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

*Sun, 18 Jul 1999 13:56:59 +0300 (EET DST)*

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[time 456] Message for time

Sender: owner-time

Precedence: bulk

Dear Matti,

We are communicating well!

Nice to hear. Only a little blunder in the end of

message(;-). I talked about infinite-dimensional configuration space

without clearly mentioning what I am talking about and you talked about LS

space. This blunder however brought into daylight important difference

between TGD and LS. In LS theory spacetime is classical (be it X^4

or W) and in TGD spacetime is quantum dynamical: this would

correspond allowance of quantum superpositions of W:s in LS framework.

Matti Pitkanen wrote:

*>
*

*> On Sat, 17 Jul 1999, Stephen P. King wrote:
*

*>
*

*> > Dear Matti,
*

*> >
*

*> > Matti Pitkanen wrote:
*

*> > snip
*

*> > > Important constraint for the fiber space is that it should explain
*

*> > > as much as possible facts unexplained by standard physics.
*

*> > > In Hitoshi's/your approach R^6/W^6 explains how local quantum
*

mechanical systems

*> > > combine with global general relativistic spacetime. Fiber abstracts
*

the

*> > > concept of local nonrelativistic quantum system. What troubles me
*

*> > > in this approach is that every point of X^4 contains local system.
*

Somehow

*> > > only some fibers are 'active'. This same feature troubles me also
*

*> > > in Bohm's theory. Only some classical orbits are 'activated' in the
*

*> > > hydrodynamical flow defined by Schrodinger amplitude and correspond
*

to

*> > > classical particles.
*

[SPK]

*> > Umm, some misunderstanding... I am proposing a Weyl geometry W
*

for the

*> > manifold into which the LSs are projected; Hitoshi uses a Riemannian
*

*> > manifold X.
*

*>
*

*> [MP]
*

*> Of course! You have general relativity
*

*> with Riemann geometry replaced by Weyl geometry.
*

Close... The local dynamics of GR are given by the local

compositions

of LS projections into W. I am considering GR to be a model of the

"glocal" structure of extremal geodesics, but as I see it, we move from

the assumption of a single Riemannian manifold X to a supermanifold W

that has as submanifolds almost disjoint X_i. Each has a slightly

different inner product, maybe? This is an attempt to model how each

observer perceives itself to be in the center of a finite universe that

has a Robertson-Walker like metric.

[MP]

Here you have the problem of defining X as a union of almost

disjoint X_i precisely. This requires probably modification

of manifold concept. In TGD framework almost disjointness is

realized in terms of sub-manifold concept: two spacetime sheets

connected by tiny wormhole are almost disjoint. The effective

p-adic topologies can be different for two sheets joined by

wormhole contacts.

Isn't the basic property of RW metric that each point is

center of the universe? All points are metrically equivalent

for given value of cosmic time.

[SPK]

*> > The R^6 refers to the 3N + 3N Euclidean space of positions
*

*> > and momenta that the LS propagator "lives" in. The breaking of scale
*

*> > invariance of the W manifold, I think, is due to the way that the LS's
*

*> > projections partition it into local logical consistent subspaces. This
*

*> > has to do with the epsilon bound on the accuracy that LSs can predict
*

*> > each other's behavior.
*

*>
*

*> > This is in the spirit that each LS has an associated M^4 that is
*

*> > constructed from W by the act of projection. This projection is an
*

*> > identification or mapping between the internal configurations of the
*

LS

*> > and a finite subset of W.
*

[MP]

*> There is probably some computationalistic motivation for this
*

*> map.
*

Yes! The computational aspect is the way that the dynamics of the

physical (material) aspects act as the "hardware" whose tendency toward

local equilibrium generates the solution of the Lagrangian of the

"next" state, the "software" is the information content. I say

poetically: "Guided by the future, powered by the past, I become"

[MP]

Hmmm..

*> Does the map to finite subset of W mean that different
*

*> particles in LS are mapped to different points of W, their positions?
*

Yes, almost, the map to finite subset of W is a model of the

"unity of

consciousness" of the LS. The quantum entanglements of the subsets

(quantum particles) of a given LS acts to unify the mapping. The

positions that are being mapped are the centers of mass of other LSs

that are being projected into W themselves. I wish I could draw a

picture of this here! The problem is that the image I have is not

reducible to 2 dimensions! :-(

[MP]

I think I understood what you mean here.

[SPK]

The notions of positions is a relative notion in my thinking. It

is

perhaps good to think of a graph were the centers-of-mass of other LSs

are the nodes and the edges are the relative overlaps in W. In this way

we define the space aspects of the observation in terms of extensions

and the time aspects in terms of durations, given the particular

internal behavior of the LS propagator.

Thus, if the LS is in a bound state, it has not time associated

and all

extensions are null, e.g. LSs that are at internal equilibrium have no

space or time associated. The consequences of this when considering how

other LSs, in interaction with such, is interesting! It looks like the

situation where a worm hole, connecting separated space-time regions in

the classical GR picture, is pinched closed.

[MP] I did not understand why bound states have no space or time.

Does it mean that LS is mapped to single point? And that there are

no relative positions and no relative times?

[SPK]

*> > The way that the Weyl scale invariance
*

*> > connects the spectra of particles and their histories, is important
*

*> > since the structure of the LS's M^4 requires that no logical
*

*> > inconsistensies are present. Each LS would have a M^4 that has a
*

causal

*> > structure that is, from the point of view of the LS in question,
*

*> > logically consistent. The objection that is used against Weyl, I am
*

*> > turning around! I say that observers do not see spectral smearing
*

*> > because they can't see all possible histories of particle motions!
*

*>
*

*> > LS that have different quantum histories will be able to
*

interact only

*> > within the bounds of the intersection of their histories, e.g. those
*

*> > part wherein they agree. This is a very relativistic notion since it
*

*> > shows that the observations of LS depend on their associated quantum
*

*> > histories. The divergence of the frequency of particles generates the
*

*> > appearence that they are moving away from each other!
*

*> >
*

[MP]

*> This looks like fiber bundle structure: different LS:s as regions
*

*> of fiber bundle related by transition functions. One could not
*

*> define uniquely single LS but would have some minimum number of
*

*> LS:s, patches of the bundle. OK? But the mapping of LS to
*

*> several points of W breaks this picture.
*

The key notion is how the "connections" are defined! LS have no a

priori connections between them, this allows connections, which define

the forces between LS, to be dependent on the local histories of the

LSs, e.g. the information content of the LS's quantum history constrains

the mapping. The fiber thus look more like a tree, N to 1 map, than a

string, 1 to 1 map.

[MP] I think I understand this. By the way, in the hierarchy of

selves selves form an infinite hierarchy describable

as infinite tree: branches in given node

are selves summing up to higher level self identified as branch

coming to that node.

[MP]

*> Generalized fiber spaces with projection mapping fiber to
*

*> several points? Could the number in image depend on base point and
*

*> could one allow the image be empty set? In this manner one
*

*> would avoid the counter argument about fiber space
*

*> realization of LS. When image is empty there is no LS.
*

Yes to all! :-) Also, we can reason that an empty LS maps to the

whole W, as the null or empty set. A singleton LS, e.g. an LS having a

single quantum particle maps to all singleton points of W.

[MP]

*> > > In my approach CP_2 geometrizes elementary particle numbers and
*

classical

*> > > gauge fields in spirit very much to that of Kaluza-Klein theories.
*

*> > > Local system is now spacetime sheet. Cartesian product x in your
*

*> > > and Hitoshi's approach is replaced by topological sum # of
*

3-surfaces

*> > > representing local system and its complement (drill holes D^3 in
*

*> > > LS and complement and connect resulting boundaries S^2 by a tube S^2
*

*> > > xD^1).
*

[SPK]

*> > Umm, your topological sum is more akin to the way that LSs are
*

composed

*> > from other LSs, not the way they fiber the base manifold X or W. The
*

*> > worm holes S^2xD^1 that you propose connect the boundaries S^2, I see,
*

*> > as a way of defining field lines in TGD. I remember the discussion in
*

*> > MTW's Gravitation... :-) I think that this is a very fruitful notion!
*

Do

*> > you think of the relationship between the LS and its complement as
*

*> > synonymous to the relationship between subject and object in an
*

*> > observation?
*

[MP]

*> More or less but quite not as I realized just now.
*

*> I try to explain.
*

*>
*

*> a) The decomposition of spacetime surface
*

*> to cognitive spacetime sheets having *finite time duration* (I stress
*

*> this since this is crucial) and material spacetime sheets has turned
*

out

*> instrumental for the model for self and binding.
*

Umm... I still have trouble with this wording, but I can see how

you use it, I think. I see "cognitive space-time sheets" and "material

space-time sheets" as Stone-Birkhoff duals of each other, as Pratt

defines the latter.

[MP] Without knowing what Stone-Birkohoff means,

I somehow feel that this identification is not correct.

Cognitive spacetime sheets provide non-faithful representations

for material spacetime sheets: they mimick some aspects of their

behaviour.

I have myself talked about geometric matter mind duality: the

phrase is misleading. One should only talk about geometric

matter-mind decomposition of spacetime.

Visualize in terms of the size and shape and topological sum.

Material spacetime sheet has infinite duration since conservation

laws does not allow it to cease in time direction. Then you take

cognitive spacetime sheet, initially vacuum, and glue it to

material sheet by topological sum. You can use several wormhole contacts.

The net result is that some energy and some momentum and other stuff

flows to cognitive spacetime sheet from material sheet and of course

also back to material sheet because otherwise conservation laws would

fail. This is a model of self. Quantum jump by quantum jump these

cognitive spacetime sheets drift gradually to the future and self

finds time running. Since self dissipates, self also finds that

self is getting old.

Could it be possible to extend the notion of local system to

something akin to a pair of material and cognitive spacetime sheets.

This would bring in matter-mind decomposition.

I know that this goes outside the standard physics and hence one should

have good motivations for doing this.

[SPK]

I see the ideas implicit in the concept of a

"space-time" as applicable to both information and matter, each has

extentional and durational attributes. The identification between the

two is modeled by the "informorphism": material event A causes material

event B if and only if the information content of B implies the

information content of A, thus A -> B iff A* <= B*; "<-" is material

causation and "<=" is logical entailment or implication.

[MP]

I understand this. In TGD cognitive spacetime sheets represent

unconscious mind geometrically. Events involve reductions of

matter-mind entanglement. The related experience could be 'I cause that

happen'.

This is not the only possibility: volition could be related solely with

the localization in zero modes characterizing various

degenerate absolute minima of Kahler action: classical nondeterminism

of Kahler action would make possible volition: this looks very nice to me.

I must be able to decide what is the truth(:-)!

[SPK]

Other key differences are in the way the "physics" of the two

work. Material "bodies" are incompressible and rotatable, information

"minds" are compressible and irrotatable. Bart Kosko explains the latter

properties in his book Fuzzy Engineering...

[MP]

For me the basic difference between mind and matter is

*finite time duration* of cognitive spacetime sheets: more generally,

cognitive spacetime sheets are *bounded* but possibly infinite (recall

the possibility of infinite primes).

*> b) In quantum jumps only the entanglement between cognitive and
*

material

*> spacetime sheets can be reduced. This generalizes von Neumann's
*

*> intuitions.
*

This idea, to me, speaks to a generalization of Pratt's notions.

The transition or quantum jump from event A to event B is a process of

selecting the particular points of W that are dual to the information

content of the LS. Umm, I have been trying to work out an idea where the

points on the surface bounding an LS encode a n-ary bit of information,

but this is still very crude. I am using the ideas of Wheeler about the

information content of a Black-Hole's event horizon.

*> c) Selves are pairs of material-cognitive
*

*> spacetime sheets unentangled with the other
*

*> selves and containing as nested subsystems lower level selfs:
*

*> Russian dolls inside Russian dolls. Self is
*

*> synonymous to observer.
*

I agree with this. I believe that the notion of a homunculus

existing inside our head with a mini-humunculus inside of its head, etc.

is generated by this p-adic hierarchy of LS selves! :-)

[MP]

There is indeed certain analogy with homunculus idea. But also important

difference. The smaller the homunculus the higher it

is at cognitive hierarchy according to the traditional homunculus

idea.

In TGD the situation is exactly the opposite. Primitive experiences of

small homunculi sum up to those of larger. All these expriences of course

exist separately in each moment of conscious experience as its separate

parts. The hierarchy also stops at elementary particle level or already

earlier, not all subsystems are able to remain unentangled under U. It

migh well be that elementary particles are not even accompanied by

cognitive spacetime sheets and thus are not able to form 'homunculi'.

*> Thus LS would correspond to a pair of matterlike and mindlike
*

*> subsystems
*

*> rather than single spacetime sheet.
*

Yes! I think of these in terms of Pratt's BODY and MIND, as

defined in ratmech.ps... An LS is a CHU space.

*> By the way, this picture works: I just worked out
*

*> a beatiful model for what happens when we wake-up or fall
*

*> asleep, or get older and eventually die. The basic phenemenology is
*

*> reproduced beatifully and one can even say definite things about what
*

*> happens in death. The Buddhist view about gradual evolution of
*

*> self to higher and higher levels of subjective existence seems to be
*

the

*> only reasonable conclusion. Amazing!
*

Umm, I am skeptical of the notion of the literal transmigration of

souls, since it assumes that the awareness of self is continuous a

priori and the idea that the self is a "rigid object" that "move in

space-time".

[MP] These are exactly the reasons why also I was sceptic about self.

The notion of self as subsystem able to remain unentangled under action

of U however mildens dramatically these conditions. Cognitive

spacetime sheet would be geometrical counterpart of a soul attached

to matter. It can born. It cand disappear. It can change its

shape and size. It is very much like material but has finite

time duration and is almost vacuum.

Without quantum jump cognitive spacetime sheet certainly cannot move in

spacetime since it is part of spacetime

itself. The *notion of quantum jump saves the situation*.

In each quantum jump the spacetimes in superposition of macroscopically

equivalent spacetimes changes as also change the precisely defined

temporal positions of cognitive spacetime sheets.

Since the future of given point of future lightcone contains much more

room than its past, cognitive spacetime sheet is bound to diffuse

or even drift to future. Some average amount of geometric

time passes per quantum jump: most naturally 10(-39) seconds

('CP_2 time'): this is arrow of psychological time.

Psychological time is quantized with this average size

of quantum. Geometrical time is continuous.

[SPK]

This contradicts the basic notion of quantum jumps. I am

claiming that the notion of rigid bodies is at best an illusion!

[MP] No, it does not! See above. The crux of matter is

finite time duration of cognitive spacetime sheet and

the fact that its temporal position changes in quantum jump.

[SPK[

The unity of "flow of consciousness" is given by the unitary evolution

of entanglements of the material particles that make up a mortal body.

When a body dies, the entanglements decohere and so does the unity of

consciousness that is associated. This idea looks very bleak, I know!

[MP]

This picture however leads to the basic difficulties of models

describing self as continuous stream of consciousness. Self

as subsystem remaining unentangled between subsequent quantum

jumps does not introduce continuous stream of cs.

Just as an example I send a short piece of text about what happens

in wake-up and fall-asleep experiences.

[SPK]

But I found another mechanism that models most paranormal phenomena as

well as the notion of transmigration. We need to consider that quantum

entanglements "connect" subsets of LSs that can have very different

space-times associated, thus we can are resonances in the information

content. Carl Jung's discussion of "synchronisities" is relevant!

[MP]

I agree that entanglement is the royal road to enlighment and explains

synchronicity. I have written about this even a chapter to

my book. There are however *two* bindings involved. Entanglement

binds experience*r*s: summation of sub-experiences of self binds

experiences and makes possible abstractions!

[MP]

*> > > The problem why the universe of conscious experience looks classical
*

while

*> > > quantum universe is nonclassical, has bothered also me. For long
*

time I

*> > > thought that the association X^3--> X^4(X^3) forced by
*

*> > > 4-dimensional General Coordinate Invariance might be all that is
*

needed

*> > > to understand this but I was wrong. The hypothesis that quantum
*

jumps

*> > > correspond to quantum measurents, which are local at the level of
*

*> > > configuration space of 3-surfaces implies
*

*> > > localization of configuration space spinor fields in zero modes:
*

this

*> > > means that moment of cs makes the world essentially classical.
*

[SPK]

*> > I, unfortunately, do not follow all of what you are saying here. :(
*

*> > Could you elaborate on what "localization of configuration space
*

spinor

*> > fields in zero modes" means?
*

[MP]

*> a) Configuration space of 3-surfaces has fiber space structure.
*

*> Fiber corresponds to cm degrees of freedom and vibrational degrees
*

*> of freedom of 3-surface: 'vibrational' motions do not change
*

*> the macroscopic shape and size nor classical Kahler field of
*

*> 3-surface.
*

What is "cm"? Have you read about the resonances of a fractal

surface?

I have a book that discusses this. It is possible that the boundary of

an LS is a fractal in most cases! The notion of tree fibers points to

this...

[MP]

cm refers to center of mass.

*> Metric of configuration space is nontrivial in
*

*> fiber degrees of freedom and quantum fluctuations occur in
*

*> these degrees of freedom. These are the degrees of freedom of
*

*> ordinary QFT.
*

How is the metric generalize to our tree-like fibers? The "leaves"

of the tree-fibers are LSs and the truck roots into a non-zero region of

W, I think... The subtleties involved is that we can invert the picture so

that the leaves are points in W and the root is an LS... The difference

in these views is the difference between the subjective and the

objective. Umm, I am confused! :-) Maybe we say that the tree is a

fibration of LS_i x X^3_j -> W_ij ? I need to think about how to put my

picture into words better...

[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.

*> b) Base corresponds to zero modes in which configuration
*

*> space line element vanishes: there is however symplectic form
*

*> so that integral can be defined. Zero modes characterize
*

*> shape size and classical Kahler field (which often reduces
*

*> to classical em field) of 3-surface. These degrees of
*

*> freedom are new and result from generalization of elementary
*

*> particle concept. They are classical degrees of freedom:
*

*> all that which we see around us and in terms of them we
*

*> formulate classical physics.
*

Umm, this seems to follow the "classical" notions. We need the

generalizations were there is not absolute space-time! The illusion of

classical emerges as a weighted averaging over many such space-times in

superposition...

[MP] I think that we are still talking about different things(;-)!

*> c) In quantum jump the state must go to an unentangled
*

*> state. The state can be expressed formally as quantum superposition
*

*> of 3-surfaces
*

*> SUM(X^3) C_nN (X^3)|n>|N>
*

*> where summation symbolizes sum over 3-surfaces and
*

*> n and N denote labels for the quantum states in fiber:
*

*> these states correspond to quantum states of
*

*> ordinary QFT. SUM(X^3) is not present in QFT since
*

*> X^3 is not dynamical.
*

Yes. The dynamics involve the changes of the X^3s which I see as

finite partitions of W. The topology changes abruptly!

*> c) Locality of NMP in configuration space requires that
*

*> quantum jump must reduce the entanglement in local manner.
*

*> This suggests that localization to single X^3 must occur:
*

*> otherwise one simply cannot get unentangled product state.
*

*> This would mean that each quantum jump leads to state
*

*> localized in single 3-surface and spacetime.
*

Yes, but I say that this occurs for each LS... The overlap of

fibers in W creates the appearance of a single space-time with a

Robertson-Walker metric, e.g. with a Hubble expansion related to the local

"age" of such...

*> This would be extremely classical but
*

*> cannot be true since various symmetries do not commute
*

*> with fiber degrees of freedom and resulting
*

*> state could not be eigenstate of say momentum.
*

Could we deal with this? What if we allowed for multiple states

and think of eigenstates as not strictly orthogonal for all fibers.

Remember that the ordinary mathematics of QFT assumes binary complete

knowledge and it is obvious that such is an idealization...

*> d) Symmetries however act
*

*> in fiber and since they are gauge symmetries one
*

*> must require that entanglement coefficients C_nN depend
*

*> *only on zero modes* but not on fiber degrees of freedom.
*

*> This means that localization in zero modes is all that
*

*> is needed. And this indeed makes the universe of
*

*> conscious experience classical!
*

I keep reading this and it makes no sense to me as a whole. :-( I

only understand pieces...

[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.

*> In each quantum jump the state UPsi_i generated
*

*> form Psi_i is reduced to state Psi_f localized completely
*

*> in zero modes. Superposition of 3-surfaces which
*

*> differ from each other only in vibrational and rotational (in
*

particular

*> color-rotational) degrees of freedom and
*

*> are macroscopically identical, is created.
*

I think I understand! :-)

*> Informational time development U makes universe classical
*

*> but moment of consciousness makes it classical again.
*

*> When Djinn comes out of the bottle universe becomes
*

*> nonclassical: when it returns to bottle the universe
*

*> becomes classical again
*

[SPK]

Umm, is this saying that during the transition from classical

space-time to another, the universe is quantum mechanical? This allows

space-times with different global topologies to be connected?

[MP]

It says that UPsi_i is non-classical. Macroscopically different

configurations, spacetimes, in same quantum superposition. Me writing this

and me walking on the beach. In quantum jump only one of these

macroscopically different configuration is selected.

The localization of spacetime surface is not compelete: small

quantum fluctuations remain but they do not affect the

size and shape of spacetime.

It might help to notice that localization in zero modes realizes

Penrose-Hameroff mechanism in TGD framework.

[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]

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]

*> > It seems to me that GCI notion is built on
*

*> > the notion that all observers live in one and the same space-time,
*

thus

*> > the need to transform a single set of physical laws, like a rigid
*

*> > structure, so that all would obey it. If we instead consider that
*

*> > observers can only interact to the degree that their own set of
*

physical

*> > laws agree, we can avoid the problems that GCI has with QT!
*

*> [MP]
*

*> Yes. I see the idea.
*

Best,

MP

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