  For nearly fifty years theoretical and experimental efforts in
nucleon-nucleon bremsstrahlung (NN$\gamma$) have been devoted to measuring
off-shell amplitudes and distinguishing among various NN potentials on the
basis of their off-shell behavior. New experiments are underway, designed
specifically to attain kinematics further off shell than in the past, and thus
to be more sensitive to the off-shell behavior. This letter shows that,
contrary to these expectations, and due to the invariance of the S-matrix under
transformations of the fields, the off-shell NN amplitude is as a matter of
principle an unmeasurable quantity in NN$\gamma$.
