6.4. Duration of events in different reference systems

Let at the point x ', fixed relative to the system K', the event takes place lasting time . The beginning of the event corresponds to the coordinate in this system. and point in time end of event - coordinate and point in time . With respect to system K, the point at which the event occurs is moved. According to the Lorentz transformations, the beginning and end of the event correspond in the system K '.

From where

or

Time counted by the clock moving with the body is called the proper time of this body. As can be seen from the equation, the proper time is always less than the time counted by the clock moving relative to the body. The relativistic effect of slowing down the course of time allows in principle to make a “journey to the future” (but not the past). In fact, let the spacecraft moving with speed (Where ) relative to the Earth, makes a flight from the Earth to a certain star and back. If the light passes the way from star to earth in time then and for the earthly observer the duration of the flight is:

That is how people on Earth will age when astronauts return. On the other hand, according to the clock set on the spacecraft, the flight will take less time which:

In accordance with the principle of relativity, all processes on a spacecraft (including the aging process of cosmonauts) proceed in the same way as on Earth, but not according to the earth clock, but according to the clock installed on the ship. Let for example = 500 years and = 0.9999. Then

years as well years old.