  Of all nuclear physics experiments none are more fundamental than ``elastic''
$p,p$ and, secondarily, $p,d$ or $d,d$ scattering. Recognizing that these
particles are themselves composite, ``elastic'' scattering may be accompanied
by temporary internal rearrangement with undetectably small energy loss. % This
paper argues that correct calculation of the spin dependence of $p,p$ elastic
scattering must account for a previously-neglected relativistic effect of
``$G$'', the anomalous magnetic dipole moment (MDM) of the scattering particles
and proceeds to describe storage ring $p,p$ scattering configurations capable
of confirming this contention. % Especially important experimentally for
protons is the existence of ``near perfect'' proton-carbon scattering
polarimetric analyzing power $A$ near $K=183.1$\,MeV laboratory kinetic energy.
% Possibilities: (i) With counter-circulating $K=200\,$MeV energy proton beams
the final spin states of coincident scattered protons can be determined with
high probability for a significantly large fraction of all scatters. For
comparison with current descriptions this corresponds roughly to proton kinetic
energy $K=400\,$MeV in the laboratory frame, close to the pion production
threshold. % (ii) In a ``DERBENEV-style'' figure-8 storage ring, independently
polarized, diametrically opposite bunches on orthogonal orbits can collide at
the beam crossover point with symmetric $K''\approx200$ MeV energies in a slow,
transversely moving frame. % (iii) $p$ and $d$ beams can counter-circulate at
the same time in a small racetrack shaped ring with superimposed electric and
magnetic bending. In this case the scattering would be ``WOLFENSTEIN-style''
with collinear incident orbits. % To investigate the consistency of quantum
mechanics and special relativity it is proposed to implement options (ii) and
(iii) in the COSY beam hall.
