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That is not a simulation and those are not fundamental constants. Because a simulation is too difficult, there are approximate formulae for computing the quant

That is not a simulation and those are not fundamental constants. Because a simulation is too difficult, there are approximate formulae for computing the quantities of interest, like the energy levels of the spectrum of the hydrogen atom. These approximate formulae include a large number of constants which are given in the paper linked by you and which are adjusted to match the experimental results. A simulation of the hydrogen atom would start from a much smaller set of constants: the masses of the proton and of the electron, the magnetic moments of the proton and of the electron, the so-called fine structure constant (actually the intensity of the electromagnetic interaction) and also a few fundamental constants depending on the system of units used, which in SI would be the elementary electric charge (determined by the charge of a coulomb in natural units), the Planck constant (determined by the mass of a kilogram in natural units) and the speed of light in vacuum (determined by the length of a meter in natural units).

fsh 3y ago
The inputs of the formulas for the hydrogen energy levels in the paper are: The Rydberg constant, the fine structure constant, the electron-to-proton mass ratio, the electron-to-muon mass ratio, the Compton wavelength of the electron, and some nuclear properties (charge radius, Friar radius, and nuclear polarizability). All inputs except the nuclear properties are as fundamental as it gets according to our current understanding of physics (note that the Rydberg constant and Compton wavelength are simple combinations of other physical constants). Nuclear physics is dominated by quantum chromodynamics which is not nearly as well developed as QED. The constants are determined by fitting the theory to the best available measurements (not only in hydrogen). This is exactly what fundamental constants do: They convert unit-less theory expressions into measurable quantities.

fsh 3y ago

The inputs of the formulas for the hydrogen energy levels in the paper are: The Rydberg constant, the fine structure constant, the electron-to-proton mass ratio, the electron-to-muon mass ratio, the Compton wavelength of the electron, and some nuclear properties (charge radius, Friar radius, and nuclear polarizability). All inputs except the nuclear properties are as fundamental as it gets according to our current understanding of physics (note that the Rydberg constant and Compton wavelength are simple combinations of other physical constants). Nuclear physics is dominated by quantum chromodynamics which is not nearly as well developed as QED. The constants are determined by fitting the theory to the best available measurements (not only in hydrogen). This is exactly what fundamental constants do: They convert unit-less theory expressions into measurable quantities.