Born reciprocity and the 1/r potential

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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14 pages, with 4 figures, Latex, requires epsf.tex and iop style files

Scientific paper

10.1007/s10701-008-9247-8

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.

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