Recent preliminary data gathered by the Fermilab MINOS Collaboration suggest with 95% confidence that the mass of the muon neutrino differs from that of its antineutrino partner, which contradicts the entrenched relativistic quantum theory notion that a free antiparticle is a negative-energy free particle compelled to travel backwards in time. Also a discrepancy of about five standard deviations in the value of the proton charge radius recently obtained from muonic hydrogen versus that previously obtained from electronic hydrogen casts doubt on the calculation of the dominant relativistic QED contributions to the effects that are actually measured (e.g., the Lamb shift): these QED contributions dominate proton charge radius contributions less in muonic hydrogen than in electronic hydrogen. The negative-energy 'free particles' of entrenched relativistic quantum theory are well-known features of the Klein-Gordon and Dirac equations, which are shown to have many other unphysical features as well. The correspondence principle for relativistic particles is incompatible with these two equations, produces no unphysical features and implies only positive energies for free particles, which eliminates the very basis of the entrenched notion of antiparticles, as well as of the CPT theorem. This principle thus requires antiparticles to arise from charge conjugation (or more generally CP) invariance, whose known breaking is naturally expected to produce mass splitting between particle and antiparticle, in consonance with the preliminary MINOS data. It also requires revamping of relativistic QED, which is in accord with the doubt cast on it by the proton charge radius results, and implies that QED is nonlocal, i.e. has no Hamiltonian density.