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A random field that is empirically equivalent to the quantizedelectromagnetic field is constructed. A mapping between the creation andannihilation operator algebras of a random field and of the quantizedelectromagnetic field provides a functor between the algebras and the Hilbertspaces generated by the vacuum states over those algebras. The functorinevitably does not extend to a functorial relationship between the localalgebras generated by the random field and by the quantized electromagneticfield, but the empirical content provided by the vacuum state restores anempirical equivalence through the Hilbert spaces. The isomorphism from onecreation and annihilation algebra to the other is not translation invariantbecause it depends on mapping positive frequency modes of one helicity toequivalent negative frequency modes, but the two theories taken independentlyare presented in equally well-defined and manifestly Lorentz and translationcovariant ways.

An empirically equivalent random field for the quantized electromagnetic field