Stephen P. King (stephenk1@home.com)
Fri, 23 Jul 1999 17:15:54 -0400
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.
> 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!
[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. :-)
> [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"?
[MP]
> > b) *Spacetime* are dynamical and not unique and quantum states
> > are superpositions of classical spacetime surface. The localization
> > in zero modes associated with every quantum jump localizes quantum
> > history to the set of spacetime surfaces which are identical in
> > macroscopic aspects characterized by zero modes.
[SPK]
> Does this implicitly assume a unique set of measuring "tools" for all
> possible observers?
[MP]
No. I think that measuring tools is not fundamental concept: it is
too 'classical'. Quantum measurement is more promising starting point.
Localization in zero modes obviously can be regarded as
*quantum measurement* of zero modes: this of course does not mean
that contents of conscious experience would contains values of
zero mode coordinates(:-)!
**
Why not? If the causal connective structure of the space-time framing
of an experience is given by a set of null rays (this is what the light
cone structure is after all!) "Localization in the zero modes" is
equivalent to my concept of "constructing a space-time"! The "values of
zero mode coordinates" is a strictly relative notion! This is why
tensors are needed to model the movement of objects in space-time. The
particular values used are irrelevant, what matters is that the
information content can be communicated.
Perhaps it would help me to explain that I believe that motion is point
to point teleportation rather than the classical motion of a
transposition of a rigid object or wave within an independently existing
space.
[SPK]
> If so, how? I am very aware that the usual
> explanation involves the notion that numbers "exist" a priori, but,
> really, how can it be affirmed that something is knowable just by
> postulating its existence?
[MP]
By no means! Objective realities exists and quantum jumps
between them make it possible to learn more and more about the
nature of objective realities. Sooner or later with respect to
subjective time these quantum jumps begin to make claims
about what these existences are and at some quantum the discovery
of the importance of the internal mathematical consistency occurs.
Subjective reality is doomed to make hypothesis about nature of
objective existences and test them. It can never be certain.
**
Yes on both counts! This is why I say that the Universe can only
experience itself via the interactions of its subsets! Only in the limit
of Eternity is absolute certainty possible! Absolute Boolean certainty
is impossible within the domain of experience because of the
NP-Completeness problem! The material resources available to a subset
LS_i of the Universe to compute the solution to the n-body problem (that
is the Langrangian of the complement of the LS_i) increase exponentially
slower that the number of subsets that become modelable by the
computation. This is Malthus in the Large!
[SPK]
> CE does not imply necessity of knowledge or
> experienciability! In order to allow for the uniqueness of the
> individual self, it is necessary and sufficient that there is at least
> one attribute that can be unique to such. The mere CE postulate is not
> enough, we need a dynamical difference. When one posits a pre-given
> metric for all and assumes that all observer exist *in* the same space,
> it is the postulation of a prison for the self from which there is no
> escape.
[MP]
I do not assume observer: self is closest to observer I can get.
Sequence of quantum jumps during which informational time development
operator does not generate p-adic entanglement. Observers
do not exist anywhere! They, or selves, correspond to sequences of
p-adically unentangling quantum jumps. This is extremely deep and
important point.
**
Umm, Yes, but, just because any given observer can not interact with
all others, does not imply that they are not "out there". I am saying
that there must exist an observer for every possible experience. Not all
experiences can be communicated within a world (remember how I define
such!). This is why we can not observer objects traveling faster than
light; we can not measure such motions because the observations of the
observers can not be logically infered within our \epsilon of accuracy.
Logic contrains observations, not some a priori defineteness! Please
recognize the failure of naive realism! Please!
snip
[MP]
> > Each quantum jump changes the macroscopic characteristics of these
> > spacetimes in quantum superposition and they seem to naturally correspond
> > to our sensory information: localization in zero modes is quantum
> > measurement of zero modes and sensory experiences seem indeed to give
> > information about zero modes. Perception is quantum measurement in this
> > sense.
>
> Sure, I can agree with that. Each person's sensory experiences can be
> explained a unique integration of many almost disjoint quantum
> measurements, thus I think of posets...
[MP]
Actually the measurement can be said to be disjoint in well
defined sense. Separate selves mutually unentangled.
**
Yes! This is why separate selves have separate indentities! I say that
experiences are "almost disjoint" since they differ in at least the
"point of identity". The notion of a fixed point under a given set of
transformations is what I considered before I has educated by Peter's
work. The Self, within Peter's formalism, is a greatest fixed point, I
think. Umm, I need to review his paper:
http://www.cs.brown.edu/~pw/papers/math1.ps
[SPK]
> But what is troubling me is the
> notion that the localization is somehow independent of what it is that
> makes the poset different for each person.
[MP]
There is big localization in entire configuration space which decomposes
into sublocalizations for selves.
**
How is the information content of this localization given? This is an
infinite NP-Complete problem that requires ETERNITY to compute! It can
not be given a priori! This is my whole point as to why naive realism
fails! "It is not even wrong"! Think of the ability to predict the
weather on Earth, the computational power needed to predict with
arditrary accuracy (limit \epsilon -> 0) instantly exceeds the available
matter in the observable world! If it can not be predicted, it can not
be said to be determined, thus can not be observed either.
The self is actualized within its own time as the interactions among
the LSs carry out the computation of "what will happen next"! We
construct our reality by interacting with each other. Read the
introduction to Frieden's book again, he is saying what I am saying!
[SPK]
> I think that if we start out
> with the notion that each measurement is informative only in comparison
> to some aspect of the measuring device, here a person, we could perhaps
> avoid the trap of classically. The idea of a pre-existing classical
> world or space-time in which all observers are "embedded" is the error,
> but it is very hard to escape it! It must be done. We need a radical
> shift in paradigm!
[MP]
I agree that the assumption about pre-existing objective reality is
error. But I do not identify objective reality as spacetime
with observers imbedded but as quantum history. Imbedding space
has nothing to do with observers nor objective realities: it
only emerges as structure related to the configuration space which
is also pregiven.
**
Umm, perhaps I am misinterpreting what you mean by "pregiven"! I use a
notion identical to what Peter uses in the definition of Interaction
Machines! What is "pregiven" by one LS is not necessarily "pregiven" by
another! There is no way of entablishing absolute precedence, we only
have finite "windows" within which an LS can have a configuration as
actual.
This is another reason why the naive realism of Newton et al is just
plain wrong! The fact is that the concurrent ordering of events is an
infinite NP-Complete problem! Laplace and Minkowski's vision of the
Universe as a static 4-manifold is just a hallucination!
[MP]
You want to give up pre-existing spacetime and replace it with something
dynamical whereas I want to give
up the notion of observer and replaced it with something quantum
dynamical.
**
YES! Matti, this is exactly what Hitoshi's model of Local Systems does!
Please read his papers again! The observer *IS* a quantum mechanical
system. Hitoshi does not get into the nitty-gritty details of the
composition of sub-LSs, but this is what your p-adic acomplish. I firmly
believe that your work is the needed generalization and extension of
Hitoshi's idea! Tis is why I get so emotional when I participate in
discussions with you! :-)
[MP]
We are locating evolution at different levels. Otherwise we agree.
**
No, we just have complementary view points! :-)
Onward!
Stephen
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