  While electromagnetic and up-down quark mass difference effects on octet
baryon masses are very small, they have important consequences. The stability
of the hydrogen atom against beta decay is a prominent example. Here we include
these effects by adding them to valence quarks in a lattice QCD calculation
based on $N_f=2+1$ simulations with 5 lattice spacings down to 0.054 fm,
lattice sizes up to 6 fm and average up-down quark masses all the way down to
their physical value. This allows us to gain control over all systematic
errors, except for the one associated with neglecting electromagnetism in the
sea. We compute the octet baryon isomultiplet mass splittings, as well as the
individual contributions from electromagnetism and the up-down quark mass
difference. Our results for the total splittings are in good agreement with
experiment.
