In this paper we derive the nonlocal Time-Energy uncertainty principle and then apply the published 229Th nuclear clock data as a first probe of the nonlocality scale EM. By using the direct clock-energy channel, we find conservative lower bounds on EM at the tens of MeV scale, with optimistic present-data estimates reaching the hundred MeV scale. Including the known nuclear sensitivity enhancement of the 229Th transition gives us stronger model dependent bounds in the GeV range, while nuclear-scale reference-energy scenarios can reach the TeV range. The conclusion we draw from this is that nuclear clocks already provide an experimental route from nonlocal time--energy uncertainty to measurable laboratory bounds on non-Planckian nonlocality.
We explore the idea of using a squeezed-state experiment with the 229Th nuclear clock to test the time--energy structure of nonlocal quantum field theory. The idea is reasonably obtainable within the near future of nuclear clock experiments. One would prepare an ensemble of thorium nuclei in a coherent superposition of the nuclear ground state and the low-lying isomeric clock state, entangle the participating nuclei through a collective interaction, and generate a family of spin-squeezed states with a tunable squeezing parameter r. Then a phase-controlled analysis pulse will rotate the selected collective nuclear quadrature into a measurable ground-isomer population difference. Near a strongly polarized collective state the normalized operators Jy/S and Jz/S obey the same approximate canonical algebra as the phase and amplitude quadratures of a squeezed optical mode. We use this experiment to either probe or bound the nonlocal energy scale EM.
The study of highly charged electronic and muonic hydrogen-like ions, provides an intriguing way to probe the internal structure of their atomic nuclei. In this work, we use nuclear structure calculations to accurately calculate the hyperfine splitting of electronic and muonic hydrogen-like ions, focusing in particular on the incorporation of finite-volume corrections, such as Bohr-Weisskopf and Breit-Rosenthal, due to the penetration of the electron and muon wavefunction into the nuclear electric charge and magnetic dipole densities. These corrections are essential for refining our understanding of the nuclear magnetic dipole and electric quadrupole moments. Our simulations use a Skyrme-Hartree-Fock-BCS model known for its effectiveness in modeling well-deformed nuclei such as 159Tb64+ and 165Ho66+, with particular emphasis on 161,163Dy65+ isotopes. It can also be generalised to multi-electron ions by studying the hyperfine anomaly between two isotopes.