The Twin "Paradox"

Let's consider the relativistic space trip to Alpha Centauri specified in the previous post, but now let's make it a roundtrip there and back. According to my previous calculations the total roundtrip should take about 12 years as measured on the Earth and about 7 years as measured on the spaceship. Let's assume there are two identical twins. One stays home and the other one is an astronaut on such a spaceship. When the spaceship returns to Earth the twin who was the astronaut is now 5 years younger than the twin who remained on Earth.

But Einstein also says in his Special Theory of Relativity that there are no privileged reference frames. Thus, the laws of physics are the same anywhere in the universe. Therefore, if we take the point of view of the twin who is the astronaut, then it is the Earth which has moved away and returned. The Earth is moving relative to the spaceship. Therefore it should be the twin on the Earth who is 5 years younger when the Earth returns to the spaceship.

Well, both twins cannot be 5 years younger than the other. Only one of them can be younger than the other one. This is an apparent paradox which stumped many physicists at the beginning of the 20th century. How can this paradox be resolved?

The paradox assumes that the situation of the spaceship and the Earth are identical. Are they in reality? Well actually, no. Although from the point of view of the spaceship the Earth appears to move away there is one crucial difference - the spaceship is accelerating but the Earth is not (actually the Earth is accelerating in its orbit around the Sun but this acceleration is negligible compared to the acceleration due to gravity at the Earth's surface - about 0.0006 g's). The time dilation effect (i.e., slowing down in time) applies only to the object that is accelerating. This explains why it is the astronaut twin who returns 5 years younger than the Earth-bound twin and not vice versa.

Actually, the concept that velocity is relative but that acceleration is absolute led Einstein to his next great theory - the General Theory of Relativity published in 1915.