stephen p. king (firstname.lastname@example.org)
Wed, 08 Sep 1999 13:59:41 -0400
I am trying to understand Matti's Strong NMP idea. He gives a
"Strong NMP says that in given quantum state=quantum history the
quantum jump corresponds to a subsystem-complement pair for which the
*entanglement entropy reduction in quantum jump is maximal*.
The first interpretation coming in mind is that the conscious
experiences is such that the information gain is maximal. Perhaps a more
natural interpretation is that entanglement entropy tells how
interesting, 'catchy', the conscious experience is and only the most
interesting experience is actually experienced."
Now, we first need to understand what "entanglement entropy" is! Does
it have to do with "quantum entropy" re: "value of quantum entropy gives
you the upper limit for how much information you can recover from a
quantum particle or collections of them."
also, this ties to Bill's event horizon thinking! :)
I think that the determination of which "subsystem-complement" pair has
the minimal quantum entropy is given by a tournament of games "played"
between the pairs. The winner of the tournament is the quantum state
that is the most informative. I see the "tournament" as modelable by a
periodic gossiping on graphs formalism.
The main ideas presupposes that "subsystem-complement" pairs can
communicate with each other. I suspect that this follows some thing like
this: Subsystem A <-> Complement B, Subsystem B <-> Complement A. If the
complement of subsystem A is subsystem B and the complement of subsystem
B the subsystem A, then subsystems A and B have identical entanglement
entropy or information.
Now, what is a given pair of subsystems do not have complete
agreements, but do share some information? (I see "information sharing"
as the existence of identical configurations in the configuration space
of each subsystem, following the logic that "identical configurations
encode identical information".) Can we model how, given an initial
common information, a pair of subsystems can evolve such that they
become equivalent? This is what happens in the periodic gossiping
situation, so I suspect that it may be useful.
The problem that I have is that I do not know how to show this
mathematically! Can you help me? :-)
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