  It is demonstrated in general that stable gravitational or electrostatic
orbits are not possible for spatial dimensions n >=4, and in particular atoms
cannot be bound by energy constraints in higher dimensions. Furthermore,
angular momentum cannot be quantized in the usual manner in 4-space, leading to
interesting constraints on mass. Thus Kaluza Klein and string theory may be
impacted since it appears that the unfurled higher dimensions of string theory
will not permit the existence of energetically stable atoms. This also has
bearing on the search for deviations from 1/r2 of the gravitational force at
sub-millimeter distances. The results here imply that such a deviation must
occur at less than ~ 10-8 cm, since atoms would be unstable if the curled up
dimensions were larger than this.
