Stephen P. King (stephenk1@home.com)
Sat, 17 Jul 1999 13:16:31 -0400
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.
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
> 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).
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
> 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.
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
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