THE SOLUTION TO THE TWIN PARADOX

THE ASTRONAUT TWIN IS YOUNGER THAN HIS BROTHER LEFT ON EARTH

The astronaut twin moves at a constant speed v in the Earth’s frame. (to head towards a star that belongs to the Earth’s frame, the Earth-star distance is therefore a well-defined length in this frame)

In the frame of the spaceship, it’s the Earth-star distance that moves towards the astronaut twin (for the astronaut twin, the moving distance is contracted and is less than the Earth-star length) and, when the star reaches the spaceship, the astronaut twin is younger than the twin left on Earth.

IF THE STAR REACHES THE SPACESHIP IN THE FRAME OF THE SPACESHIP, THE SPACESHIP REACHES THE STAR IN THE FRAME OF THE EARTH!

In the Earth’s frame the spaceship travels a “longer” distance, the time spent on Earth is necessarily greater than the time spent on board the spaceship!

THE ERROR

Since the Earth is moving relative to the spaceship, it could be assumed that the twin left on Earth is younger but this is wrong (even in Special Relativity) because the astronaut twin knows very well that the moving distance has a shorter length.

The astronaut twin also knows that, in the Earth’s frame, it is he himself who moves in the opposite direction to that of the Earth (towards the star) and therefore, if he has to travel a greater distance, also the time spent in the Earth’s frame is greater. (the brother who remained on Earth is older even according to the astronaut twin, the latter knows the phenomenon of the contraction of lengths!)

INSIGHTS

If an object A is launched from the spaceship (at speed v with respect to the spaceship) towards the direction in which the Earth is moving away, then the object itself, moving in the frame of the spaceship, is younger than the astronaut twin. It is this launched object that is younger than the astronaut twin, it is not the terrestrial twin that is younger.

The “problem” is that, when we think of the phenomenon of time dilation, we confuse the Earth with object A. (AND THIS IS WHAT CREATES AND FEEDS THE PARADOX)

It is one thing to consider an object in motion with respect to the spaceship (only object A) and another is to consider the distance Earth-star in motion (always with respect to the spaceship), I remember once again that the Earth-star distance has a length well defined in the Earth’s frame.

CONCLUSIONS

The astronaut twin is always younger than his brother, even though he continues to travel at a constant speed in the Earth’s frame and does not come back. (and, of course, object A is always younger than the astronaut twin if he continues to move with uniform rectilinear motion)

In my opinion it is not necessary to consider the accelerations and bring up General Relativity, it is possible to resolve the paradox simply by considering the phenomenon of the contraction of lengths.

Atmospheric muons also travel on a one-way journey (at constant speed), and always with a travel time t_1 less than the time t which is measured in our terrestrial frame. (The reverse has never happened!)

The Earth and object A move at speed v with respect to the spaceship, what is “paradoxical” is that the terrestrial twin is the older twin (the spaceship moves in the Earth’s frame) and that the object A is younger than the astronaut twin. (object A moves in the frame of the spaceship)

Yes, it seems a paradox, but this is how the phenomenon of length contraction works. The important thing is that only one of the twins is the youngest, and this must be true in both inertial frames of reference. (it is only necessary to consider the exact time dilations, the Lorentz Transformations are enough!)

Massimiliano Dell’Aguzzo