I am putting this out in order to clarify my understanding - hopefully the 
MWI experts out there can help me out here. A while back I asked whether 
the past can be undefined at a quantum level the way the future is. I asked 
this because I recall (somewhat vaguely unfortunately) reading or hearing 
something from Stephen Hawking in which he appeared to argue that at a 
certain very early point in the universe, there is no longer a single 
history, but quantum uncertainty comes into play, with important 
implications. Anyway, the response to my question indicated that most 
people still assume that history represents a single, well-defined line 
through the multiverse (I'm assuming MWI here, even though I know it's not 
the dominant theory/interpretation). 

I have been thinking about this and it occurs to me that firstly, the 
single history is only partially true. Since quantum interference patterns 
occur in MWI due to interference between universes, which can only occur if 
universes can merge again after splitting, then at least at this level, the 
past is not well defined. If a universe merges back with another from which 
it had temporarily diverged, then an observer within that universe cannot 
say which path he followed to get there. She followed all possible paths. 
Of course those divergent universes were only trivially different, or else 
decoherence would have made the merging impossible. But of course in any 
real universe, there will be a vast number of such "nanohistories", because 
of the immense number of quantum interactions where merging occurs. So at 
this very short time/space scale level at least, it is impossible to define 
a single history. Correct?

However at a macroscopic scale, it appears difficult for history to be 
intrinsically ambiguous. In other words the network of "nodes" of the 
multiverse is like a tree not a net. There may be tiny branches that rejoin 
one another at the smallest scale, but the limbs of the tree cannot merge 
back together. I can always define a single route back to the trunk, though 
if I go further up the tree, I will be forced to decide repeatedly which 
way to go. This branching is defined by time, so doesn't this effectively 
give an "arrow of time"? Yet the laws of physics are not supposed to be 
directional in time except through aggregation of effects as entropy. Are 
these two "arrows" related? How?

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