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The result of a recent measurement of the size of the proton [R. Pohl et al.,Nature 466, 213] performed on the base of the muonic hydrogen spectroscopyturned out to be significantly different, by five standard deviations, from theresults derived from the atomic hydrogen spectroscopy. This large discrepancycould come from the calculations of the Lamb shift in atomic hydrogen andmuonic hydrogen. Here we show that there is a gap in the standard bound-stateQED that may be the source of the discrepancy. This gap originates in the factthat within the framework of this theory the QED corrections are described interms of the respective Green functions. The character of the time evolution ofa system which should manifest itself in the general definition of bound statesas stationary states of the system cannot be described in terms of the Greenfunctions. We present a consistent way of solving the bound-state problem inQED starting from the condition of stationarity of the bound states. Formulaefor the energies and the vectors of the states of one-electron (muon) atomsderived in this way indicate that the standard bound-state QED does not obeythe exact description of the atomic states and, as a result, the Lamb shiftobtained in its framework should be supplemented by an additional "dynamical"energy shift. It is shown that in this shift natural nonlocality of theelectromagnetic interaction that in describing the S matrix and the Greenfunctions is hidden in the renormalization procedure manifest itselfexplicitly.

Proton radius, bound state QED and the nonlocality of the electromagnetic interaction