ASU and CS would like to thank Prof. David Hinde for useful discussions regarding the neutron clock. This work was partially supported by the STFC grant Nos. ST/M006433/1, ST/P003885/1, and ST/P005314/1, by the Polish National Science Center under Contract Nos. 2018/31/B/ST2/02220, 2018/30/Q/ST2/00185, and 2017/27/B/ST2/02792; by JSPS KAKENHI Grant Number JP19K03861; by the National Natural Science Foundation of China under grant Nos. 11875225 and 11790325; by the U.S. Department of Energy under grant Nos. DE-SC0013847, DE-SC0019521, DE-SC0013365, DE-SC0018083, DE-NA0003885, and DE-SC0019521; by Spanish Ministry of Economy and Competitiveness (MINECO) grant No. PGC2018-094583-B-I00; by the Fonds de la Recherche Scientifique (F.R.S.-FNRS) and the Fonds Wetenschappelijk Onderzoek - Vlaanderen (FWO) under the EOS Project nr O022818F; and by the Australian Research Council grant No. DP190100256. This work was partly performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (NS). The work was also supported by the US Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 654002. JR wishes to acknowledge the Yukawa Institute for Theoretical Physics in Kyoto for its generous support of his participation is this project.