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

*Sat, 17 Jul 1999 21:59:37 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 455] Re: [time 454] Re: [time 450] Re: Fibering, manifolds and sums"**Previous message:**Stephen P. King: "[time 453] Re: [time 450] Re: Fibering, manifolds and sums"**In reply to:**Matti Pitkanen: "[time 450] Re: Schommers' work"**Next in thread:**Stephen P. King: "[time 455] Re: [time 454] Re: [time 450] Re: Fibering, manifolds and sums"

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
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*> > combine with global general relativistic spacetime. Fiber abstracts the
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*> > concept of local nonrelativistic quantum system. What troubles me
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*> > in this approach is that every point of X^4 contains local system. Somehow
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*> > only some fibers are 'active'. This same feature troubles me also
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*> > in Bohm's theory. Only some classical orbits are 'activated' in the
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*> > hydrodynamical flow defined by Schrodinger amplitude and correspond to
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*> > classical particles.
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*>
*

*> Umm, some misunderstanding... I am proposing a Weyl geometry W for the
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*> manifold into which the LSs are projected; Hitoshi uses a Riemannian
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*> manifold X.
*

[MP]

Of course! You have general relativity

with Rieman geometry replaced by Weyl geometry.

*>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
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*> projections partition it into local logical consistent subspaces. This
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*> has to do with the epsilon bound on the accuracy that LSs can predict
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*> each other's behavior.
*

*> This is in the spirit that each LS has an associated M^4 that is
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*> constructed from W by the act of projection. This projection is an
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*> identification or mapping between the internal configurations of the LS
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*> and a finite subset of W.
*

There is probably some computationalistic motivation for this

map. Does the map to finite subset of W mean that different

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

*> The way that the Weyl scale invariance
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*> connects the spectra of particles and their histories, is important
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*> since the structure of the LS's M^4 requires that no logical
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*> inconsistensies are present. Each LS would have a M^4 that has a causal
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*> structure that is, from the point of view of the LS in question,
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*> logically consistent. The objection that is used against Weyl, I am
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*> turning around! I say that observers do not see spectral smearing
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*> because they can't see all possible histories of particle motions!
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*> LS that have different quantum histories will be able to interact only
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*> within the bounds of the intersection of their histories, e.g. those
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*> part wherein they agree. This is a very relativistic notion since it
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*> shows that the observations of LS depend on their associated quantum
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*> histories. The divergence of the frequency of particles generates the
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*> appearence that they are moving away from each other!
*

*>
*

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.

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.

*> > In my approach CP_2 geometrizes elementary particle numbers and classical
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*> > gauge fields in spirit very much to that of Kaluza-Klein theories.
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*> > Local system is now spacetime sheet. Cartesian product x in your
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*> > and Hitoshi's approach is replaced by topological sum # of 3-surfaces
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*> > representing local system and its complement (drill holes D^3 in
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*> > LS and complement and connect resulting boundaries S^2 by a tube S^2
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*> > xD^1).
*

*>
*

*> Umm, your topological sum is more akin to the way that LSs are composed
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*> from other LSs, not the way they fiber the base manifold X or W. The
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*> worm holes S^2xD^1 that you propose connect the boundaries S^2, I see,
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*> as a way of defining field lines in TGD. I remember the discussion in
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*> 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
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*> synonymous to the relationship between subject and object in an
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*> observation?
*

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 fo self and binding.

b) In quantum jumps only the entanglement between cognitive and material

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

intuitions.

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.

Thus LS would correspond to a pair of matterlike and mindlike subsystems

rather than single spacetime sheet.

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!

*>
*

*>
*

*> > The problem why the universe of conscious experience looks classical while
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*> > quantum universe is nonclassical, has bothered also me. For long time I
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*> > thought that the association X^3--> X^4(X^3) forced by
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*> > 4-dimensional General Coordinate Invariance might be all that is needed
*

*> > to understand this but I was wrong. The hypothesis that quantum jumps
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*> > correspond to quantum measurents, which are local at the level of
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*> > configuration space of 3-surfaces implies
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*> > localization of configuration space spinor fields in zero modes: this
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*> > means that moment of cs makes the world essentially classical.
*

*>
*

*> 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?
*

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. 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.

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.

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.

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.

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.

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!

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.

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

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

*> the notion that all observers live in one and the same space-time, thus
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*> the need to transform a single set of physical laws, like a rigid
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*> structure, so that all would obey it. If we instead consider that
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*> observers can only interact to the degree that their own set of physical
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*> laws agree, we can avoid the problems that GCI has with QT!
*

*>
*

[MP]

Yes. I see the idea.

Best,

MP

**Next message:**Stephen P. King: "[time 455] Re: [time 454] Re: [time 450] Re: Fibering, manifolds and sums"**Previous message:**Stephen P. King: "[time 453] Re: [time 450] Re: Fibering, manifolds and sums"**In reply to:**Matti Pitkanen: "[time 450] Re: Schommers' work"**Next in thread:**Stephen P. King: "[time 455] Re: [time 454] Re: [time 450] Re: Fibering, manifolds and sums"

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