Testing distinguishability and determinism in atoms

We propose and analyze experiments to test distinguishability and determinism in atoms. As a first step, we consider experiments to test if atoms are distinguishable from each other due to small differences in the nuclear magnetic moment. The idea is to measure the hyperfine splitting for stable isotopes that are confined to ion traps, by accumulating statistics over time with different atoms. The three cases analyzed are strontium-87 with an odd number of neutrons, lutetium-175 with an odd number of protons, and lutetium-176 with an odd number of protons and neutrons. We then consider the possibility of performing the same tests on newly created stable isotopes. We also propose that a time-dependent nuclear magnetic moment may enable deterministic tracking of the life cycle of an isotope, and prediction of age since creation and time until decay of radioisotopes. The case of thulium-170 is considered, it is particularly interesting as a radioisotope with an odd number of protons and neutrons. More generally, we argue that any atomic transition could change in time, either due to the atomic nucleus or to the electron charge distribution. The latter could be tested in a dual atomic clock in a ladder configuration to search for the aging of an electronic transition.