**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Thu, 9 Sep 1999 08:36:54 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**WDEshleman@aol.com: "[time 726] My Paradigm Shift"**Previous message:**Matti Pitkanen: "[time 724] Quantum jump as ultimate synhronizer"**Next in thread:**Stephen P. King: "[time 729] Re: [time 725] Entanglement defines the fundamental bi-simulation?"

Hi Stephen et al,

*****

[SPK] Hi All,

I am trying to understand Matti's Strong NMP idea. He gives a

definition:

From: http://members.home.net/stephenk1/Outlaw/MattiQMind.htm

"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."

[MP] Consider entangled state

|A,B > = SUM(m,M) c_mM |m>|M>

m and M refer to states of subsystem and its complement inside self.

One can always find state basis m and M such that entanglement

coefficients

c_mM are 'diagonal'

|A,B > = SUM(m) c_m |m>|M(m)>

m is state of subsystem and M(m) is state of its complement.

Density matrix represents the state of subsystem and is diagonal

in the basis just defined. Its diagonal elements are just

*entanglement probabilities*

P_mn = p_m delta(m,n) = |c_m|^2 delta (m,n)

telling the probability for that quantum jump occurs to state m

in measurement of density matrix.

Entanglement entropy is the Shannon entropy associated with the

probabolities p_m:

S=-SUM(m) -p_m log(p_m)

Here it is!

In p-adic context one must defined logarithm appropriately

and this leads to some exotic effects (entanglement without

entanglement entropy).

***************

[SPK]

http://www.aip.org/physnews/preview/1997/qinfo/sidebar2.htm

also, this ties to Bill's event horizon thinking! :)

http://xxx.lanl.gov/abs/hep-th/9811122

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.

http://www.cs.wvu.edu/~chif/cs418/1.html

[MP] This would represent attempt to reduce quantum jump to

classical computation. What makes me sceptic are Bell inequalities

plus my belief that genuine (not completely) free will resides in quantum

jump. Quantum jump is not reducible to process, quantum jump

is the Spirit, the Godly.

[SPK] 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.

[MP] I have for a long time pondered the problem whether this is

the case and I have been even enthusiastic about this idea: its

indeed suggested by quantum measurement theory.

The notion of self seems to resolve the question finally:

communication is *not* in question in the sense one might

think. The self containing *both* the subsystem *and* its complement is

the basic experiencer. Not the subsystem or/and its complement.

Note: the map m-->M(m) defined by the diagonalized

density matrix maps the states of the subsystem

of self to the states of its complement in self and is

perhaps analogous to *'bi-simulation map'* that Stephen has

been talking.

Entanglement would define the fundamental bisimulation.

Subsystems of self would simulate each other just at the

moment when they wake-up and reduce quantum entanglement

to zero. When they are selves they do not anymore bisimulate.

This would be sub-conscious bisimulation. Note that

any entangled subsystem of self would unconsciously bisimulate its

complement.

[SPK]

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? :-)

[MP] This would require precise specification of a model for

interaction. As I mentioned: quantum entanglement defines

a map between states of subsystem and its complement

resembling bisimulation: M(m) simulates m and vice versa.

Schrodinger cat bravely simulates atomic nucleus whose

transition leads to the opening of the bottle of poison.

Best,

MP

**Next message:**WDEshleman@aol.com: "[time 726] My Paradigm Shift"**Previous message:**Matti Pitkanen: "[time 724] Quantum jump as ultimate synhronizer"**Next in thread:**Stephen P. King: "[time 729] Re: [time 725] Entanglement defines the fundamental bi-simulation?"

*
This archive was generated by hypermail 2.0b3
on Sat Oct 16 1999 - 00:36:40 JST
*