  It is shown that Maxwell's equation cannot be put into a spinor form that is
equivalent to Dirac's equation. First of all, the spinor \psi in the
representation \vec{F} = \psi \vec{u} \bar{\psi} of the electromagnetic field
bivector depends on only three independent complex components whereas the Dirac
spinor depends on four. Second, Dirac's equation implies a complex structure
specific to spin 1/2 particles that has no counterpart in Maxwell's equation.
This complex structure makes fermions essentially different from bosons and
therefore insures that there is no physically meaningful way to transform
Maxwell's and Dirac's equations into each other.
