6.4. Duration of events in different reference systems

Lecture



Let at the point x ', fixed relative to the system K', the event takes place lasting time   6.4.  Duration of events in different reference systems . The beginning of the event corresponds to the coordinate in this system.   6.4.  Duration of events in different reference systems and point in time   6.4.  Duration of events in different reference systems end of event - coordinate   6.4.  Duration of events in different reference systems and point in time   6.4.  Duration of events in different reference systems . 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 '.

  6.4.  Duration of events in different reference systems

From where

  6.4.  Duration of events in different reference systems

or

  6.4.  Duration of events in different reference systems

Time   6.4.  Duration of events in different reference systems 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   6.4.  Duration of events in different reference systems (Where   6.4.  Duration of events in different reference systems ) relative to the Earth, makes a flight from the Earth to a certain star and back. If the light passes the way   6.4.  Duration of events in different reference systems from star to earth in time   6.4.  Duration of events in different reference systems then   6.4.  Duration of events in different reference systems and for the earthly observer the duration of the flight is:

  6.4.  Duration of events in different reference systems

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   6.4.  Duration of events in different reference systems which:

  6.4.  Duration of events in different reference systems

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   6.4.  Duration of events in different reference systems = 500 years and   6.4.  Duration of events in different reference systems = 0.9999. Then

  6.4.  Duration of events in different reference systems years as well   6.4.  Duration of events in different reference systems years old.


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Physical foundations of mechanics

Terms: Physical foundations of mechanics