Why Observable Space Is Solely Three Dimensional

TL;DR

This paper argues that observable space is limited to three dimensions due to quantum and classical energy constraints, which prevent stable atoms and planetary orbits in higher or lower dimensions, supported by novel theoretical analyses.

Contribution

It introduces a new virial theorem analysis and detailed energy calculations demonstrating the impossibility of stable structures in dimensions other than three.

Findings

Atoms cannot exist in 1 or 2 dimensions due to energy constraints.

Stable orbits are not possible in dimensions greater than three based on energy considerations.

Deviations from inverse-square gravity should occur below 10^-10 meters if extra dimensions exist.

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.