Matti Pitkänen (matpitka@pcu.helsinki.fi)
Tue, 30 Nov 1999 06:33:42 +0200
----- 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
>
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