Spin Independence,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>Spin, Parity, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>SU</mml:mi><mml:mo>(</mml:mo><mml:mn>6</mml:mn><mml:mo>)</mml:mo><mml:mn/></mml:math>Symmetry

The assumption of strict spin independence of strong interactions between elementary particles forbids all three-meson and meson-baryon-baryon couplings, such as $\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}$, $\mathrm{NN}\ensuremath{\pi}$, and ${N}^{*}N\ensuremath{\pi}$. It is shown that these catastrophies may be avoided, even in the nonrelativistic limit, by adopting a modified definition of spin independence, i.e., $W$-spin independence. A nonrelativistic definition of $W$ spin is obtained which requires only a trivial change to yield the relativistic description. The consequences of the assumption of $W$-spin independence are explored.