Popular expositions of general relativity start with a thought experiment showing that it is impossible to distinguish a constantly accelerating frame of reference in a free fall from a free floating frame of reference.
Person A is a small closed box, free-falling towards earth. Person B is in a small closed box floating around in space. If they both do the same experiments, they should see the same results. For example, if they have a small ball and toss it inside their box, they would both see that ball travel in a straight line (not curving) towards the wall. They would also both feel themselves floating around as if there was no gravity.
The same thought experiment could be applied to a frame undergoing a constant jerk. Does that lead to a new theory of relativity?