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The twin paradox

The paradox of the twins of Paul Langevin, proposed to the sagacity of his colleagues at the congress of Bologna in 1911 tells that at the age of 20, twins separate and one of the two, leaves to make an interstellar voyage in a rocket moving at near the speed of light, such that, seen from Earth, time dilation makes one second for the rocket last two seconds on earth. After 20 years, the Earthlings see the rocket make a U-turn and return at the same speed to arrive 20 years later, after a 40-year journey. The twin who remained on Earth is 60 years old, he welcomes his traveling brother, who is only 40. He has aged by half due to the dilation of time observed by the Earth.

The paradox lies in the fact that the traveler has aged 40 years in his own landmark in motion, since precisely, in his landmark, he was not in motion. It is the Earth that moved away and then returned in the space of 20 years, while the traveler lived 40 years. It is therefore the traveler who is 60 years old and who finds his 40-year-old brother.

A little clever then points out that each of the twins has lived 40 years in his own landmark, and that they are therefore both 60 years old.

Faced with these three possible answers, the most shared opinion according to the literature tells us that the traveler has aged less, on the grounds that when the rocket departs, when it makes a U-turn and when it arrives, it is no longer in an inertial Galilean frame of reference but in accelerated frames of reference.

We do not share this idea: the non-inertial frames of reference are supposed to be neglected, if there is a difference in age it will be due to the accelerations which affect the time in the traveler's frame of reference. If we are only interested in the inertial part, time passes there in the same way as on Earth. For us, the twins have both lived 40 years in their own frame of reference and are both 60 years old.

We refer you to the founding article of special relativity in §2 ON THE RELATIVITY OF LENGTHS AND TIMES of the kinematics part. Einstein explains very well there that in the moving frame of reference everything happens as in the immobile frame of reference and this is what is called "the relativity of movement" There is movement only in relation to another frame of reference, never in absolute.

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