Does antihydrogen 1S-2S match hydrogen at 1e-15?
In plain words
Antihydrogen (an antiproton bound to a positron) should have exactly the same energy levels as hydrogen if matter and antimatter mirror each other perfectly. The main ultraviolet line has been compared to a few parts in $10^{12}$; hydrogen itself is known about a thousand times better.
Precise statement
ALPHA measured the antihydrogen $1\mathrm{S}-2\mathrm{S}$ two-photon frequency in agreement with hydrogen at about 2e-12 relative precision (2018). Determine whether nu_1S2S(Hbar) - nu_1S2S(H) is nonzero at the 1e-15 level, approaching the hydrogen precision of about 4e-15.
What would settle it
Antihydrogen 1S-2S spectroscopy with laser-cooled, magnetically trapped atoms reaching sub-kHz resolution and 1e-15 accuracy.
Status in the literature
ALPHA demonstrated laser cooling of antihydrogen in 2021, a prerequisite for the next precision step.