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Simultaneity of Events in Different Frames of Reference

If no forces act on a material point it will not be accelerated. | AFTER STUDYING THE TOPIC A STUDENT IS TO | Active vocabulary | Moment of inertia | Active vocabulary | The mechanics laws are invalid with respect to this frame of reference | Forces of Inertia in Rotating Frame of Reference | Centrifugal force of inertia | Coriolis force of inertia | Space-Time Interval |


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Let an instantaneous event occur in point in the space. Let’s suppose that the clock of an observer in frame indicates the moment of time when this event occurs. Another event occurs in point and is fixed by the clock at the moment of time . Another observer located in frame fixes these two events at two corresponding moments of time, and , respectively. Let the difference of the two moments of time in frame be positive, i.e. . What will the difference of the two moments of time in be?

.

.

We conclude that . Let us analyse the details of the relationship between and .

1) Let’s suppose . How small or large is in this case? We get:

.

Note that also equals zero in any of two cases: a) if - classical physics and b) if , that is both events take place in the same point.

2) Let . Three variants for are possible: , and . It means that the consequence of the events and is arbitrary: the event may precede the event and v.v. This case does not raise doubts if the two events are independent: any one may precede the other. But the situation differs if the two events are mutually related. Let’s consider an example of two related events: the birth of your grandmother and your own birth. It is obvious that at first the grandmother was born and later it was the turn of her grandson. But as there are different variants for (<0, =0, >0) the possibility for the grandson to be born prior to his grandmother seems to exist.

The explanation of such a strange situation does not cause difficulties. If there are two events with cause-and-effect relation, the time is needed to transmit information from to , this time is . The expression ; is always less than and both and have the same sign.


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