Suppose that one twin stays home and the other twin gets in a rocket and travels to and back from a far-away star at great speed. According to the Theory of Relativity, the travelling twin will be younger than the resident twin, and the difference gets greater when the traveller stays near the speed of light for longer.
For example, if the journey is to the nearest star outside of the Solar System and back (to α Centauri at 4.3 lightyears), if the traveller turns back immediately, and if the rocket has an acceleration or deceleration equal to the acceleration of gravity on Earth (so that the traveller feels the same weight as on Earth), then the greatest speed of the traveller is 0.95 times the speed of light, compared to the Earth-bound twin. According to the resident twin, the whole journey covers 8.6 lightyears and 11.86 years, but according to the travelling twin the journey took only 7.12 years, so at the end of the trip the traveller's age is 4.74 years less than that of the resident twin. The average speed of the traveller was (according to the resident twin) 8.6/11.86 = 0.73 times the speed of light.
It now seems as if the traveller has covered 8.6 lightyears in 7.12 years and hence has travelled at an average speed of 8.6/7.12 = 1.21 times the speed of light, which seems to go against the Theory of Relativity. However, this is a fake problem, because a distance as measured by the resident twin is compared with a time measured by the travelling twin, and the only speeds that really mean something compare a distance and a time as observed by the same observer. Not just the measure of time is relative (and can be different for different observers), but also the measure of space.
According to the Theory of Relativity, a moving object appears shorter in the direction of motion, so the same would hold for a ruler that stretches from the beginning to the end of the journey, and hence also for the distance between the beginning and end. According to the traveller the distance was not 8.6 lightyears but only 4.53 lightyears, covered in 7.12 years, so the average speed of the traveller according to the traveller was 4.53/7.12 = 0.64 times the speed of light.
For example, if the journey is to the nearest star outside of the Solar System and back (to α Centauri at 4.3 lightyears), if the traveller turns back immediately, and if the rocket has an acceleration or deceleration equal to the acceleration of gravity on Earth (so that the traveller feels the same weight as on Earth), then the greatest speed of the traveller is 0.95 times the speed of light, compared to the Earth-bound twin. According to the resident twin, the whole journey covers 8.6 lightyears and 11.86 years, but according to the travelling twin the journey took only 7.12 years, so at the end of the trip the traveller's age is 4.74 years less than that of the resident twin. The average speed of the traveller was (according to the resident twin) 8.6/11.86 = 0.73 times the speed of light.
It now seems as if the traveller has covered 8.6 lightyears in 7.12 years and hence has travelled at an average speed of 8.6/7.12 = 1.21 times the speed of light, which seems to go against the Theory of Relativity. However, this is a fake problem, because a distance as measured by the resident twin is compared with a time measured by the travelling twin, and the only speeds that really mean something compare a distance and a time as observed by the same observer. Not just the measure of time is relative (and can be different for different observers), but also the measure of space.
According to the Theory of Relativity, a moving object appears shorter in the direction of motion, so the same would hold for a ruler that stretches from the beginning to the end of the journey, and hence also for the distance between the beginning and end. According to the traveller the distance was not 8.6 lightyears but only 4.53 lightyears, covered in 7.12 years, so the average speed of the traveller according to the traveller was 4.53/7.12 = 0.64 times the speed of light.