Comments on the Three-Slit Experiment and Quantum Mechanics

TL;DR

The paper critiques the idea that a three-slit experiment could challenge quantum mechanics by showing that proper interpretation and measurement procedures uphold the Born rule and superposition principle.

Contribution

It clarifies how correct quantum measurement interpretation ensures the three-slit experiment does not violate fundamental quantum principles.

Findings

Proper quantum interpretation yields $ppa_S=0$

No fundamental difference between quantum and classical interference in this context

Misinterpretation of measurement procedures can lead to incorrect conclusions

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 $\kappa_S$, 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 proper interpretation of the procedures involved in a physical determination of $\kappa_S$ does not necessarily lead to $\kappa_S=0$. In order to show this we consider a mono-chromatic source of photons prepared in an {\it 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 $\kappa_S=0$. 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.