Born reciprocity and the 1/r potential

TL;DR

This paper explores Born reciprocity invariance in physics, proposing a scale transformation that leaves the Hamiltonian unchanged, and suggests it could explain galactic rotation curves without dark matter.

Contribution

It investigates the implications of Born reciprocity for atomic and galactic physics, introducing a scale parameter that could account for galactic rotation.

Findings

Negligible effect on atomic physics at the proposed scale

Potential explanation for galactic rotation curves

No need for dark matter hypothesis at this scale

Abstract

Many structures in nature are invariant under the transformation (p,r)->(br,-p/b), where b is some scale factor. Born's reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We investigate this idea for atomic physics and galactic motion, where one is basically dealing with a 1/r potential and the observations are very accurate, so as to determine the scale $b = m\Omega$. We find that an $\Omega \sim 1.5\times 10^{-15}$ Hz has essentially no effect on atomic physics but might possibly offer an explanation for galactic rotation, without invoking dark matter.