# [time 469] Re: [time 464] Parallel transport, etc....

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Fri, 23 Jul 1999 08:03:18 +0300 (EET DST)

On Thu, 22 Jul 1999, Stephen P. King wrote:

> Dear Matti,
>
> I pasted your response to my last query at the end...
>
> Matti Pitkanen wrote:
> >
> > Below continuation to the answer of earlier message.
> >
> > On Tue, 20 Jul 1999, Stephen P. King wrote:
>
> > > > [MP] I think that we talk about different fiber
> > > > spaces! I am talking about the fiber space structure of
> > > > the space of the infinite-dimensional space of 3-surfaces. You are
> > > > talking about finite dimensional space having W as base: this space
> > > > corresponds to M^4_+xCP_2 in my framework.
> [SPK]
> > > Yes. Can we talk about the "connections" involved? Particularly, I
> > > would like to understand how "parallel transport" is modeled in your
> > > theory.
> [MP]
> > Parallel transport and connections emerge both at the level
> > of spacetime geometry and configuration space geometry.
>
> > a) At spacetime level all geometric structures are induced
> > from those of imbedding space. Although imbedding space
> > geometry is nondynamical, spacetime geometry is dynamical.
> > This is metaphorically dynamics of shadows: object is u
> > nchanged but shadow varies when object moves.
>
> This "parallel transport" notion is what Weyl made a careful analysis
> of in his work and why he reasoned that Riemannian geometry needed to be
> generalized! But, Weyl did not consider the possibility that multiple
> space-times are needed to model multiple observers. He assumed, as do
> most, that there is only one M^4 and its related fields/connections for
> all...

Parallel transport is extremely general concept: 'connection' in fiber
bundle with structure group G. Very abstractly. Metric (Riemann)
connection special case: in this case inner product defined by Riemann
metric is conserved in parallel transport. For Weyl connection only
angles between vectors are conserved. In gauge theories one just
postulates some structure group G (say standard model group SU3 times U2)
for connection.

> Parallel transport is the conceptual tool to model motions of the
> "shadows", but fact is that that which is projecting the shadows is not
> a "ONE" in the ontological sense, it is the "MANY" possible finite
> subsets of U. They project onto each other...

Is there slight misformulation here.
In case of 'shadows' it is the induction of parallel transport which
occurs. Parallel transport in imbedding space is projected to spacetime.
Induction and parallel transport are two different things. Parallel
transport is the great construction principle of GRT and gauge theories
and in fact all recent QFT:s. Induction is purely TGD:eish addition
to the conceptual arsenal used.

> This is a very important point that becomes obvious in a discussion
> about the difference between "actual" and "potential" infinities... What
> is ontologically a priori is the Universe, which is an "Actual"
> infinity, thus it is ONE. The dynamics of the shadows are "potential"
> infinities, thus are "MANY", thus the uncertainty formalism that Hitoshi
> has discovered and discussed in his papers connects the time of the LS
> to its measure of uncertainty.
> The idea that the Universe, as a "static, pre-given entity" is
> non-dynamical is part of my thinking and that of Hitoshi and,
> appearently yours.

But what one means by Universe! I do not mean by Universe imbedding space.
Rather, Universe is one possible spacetime surface classically. Single
configuration space spinor field quantum mechanically. And Universe
in latter sense is replaced by a new one in any quantum jump. It can
quite well occur that the sequence of quantum jump produces almost
fixed points: at least parts of universe can become almost fixed points:
this is what self organization by quantum jump produces.
But basically there is endless evolution: the prime characterizing p-adic
topology of universe increases all the time.

> Michael C. Mackey also addresses this notion in his
> book Time's Arrow with his "God Theorem"... The key notion that we all
> seem to agree on is that the "parts" can have dynamical behavior (are
> not at equilibrium) while the "whole" is static. The notion of time is
> given in the manner that the parts, by interacting among themselves,
> evolve toward equilibrium, e.g. evolve toward isomorphism with the
> whole: the "Union with All" of mystics. But the key notion is that this
> process literally takes forever to accomplish!
>
p-Adic evolution indeed never ends. Even God as the self of entire
universe is evolving all the time!

> > b) In accordance with this parallel transport in spacetime surface
> > reduces to parallel transport in imbedding space. Measuring of
> > distances reduces to that in imbedding space. Etc...
> > Especially important induced quantity is CP2 Kahler form
> > whose projection on spacetime surface defines Maxwell field.
>
> The argument about "a priori orderings" that I have been trying to
> communicate since the beginning of the Time List relates to this! The
> Oneness aspect of the Universe is forever out of reach since it is
> Everything simultaneously. It would have at least a multiple connected
> topology - everything mapping isomorphically to everything else... I am
> proposing that the subsets of U are simply-connected manifolds, up to
> isomorphism in the classical limit of hbar = zero.

I understand your point completely. But this is simply all about basic
philosophy.

I accept three ontological levels. Material existence (spacetime
surfaces), subjective existence (sequence of quantum jumps as moments of
cs and objective/informational/whatever existence (single quantum history).

Correct me if I am wrong: You accept only single ontological
level: experiences/subjective existence and since this subjective
existence obviously gives very limited information about spacetime
etc... Thus it is logical that you want replaced the Riemannian geometry
etc... by more primitive concepts containing not so much information.

> Here is a crude sketch of my idea about the applicability of Weyl's
> geometry:
> "The necessary and sufficient condition that a Weyl geometry may be
> reduced to a Riemannian geometry is that a vector keep its original
> length after transplantation along an arbitrary closed trajectory.
> Indeed, the condition of such a length preservation is ...
>
> (15.40) \surface integral_C of dl/l = \surface integral_C \PHI_\alpha
> dx^\alpha = 0
>
> [forgive my terrible ascii]
>
> and it is well known that \PHI_\alpha|\beta - PHI_\beta|\alpha
> \equivalent 0 is the necessary and sufficient condition for the
> integrability requirement of (15.41) in simply connected regions."
> [from Introduction to General Relativity by Adler, Bazin and Schiffer,
> 1975. pg. 496]

OK. This is obvious.

> These "simply-connected regions" would have properties that are
> represented by Maxwell field equations. These define the patterns of
> causal connections that M^4's represent. They have the appearance of
> being unique from the point of view of an observer O because they are
> the framing within which an observation by O is possible. If we consider
> for the sake of illustration the ability to observe this projection
> process "from a divine point of view" we would see that each O (an LS)
> has its own M^4 constructed piece by piece by mappings between its
> internal propagator's (quantum mechanical) dynamic's configuration space
> and points in the manifold W.
> What is difficult to grasp is that the "points" that make up W are the
> possible exteriors as centers of mass ("cm"). In other words, the
> "exteriors" of LS are ontologically different from the "interiors"! The
> former are facets of the "MANY" and thus appear "classical" while the
> latter are finite facets of the "ONE" and are quantum mechanical! The
> ONE and the MANY are co-inductive aspects of the Universe, they define
> each other, but the "meaning" of such definition is only possible for CE
> reasons as being "in time" and since each LS, as a unique facet of U,
> has its own time and gauge scale, it constructs its own local consistent
> "reality".
>
> > c) This means geometrization of classical
> > gravitational and classical gauge fields.
> > Metric, the vector formed by components of spinor connection
> > of imbedding space, etc are projected to corresponding
> > tensor quantities defined on spacetime surface.
> > Note that since shadow is created by projection map,
> > dynamics of shadows is indeed in question in precise sense!
>
> Umm, I fail to see how it is necessary and sufficient to require that
> spinoral properties be aspects of the ONE.

What is beautiful is that spinor structure is direct concomitant of
Riemannian geometry. Under very general conditions Riemann geometry
defines spinor structure uniquely. Spin is thus purely geometric
property. In case of infinite-dimensional configuration space
spin is extremely abstract concept and does not have interpretation as
spin as rotation. Different many particle states are in
infinite-dimensional context analogous
to different spin states of ordinary spinor.

>I see them as constructed
> dynamically in the act of observation in that they are aspect of the
> framing. Thus I do not see them as a priori givens! Is it not enough to
> show that the "shadow" is a construction of the mapping between LSs? Do
> we really have to suppose that the "statue" exists "out there" prior to
> the sculptor's work?!

This is a good question. Your point of view makes possible to avoid
dualism: observations contra world out there.

But so does also my approach. I see painting and landscape as one and the
same thing! Painter exists only in the moment of consciousness when
painting/landscape is replaced with a new one. Painter experiences some
of the beauty of painting and, by artst's vanity concludes that he did
it!

I see as the difficulty of your approach the necessity to provide
formula for the contents of consciousness: this indeed seems to be the
case if you identify reality as observations.
*********

It "exists" only in the sense of being a
> possibility! The metric or related properties are given by the act of
> observation which is determined by the local logical entailment aspect
> of the informorphism that is the interaction between LSs.
> To be sure, I need to discuss the "compactness" notion that you
> mentioned before with regards to the W(r)...
>
This leads to the problems in the following sense. Our observations give
extremely limited information about spacetime. I do not experience
all the values of the metric tensor or classical gauge fields defined
on it. Does this mean that one should give up entirely the notion
of spacetime and what should be left? Some set discrete points perhaps:
but how can you understand in this kind of context how observes
invent concepts like moral and freedom and how the idea of infinity
arises?

> > d) Thus everything is classical mathematics: even induction
> > procedure which is standard mechanism of building new bundles
> > by mapping manifolds to base spaces of bundles but not noticed
> > by say string model people.
>
> Umm, I an missing something! :-( I say that each LS observes a
> classical like world, thus can be approximated and modeled by classical
> math, but we need to consider co-induction, not just classical
> induction... Perhaps I am misunderstanding you!
>

This induction is not induction in the sense as co-induction defines it.
Induction in the sense of Faraday! When you have metric in some space
you have also natural metric for its submanifolds: distances are measured
using the length units of imbedding space.

> > At the level of configuration space the metric is also inherited
> > from that of the imbedding space in well defined sense but this
> > is rather technical. Suffice it to say that basic idea
> > is to generalize the notion of the symmetric space to
> > infinite-dimensional context so that symmetries fix the metric
> > totally.
>
> Sure, the particular symmetries "fix the metric", but I argue that this
> fixing is a computational act, not an a priori synthetic! This is
> metaphorically similar to the situation of a new-born baby; it has the
> potential to become many different adults, what determines the actual
> adult it becomes depends on both its interactions with the world
> constrained by the consistency requirements of the world determined by
> others that are interacting wherein. The World is not a priori given in
> an ontological sense, it is co-indictively defined by the interactions
> of its members, it is the intersection of its member's possibilities
> that define it!

> The way that M^4s are constructed "piece-by-piece" is well illustrated
> in Penrose's discussion of quasi-crystals and it highlighted in by
> Forbidden Symmetry paper:
> http://members.home.net/stephenk1/Outlaw/forbiden.html

[MP]
I agree that this what you are saying applies to how our ideas about
spacetime evolve.

>
> [MP]
> > > > OK. I think that we were indeed thinking about different things.
> > > > Configuration space is the space in question: it presumably does not
> > > > have any counterpart in LS framework because X^4/W is purely classical
> > > > so that one does not have superpositions of parallel W:s.
> > > > Configuration space in LS context would be the space of all possible W:s.
> [SPK]
> > > The postulation of a configuration space seems to presuppose an
> > > ordering and a basis for observations prior to the act of the particular
> > > observation itself. This is very similar to the Minkowskian notion that
> > > there exists a single space-time manifold that just "exists". The
> > > serious problem that I have with this notion is that it presupposes that
> > > their exists a Cauchy hypersurface of positions and momenta with
> > > definite a priori status.
> [MP]
> > The mere existence fixes that which exist essentially uniquely
> > in infinite-dimensional context: this is the basic idea. One cannot
> > construct dynamics for the metric of infinite-dimensional configuration
> > space because it is fixed already by the requirement that it
> > exists! The existence of Cauchy hypersurface poses problems when
> > one assumes dynamical spacetime and tries to quantize metric.
> > Now imbedding space is given and these problems disappear.
>
> But how do we derive particular actual properties by merely evoking the
> fact that they exist? Existence is "outside of time", it is tenseless.
> The dynamics that define sharp properties only occur "in time", in fact,
> I propose that in a subtle sense, they ARE time, but since each LS has
> its own unique dynamics (defined by its internal QM propagator), each
> has their own time and thus their own length scale or gauge. Thus I say
> that each LS constructs its space-time M^4 framings by interaction with
> other LSs.

We have articulated rather precisely the differences in our philosophy.
For you LS:s are all that is. For me LS:s could represent models for
contents of conscious experiences of selves but besides this
the realities behind these experiences would exist.

> The Cauchy problem holds in the static case since the Uncertainty
> principle prohibits the a priori definite "sharp" properties!

This is true if one consdier QFT in Minkowski space. One can fix
only E or B. Similar conclusion holds for the components of
spacetime metric regarded as small perturbation of Minkowski metric.
It is nonsensical to speak about entire spacetime metric as given.
Only some of its components commute at given time =constant section.
But as we know, this approach to quantum gravitation does not work!
TGD approach is quite different and in complete accordance with
uncertainty principle. There is no quantization of
metric or other classical gauge fields.

> It is for
> this reason that Einstein was very opposed to QM! His statement "GOD
> does not play with dice" [to determine the properties of the world]
> speaks directly to this!

Einstein's argument relied on spacetime concept he had invented: the
idea about quantum jump occurring at definite value of time is in violent
conflict with space-time democracy. It breaks general coordinate
invariance and it breaks the hypothesis about deterministic
field equations. Quantum jump between quantum histories concept was
originally forced by the requirement of General Coordinate Invariance and

>
> > The point is that I do *not* identify observations as points of
> > spacetime or configuration space. They are not active 'events'.
> > Quantum jumps between quantum states= quantum histories are events and one
> > cannot localize them to anywhere (one can of course, identify
> > these events as pairs of possible initial and final quantum histories
> > so that one can speak about the space of all possible experiences).
>
> I say that observations are co-inductively related posets of points (as
> an abstraction since true infinitesimal points can not be distiguised
> from each other as they can not encode any information!!!), not
> individual points per say.

I undestand that you great idea is identify observations with geometrical
structures, 'posets of points of space'. I also parametrize
the set of all possible observations: not as posets but as
allowed quantum history pairs: but this parametrization tells
anything about content of observation: it is just labelling: the only
thing that matters that this naming scheme is one-to-one. I believe
that the content of observation/cs experience cannot be expressed by any
mathematical formula.

> To call them "space-time framings" speaks to
> the fact that we always make observations in terms of a M^4 frame... The
> quantum jumps are more epiphenomena that objective, but the restriction
> that observers can only communicate effectively about M^4 framings that
> do not logically contradict each other follows from CE! The
> schizophrenic is an example of an observer that is attempting to
> communicate about a M^4 framing that is logically inconsistent with
> another's!
>
But there is the notion of observer. You take it as granted. I take
observation fundamental.

> > I see no problems with Heisenberg's uncertainty relations: informational
> > time development operator U reduces at QM limit to Schrodinger equation.
> > Metric, etc.. classical gauge fields are *not* quantized in TGD.
> > Neither spacetime coordinates are quantized. There is
> > absolutely no quantization, only classical geometry of
> > infinite-dimensional configuration space and classical spinor fields of
> > configuration space. Oscillator operator algebras etc are geometrized in
> > this approach.
>
> I see the evolution of information in terms of the evolution of the LSs
> as they interact. Thus the act of the Universe 'experiencing itself' is
> an ongoing process. It is what "concurrent computation" is all about is
> a fundamental sense! Again, this is why I find Peter's work so useful!
> :-)
>

Here here agree completely. But 'universe=experience about universe'
is where I cannot follow you. This is simply too strong assumption and
leads to the hopeless attempt of writing formula for the contents
of cs experience.

> > One must distinguish between coordinates of spacetime which are
> > completely classical quantities and position and momenta of particle
> > in spacetime, which are operators in wave mechanics. They are
> > quite different things. Quantum group people have tried to
> > make spacetime coordinates operators but it has not led to successes:
>
> I hope to discuss this when you receive the copy of Schommers' paper...
>
OK.

> > I just saw a paper in which it was shown that divergence problem is
> > not solved by noncommutatitivy of the spacetime coordinates. There is also
> > problem with the loss of general coordinate invariance. One must assume
> > special coordinates and very high symmetries if one wants
> > special coordinates.
>
> Could you give me the reference of this paper? I can order a copy from
> the library! :-)

It was paper by my 'boss' Masud-Chaichian and Peter Presnajder and third
theoretician. They constructed noncommutative QFT in two-dimensional case.
For cylinder it worked but for more general case they found infinities.
They also suggested generalization of results to higher dimensional case.
I do not have the paper here but I could ask for bibliodata.

> The loss of "general coordinate invariance" does not
> bother me at all, in fact, I say that it is an illusion that results
> from the fact that LSs can not communicate if they have different
> histories. I say: LSs can interact only to the degree that their
> histories are not inconsistent with each other. If the think of the LS's
> histories in terms of M^4s, we see that to be consistent is for there be
> isomorphisms between at least one point and that the "Hamming distance"
> between points in the the Powersets of the LSs observations is
> equivalent to the degree of mutual consistency or "agreement" between
> the LSs.
>

Here I could not quite follow but I understand your philosophy. I do not
thinkg that technical details are so important.

> [SPK]
> > > This is completely contradicted by the
> > > Heisenberg's Uncertainty relation. The interpretation of this aspect of
> > > QM is the most troublesome for physicists! What I see is that the very
> > > notion of a configuration space has serious problems! If we are going to
> > > insist on using them then we much at least make their status
> > > statistical, so we talk about statistical distributions of properties
> > > given such and such conditions. This idea seems to be the best aspect of
> > > the Multiple World interpretation of QM.
> > > My problem is that I see an unanswered question being swept under the
> > > proverbial rug: What makes the world run? We can't just postulate that a
> > > God or Singularity "started" the world! Why do we experience time in the
> > > first place? Why has everything not already happened?
> [MP]
> > God of Singularity concept is based on traditional concept of
> > psychological time. Also the question why everything has not already
> > happened is created by the same concept of psychological time.
>
> Yes, but here the error is in the tacit (subconscious) assumption that
> the psychological time of one person is one and the same of that of
> another! The clocking by the QM propagator of the LS defines the
> individual time of the LS, thus representing psychological time very
> well!

Also that. But the real blunder is the identification
is the assumption that *contents of cs experience correspond to
time=constant snapshot*.
Neurophysiologists tell us that this is not the case. Consdier music
as example. We are able to experience frequencies, which
is nonlocal concept with respect to time.

> The "everything has not already happened" notion is indeed related to
> psychological time, but in the sense stated above. "Everything" much
> included all possible "actual" experiences, and obviously, these involve
> NP-complete computational issues! This later notion is at the heart of
> my argument.
>
> > I regard this concept as badly wrong. In TGD framework subjective time
> > corresponds to quantum jumps and there can be *no first quantum jump*.
>
> I am not communicating my notion since your are not aware of the
> NP-completeness problem! Karl Svozil's papers point the way! We agree
> that "there can be *no first quantum jump*"! The ideas of co-induction
> and related issues involved are in Peter's papers...

I have studied Peter's papers (rather technical!). My view is that cannot
start from so technical concept like NP-completeness in building model
for universe: the reason is that I do not believe that universe computes
itself into existence: it just exists! Even more, it is able to replace
itself with a new one again and again and do also some computation
besides that!

>
> > This requirement plus p-adic evolution
> > as gradual statistical increase of p-adic prime of the universe
> > immediately leads to the requirement that
> > also infinite p-adic primes are possible and that recent universe
> > must correspond to infinite prime. Every moment of consciousness
> > decomposes to infinite number of subexperiences with values of
> > psychological time ranging from zero to infinity. What we really 'know' is
> > that local arrow of psychological
> > time exists: if one is satisfied with this then paradoxes disappear.
> > Universe becomes *4-dimensional* living being getting conscious
> > information about its entire 4-dimensional body in every quantum jump.
> > Cognitive spacetime sheets are the sensory organs of this infinitely
> > large 4-dimensional living system.
>
> The notion of "gradual statistical increase of p-adic prime of the
> universe" is given in my thinking in the sense that the overall
> concurrent interactions of LSs are modelable in this way. It would be a
> representation of the accumulated "experience of the Universe", but with
> the caveat that it is information that can not be gotten in finite time
> or finite energy with arbitrary accuracy. The operator formalisms that
> Schommers talks about, I believe, is useful to us in thinking about
> this!
>

Yes: I have grasped the universe computes itself into existence philosophy
but....

> > > > [SPK]
> > > > This notion is very different from Hitoshi's idea, but perhaps the
> > > > difference is due to the different ways that time is treated.
> > > > I still see these as complementary! You see space-times as a priori
> > > > surfaces, subsets of the totality U that are connected by quantum jumps
> > > > "in time", Hitoshi, as I understand, sees space-times as the "clocked"
> > > > poset of observations of LS, which are a priori quantum mechanical
> > > > systems existing tenselessly as subsets of the totality U.
> > > > Thus you are proposing space-times as a priori and Hitoshi
> > > > proposes quantum local systems as a priori, this is a chicken-egg
> > > > complementarity! We need to see that this is just a matter of
> > > > perspective!
> [MP]
> > I have the feeling that this is not a matter of perspective. Our
> > basic philosophies are different.
>
> In a way, yes. You are a Platonist, and I something different. I think
> that Plato's Idea Reality *is* the Universe in-itself, but as Kant
> argued well, is not knowable in-itself. I see it as Existence itself!
> All experiences, measurements, observations, qualia or what ever, are
> not given directly by their mere existence (as all exist in the
> ontological sense), but have finite properties given by the interactions
> between the finite subsets or "facets" or LSs of the Universe. We can
> only observe shadow, consciousness is not capable of knowling the
> "in-itself"!

Funny thing, reading this I find that I agree completely. But somewhere
the differences emerge: computationalism is one of the division lines.

>
> > > > [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.
> >
> > I meant that there is single spacetime, not a superposition of them (or
> > 3-geometries).
>
> How could this be? The very definition of such requires the a priori
> computation of the causal structure of such a space-time!

Certainly in computationalistic framework. If universe computes itself
into existence you are quite right. But I believe that it just
shamelessly and majestetically exists!

> 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!

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.
One can even consider the promordial 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.

> I am trying to model this by using a generalization of Weyl's ideas...
>
> [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?

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.

>
> > 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.
>
> Does this implicitly assume a unique set of measuring "tools" for all
> possible observers?

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(:-)!

> 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?

By no means! Objective realities exists and quantum jumps
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.

> 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.

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.

>
> > This brings in also psychological time as center of mass coordinate of
> > cognitive spacetime sheet, which is zero mode too.
>
> This seems to follow from Hitoshi's theory...
>
> > 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...

Actually the measurement can be said to be disjoint in well
defined sense. Separate selves mutually unentangled.

> 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.

There is big localization in entire configuration space which decomposes
into sublocalizations for selves.

> 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
>

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.

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.

We are locating evolution at different levels. Otherwise we agree.

MP

> Matti Pitkanen wrote:
> >
> > On Thu, 22 Jul 1999, Stephen P. King wrote:
> >
> > > Dear Matti,
> > >
> > > Just a quits question that comes to mind as I read you post on parallel
> > > transport: What is the embedding space? What are its properties? Is it a
> > > "static" entity? (You relate it to Plato's Ideal world) Most off all, is
> > > it similar to the "Totality of Existence" in-itself?
> >
> > Sorry for not making clear what I meant with the concept.
> > Embedding space refers to the 8-dimensional M^4_+ xCP_2, future lightgone
> > times complex projective space of 4 real dimensions. Isometry group
> > is Poincare times SU(3), color group, the symmetry group of strong
> > interactions (quarks, gluons). CP_2 spinor connection has as its holonomy
> > group (group of parallel translations around closed curve in given point)
> > electroweak gauge group.
>
> Again, I fail to see how you propose to claim that a unique M^4_+ xCp_2
> *is* the TOTALITY OF EXISTENCE! These are definite actual properties and
> as such can only be given within the context of particular experiences!
> The Universe in itself can only *exist* by CE reasoning, the
> construction of M^4_+ xCP_2 is a subjective projection; it is phenomena,
> not noumena, e.g. I believe that the particular patterns of behavior
> that is called "physics" is derived from observation, it is not priori
> to it. This is the case presented by Frieden!
> Is is the "behavioral form" that the "shadows" take that is given by
> the interactions between the finite facets of the Universe. All we can
> observe is the shadows and the "wall" upon which they think that they
> are "projected" is just the Powerset of the set or equivalence class of
> Again we are merely debating the semantics of our perspective model of
> our worlds, and thus it is the usefulness of our notions that matters in
> the long run... :-)
>
> > Embedding space is stati, pregiven entity.
> > Imbedding space provides only geometric frames for existence. It is
> > only finite-dimensional, etc..
> > Totatility of existence is the space of all configuration space
> > spinor fields=quantum histories.
>
> I agree with this only in the sense that all possible quantum histories
> "exists", but the "ordering" of them, that makes consciousness "flow" is
> not a priori! This is the basis of the computation argument!
>
> > Best,
> > MP
>
> Onward!
>
> Stephen
>
> PS I am very tired mentally so my arguments may very well be just a lot
> of noise! :-)
>

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