On 1/20/2014 5:18 PM, Pierz wrote:
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?
I think this is right; at least it's the way I think about it. The arrows are related
just by the increasing number of states available to the micro-dynamics. Per QM even the
"trunks" of the tree are not independent. The net information doesn't increase under the
unitary evolution, so there is negative information encoded in the entanglement between
different twigs, branches, and trunks. But in the coarse graining that we can observe in
whatever trunk we find ourselves, entropy is increasing and that's time's arrow.
Brent
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