The modified twins paradox

We would remind that in classical physics results are obtained by one observer can be used by any other observer (including investigators not participating in experiments). In such a case, our goal is to formulate some symmetric setting of a problem with results which are evident from the common sense. Relativists renounce the common sense permanently! Therefore, to prove the lack of contradictions and observability of relativistic effects, they must consider different results from the viewpoint of different observers and compare all results between themselves. However, for some reason they do not aspire to the Truth in this question. But few investigators, who carried out such analysis, either ascertained the lack of observable relativistic effects for two-observer schemes (and announced it), or discovered the presence of contradictions for a larger number of observers (the most honest-minded peoples even passed to the camp of critics of RT).

Let two colonies of Earth's inhabitants $A$ and $B$ be at some large distance from each other (Fig. 1.1). A beacon $O$ is at the middle of this distance. It sends a signal (the light sphere), and when it reaches both colonies (simultaneously), each launches a spacecraft piloted by one twin. The laws of acceleration (to reach a large equal speeds) are chosen equal in advance.

Figure 1.1: The modified twins paradox.

At the time each twin passes the beacon, at a high relative velocity, each will believe that his counterpart should be younger. But this is impossible, since they can photograph themselves at this instant and write their age on the back side of a picture (or even exchange pictures by the digital method). It is nonsense, if wrinkles will appear on a pictured face of any astronaut during the deceleration of another one. Besides, it is unknown beforehand if one of astronauts will wish to move with acceleration in order to turn around and catch up to the other one.

This paradox can be more reinforced and be formulated as a paradox of coevals - people born in the same year. (In SRT it is declared a change of time course rather than a transfer of initial time, as the time zone on the Earth, for example.) Let now the spacecrafts be launched with families of astronauts. Babies are born on each spacecraft just after accelerations became equal to zero (accelerations were chosen equal in advance). And these babies are chosen for a comparison of age. All previous history of motion (to the points $A_1$ and $B_1$ respectively) does not exist for theirs. The observers at the points $A_1$ and $B_1$ can confirm the fact of the baby birth. The babies differ in that they moved relative to each other at speed $2v$ all the time. They travelled the equal distances $\vert OA_1\vert=\vert OB_1\vert$ to the meeting. This is just the pure experiment to compare the time duration and to verify SRT. Let, for example, the flight of the baby 1 with the constant speed $v$ take place for a time 15 years. Then, from the SRT viewpoint, the first baby will reason in the following manner: the second baby moved relative to me with a large velocity for all my life (15 years); therefore, his age must be less than mine. Besides, if he will count out the age of the second baby starting from the moment of the receipt of signal from $B_1$, then he will believe that he will see infant in arms at the meeting. But the second baby will reason about the first baby in the same manner. However, owing to full symmetry of the motion, the result is obvious: the age of both astronauts are the same (this fact will be confirmed by the observer at the beacon).

Recall the explanation of the classical paradox of twins (one an astronaut and one an Earth's inhabitant). These twins have "unequal in rights," since only one of them accelerates (it is just this person who was declared to be younger than the other one). But before acceleration each of the twins thought that the other one should be younger! And, in fact, if one twin is accelerated, then the other grows old faster. (Maybe, it makes sense to prohibit accelerating astronauts and sportsmen in order that everybody around could grow old to a less extent?). Even the "explanation" of the classical twins paradox certainly contains some contradictions. First, everything could have been done symmetrically; the astronauts can take photographs before and after accelerations and even exchange pictures at the center (Can wrinkles appear on photos?!). Second, the explanation cannot lie in the acceleration. We see again at Fig. 1.1 (the modified twins paradox): even with initial equal accelerations, the twins can fly at the same high relative velocity for different times (due to different initial distance $\vert AB\vert$, for example). For example, we choose these accelerations to be equal to the acceleration of free fall on the Earth. Then, the driving at high relativistic speed requires about one year (but all the distance can be chozen much more: 100 or 1000 light years). It is obvious that neither "accelerated ageing" nor "accelerated rejuvenation" can occur during this year (we can remember the equivalence of accelerated systems and systems in gravitational field from the general relativity theory: just now we have conditions which are analogous to the usual Earth conditions!). It then occurs that accelerations the same in magnitude and in time of action at the same distances $\vert AA_1\vert$ and $\vert BB_1\vert$ may cause different aging - depending on the time of previous motion (100 or 1000 years) at constant relative velocity (due to time slowing from SRT), i.e. there obtains a violation of causality. Further developing this idea, one can permanently change the sign of acceleration ($<v> = 0$), and an arbitrary additional aging will take place in this case (in such a case the SRT formulas for time slowing at a constant rate make no sense). Third, the accelerations and velocities may be different for different astronauts in the process of their motion, but their meeting can always be organized at the same point, and, by the opinion of each of astronauts, the age of the same object will be different, that is nonsense.

Let us consider, for example, a modified paradox of "n twins" (Fig. 1.2). Let them depart on flights in different directions from the same center $O$, so that all departure angles are different in any pairs (we shall have an irregular $n$-gon).

Figure 1.2: The paradox of "n twins".

The schedule of velocities and accelerations is chosen the same beforehand (all spacecrafts are always "situated" at some sphere with the center $O$). Because of vector character of quantities, all relative velocities and accelerations will be different in pairs. By the opinion of some selected astronaut, each another astronaut must grow old to a different age (and this takes place from the viewpoint of each astronaut), which is impossible (again all astronauts can photograph themselves before each acceleration and after it).

Attempts look naive when "explanations" of different versions of the classical twins paradox are "made" with artificially fabricated auxiliary diagrams: relativists are again cunning and do not check results as a matter of contradictions from viewpoint of all observers (will somebody claim that the Lorentz transformations are insufficient ones, but diagrams present something more thing? really?). Physics and mathematics are "slightly" different sciences to put it mildly. Possible, someone could be interested how pure geometric drawings (a rhombus, a parallelogram, a triangle etc.) can be turned or transformed to pseudo-scientifically rescue the SRT. But these recommendations resemble the proud INSTRUCTIONS "how one can scratch the right-hand ear with the left-hand heel, when this leg is twice wound round the neck, and can provoke the same sensations (they must be elucidated beforehand!) as the normal man (which satisfies his requirements in more natural manner). But even for such "a state of affairs", the following fact is remarkable. In classical physics any logically consistent way leads to the same objective result (each observer can imagine reasoning of any other observer and even appropriates they). The matter is quite different for SRT: it is "necessary" to arbitrarily postulate some reasonings from absolutely single-type ones as false (i.e. there occur the fitting the choice of a way to the classical result). The resulting theory is "surprising": "here we read, here we do not read, here we turn over a page by this manner, here we turn inside out by that manner", and, as it is sung in the song: "and in other things, the beautiful marchioness, a nice how-d'ye-do...". It is concocted artfully.