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Symmetric twins paradox

Запись от IGPIGP размещена 13.06.2020 в 14:17
Обновил(-а) IGPIGP 13.06.2020 в 15:28

We all know the classic twins paradox and the way it is “refuted” by the Theory of Relativity supporters.
one of them remains on the Earth (being close to the inertial reference frame), and the other moves: accelerates, moves uniformly rectilinearly, decelerates to zero speed relative to the Earth, accelerates back to Earth, moves uniformly rectilinearly, decelerates to zero speed relative to the Earth, to stop right by the Earth
fraud is not noticeable. They say that acceleration created an asymmetry, which leads to the fact that the one who remained on Earth is elder at the end of the experiment. Acceleration (relative to the inertial reference frame) is equivalent to the action of gravity and due to its decelerating effect on time during acceleration of the reference frame (relative to the inertial reference frame) the traveler brother should be younger. They do not even notice that the sum of the stretchs of accelerations and the sum of the stretchs of uniform rectilinear motion in a straight line do not depend on each other and can be chosen arbitrarily.

Well. Let's try to eliminate the asymmetry, preserving the fact that the twins move relative to each other so that the time dilation effect of each brother observed from the system of the other brother remains a valid physical fact.

Now imagine - both brothers start from Earth and move in opposite directions. Imagine that we choose stretchs of uniform rectilinear motion so that their total duration in local time (the proper time of each twin) is much greater than the total duration of the acceleration stretchs. In all other conditions, the nature of the movement of each twin symmetrically repeats the movement of his brother. It should turn out that the time of any brother becomes less, relative to the other brother. The stretchs of acceleration , due to their symmetry with respect to the inertial system, should act equally on the local time of the twins and these regions can be excluded from the analysis. There are two, for each brother, stretchs of uniform rectilinear motion, relative to the inertial system. These stretchs are synchronous (according to the experiment) and in these stretchs the both twins are inertial a framess moving relative to each other. But the Lorentz transformations with respect to time are inexorable. They require that the time of each of the twins flow more slowly from the point of view of the other twin, who considers himself an observer, and his system is at rest, while the brother's system, from the point of view of the observer, moves with a total speed which is relativistic sum:

https://www.cyberforum.ru/cgi-bin/latex.cgi?v_{brobro} = \frac {2 \cdot v _ {broEarth}} {1+ \frac {{v _{broEarth}} ^ { 2}} {C ^ {2}}}
This is nonsense. When they meet at the final point (on Earth), each of them should see his brother younger. Both! And that is not possible. This is the reason for both to synchronously say: "This is bullshit!".
If it is true, decide for yourself.
Размещено в Theory of relativity
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