Noninteger Dimensional Spaces and the Inverse Square Law

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.