**Stephen P. King** (*stephenk1@home.com*)

*Sat, 17 Jul 1999 13:16:31 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 454] Re: [time 450] Re: Fibering, manifolds and sums"**Previous message:**Stephen P. King: "[time 452] Re: [time 451] Some New Mathematics"**In reply to:**WDEshleman@aol.com: "[time 451] Re: [time 447] Re: [time 446] Some New Mathematics"**Next in thread:**Matti Pitkanen: "[time 454] Re: [time 450] Re: Fibering, manifolds and sums"

Dear Matti,

Matti Pitkanen wrote:

snip

*> Important constraint for the fiber space is that it should explain
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*> as much as possible facts unexplained by standard physics.
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*> 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

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

manifold X. 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. 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!

*> 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).
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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?

*> 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
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*> 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.
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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? 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!

Kind regards,

Stephen

**Next message:**Matti Pitkanen: "[time 454] Re: [time 450] Re: Fibering, manifolds and sums"**Previous message:**Stephen P. King: "[time 452] Re: [time 451] Some New Mathematics"**In reply to:**WDEshleman@aol.com: "[time 451] Re: [time 447] Re: [time 446] Some New Mathematics"**Next in thread:**Matti Pitkanen: "[time 454] Re: [time 450] Re: Fibering, manifolds and sums"

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