, Volume 38, Issue 11, pp 995-1010
Date: 11 Oct 2008

Born Reciprocity and the 1/r Potential

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Many structures in nature are invariant under the transformation pair, (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 bmΩ. We find that an Ω∼1.5×10−15 s−1 has essentially no effect on atomic physics but might possibly offer an explanation for galactic rotation, without invoking dark matter.