[time 454] Re: [time 450] Re: Fibering, manifolds and sums

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sat, 17 Jul 1999 21:59:37 +0300 (EET DST)

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.
> 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.

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
> 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.

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
> 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!

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
> > 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?

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

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
> > 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?

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
> 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!

Yes. I see the idea.


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