  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.
