I debated over whether to include this in the HPMOR thread, but it's not specific to that story, and, well, it is kind of a stupid question.

How does backwards-only time travel work? Specifically, wouldn't a time traveler end up with dozens of slightly older or younger versions of herself all living at the same time? I guess "Yes" is a perfectly acceptable answer, but I've just never really seen the consequences addressed. I mean, given how many times Harry has used the Time Turner in HPMOR (just a convenient example), I'm wondering if there are like 13 or 14 Harries just running around acting independently? Because with backwards-only time travel, how is there a stable loop?

Think about a situation with a six-hour Time Turner and three versions of the same person: A, A' (three hours older than A), and A'' (three hours older than A'). Let's say A' gets to work and realizes he forgot his briefcase. If he had a backwards and forwards time machine, he could pop into his home three hours ago and be back in literally the blink of an eye - and because he knows he could do this, he should then expect to see the briefcase already at his desk. Sure enough, he finds it, and three hours later he becomes A'', and goes back to plant the briefcase before the meeting. This mostly makes sense to me, because A'' would plant the briefcase and then return to his own time, through forwards time travel, rather than the slow path. A'' would never interact with A', and every version of A to reach the point of the meeting would be locked deterministically to act exactly as A' and A'' acted.

But I'm really confused about what happens if A has a Time Turner, that can go backwards but not forwards. Then, when A' realizes he forgot his briefcase, wouldn't there actually be two ways this could play out?

One, A' finds the briefcase at his desk, in which case three hours later, he would become A'' and then come back to plant the briefcase. But what does A'' do after he plants the briefcase? Can he do whatever he wants? His one job is over, and there's another version of him coming through from the past to live out his life - could A'' just get up and move to the Bahamas or become a secret agent or something, knowing that A' and other past versions would take care of his work and family obligations? Isn't he a full-blown new person that isn't locked into any kind of loop?

Two, A' doesn't find the briefcase at his desk, in which case he goes back three hours to remind A to take his briefcase - does that violate any time looping laws? A' never had someone burst in to remind him to take a briefcase, but does that mean he can't burst in on A now? A' can't jump back to the future and experience firsthand the consequences of having the briefcase. If he goes back to talk to A, isn't this just the equivalent of some other person who looks like you telling you not to forget your briefcase for work? Then A can get the briefcase and go to work, while A' can just...leave, right? And live whatever life he wants?

Am I missing something really obvious? I must be, because Harry never stops to consider the consequences of dozens of independently operating versions of himself out there in the world, even when there are literally three other versions of him passed out next to his chair. What happens to those three other Harries, and in general what happens with backwards-only time travel? Is there no need for forwards time travel to "close the circuit" and create a loop, instead of a line?