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I am a little confused about the implications of special relativity on causality and simultaneity.

Are the following two statements true?

  1. For two events A and B that are close enough in space and time such that A could possibly cause B, no matter how what inertial reference frame, A will always occur before B.

and

  1. For two events A and B that are far enough in space and time such that neither could not possibly cause the other, depending on your inertial reference frame, A could occur before B, or B before A.
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Both statements are true.

It would be more precise to say that for timelike separated points the temporal order is always preserved while for spacelike separated points it is not.

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Are the following two statements true?

  1. For two events A and B that are close enough in space and time such that A could possibly cause B, no matter how what inertial reference frame, A will always occur before B.

Yes: if event A could possibly have caused event B, i.e.
- if (at least) one identifiable participant observed event A coincident with participanting in event B (where A and B are distinct events, of course), or
- if (at least) one identifiable participant first took part in event A and subsequently in event B,
then event A is said to have occured before event B,
and events A and B are correspondingly said to be "light-like" related to each other, or "time-like" related to each other.

  1. For two events A and B that are far enough in space and time such that neither could not possibly cause the other, depending on your inertial reference frame, A could occur before B, or B before A.

No: pairs of distinct events which are neither "light-like" nor "time-like" related to each other (but which are therefore called "space-like" related to each other) are not said to have a particular "temporal order", as entire events. Instead, there may be particular temporal order relations ("before" vs. "after", or "simultaneous") between indications of pairs of participants at those events who were at rest to each other.

If, for a given pair of "space-like" related events A and B there can be found a pair of participants, one having taken part in event A, the other having taken part in event B, who were at rest to each other, and such that their two indications "at" these two events were simultaneous to each other,
then other pairs of participants can be thought of, or even be found, one having taken part in event A, the other having taken part in event B, who were at rest to each other, and such that their two indications "at" these two events were not simultaneous to each other (but "dissimultaneous"; one "before" and the other "after").

This fact, which arises from the defintion of how to determine mutual rest of participants and simultaneity, or dissimultaneity, of their indications, and which precludes the attribution of any such temporal order to entire events, is known as "relativity of simultaneity".

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