  We derive two relations involving spin polarizabilities of a spin-1/2
particle and consider their empirical implications for the proton. Using the
empirical values of the proton anomalous magnetic moment, electric and magnetic
charge radii, moments of the spin structure functions $g_1$, $g_2$, and of two
spin polarizabilities, the present relations constrain the low-momentum
behavior of generalized polarizabilities appearing in virtual Compton
scattering. In the case of the proton, the dispersive model evaluations of the
spin and generalized polarizabilities appear to be consistent with these
relations. The ongoing measurements of different electromagnetic observables at
the MAMI, Jefferson Lab, and HI$\gamma$S facilities may be able to put these
relations to a test, or use them to unravel the low-energy spin structure of
the nucleon.
