Maxwell theory is usually treated in the lab frame under the standard time order (light-signal clock synchronization). Particle tracking in the lab frame usually treats time as an independent variable. Then, the evolution of electron beams is treated according to the absolute time convention (non-standard clock synchronization). This point has never received attention in the accelerator community. There are two ways of coupling fields and particles. The first, Lorentzs way, consists in `translating Maxwells electrodynamics to the absolute time world-picture. The second, Einsteins way, consists in `translating particle tracking results to the electromagnetic world-picture. Conventional particle tracking shows that the electron beam direction changes after a transverse kick, while the orientation of the microbunching fronts stays unvaried. We show that under Einsteins time order, in the ultrarelativistic asymptote the orientation of the planes of simultaneity is always perpendicular to the electron beam velocity. This allows for the production of coherent undulator radiation from a modulated electron beam in the kicked direction without suppression. We hold a recent FEL study at the LCLS as experimental evidence of microbunching wavefront readjusting after a large kick. In a previous paper we quantitatively described this result invoking the aberration of light, corresponding to Lorentzs way of coupling fields and particles. Here we give details of the Lorentzs approach used in that paper. We also demonstrate that an `inverse translation of particle tracking results to the standard time order resolves puzzles related with the strong qualitative disagreement between simulations and experiments. Previous simulation results in ultrarelativistic electron beam physics should be reexamined in the light of the difference between particle tracking and electromagnetic world-pictures.
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