the stationary observer. The time delay can be easily regulated by the distance between the internal mirrors; as stationary as moving observer can regulate on his instruments when correcting the time interval.

As we see, the clock timing problem is difficult (as many things in the issues of metrological standards) but quite realisable. With it, all clocks in the inertial frame are timed equally without any transformation of the time unit. The only thing is needed - observers to be just observers, not Einstein's guinea-pigs.

We regret much saying it, but this is so.

All the best to you,

Sergey and Olga Karavashkin

18.12.2004

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S.B. Karavashkin and O.N. Karavashkina