Quantum Mechanics “explains” the lack of radiation from electrons in the ground state of an atom by telling us that our idea of electrons (or anything else) as discrete particles with well-defined positions and momenta is wrong – and that the bound electron is not in fact accelerating on a curved path around the nucleus, but rather has a range of possible values for our attempts to measure its positions and momenta at different times (with the property that the probability distribution of these values is concentrated around the nucleus but invariant with respect to time).