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

*Tue, 30 Nov 1999 06:33:42 +0200*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**WDEshleman@aol.com: "[time 1066] I've got Hamiltonians now!"**Previous message:**I.Vecchi: "[time 1064] Re: [time 1056] Re: [time 1055] "The Un-logic" of Thermodynamics"**In reply to:**Koichiro Matsuno: "[time 1055] RE: [time 1048] Re: [time 1045] Re: [time 1044] The Un-logic"

----- Original Message -----

From: Koichiro Matsuno <kmatsuno@vos.nagaokaut.ac.jp>

To: Matti Pitk$BgO(Ben <matpitka@pcu.helsinki.fi>

Sent: Tuesday, November 30, 1999 2:27 AM

Subject: reply

*> Dear Matti:
*

*>
*

*> Thanks for your reply to my posting to the Time list. It seems that you
*

*> are concerned with a dilation scheme or a hierarchy of subdynamics when
*

you

*> talk about jumps in quantum mechanics.
*

*> My cursory understanding of yours is
*

*> that the density matrix and entropy you have mentioned is referred to in
*

the

*> present perfect tense.
*

The definitions of density matrix and associated entanglement entropy are

actually not at all trivial since quantum states are quantum histories

(spinor

fields in infinite dimensional configuration space of 3-surfaces of

M^4_+xCP_2).

Density matrix is *not* defined for time=constant snapshot as it would be

in standard

quantum mechanics. The details of subsystem concept are still not completely

understood. So these concepts are "timelessness" in TGD framework.

If the dynamics determining spacetime surfaces as absolute minima

of Kaehler action were strictly causal, one could by general

coordinate invariance define density matrix using the

restrictions of configuration space spinor field in the set

of 3-surfaces contained on lightcone boundary delta M^4_+x CP_2,

7-dimensional moment of big bang. This kind of reduction

would be the counterpart of *quantum holographic principle*

of string models. In this case everything would reduce to lightcone

boundary and one would lose time just as

one does in General Relativity.

The classical nondeterminism of Kaehler action saves the day

and brings in psychological time.

a) The huge (really!) classical nondeterminism of Kaehler action implies

that there are large number of absolute minimum 4-surfaces

having same intersection with lightcone boundary (think

this in terms of 4-dimensional soap films with 3-dimensional frame

on lightcone boundary: also soap films can have several

absolute minimum areas). Cognitive spacetime sheets having finite

time duration glued to material spacetime sheets represent

one aspect of this nondeterminism.

b) Classical nondeterminism means that, in order to achieve

classical determinism in generalized sense, one

generalize the notion of 3-surface by allowing 3-surfaces which

consist of component on lightcone boundary and some minimal number

of components on geometric future. In this manner one can

fix absolute minimum (soap film going through given frame plus

auxiliary frames fixing the film uniquely) uniquely.

c) I call these temporal sequences associations sequences, they

can be regarded as geometrical correlates of thinking matter.

They bring in discrete degrees of freedom distinguishing between different

absolute minima and these degrees of freedom are responsible

for psychological time. Cognitive spacetime sheets

are geometric counterparts of selves.

***

So, I return to the definition of entanglement entropy after this

digression.

The generalization of the concept of 3-surface must be taken

into account in the definition of density matrix and this brings in

contributions describing entanglment of cognitive spacetime

sheets with the surrounding world. These contributions are

labelled by some time coordinate specifying of center of mass

temporal position for cognitive spacetime sheet on material

spacetime sheet.

*> My primary concern is on something in the present
*

*> progressive. Of course, the transference from the present progressive to
*

the

*> present perfect is a crucial matter. Let me have a time to study yours
*

more.

Could you explain what the concepts

'present perfect tense' and and 'present progressive' mean.

I hated grammatics in school time(;-) and

I am not at all sure whether I understand them correctly!

Best,

MP

*>
*

*> All the best,
*

*> Koichiro
*

*>
*

**Next message:**WDEshleman@aol.com: "[time 1066] I've got Hamiltonians now!"**Previous message:**I.Vecchi: "[time 1064] Re: [time 1056] Re: [time 1055] "The Un-logic" of Thermodynamics"**In reply to:**Koichiro Matsuno: "[time 1055] RE: [time 1048] Re: [time 1045] Re: [time 1044] The Un-logic"

*
This archive was generated by hypermail 2.0b3
on Wed Dec 01 1999 - 01:15:41 JST
*