The solution can be found in Einstein's theory of Special Relativity. When travelling at speed v, time actually slows down according to the equation:
By the principle of relativity, it would seem to an observer in the car that clocks outside the car slow down compared to his own.
Suppose there are two twins before us. One of them will ride down a road at a constant speed, make a turn and return to where he started out. During the journey, each twin will see the other as being aging at a slower rate than himself, because either twin could regard the other as moving away. This leads to question: who is the younger twin?
In reality, it is possible to determine which twin was in motion because he would have experienced acceleration during three stages of his journey- starting up, turning around and stopping. Only the twin who remained at the same spot throughout the journey is right in claiming that his twin aged less than he did. Time did pass more slowly for the twin who was in the car. In fact, the times taken for the journey as measured by the two twins can be given by the equation above.
Let us examine the following space-time diagram.
The diagram shows the position of each twin with respect to time. Each line (called a world-line) on the diagram represents the position of a twin. For Kaluza, the twin remaining stationary, his world-line is parallel to the time axis. Note that the world-lines for light rays are inclined at an angle of 45 degrees to the time axis. As the other twin, Klein, is moving to and fro at 0.8c, his world-line is bent. Each dot on a world-line represents the point when a light signal is sent out to the other twin, at intervals of one second.
It can be seen clearly that Kaluza will measure 10 seconds for the journey while Klein measures 6 seconds. The first signal sent out by Kaluza in the first second reaches Klein only after the third second according to Klein's time, and so Klein assumes that time passes more slowly for Kaluza. On the other hand, the first light signal sent off by Klein in his first second reaches Kaluza only in the third second of Kaluza's time. Hence, Kaluza observes that Klein's time passes more slowly compared to his. In the last 3 seconds of Klein's time, he receives 3 signals per second and so concludes that time speeds up for Kaluza. Kaluza receives signals at a slow rate for 9 seconds and at a rapid rate for 1 second. Although to Kaluza it seems as if the car travelled back at a speed faster than that of light, it is only an illusion that arose as a result of the time taken for light to travel from Klein to Kaluza. At the end of the journey, Klein received 10 signals in all and Kaluza received 6 signals. Therefore, they can both agree on the fact that a shorter length of time passed for Klein and so he aged less.