On the three-slit experiment and quantum mechanics

Abstract

It has been suggested by Sorkin that a three-slit Young experiment could reveal the validity a fundamental ingredient in the foundations of one of the cornerstones in modern physics namely quantum mechanics. In terms of a certain parameter κS, it was argued that a non-zero value could imply a breakdown of the fundamental Born’s rule as well as the superposition principle. Here we argue that a physical realization of such arguments could lead to an erroneous conclusion and contradict the basic rules of quantum mechanics. In fact, we argue that a straightforward interpretation of the procedures involved in a physical determination of κS does not necessarily lead to κS=0. In order to show this we consider a mono-chromatic source of photons prepared in an arbitrary quantum state and a simple version of the well-established photon detection theory of Glauber which, by construction, obeys all the rules of quantum mechanics. It is, however, also argued that after a proper identification of the relevant quantum-mechanical probability amplitudes one can be reach κS=0. As long as one only consider a single photon detector, it is verified that, in this context, there is no fundamental difference between quantum-mechanical interference and interference as expressed in terms of classical electro-magnetic waves.