Simultaneity and Spacelike Interval

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SUMMARY

The discussion centers on the concept of simultaneity and spacelike intervals in the context of special relativity. Events connected by spacelike intervals lie outside the past and future light cones of a reference event, such as "Event 1." It is established that while two events may appear simultaneous in one frame of reference, they are not in another, as demonstrated by the example of an event occurring at the Sun and the observer's location. The discussion highlights that extreme acceleration could theoretically allow an observer to receive information from the Sun before the light from that event reaches them, emphasizing the non-simultaneity of events across different frames of reference.

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anxmetal
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All the events that are connected with a particular "Event 1" by spacelike intervals lie outside the past and future light cones of Event 1. But in some other frame of reference these events which are connected to Event 1 by spacelike intervals can appear to occur simultaneously with Event 1. Any explanation?
 
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Well, any two events which are simultaneous but at different locations wrt some frame of reference are outside the light cones of each other.

For example, an event occurring at the Sun at this very moment wrt my ordinary frame of reference is outside the light cone of the event that I am sitting here, now. I will get no knowledge of the event at the Sun until after eight minutes, at the event that I'm sitting here in eight minutes from now.
 
Erland said:
Well, any two events which are simultaneous but at different locations wrt some frame of reference are outside the light cones of each other.

For example, an event occurring at the Sun at this very moment wrt my ordinary frame of reference is outside the light cone of the event that I am sitting here, now. I will get no knowledge of the event at the Sun until after eight minutes, at the event that I'm sitting here in eight minutes from now.

So you have defined three events. Two simultaneous events in your original frame (one at the sun, one at you) and third event when information from the first event reached the location of the second eight minutes later.

If we look at this system from a frame with a relative motion in the instantaneous radial direction the original events would no longer be simultaneous. In principle is is possible to find a frame where the original event at the sun and any event you experience between now and eight minutes from now are simultaneous.

With extreme acceleration we could theoretically out run the news from the sun, if say, other indicators showed that it should have gone super nova two minutes ago.

Once the eight minutes has passed, the events on the sun are irrevocably in our past.
 

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