Abstract
It has been a long-standing problem that there is no consistent definition of the photon position operator or photon number density in the context of quantum theory. In this paper, we derive the photon detection operator, which defines the location of photon absorption, by applying the theory of indirect measurement to quantum electrodynamics. It is shown that the photon detection probability depends on the properties of a photon-absorbing atom, in particular, on both electric and magnetic dipole moments of the atom. An experiment is proposed in which the complementarity of wave–particle nature of light will be tested. It is also discussed that the complementarity is related to the non-commutativity of the electric and the magnetic fields. (When this work was presented at the conference CEWQO2013, it had the title ‘Photon position operators and complementarity between electric detector and magnetic detector’.)
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