  A hypothesis of general relativity is that spacetime torsion vanishes
identically. This assumption has no empirical support; in fact, a nonvanishing
torsion is compatible with all the experimental tests of general relativity.
The first part of this essay specifies the framework that is suitable to test
the vanishing-torsion hypothesis, and an interesting relation with the
gravitational degrees of freedom is suggested. In the second part, some
original empirical tests are proposed based on the observation that torsion
induces new interactions between different spin-polarized particles.
