Simultaneity and Spacelike Interval

[anxmetal]

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?

 

[Erland]

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.

 

[utesfan100]

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.