  A new duality is proposed in four-dimensional flat space, which exchanges
between spin and orbital degrees of freedom. This is motivated by a Hodge
decomposition of the angular-momentum bivector for massive fields, along which
spin and orbital angular momentum are Hodge duals of one another. The duality
respects Poincar\`e symmetry and is shown to transform between complementary
spacelike regions, projecting a fixed three-dimensional de Sitter world-tube
(around the center of mass) into the bulk of four-dimensional spacetime and
vice versa. This state of affairs is interpreted as a realization of the
holographic principle. The dual theory living on that tube turns out to be
noncommutative and entirely defined by the Casimir elements of the Poincar\`e
algebra. In fact, the mass is now an ultraviolet cutoff. This naturally
suggests that, for a Poincar\`e or just Lorentz-invariant quantum theory with
massive fields of nonzero spin, spacetime is quantized at the fundamental
level.
