  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,
Lorentz's way, consists in `translating' Maxwell's electrodynamics to the
absolute time world-picture. The second, Einstein's 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 Einstein's 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 Lorentz's way of coupling
fields and particles. Here we give details of the Lorentz's 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.
