Why observable space is solely three dimensional

Abstract

Quantum (and classical) binding energy considerations in n-dimensional space indicate that atoms (and planets) can only exist in three-dimensional space. This is why observable space is solely 3-dimensional. Both a novel Virial theorem analysis, and detailed classical and quantum energy calculations for 3-space circular and elliptical orbits indicate that they have no orbital binding energy in greater than 3-space. The same energy equation also excludes the possibility of atom-like bodies in strictly 1 and 2-dimensions. A prediction is made that in the search for deviations from r^-2 of the gravitational force at sub-millimeter distances such a deviation must occur at < ~ 10^-10 m (or < ~10^-12 m considering muoniom), since atoms would disintegrate if the curled up dimensions of string theory were larger than this. Callender asserts that the often-repeated claim in previous work that stable orbits are possible in only three dimensions is not even remotely established. The binding energy analysis herein avoids the pitfalls that Callender points out, as it circumvents stability issues. An uncanny quantum surprise is present in very high dimensions.