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## Two events A and B are simultaneous but occur at different locations in frame S. In a different frame S' (A) the events could be simultaneous and occur at the same location. (B) the events could either be simultaneous or occur at the same location, but not both. (C) the events could be simultaneous but cannot occur at the same location. (D) the events cannot be simultaneous but could occur at the same location. (E) the events cannot be simultaneous and cannot occur at the same location.

5 years ago

The correct option is (E).

Let us consider two events A and B occurring at the two points X and Y which are fixed in inertial frame S. since the velocity of light is c in all directions, the criterion of these events to be simultaneous relative to system S is obviously that the two light signals emitted from X and Y at the moment when the events occur shall meet in the center O of the line connecting X and Y. A similar criterion for simultaneity is also true relative to system Sʹ, having a constant velocity v relative to system S.

Now let us consider that the two events are simultaneous relative to system S and also the line connecting X and Y is parallel to the direction of velocity v of system Sʹ relative to system S. Then consider two points Xʹ and Yʹ in system Sʹ which, at the moment the events occur, coincide with the points X and Y. Then simultaneously the center Oʹ between Xʹ and Yʹ will coincide with O. Since now Oʹ, just as Xʹ and Yʹ, moves together with system Sʹ with a velocity v relative to system S. Oʹ will not coincide with O at the moment light signals from X and Y meet in O. The light signals with thus not met in Oʹ and hence, according to above mentioned criterion, the two events are not simultaneously relative to system Sʹ.

Thus simultaneity is a relative concept, not an absolute one. Hence the concept of simultaneity between two events in different space points has an exact meaning only in relation to a give inertial system. In other words each frame of reference has its own particular time. Therefore, two events A and B are simultaneous but occur at different locations in frame S. In a different frame Sʹ, the event cannot be simultaneous and cannot occur at the same location. Therefore option (E) is correct.

5 years ago

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