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Coexist vs Simultaneous


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You're describing a (frame-dependent) moment, or an instant in time, rather than an interval of time. To describe things like "bolt here, one there" etc., you're describing events, ie. anything with a location and a time. The coordinates you use to describe the events come from a system of coordinates, in this case you're using the coordinate system of the observer, ie. the inertial frame in which your chosen observer is at rest. In those coordinates, the 2 lightning events have the same time value.

The relationship you're talking about describes any pair of events separated by a space-like interval in flat spacetime, because you can always find an inertial frame in which 2 space-like separated events happen at the same time. Or, find other observers where the lightning bolts aren't simultaneous. So, there's nothing special about the 2 events being simultaneous, unless there's something special about the observer you chose. "The interval between the events is space-like" is something all observers agree on, to describe the relationship.

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