  A recent "beam splitting" experiment at LCLS apparently demonstrated that
after a microbunched electron beam is kicked on a large angle compared to the
divergence of the FEL radiation, the microbunching wave front is readjusted
along the new direction of motion of the kicked beam. Therefore, coherent
radiation from an undulator placed after the kicker is emitted along the kicked
direction without suppression. This strong emission of coherent undulator
radiation in the kicked direction cannot be explained in the framework of
conventional synchrotron radiation theory. In a previous paper we explained
this puzzle. We demonstrated that, in accelerator physics, the coupling of
fields and particles is based, on the one hand, on the use of results from
particle dynamics treated according to the absolute time convention and, on the
other hand, on the use of Maxwell equations treated according to the standard
(Einstein) synchronization convention. Here lies the misconception which led to
the strong qualitative disagreement between theory and experiment. After the
"beam splitting" experiment at LCLS, it became clear that the conventional
theory of synchrotron radiation cannot ensure the correct description of
coherent and spontaneous emission from a kicked electron beam, nor the emission
from a beam with finite angular divergence, in an undulator or a bending
magnet. However, this result requires further experimental confirmation. In
this publication we propose an uncomplicated and inexpensive experiment to test
synchrotron radiation theory at 3rd generation light sources.
