/ 97 11 02 9 v 2 2 D ec 1 99 7 Do we need photons in parametric down conversion ?

The phenomenon of parametric down conversion from the vacuum may be understood as a process in classical electrodynamics, in which a nonlinear crystal couples the modes of the pumping field with those of the zeropoint, or “vacuum”, field. This is an entirely local theory of the phenomenon, in contrast with the presently accepted nonlocal theory. The new theory predicts a hitherto unsuspected phenomenon — parametric up conversion from the vacuum. PACS numbers: 03.65, 42.50 The widely accepted description of parametric down conversion (PDC) by a pumped nonlinear crystal (NLC) is based on a hamiltonian (for simplicity we confine attention to the scalar version) H = ∑ h̄ωka † k ak + ∑ gkk′a † k a k e0 . (1) The interaction part of H is interpreted to mean that (I prefer to say “was constructed so that”) an incoming laser photon of frequency ω0 down converts into a correlated pair of photons with frequencies ω and ω0 − ω. Such a process is depicted in Fig.1. Naturally, since we know that E = h̄ω, that means ` ` ` ` ` ` ` ` ` ` ` NLC z : Figure 1: PDC — photon-theoretic version. A laser photon down converts into a conjugate pair of PDC photons with conservation of energy. energy is conserved in the PDC process. The correlation in the properties of the two outgoing photons, according to this description, can only be described as bizarre[2, 3]. Indeed, attempts, by supporters of the theory, to describe effects such as “entanglement” to a nonspecialist public, have used the words “mind boggling”[4] and, in another context, “absurd”[5], but these authors’ implication is that the theory must nevertheless be correct. The mind boggling feature of the standard theory of PDC, and also of atomic transitions, is its nonlocality. This feature is already clear in Fig.1, which implies that photons, or plane waves filling the whole of space, are created instantaneously by the action of H. But we do not have to believe Fig.1 represents what really happens. The alternative to photons is almost as old as photons themselves, namely the zeropoint electromagnetic field of Max Planck[6, 7]. I have reviewed elsewhere[8] how nonlocal photon descriptions may be more or less systematically replaced by local descriptions which incorporate Planck’s field. This systematic replacement includes, indeed begins with, the celebrated experiments on Bellinequality tests in atomic cascades[9]. Most specialists, possibly quite rightly, are not impressed, because, although the treatment of the field is unambiguously maxwellian, we have had to improvise, in a rather crude manner, the description of the atomfield interaction. Nobody has yet succeeded in doing, for the Dirac field, what Planck did for the Maxwell field. Now when it comes to PDC we do not need to know any details about the atom-field interaction; only the relation between the current and the field inside the crystal is relevant at optical and near ultraviolet frequencies. So a purely maxwellian theory of the type I have outlined[8, 10], and which I call the Field Theory, can engage with the theory generated by eq.(1) and Fig.1, which I call the Photon Theory, on equal terms. But the Field Theory is manifestly local and causal; the incoming fields generate a cur-