Constraints on the Dimensionality of Space

Abstract

Complex structures can only form in a universe that allows for bound states. While this is clearly observed in three-dimensions, added degrees of freedom in a higher-dimensional space preclude the immediate assumption that binding potentials can in fact exist. In this paper, we derive a constraint on the dimensionality of a universe in the presence of an arbitrary set of forces. We then apply this constraint to systems with several example potentials. In doing so, we find that bound states in higher than 3 dimensions are in fact possible under specific circumstances which we characterize.