  Particle experiments are difficult at weak coupling because interactions are
rare and a huge number of collision attempts are needed to attain significant
precision. One often hears that "one Higgs boson is produced in a billion of
collisions at LHC." In this essay, we fantasize about possible advantages
afforded in this regard by performing experiments in anti-de Sitter (AdS)
spacetime instead of a usual collider in a nearly-flat spacetime. Being a
perfectly resonant cavity, the AdS spacetime enhances all nonlinear
interactions, which therefore produce effects of order one no matter how small
the couplings are, provided that one waits long enough. These effects are
encoded in spectroscopic data, namely, the fine splittings of the energy levels
which would have been highly degenerate in AdS if no interactions were present.
Over long times, such energy shifts let different components of wavefunctions
drift completely out-of-phase, producing large effects for arbitrarily small
interactions.
