Cobe Satellite Measurement, Hyperspheres, Superstrings and the Dimension of Spacetime
✍ Scribed by M.S. El Naschie
- Book ID
- 104363907
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 512 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0960-0779
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✦ Synopsis
The _rst part of the paper attempts to establish connections between hypersphere backing in in_nite dimensions\ the expectation value of dim E " # spacetime and the COBE measurement of the microwave background radiation[ One of the main results reported here is that the mean sphere in S " # spans a four dimensional manifold and is thus equal to the expectation value of the topological dimension of E " # [
In the second part we introduce within a general theory\ a probabolistic justi_cation for a com! pacti_cation which reduces an in_nite dimensional spacetime E " # "n # to a four dimensional one "D T n 3#[ The e}ective Hausdor} dimension of this space is given by ðdim H E " # Ł d H 3¦f 2 where f 2 0:ð3¦f 2 Ł is a PV number and f "z4-0#:1 is the Golden Mean[
The derivation makes use of various results from knot theory\ four manifolds\ noncommutative geometry\ quasi periodic tiling and Fredholm operators[ In addition some relevant analogies between E " # \ statistical mechanics and Jones polynomials are drawn[ This allows a better insight into the nature of the proposed compacti_cation\ the associated E " # space and the Pisot!Vijayvaraghavan number 0:f 2 3[125956866 representing it|s dimension[ This dimension is in turn shown to be capable of a natural interpretation in terms of Jones| knot invariant and the signature of four manifolds[ This brings the work near to the context of Witten and Donaldson topological quantum _eld theory[ Þ 0887 Elsevier Science Ltd[ All rights reserved[