Reverse Physical Processes, not Time
Here is the way to solve this problem. Now, I don’t think this solution works for the actual world, but it at least possible and it also makes sense of character motivations. (It also makes sense of the stupid thing Superman did in the 1970s film. Not sure about similar ideas, such as those in Looper — why was he wearing shoes???).
What we need to do is distinguish between the arrow of time and what I’ll call here the physical sign or appearance of the arrow of time. The arrow of time is the actual order of events in time. But the physical sign of time’s arrow is the typical physical pattern that maps onto such order. I mean though typical sequences of physical events (Actually, I don’t like this term ‘physical sign’ but am not sure of a better term –).
Here is an example of the difference: Imagine an egg smashing onto the ground. Now imagine a smashed egg spontaneously leaping off the ground and reassembling into the shape of a solid egg.
At the very least, I think the following is the case: the order of the first situation is a physical sign of time’s arrow — because it is a typical sequence of events. The second is a physical sign of reversed time.
I say at the ‘very least’ they are a sign. They might be more: they might actually be time reversing: when an egg reassembles, it is a case of time reversing. But I don’t think this has to be the way of putting it; this depends on how you understand temporal order, the arrow of time, in relation to the typical sequence of events in time.
Insert: Reducing Time’s Arrow
There is an issue here with whether or not one should or can reduce time’s arrow to something else to do with physical events. Over the years, attempts have been made to reduce temporal order to causal order and to increases of entropy (I’ll not give any examples here — but a relatively old popular physics book ‘The Arrow of Time’ by Coveney and Highfield might be a good non-philosophical start).
If you think that the arrow of time just is — or just is a product — of typical sequences of events, then you might also think the arrow of time follows the typical sequence even if it seems to be the opposite of the typical sequence, i.e., if we have a reverse of a typical sequence, then we also have a reversed arrow of time. E.g., when the smashed egg reforms into a whole egg, the arrow of time reverses (for that egg at least), In that case, time does reverse for one process relative to other processes: time runs backward for the smashing egg relative to other processes so that, to other processes, it seems to reassemble (also, it reverses for the other processes relative to the one process, i.e., to the smashing egg, the rest of the universe runs backward).
I’ll put aside whether or not there is a reducible arrow of time here. As said, this is not a situation for the actual world. Anyhow, for an observer watching the processes in the imagined situation, one of these processes seems to reverse, while the other does not. This does not require a reversal of time’s arrow; it only requires that one of the processes reverse (albeit, if that’s all there is to time’s arrow, then it is enough for the arrow to reverse).
Were you to witness both reassembling and smashing of the egg, the sequence of events would be of the same temporal order for both. It’s just that one — the re-assembling egg — is unusual. It’s still the case that, for you, in the strange event, the egg is smashed and then the egg is whole; for the typical event, the egg is whole and then the egg is smashed. Tempora; order is captured by the ‘and then’: Smashed egg followed by whole egg.
Back to the plot of Edge of Tomorrow: one can make sense of it if one does the following. When A ‘goes back in time’, A doesn’t necessarily go back in time at all. What happens is that everything in the universe reverses processes back to how it was at a certain point in time. Time itself mightn’t reverse in this case (if temporal order is more than typical physical order). All that happens is that physical signs of time reverse (again, this might be all you need for temporal order reversing — but I’m not assuming that).
It is like a fishing line: you throw it out then rewind it back in. Then throw it out again.
Let’s develop the egg example: At the restart moment, to which A keeps going back and waking, an astronaut accidentally drops a raw egg in space. That egg floats away out of reach and tumbles throughout the day until, several hours later, it smacks another astronaut’s visor. Say A dies just as the egg smacks the astronaut. Then what happens is that all physical processes, including the egg-smack, reverse. The egg’s disparate parts are pulled off the mask toward each other, and reassemble back into an egg. Following that, the whole egg floats back the way it came, eventually into the fumbling hand of the original astronaut.
The important point is this: time itself does not reverse. it continues on, filling up the hours. As such, it is still several hours later when the egg finally reaches the original place. When it does, at that moment, A wakes up. The astronaut drops the egg, and it begins its slow fall toward smacking the other unwitting astronaut several hours later (unless A dies in the meantime).
Over and over and over again, without remembering. The trick with A is that A remembers the unreversed sequence of physical events (but, so far as the story goes, not the reversed sequence).
This then answers the questions above.
Next page (page 4 below): Answering the Questions