O.K.In the particular situation we were discussing, A and B are non inertial observers onboard an accelerating rocket and are spatially separated along the axis parallel to the accelerating motion of the rocket. Both A and B feel and measure proper acceleration.
Did I say that?C is an inertial observer not on board the accelerating rocket.
I'm fairly certain that C and D need only accelerate with, and in the same direction as A and B. However, since I did not accurately represent what you were calling C, would it be O.K. to let C and D be co-located with events that A and B agree are simultaneous?If you wish to introduce a fourth inertial observer D that is spatially separated from C, then C and D should be on a line parallel to the line joining A and B.
O.K.The situation we were discussing is the Rindler spacetime drawn on a Minkowski diagram with one space dimension and one time dimension.
Consider this: with only one space dimension to work with, any pair of simultaneous events would necessarily have to occur at the same point. Overlooking this, A and B will certainly agree upon the simultaneity of any two such events, but they will not observe the events simultaneously.Under those conditions, my original assertion:
remains true and can be extended to :
1) A and B agree at all times on matters of simultaneity.
How so? If A and B agree that any two co-located events are simultaneous, why wouldn't/couldn't any number of additional observers agree on the same thing?1) If A and B agree that two events are simultaneous then C and D do not agree those events are simultaneous.
Hmmm.. If I modify what I stated and let C and D simply have a relative displacement that is perpendicular to, and symmetric about the instantaneous velocity of A and B, I think you will find that all four can agree on simultaneity (although they may disagree on time).Your counter argument is based on all the observers (A,B, C and D) being inertial observers which is not the situation that was under discussion.