Matti Pitkanen (matpitka@pcu.helsinki.fi)
Wed, 25 Aug 1999 08:09:17 +0300 (EET DST)
On Tue, 24 Aug 1999 WDEshleman@aol.com wrote:
> In a message dated 8/24/99 2:19:56 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.
String modelists have similar dream but they have not realized that
infinite-dimensional geometry is the proper framework to realize this
dream.
The main motivation for this dream comes from the fact that in
infinite-dimensional calculus infinities are encountered at
every step. In infinite-dimensional geometry, existence of Riemann
connection forces huges isometry group and structure
of infinite-dimensional symmetric space G/H, finite Ricci tensor
forces vacuum Einstein equations for configurations space, etc..
G/H structure has strong implications: finite-dimensional symmetric spaces
have been listed by Cartan. Physically it says that all points
of symmetric space are physically equivalent: cosmological principle
generalized.
My original motivation came from a work of mathematician Frieden who
constructed Kahler geometry of loop space (maps from circle to
Lie group) and demonstrated that
it was unique and had infinite-dimensional Kac Moody type group
as group of isometries. This geometry had one failure: Ricci
scalar was infinite, which suggests that strings are not yet
the final story. Second failure: loop group geometry is
not Diff^2 invariant (you read correctly: Diff^2!: in TGD Diff^4
acts as gauge symmetry in space of 3-surfaces).
Best,
MP
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