  If the Einstein-Hilbert action ${\cal L}_{\rm EH}\propto R$ is re-expressed
in Riemann-Cartan spacetime using the gauge fields of translations, the
vierbein field $h^\alpha{}_\mu$, and the gauge field of local Lorentz
transformations, the spin connection $A_{\mu \alpha}{}^ \beta $, there exists a
new gauge symmetry which permits reshuffling the torsion, partially or totally,
into the Cartan curvature term of the Einstein tensor, and back, via a {\em new
multivalued gauge transformation\/}. Torsion can be chosen at will by an
arbitrary gauge fixing functional. There exist many equivalent ways of
specifing the theory, for instance Einstein's traditional way where ${\cal
L}_{\rm EH}$ is expressed completely in terms of the metric $g_{\mu \nu}=h^
\alpha {}_\mu h_ \alpha {}_ \nu $, and the torsion is zero, or Einstein's
teleparallel formulation, where ${\cal L}_{\rm EH}$ is expressed in terms of
the torsion tensor, or an infinity of intermediate ways. As far as the
gravitational field in the far-zone of a celestial object is concerned, matter
composed of spinning particles can be replaced by matter with only orbital
angular momentum, without changing the long-distance forces, no matter which of
the various new gauge representations is used.
