  A random field that is empirically equivalent to the quantized
electromagnetic field is constructed. A mapping between the creation and
annihilation operator algebras of a random field and of the quantized
electromagnetic field provides a functor between the algebras and the Hilbert
spaces generated by the vacuum states over those algebras. The functor
inevitably does not extend to a functorial relationship between the local
algebras generated by the random field and by the quantized electromagnetic
field, but the empirical content provided by the vacuum state restores an
empirical equivalence through the Hilbert spaces. The isomorphism from one
creation and annihilation algebra to the other is not translation invariant
because it depends on mapping positive frequency modes of one helicity to
equivalent negative frequency modes, but the two theories taken independently
are presented in equally well-defined and manifestly Lorentz and translation
covariant ways.
