Matti Pitkanen (matpitka@pcu.helsinki.fi)
Wed, 25 Aug 1999 13:22:24 +0300 (EET DST)
On Wed, 25 Aug 1999 WDEshleman@aol.com wrote:
> In a message dated 8/25/99 1:10:11 AM Eastern Daylight Time,
> matpitka@pcu.helsinki.fi writes:
>
> > > > In any case, the basic philosophy of quantum TGD is eliminative:
> > > > this means that entire quantum physics (apart from quantum jump)
> > > > is reduced to infinite-dimensional configuration space geometry
> > > > with spinor structure. The success of this philosophy
> > > > convinces me even more than indidividual applications.
> > >
> > > Matti,
> > > An "infinite-dimensional configuration space geometry" subjectively,
> > > but not an "infinite-dimensional space geometry" objectively?
> >
> > Infinite-dimensional configuration space geometry as something objective,
> > pregiven, totally fixed by the mere requirement of mathematical existence
> > implying huge symmetries fixing the metric and spinor structure
> > completely.
> >
>
> Matti,
>
> I sorry to be so dense (and I mean that), but is your next level of
> objective space that of 16-dimensions?
There is no necxt level of objective space! There must be some
misunderstanding here. Perhaps related to the notions
of imbedding space and configuration space of 3-surfaces.
Perhaps the explanations below might help.
> Or do you effectively add
> them on 1-dimension at a time? Does your observer located on
> a 4-D sheet see what is objectively true? I'm still having trouble
> with those extra dimensions being real and therefore not being
> the creation of a subjective observer. If those extra dimensions
> are real, I would expect them to be in the initial object; as you
> know, where I would prefer them to be.
1. String models
It is perhaps could to relate this to string models. In super string
models 'spacetimes' are 2-dimensional orbits of strings and
live in 10-dimensional spacetime. In TGD spacetime surfaces
are 4-dimensional and live in 8-dimensional spacetime.
2. Observer in TGD
In TGD observer can itself be regarded as spacetime sheet, so called
cognitive spacetime sheet X^4. This is new and would need long
explanation! In any case, cognitive spacetime
sheet has *finite* time duration (small
energy flows from material spacetime sheet when X^4 begins and
back to material spacetime sheet when X^4 ends.
The basic philosophy is that basic dynamical objects must be 3-dimensional
because we ourselves experience us as 3-dimensional. This excludes
string models.
3. Imbdding space is nondynamical
The 8-dimensional spacetime is *non-dynamical*. This is required
by the consistency of the theory. In string models 10-dimensional
space must be assumed to be dynamical since otherwise one does
not obtain dynamical Einsteinian spacetime: now it is obtained
by Kaluza-Klein trick and spontaneous compactification. This has however
turned out to be the weak point of string models: essentially no progress
has occurred during these ten 15(!) years in this respect.
The most horrible thing is that field theory limit is nonrenormalizable:
this should make anyone VERY cautious. In TGD there is no
need to this since basic object is spacetime surface. The concept
of spacetime is generalized dramatically however: particles
are small spacetimes glued to larger spacetimes glued to...
to macroscopic spacetime.
4. Infinite dimensional configuration space
Basic infinite-dimensional structure is configuration space
of 3-surfaces. Local coordinates for this space could correspond to
Fourier coefficients for small deformations of 3-surface
in 8-dimensional space. Clearly there are infinite number
of Fourier coefficients so that space is infinite-dimensional.
In string models all possible configurations of string would
be corresponding space.
>
> I am reminded of when I performed some simulations of insect
> population dynamics. No matter what initial population ratio
> of eggs : larva : pupa : adult, the final result always converges
> on a constant ratio. If you then use the final ratio as an initial
> condition, the solution never changes that ratio. Likewise, if
> it was appropriate (and easy) to substitute your infinite-dimension
> result for the 4-D surface in a 8-D space object, and again
> substitute the result obtained by the previous substitution,
> over and over, would not this procedure converge on a final
> objective infinite structure requiring no further modifications?
> I believe such a structure would interpret itself so-to-speak.
> I speculate that the converged on structure would be a
> doubling structure consistant with your initial object,
> consistant with my analysis of particular infinite product
> identities, and preserving the most important predictions
> of TGD.
I am not quite sure: perhaps we have different basic interpretation
but I do not quite get you idea.
>
> Sincerely,
> Bill
>
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