system
Given the following post, respond as if you're commenting on Reddit:
human
Is there a possible scenario where two events, A and B, can occur as: A then B, A and B simultaneously, and B then A, all using three different relativistic frames?

~~It's been a while since I've caught up with GR.~~ Say two events occur: A and B. Is it possible to have a frame R experience A then B, a frame R' experience A and B simultaneously, and a frame R'' experience B then A, all within our universe of physics? I am unsure if this would imply that it is simply three frames with three different accelerations, or if one frame would require time to be moving in the negative direction. 

EDIT: Thank you for the well put responses.
gpt
Let's answer this in SR. Forget about GR.

Given two events A and B, we can consider the invariant spacetime interval between them:

> (Δs)^(2) = -(Δt)^(2)+(Δx)^(2)+(Δy)^(2)+(Δz)^(2)

The notation "Δt" means the difference in the time coordinate between the events, and similarly for Δx, Δy, and Δz. The two events can be classified into three categories (assume that A and B are different events):

* timelike separated: (Δs)^(2) < 0
* lightlike separated: (Δs)^(2) = 0
* spacelike separated: (Δs)^(2) > 0

Timelike separated events are those events for which a massive particle can, in principle, travel between them. Lightlike separated events are events connected by a light signal. Spacelike separated events are events so far apart that not even a light signal could have traveled between their spatial locations in the required time. Note that the number (Δs)^(2) is the same in all reference frames. So if A and B are timelike separated in one frame, they are timelike separated in all frames. (Similarly for lightlike and spacelike separated events.)

Now to answer your question:

* The temporal order of A and B is the same in *all* reference frames IF AND ONLY IF the events can be joined by a signal traveling at or below the speed of light.

 * It follows that if A and B are timelike or lightlike separated, then their temporal order is the same in all reference frames.
 * It follows that if A and B are spacelike separated, then given any temporal order of A and B (A before B, A and B at same time, or A after B), there is a reference frame in which that temporal order occurs.

There are some other interesting properties these events must satisfy:

* If A and B occur at the same space location in the frame *S* (from which it follows that A and B are timelike separated), then their temporal order is the same in all reference frames and the least time separation between A and B occurs in that frame *S*.

* If A and B occur at the same time in the frame *S* (from which it follows that A and B are spacelike separated), then there is no limit on their time separation (it can be any real number) and the least space separation between A and B occurs in that frame *S*.