Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sat, 24 Jul 1999 11:46:13 +0300 (EET DST)
Here begins my reply to your second email about parallel
translations etc...
On Fri, 23 Jul 1999, Stephen P. King wrote:
> Dear Matti,
>
> Continuing...
>
>
> > > > > [MP]
> > > > > Hitoshi assumes fixed spacetime which is classical
> > > > > and satisfies field equations of GRT and puts the quantum
dynamics
> > > > > to the fiber R^6. In TGD the quantum state is superposition of
classical
> > > > > spacetimes since spacetime is made quantum dynamical.
Localization in
> > > > > zero modes however effectively makes dynamics by quantum jumps
to hopping
> > > > > in zero modes: like Brownian motion.
> > [SPK]
> > > > Umm, I did not get this thought from reading Hitoshi's
papers! He
> > > > points out that GRT field equations problematic and outlines a way
out.
> > > > His theory is incomplete in this sense, again as I see it. I do
not
> > > > suppose that a fixed space-time is necessary for LS theory, it
gives us
> > > > a way to model an alternative.
> [MP]
> > > I meant that there is single spacetime, not a superposition of them
(or
> > > 3-geometries).
> [SPK]
> > How could this be? The very definition of such requires the a
priori
> > computation of the causal structure of such a space-time!
> [MP]
> Certainly in computationalistic framework. If universe computes itself
> into existence you are quite right. But I believe that it just
> shamelessly and majestically exists!
> **
>
> OK, on this point let me be clear: The Universe "just exists"! It
is
> the experiences that are computed by the interactions (observations) of
> the finite subsets (LSs) of the Universe.
I can agree here in the following sense. Each quantum jump
is quantum computation in the manner I explained in
part IV of my reply to earlier posting. Infinitely large
quantum computer performing infitely long quantum computation
and halting: Psi_i--Z UPsi_i-->Psi_f.
Actually the sequences of computations of this kind represent thoughts
which generate cascades of selves. Infnite number of
simultaneous experiences by the hierarchy of dynamical selves
forming abstractions about the experiences of their subselves.
NP-computability is replaced by quantum computability in this
sense in TGD framework.
>
> > Newton et al,
> > assumed that God did this "in the beginning" and thus they give us a
> > "clock-work" paradigm of the world. I am speaking to a paradigm that
is
> > more like a network of CGI (computer graphic interface) that is
> > constructed by the very act of interaction, thus the "means" of
> > communicating between LSs is given simultaneously with the "ability"
to
> > communicate! There is no "absolute" ex nihilo beginning and no
absolute
> > pre-defined causal ordering and thus no pre-given M^4!
> [MP]
> I could agree to high degree if we would replace M^4 with configuration
> space spinor field. This is what indeed evolves in TGD. It is located
> to definite sector D_p of configuration space and p increases.
> **
>
> Perhaps I am not understanding how the "definite sector D_p of the
> configuration space" is selected. I say that the act of observation is
> the act of selection, in the sense that a given transition A -> B on the
> material configuration involved in the particular observation is allowed
> iff the information content of B implies the information content of A.
> This is the essence of an infomorphism!
>
Configuration space decomposes into sectors D_p allowing effective
p-adic topology with prime p. The localization of state
to D_p is forced by Generalized Unitarity.
The requirement that quantum jump corresponds to measurement
which is local at the level of configuration space sharpens
localization hypothesis: localization occurs to definite
values of zero modes characterizing the classical features of
spacetime.
One could say tha selection is involved at the level of zero modes.
Our volition probably corresponds to selection between degenerate
absolute minima of Kahler action characterized by *discrete* zero
modes: no experience selection in continous zero modes
since it is not possible to experience what it is to select
between continuum of alternatives.
I do not assume quantum jump A-->B means that information content
of B implies information content of A. This is too strong requirent.
p-Adic evolution however implies that information gains tend to increase.
Note also that there are infinitely many types of informations
and each is characterized by its own information measure:
not only single abstract information.
> [MP]
> One can even consider the primordial chaos obtained formally by putting
> p=1: effective topology is roughest possible: distance between two
> points is zero or one. I have essentially you picture but
> at the level of effective experienced topology.
> **
>
> This is modeled by the Chu_{0,1} that Pratt discusses in
ratmech.ps! I
> am using the generalization that would be modeled by a Chu_[0,1], it
> allows the modeling of \epsilon accuracy involved in dissipative
> transitions of the configurations, e.g. memory fades, spectra shift to
> red, entanglements decohere, etc. I wish I had a better grasp of the
> formal language needed to communicate this precisely, but I guess that
> that it why I am a philosopher, not a physicist. :-)
>
I have the eeling that Chu spaces might enter TGD in description of
cognition as cascades of selves created with selves.
> > [SPK]
> > > > I would like to discuss the basic notion that observations are
the way
> > > > that the Universe realizes the existence of consciousness and that
> > > > partial orderings of observations can, allowing for the group
theoretic
> > > > properties, generate space-time framings (subjective views) that
can
> > > > overlap (have configurations that are similar) such that the
appearance
> > > > of a single finite universe results.
> > > > Can we put the details of p-adics aside and just talk about
> > > > space-time's ontological status? Is it necessary and sufficient to
> > > > assume that a single unique space-time exists? If so, how?
> > [MP]
> > > Let me put my recent view in nutshell:
> > >
> > > a) My view is that one assume single unique *imbedding space*,
> > > 8-dimensional space M^4_+xCP_2. I have explained the reasons for
this.
> > > Configuration space
> > > of 3-surfaces must allow metric with Riemann connection and finite
Ricci
> > > tensor and Ricci scalar. Also spinor structur is needed. This does
not
> > > leave many possibilities. Configuration space decomposes into
> > > union of constant curvature spaces satisfyin Einstein equations:
> > > these spaces are labelled by zero modes.
> >
> > Is there any relationship between "zero modes" and "null
geodesics"?
> > Could there exist an infinity of almost disjoint hull hypersurfaces?
> [MP]
> All curves in zero modes are null geodesics formally. I do not
> believe that this is however a useful concept. The space of zero
> modes is infinite-dimensional. And each surface in this space
> as formally vanishing metric. Or better to say: no metric at all.
> Only symplectic structure making integration possible.
> **
>
> Interesting! Is it true that we could find every possible set of
null
> geodesic somewhere "in" this space of zero modes? Could you elaborate
> about the role of this "symplectic structure"?
All curves would be null geodesics since line element vanishes:
thefore the concept of geodesics becomes useless.
Symplectic structure is defined by antisymmetric tensor J^kl.
One can define J_kl by the condition
J^kr J_rl = -delta^k_l, Kronecker delta.
Note that metric is not needed: it emerges
only when one wants to define J^k_l by index raising operation
applied to J_kl.
J^kl defines Poisson bracket in the space of functions define
on manifold
{f,g}= J^{kl}f_lg_k
_l means partial derivative. Poisson bracket is antisymmetric and makes
function algebra infinite-dimensional Lie-algebra. Jacobi identities are
indeed satisfied. Functions generate canonical transformations generated
by the vector fields
X^k = J^{kl}f_l, f arbitrary function.
Canonical transformations preserve all 2n dimensional integrals
defined as integrals of J^J...^(n J:s ) over 2n-dimensional
submanifolds.
Canonical transformations are the isomorphisms of canonical
formalism of classical mechanics. The are crucial also for
canonical quantization. Quantization in standard QM means
the replacement of function algebra with the algebra
of Hilbert space operators and the replacement of Poisson
bracket with operator commutator AB-BA.
Best,
MP
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