Noninteger Dimensional Spaces and the Inverse Square Law
- Subhash Kak
Abstract
Noninteger dimensionality, which shows up in many fields of physics and
engineering, is generally viewed from the perspective of fractals and
measured by the Hausdorff dimension. Motivated by information theoretic
considerations and by extending the principle of complementarity, we
propose a new interpretation in which it engenders a potential. The
inverse square law may then be seen to originate from the properties
associated with the noninteger dimensional space, and it further
indicates a relationship between the dynamics and the actual value of
the dimensions that may be used for experimental test of the
interpretation.