  Nucleon-nucleon bremsstrahlung has long been considered a way of getting
information about the off-shell nucleon-nucleon amplitude which would allow one
to distinguish among nucleon-nucleon potentials based on their off-shell
properties. There have been many calculations and many experiments devoted to
this aim. We show here, in contrast to this standard view, that such off-shell
amplitudes are not measurable as a matter of principle. This follows formally
from the invariance of the S-matrix under transformations of the fields. This
result is discussed here and illustrated via two simple models, one applying to
spin zero, and one to spin one half, processes. The latter model is very
closely related to phenomenological models which have been used to study
off-shell effects at electromagnetic vertices.
