# Does coordinate acceleration match proper acceleration when $v=0, s=0$?

Alice and Bob are riding in their rocket at arbitrary proper acceleration through an arbitrary region of spacetime.

Bob steps out of the space ship right next to Alice, such that at $$t=t'=0$$, $$v=0$$, displacement $$s=s'=0$$ and Bob's proper acceleration is $$0$$. Alice's proper acceleration is $$A$$.

Alice gets the primed frame.

At that moment, do Bob and Alice measure Alice and Bob respectively accelerating away with coordinate acceleration $$a(t=0)=a'(t'=0)=A$$ for all $$A$$ in all regions?

Context: This question came to mind in relation to the comments on my old answer here.

• I have put the general relativity tag back on this question because "special relativity describes this situation" is a complete answer to the question.
– g s
Commented May 22 at 20:03

Yes. We can think for example that Alice and Bob are both in a airplane. In the moment that Bob jumps, Alice has a coordinate acceleration $$g$$ upward for him. Bob has a coordinate acceleration $$g$$ downward for her.