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

*Wed, 25 Aug 1999 13:22:24 +0300 (EET DST)*

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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)
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*> > > > is reduced to infinite-dimensional configuration space geometry
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*> > > > with spinor structure. The success of this philosophy
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*> > > > convinces me even more than indidividual applications.
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*> > >
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*> > > Matti,
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*> > > An "infinite-dimensional configuration space geometry" subjectively,
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*> > > but not an "infinite-dimensional space geometry" objectively?
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*> >
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*> > Infinite-dimensional configuration space geometry as something objective,
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*> > pregiven, totally fixed by the mere requirement of mathematical existence
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*> > implying huge symmetries fixing the metric and spinor structure
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*> > completely.
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*> >
*

*>
*

*> 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
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*> the creation of a subjective observer. If those extra dimensions
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*> 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
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*> population dynamics. No matter what initial population ratio
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*> of eggs : larva : pupa : adult, the final result always converges
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*> on a constant ratio. If you then use the final ratio as an initial
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*> condition, the solution never changes that ratio. Likewise, if
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*> it was appropriate (and easy) to substitute your infinite-dimension
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*> result for the 4-D surface in a 8-D space object, and again
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*> substitute the result obtained by the previous substitution,
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*> over and over, would not this procedure converge on a final
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*> objective infinite structure requiring no further modifications?
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*> I believe such a structure would interpret itself so-to-speak.
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*> I speculate that the converged on structure would be a
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*> doubling structure consistant with your initial object,
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*> consistant with my analysis of particular infinite product
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*> identities, and preserving the most important predictions
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*> 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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