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Springer eBooks

A position operator for the photon. Giving up the complementarity principle

Published Nov 22, 2005• 0 citations
Publisher
DOI
10.1007/bfb0019325

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It had been a long standing problem that there is no consistent definition of photon position operator nor photon number density in the context of quantum theory. In this paper we derive the photon detection operator, which defines location of photon absorption, by applying the theory of indirect measurement to quantum electrodynamics. It is shown that the photon detection probability depends on electric 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.
Bohr's principle of complementarity predicts that in a welcher weg ("which-way") experiment, obtaining fully visible interference pattern should lead to the destruction of the path knowledge. Here I report a failure for this prediction in an optical interferometry experiment. Coherent laser light is passed through a dual pinhole and allowed to go through a converging lens, which forms well-resolved images of the respective pinholes, providing complete path knowledge. A series of thin wires are then placed at previously measured positions corresponding to the dark fringes of the interference pattern upstream of the lens. No reduction in the resolution and total radiant flux of either image is found in direct disagreement with the predictions of the principle of complementarity. In this paper, a critique of the current measurement theory is offered, and a novel nonperturbative technique for ensemble properties is introduced. Also, another version of this experiment without an imaging lens is suggested, and some of the implications of the violation of complementarity for another suggested experiment to investigate the nature of the photon and its "empty wave" is briefly discussed.