100 years of spin: fundamental physics, dark matter, exotic interactions, and all that

Abstract

For a century, spin has been an indispensable probe of the fundamental laws of nature. A reflection on the role of spin in shaping modern physics is presented, from the early days of quantum mechanics to the latest precision tests of the Standard Model. The significance of magnetic and electric dipole moments in testing CP and CPT symmetries is surveyed, along with the ongoing searches for exotic spin-dependent interactions that may reveal the nature of dark matter and its connection to spacetime geometry. Through these vignettes, it is shown that spin continues to provide a fresh perspective on the most profound questions in physics today.

Figures (6)

• Figure 1: Magnetic resonance of a single antiproton spin Latacz2026_BASE_Nature and fractional resolution achieved in measurements of the antiproton magnetic moment as a function of time. Above: The plot shows the most recent results from the BASE collaboration (resonance width of 0.156(4) Hz FWHM, blue points) and the least-squares fit of a Voigt profile to the data (red line). The gray data points and fit are from the previously measured antiproton resonance with a width of 2.5(2) Hz FWHM Smorra2017_BASE_Nature. Below: A fractional accuracy on the $10^{-3}$ level was reached with exotic-atom spectroscopy reached (orange); measurements in single Penning traps achieved resolutions at the ppm level. Upon approval, the BASE collaboration measured the antiproton magnetic moment with a frational resolution at the $10^{-9}$ level. It is expected that recently introduced coherent spectroscopy will allow for triple-trap measurements at the level of $\approx0.1\,$ppb. BASE is currently developing a single-particle double-trap technique with cyclotron frequency measurements based on phase sensitive detection, with projected fractional resolution $<20\,$ppt. Figure courtesy S. Ulmer (BASE).
• Figure 2: Wiggle-plot showing detected-analyzed positrons above a fixed energy threshold. Dashed lines indicate decay of muons in the lab frame. Adapted from Aguillard2023_Muongm2Run23.
• Figure 3: History of muon $g-2$. Measurements and Standard-Model calculations with semi-empirical (labeled WP2020) and Lattice-QCD (labeled WP2025) hadronic vacuum-polarization contributions. Adapted from Aguillard2025_FinalMuongm2.
• Figure 4: Nucleon EDM limits. The history of direct limits on the neutron EDM from the first experiment Smith1957 until today at $2\times10^{-26}e$cm Abel2020 along with the EDM limits for the $^{199}$Hg atom, providing the most precise directly measured limit of any EDM today at $7.4\times10^{-30}e$cm Graner2016Graner2017. From the $^{199}$Hg measurement, one can with some disputed large uncertainties and some suppression factor, also derive indirect limits on the neutron and proton EDMs Dmitriev2003, displayed without uncertainties. The direct and indirect neutron limits are about equal, for the proton no direct limit is available yet. Figure credit: T. Hume, PSI.
• Figure 5: Electron and muon EDM limits. The history of electron EDM limits, indirectly derived from various systems. The most sensitive measurements today use molecules, the best one on the HfF$^+$ ion setting a limit of $5\times10^{-30}e$cm for the electron Roussy2023. Opposite to the case of the diamagnetic $^{199}$Hg atom with its suppression factor (see Fig. \ref{['fig:nucleonEDM']}) the paramagnetic atoms and molecules exhibit large amplification factors. Also shown are the limits on the muon EDM, the best one published today still coming from the BNL muon $g$-2 experiment Bennett2009. Interestingly, the muon is the only measurement on a bare fundamental particle. Figure credit: T. Hume, PSI.