Information Theory of Evolutionary Stages in Noninteger Dimensional
Spaces
- Subhash Kak
Abstract
This paper investigates evolution of a physical system through
intermediate noninteger dimensions to provide a phenomenological
explanation for the system's emergent properties. In recent papers it
was shown that physical space is associated with noninteger
dimensionality and its value is associated with the strength of
attractive inverse square law and this has applications to diverse
fields including the design of metamaterials. Here this
information-theoretic analysis is applied to cosmology to yields a novel
noninteger dimensional explanation for filaments and sheets of matter,
inflation, and the accelerating expansion of the universe, without the
need to postulate inflation field or dark energy as the drivers of this
expansion. Furthermore, the analysis shown that in the future as the
zero-dimension residual potential declines further, the expansion will
slow and then reverse. Evolution across noninteger spaces has potential
relevance for the study of materials that emerge from compressing
three-dimensional volumes into lower dimensions.