If the particle is moving at a relativistic velocity, the usual relativistic corrections for time dilation must be made.

Following table illustrates the relativistic corrections in energy and it can be seen how the relativistic correction scales with the atomic number of the system.

We can use this result to further calculate the relativistic correction:

On final calculation, the order of magnitude for the relativistic correction to the ground state is .

Only using 2 as the g-factor, we can match the energy level in the 1st order approximation of the relativistic correction.

And when relativity came, Newton's equations were found wanting but not Maxwell's; they needed no relativistic correction.

It should be noted that one needs to include relativistic and quantum electrodynamic corrections to get full agreement with experiment to spectroscopic accuracy.

The fine structure also results in single spectral lines appearing as two or more closely grouped thinner lines, due to relativistic corrections.

His work was the basis of general relativistic correction being properly included in the Global Positioning System.

Thus Richard could only approximate the relativistic corrections necessary to transform their own time basis into the one being experienced on the Earth.