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I think something like this really works.* Here's how mainstream physicists would describe it. Let's use particle-physics natural units ($c=\hbar=1$). Then we have just one dimensionful unit, usually the eV. Nothing is stopping you from using a different unit, the cV (short for "crazy eV"), where the conversion is 1cV = 1eV in this galaxy, but 1cV=0.99eV in ...


The OP acknowledges that $m_e/m_p$ is constant and correctly points out that the fine sturcture energy levels of the hydrogen atom are proportional to $m_e$ (as opposed to $m_e/m_p$). It is also true that the energy levels of the Lamb Shift are proportional to $m_e$. However, the hyperfine structure of the hydrogen atom is proportional to $m_e/m_p$. ...

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