This started with wondering about the nature of certain physical quantities under time-reversal - chiefly, that acceleration retains its magnitude and direction at a given time regardless of the 'direction of time' used; this is different to say momentum, which may be reversed under time-reversal (in the sense that we are integrating forward in time from our perspective, along the backward direction in time).
There may be already agreed-upon conventions I'm not aware of regarding which quantities would be reversed, but the essence of the idea is that some quantities or some combinations of quantities need to be reversed, while others (such as acceleration) don't.
With respect to the twin paradox, this got me wondering if it works under non-trivial time reversal regarding the acceleration periods of the paradox. That is, suppose it isn't enough to simply reverse the order of events; if we assume everything runs in reverse, could we start off with two people of different ages, and due to relative reverse motion cause one twin to 'catch up' in 'getting younger' such that at some future (ie their past) they are of the same age?
To put the question more simply: Given that acceleration retains direction going forward and backward in time while velocity (or momentum) may not, do the relativistic effects remain the same (and do they make physical sense) from the perspective of a forward-time observer watching events unfold in reverse?
More generally: By virtue of acceleration having the same magnitude in both directions of time, does it mean it is impossible to discern a direction of time from any measurable acceleration alone? (further questions tempt relevance)