Matti Pitkanen (matpitka@pcu.helsinki.fi)
Fri, 27 Aug 1999 12:41:02 +0300 (EET DST)
On Fri, 27 Aug 1999, Stephen P. King wrote:
> Dear Matti,
>
> Matti Pitkanen wrote:
> >
> > When this book is published?
>
> I can find the origional reference but I think it was in the early
> '70s...
>
> > By the way, 8-dimensional imbedding space is of maximal dimension in the
> > sense that only in this dimension two 4-surfaces in general intersect
> > in point just as two curves in plane intersect generalically
> > but miss each other in dimensions D>2.
>
> Yes, I agree! I will be looking into Pratt's Chu_8 spaces, there is a
> relation there!
>
> > This might have some deep implications. For instance, cognitive
> > spacetime sheets would generically intersect material
> > spacetime sheets in D=8 but not in D>9. D<9 maximimizes
> > geometric contact interactions in well defined sense.
>
> Wow! That would be great if we could prove it.
>
> > Furthermore, two 3-surfaces in 7-dimensional lightcone
> > boundary delta M^4_+c xCP_3 or in a=constant hyperboloid can get
> > linked just as curves in 3-space get linked. Could the linking
> > of 3-surfaces can have any physical effects? It could if
> > the topological reaction destroying the linking requires
> > large enough energy: in this case linked 3-surface would be
> > confined.
>
> Could the linking be use to define entanglement or locality? It does
> seem that a Planck energy is needed in a Planck volume to achive grand
> symmetry, perhaps it is here were topological variations occur... I
> don't know...
No. Quantum entanglment is purely Hilbert space concept related
with tensor product. Of course, 'ontogeny recapitulates phylogeny'
suggests that there is geometric counterpart for entanglement.
Join along boundaries for 3-surface makes interaction between them
possible and is excellent candidate for geometric prequisite
of quantum entanglement. Also linking certaily correlates
the quantum positions of two 3-surfaces and might imply entanglement
in position coordinates.
Best,
MP
>
> Later,
>
> Stephen
>
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