Quantum theory of an electromagnetic observer: Classically behaving macroscopic systems and the emergence of the classical world in quantum electrodynamics

Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such “mesoscopic quantum electrodynamics” is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to “doing quantum electrodynamics while thinking classically,” allowing one to substitute essentially classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.

Figure 1

From response characterization of devices (a) to that of an interacting pair (b). Circles surrounded by curved dashed arrows symbolize “dressed” macroscopic devices, with all electromagnetic self-actions accounted for. Straight dashed arrows symbolize interactions of dressed devices. The detectors are a reminder that the time-normal ordering originates in photodetection theory. In the classical case of Sec. 3, disregard hats in the pictures and the remark on the time-normal ordering here.

Figure 2

The two-device model without external $c$-number sources. Dashed lines with arrows symbolize electromagnetic interaction. Circles surrounded by curved dashed arrows symbolize “dressed” devices regarded as macroscopic entities. (a) Separation of interactions from self-actions emerges as a consequence of distinguishability. At this stage, electromagnetic actions and back-actions are not formally distinguished. This is emphasized by making all “electromagnetic arrows” bidirectional. (b) The same with propagating waves introduced through the wave quantization formula (33). The “electromagnetic arrows” are directional as in Fig. 1.

Figure 3

The $c$-number sources and macroscopic detectors as a macroscopic approximation. (a) The photodetection problem. The macroscopic back-action of the detector (dotted arrow) is neglected. The dashed oval isolates the $\mathrm{source}+\mathrm{field}$ entity, operating independently of the detector. Formally, this entity is characterized by functional (E9) in Appendix pp5. (b) The four-device arrangement, to which response characterization of the two-device model [cf. Fig. 1] is an approximation. Neglected macroscopic actions and back-actions are shown as dotted arrows.

Figure 4

Schematics of information flow in an optical experiment. Solid lines indicate “the classical” and dashed ones “the quantum.” Thick dotted lines show possible choices of the quantum-classical boundary: “minimal” ($M$), “intermediate” ($I$), and “strict” ($S$).